Daily Papers

Efficient deployment of large language models (LLMs) requires extreme quantization, forcing a critical trade-off between low-bit efficiency and performance. Residual binarization enables hardware-friendly, matmul-free inference by stacking binary (pm1) layers, but is plagued by pathological feature co-adaptation. We identify a key failure mode, which we term inter-path adaptation: during quantization-aware training (QAT), parallel residual binary paths learn redundant features, degrading the error-compensation structure and limiting the expressive capacity of the model. While prior work relies on heuristic workarounds (e.g., path freezing) that constrain the solution space, we propose RaBiT, a novel quantization framework that resolves co-adaptation by algorithmically enforcing a residual hierarchy. Its core mechanism sequentially derives each binary path from a single shared full-precision weight, which ensures that every path corrects the error of the preceding one. This process is stabilized by a robust initialization that prioritizes functional preservation over mere weight approximation. RaBiT redefines the 2-bit accuracy-efficiency frontier: it achieves state-of-the-art performance, rivals even hardware-intensive Vector Quantization (VQ) methods, and delivers a 4.49times inference speed-up over full-precision models on an RTX 4090.

Weight-only post-training quantization (PTQ) can alleviate the computational burden of serving large language models (LLMs) at scale. However, existing PTQ methods often fail to generalize across models and suffer severe accuracy loss below 2 bits. Many leverage unstructured sparsity to mitigate this loss, but at the cost of regularity and GPU-friendly execution. We present QTEA, a sub-2-bit PTQ framework that quantizes weights into ternary values and uses salient weights as residual error compensators. To maintain hardware efficiency, residuals are assigned to selected columns with semi-structured \(1{:}4\) sparsity within the salient columns. We further add column-wise rescale refinement to GPTQ-style column-by-column quantization, alternately updating per-column scales and ternary assignments to reduce reconstruction error. We also identify order-dependent error propagation in GPTQ and introduce error decay to attenuate late-stage error accumulation. On Qwen3-14B, QTEA compresses all weights to an effective 1.7 bits per weight while improving average accuracy over the strongest ternary PTQ baseline by 16.7\%. It also achieves 1.40\(\times\) and 2.61\(\times\) lower perplexity on WikiText and C4 respectively. This trend holds on Llama3-8B, where QTEA obtains a 6.6\% accuracy gain and 1.34\(\times\)/1.95\(\times\) lower perplexity on the same datasets. Finally, we develop a lookup-table based kernel that achieves 7.2\(\times\) faster per-token generation over an FP16 baseline. Code is available at https://github.com/Intelligent-Microsystems-Lab/QTEA.

Modern distributed training relies heavily on communication compression to reduce the communication overhead. In this work, we study algorithms employing a popular class of contractive compressors in order to reduce communication overhead. However, the naive implementation often leads to unstable convergence or even exponential divergence due to the compression bias. Error Compensation (EC) is an extremely popular mechanism to mitigate the aforementioned issues during the training of models enhanced by contractive compression operators. Compared to the effectiveness of EC in the data homogeneous regime, the understanding of the practicality and theoretical foundations of EC in the data heterogeneous regime is limited. Existing convergence analyses typically rely on strong assumptions such as bounded gradients, bounded data heterogeneity, or large batch accesses, which are often infeasible in modern machine learning applications. We resolve the majority of current issues by proposing EControl, a novel mechanism that can regulate error compensation by controlling the strength of the feedback signal. We prove fast convergence for EControl in standard strongly convex, general convex, and nonconvex settings without any additional assumptions on the problem or data heterogeneity. We conduct extensive numerical evaluations to illustrate the efficacy of our method and support our theoretical findings.

Methods based on weight compensation, which iteratively apply quantization and weight compensation to minimize the output error, have recently demonstrated remarkable success in quantizing Large Language Models (LLMs). The representative work, GPTQ, introduces several key techniques that make such iterative methods practical for LLMs with billions of parameters. GPTAQ extends this approach by introducing an asymmetric calibration process that aligns the output of each quantized layer with its full-precision counterpart, incorporating a residual error into the weight compensation framework. In this work, we revisit the formulation of the residual error. We identify a sub-optimal calibration objective in existing methods: during the intra-layer calibration process, they align the quantized output with the output from compensated weights, rather than the true output from the original full-precision model. Therefore, we redefine the objective to precisely align the quantized model's output with the original output of the full-precision model at each step. We then reveal that the residual error originates not only from the output difference of the preceding layer but also from the discrepancy between the compensated and original weights within each layer, which we name the 'compensation-aware error'. By inheriting the neuron decomposition technique from GPTAQ, we can efficiently incorporate this compensation-aware error into the weight update process. Extensive experiments on various LLMs and quantization settings demonstrate that our proposed enhancements integrate seamlessly with both GPTQ and GPTAQ, significantly improving their quantization performance. Our code is publicly available at https://github.com/list0830/ResComp.

Model families train every size from scratch. Can a pretrained large model be converted into a smaller sibling? We characterize the 1.4B->410M conversion in the Pythia family end-to-end: (i) representations align strongly across sizes (ridge R^2=0.84) while parameters align weakly; (ii) dense weight projection is functionally destructive -- provably not an assembly artifact -- because basis mixing breaks rotary, per-head, GELU, and LayerNorm structure; (iii) after the best-fit linear operator, weight residuals are statistically indistinguishable from noise under shuffle controls; (iv) conversion value therefore lives in initialization. In matched-budget continued pre-training we decompose conversion into two independent levers -- least-squares compensation (function: best zero-shot) and variance-preserving rescale (dynamics: best endpoints). Compensation is a token-efficient, low-budget win rather than a universal one: at 30M tokens it beats the strongest subcloning variant on both a width-reduced pair (84.0 +/- 1.8 vs. 89.7 +/- 3.7, 3/3 seeds) and a held-out depth-reduced pair (109.3 vs. 117.9, 3/3 seeds), reaching a given quality with fewer tokens; at a 33x larger budget the two converge to parity (40.0 vs. 40.0), both far ahead of from-scratch, which transfer initialization always beats -- by up to 18x at low budget, the margin narrowing at convergence and at the largest scale. We further map the method's boundary: at ~5x the donor scale (6.9B->1.4B) stacking both levers over-corrects, which we trace to ill-conditioning of the compensation solve at large width, pointing to dimension-aware regularization as the fix. Code, checkpoints, and the frozen evaluation corpus are released.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

Lower numerical precision reduces storage and memory traffic but raises the perturbation floor. We study rank compensation: reinvesting saved memory in a larger approximation rank. For matrices, the singular-value error identity yields a directly testable sufficient condition requiring the additional singular component to offset the perturbation from storing the rank-augmented approximation in lower precision. On ten SuiteSparse matrices, all 100 truncation-dominated configurations (50 FP32 and 50 FP16) are certified non-increases and strict accuracy wins, with mean error ratio 0.963 and storage ratios 58.8% and 29.4% relative to the FP64 baseline. FP16 failures occur only in tail-rank stress tests near the perturbation floor. At the largest resident matrix-application batch, compensated FP32 and FP16 achieve geometric-mean A100 speedups of 1.28times and 2.12times; neither accelerates the smallest batch. For Tensor-Train (TT) approximation, we give a conditional a posteriori extension based on the measured truncation gain and rounded-core perturbation. Across three-way and six-way synthetic tests, FP32 and FP16 achieve combined accuracy-memory wins in 10 of 20 and 14 of 20 trials. On public hyperspectral tensors and FROSTT top-active subtensors, the corresponding counts are 44 of 60 and 54 of 60; four FP16 Salinas-A tail-stress cases fail. No certified TT case exceeds the FP64 error beyond numerical tolerance. Reconstruction of six public tensors yields geometric-mean compensated speedups of 1.38times (FP32) and 1.94times (FP16). Timings cover resident downstream kernels, not factorization, transfers, or end-to-end acceleration.

Reinforcement Learning with Verifiable Rewards (RLVR) can elicit strong multi-step reasoning, yet it often encourages overly verbose traces. Moreover, naive length penalties in group-relative optimization can severely hurt accuracy. We attribute this failure to two structural issues: (i) Dilution of Length Baseline, where incorrect responses (with zero length reward) depress the group baseline and over-penalize correct solutions; and (ii) Difficulty-Penalty Mismatch, where a static penalty cannot adapt to problem difficulty, suppressing necessary reasoning on hard instances while leaving redundancy on easy ones. We propose Dynamic Decoupled Conditional Advantage (DDCA) to decouple efficiency optimization from correctness. DDCA computes length advantages conditionally within the correct-response cluster to eliminate baseline dilution, and dynamically scales the penalty strength using the group pass rate as a proxy for difficulty. Experiments on GSM8K, MATH500, AMC23, and AIME25 show that DDCA consistently improves the efficiency--accuracy trade-off relative to adaptive baselines, reducing generated tokens by approximately 60% on simpler tasks (e.g., GSM8K) versus over 20% on harder benchmarks (e.g., AIME25), thereby maintaining or improving accuracy. Code is available at https://github.com/alphadl/DDCA.

This article explores the adaptive relationship between Encoder Layers and Decoder Layers using the SOTA model Helsinki-NLP/opus-mt-de-en, which translates German to English. The specific method involves introducing a bias-free fully connected layer between the Encoder and Decoder, with different initializations of the layer's weights, and observing the outcomes of fine-tuning versus retraining. Four experiments were conducted in total. The results suggest that directly modifying the pre-trained model structure for fine-tuning yields suboptimal performance. However, upon observing the outcomes of the experiments with retraining, this structural adjustment shows significant potential.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

In this work, we re-formulate the model compression problem into the customized compensation problem: Given a compressed model, we aim to introduce residual low-rank paths to compensate for compression errors under customized requirements from users (e.g., tasks, compression ratios), resulting in greater flexibility in adjusting overall capacity without being constrained by specific compression formats. However, naively applying SVD to derive residual paths causes suboptimal utilization of the low-rank representation capacity. Instead, we propose Training-free Eigenspace Low-Rank Approximation (EoRA), a method that directly minimizes compression-induced errors without requiring gradient-based training, achieving fast optimization in minutes using a small amount of calibration data. EoRA projects compression errors into the eigenspace of input activations, leveraging eigenvalues to effectively prioritize the reconstruction of high-importance error components. Moreover, EoRA can be seamlessly integrated with fine-tuning and quantization to further improve effectiveness and efficiency. EoRA consistently outperforms previous methods in compensating errors for compressed LLaMA2/3 models on various tasks, such as language generation, commonsense reasoning, and math reasoning tasks (e.g., 31.31%/12.88% and 9.69% improvements on ARC-Easy/ARC-Challenge and MathQA when compensating LLaMA3-8B that is quantized to 4-bit and pruned to 2:4 sparsity). EoRA offers a scalable, training-free solution to compensate for compression errors, making it a powerful tool to deploy LLMs in various capacity and efficiency requirements.

Structural fidelity is essential to scientific methodology diagrams. To communicate research logic, these diagrams must faithfully render components, directional relations, and textual annotations. Since a single error, such as a reversed arrow or an unreadable equation, can invalidate the entire figure, structural fidelity is inherently conjunctive: correctness on one axis cannot compensate for failure on another. Current open-source models fail to satisfy this criterion. Supervised fine-tuning (SFT) learns plausible layouts but cannot reliably ensure structural correctness, while scalar reward-based post-training obscures which structural dimension has failed. To address this, we introduce SciForma, a framework for the structure faithful generation of scientific methodology diagrams. Specifically, SciForma decomposes diagram quality into three structural axes: Component, Arrow, and Text, guided by a structural inventory. Built on this foundation, we curate SciFormaData-700K for structured training and SciFormaBench-2K for logic-verified evaluation. To close the gap left by SFT, we develop Multi-Dimensional Conjunctive Preference Optimization (M-DPO), which enforces simultaneous correctness across all axes and adaptively routes gradients to the most deficient dimension in post-training. The same structural inventory also enables iterative editing at inference time to correct residual errors. This combination allows SciForma-9B to exceed all open-source baselines and GPT-Image-1.5 on both SciFormaBench-2K and AIBench, bringing open scientific diagram generation close to proprietary-level structural fidelity. Our code and data will be available at: https://github.com/microsoft/SciForma.

We present a method for classifying syntactic errors in learner language, namely errors whose correction alters the morphosyntactic structure of a sentence. The methodology builds on the established Universal Dependencies syntactic representation scheme, and provides complementary information to other error-classification systems. Unlike existing error classification methods, our method is applicable across languages, which we showcase by producing a detailed picture of syntactic errors in learner English and learner Russian. We further demonstrate the utility of the methodology for analyzing the outputs of leading Grammatical Error Correction (GEC) systems.

Multi-agent systems (MAS) are increasingly capable of tackling complex real-world tasks, yet their reliance on inter-agent coordination, tool use, and long-horizon reasoning makes error recognition particularly challenging. Minor errors can propagate across agents, escalating into task failures while producing long, intertwined execution trajectories that impose significant costs for both human developers and automated systems to debug and analyze. Our key insight is that, despite surface differences in failure trajectories (e.g., logs), MAS errors often recur with similar structural patterns. This paper presents CORRECT, the first lightweight, training-free framework that leverages an online cache of distilled error schemata to recognize and transfer knowledge of failure structures across new requests. This cache-based reuse allows LLMs to perform targeted error localization at inference time, avoiding the need for expensive retraining while adapting to dynamic MAS deployments in subseconds. To support rigorous study in this domain, we also introduce CORRECT-Error, a large-scale dataset of over 2,000 annotated trajectories collected through a novel error-injection pipeline guided by real-world distributions, and further validated through human evaluation to ensure alignment with natural failure patterns. Experiments across seven diverse MAS applications show that CORRECT improves step-level error localization up to 19.8% over existing advances while at near-zero overhead, substantially narrowing the gap between automated and human-level error recognition.

Self-improving LLM agents increasingly learn from experience without updating any weights. Each episode is stored in an external memory, scored, and retrieved for similar future tasks to shape later behavior. Viewed through a reward lens, the stored score is a proxy reward for an implicit, non-parametric policy. Each retrieved episode then becomes a policy-improvement step whose reliability hinges on how that score is produced. In deployment, ground-truth labels are unavailable, so the stored reward is at best an LLM assessment. This substitution creates a failure mode, the *Echo Gap*, across the memory-based self-improving agents and model families studied. Incorrect episodes receive inflated rewards; thus, the agent preferentially reuses the very mistakes it has most confident in. Because the error compounds through memory rather than averaging out and the confirming judge's errors remain correlated with the original self-grading bias, so it cannot identify which memories are overvalued. The missing property is formalized as the *Error-Independence Assumption* (EIA), which we prove is a *necessary* condition for correcting the inflation, not merely a description of a good verifier: a usable signal must track truth *and* decorrelate its error from the memory bias, and the recoverable payoff is a closed-form function of exactly those two quantities. We further show the inflation compounds not only when retrieval ranks by the stored score but also under plain similarity retrieval which is the regime the deployed agent uses. Finally, the answer-free de-inflation algorithm LUCID delivers a consistent end-to-end gain on the BIRD text-to-SQL benchmark. It raises execution accuracy to 56.9%, above both a Memento-style self-graded agent (54.0%, a +2.9-point mean gain across seeds) and a memory-less agent of identical architecture (52.4%).

The rapid growth in the parameter scale of large language models (LLMs) has created a high demand for efficient compression techniques. As a hardware-agnostic and highly compatible technique, low-rank compression has been widely adopted. However, existing methods typically compress each layer independently by minimizing per-layer reconstruction error, overlooking a critical limitation: the reconstruction error propagates and accumulates through the network, which leads to amplified global deviations from the full-precision baseline. To address this, we propose Self-Adaptive Error Suppression SVD (SAES-SVD), a LLMs compression framework that jointly optimizes intra-layer reconstruction and inter-layer error compensation. SAES-SVD is composed of two novel components: (1) Cumulative Error-Aware Layer Compression (CEALC), which formulates the compression objective as a combination of local reconstruction and weighted cumulative error compensation. Based on it, we derive a closed-form low-rank solution relied on second-order activation statistics, which explicitly aligns each layer's output with its full-precision counterpart to compensate for accumulated errors. (2) Adaptive Collaborative Error Suppression (ACES), which automatically adjusts the weighting coefficient to enhance the low-rank structure of the compression objective in CEALC. Specifically, the coefficient is optimized to maximize the ratio between the Frobenius norm of the compressed layer's output and that of the compression objective under a fixed rank, thus ensuring that the rank budget is utilized effectively. Extensive experiments across multiple LLM architectures and tasks show that, without fine-tuning or mixed-rank strategies, SAES-SVD consistently improves post-compression performance.

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.

End-to-end automatic speech recognition systems frequently hallucinate rare entities and domain-specific terms, especially in low-resource languages. While retrieval-augmented generation frameworks can mitigate these errors using large language models, current architectures face significant challenges. They either rely on standard sparse retrieval that ignores phonetic misrecognitions or utilize heavyweight cross-modal embeddings that introduce high latency. This letter proposes a highly efficient, purely lexical error-aware framework designed to explicitly resolve phonetic and loop hallucinations. Our approach integrates a symmetric text normalization module with a novel error-aware term frequency-inverse document frequency algorithm. By constructing a sparse diagonal penalty matrix based on historical errors, the retriever mathematically prioritizes corrective documents containing specific high-risk misrecognitions. Evaluated on the Persian subset of the FLEURS dataset, our method increased the error-aware hit rate from 53.7% to 90.9%. In end-to-end evaluations, the integrated framework reduced the final word error rate from 23.06% to 18.83%, achieving significant accuracy gains with near-zero inference latency.

Post-training quantization (PTQ) is widely used to reduce the cost of serving large language models (LLMs), but its accuracy cost is uneven and is often tuned per model. We study where quantization damage occurs and how to allocate a small additional precision budget. Using causal mixed-precision intervention as ground truth (raise each layer to 8-bit in turn and measure the accuracy it recovers) across 9 open-weight models in 4 architecture families, we test 3 intuitive hypotheses: that quantization damage lives in task circuits, where the model computes, or in weight statistics. None of them predicts which layers benefit from restored precision. Recovery is instead diffuse: for 8 of 9 models, recovering 75% of the gap takes roughly half the layers; the lone exception, Qwen3-8B, is sharply concentrated. At a matched precision budget, spending it globally on finer quantization granularity beats locally repairing the most recoverable layers for all 8 group-128-compatible models (all but OpenLLaMA, whose width rules out group-128), by 21-52 points, including the concentrated Qwen3-8B. We report 2 secondary findings: the residual is budget-limited (8-bit is near-lossless in our evaluation across RTN, GPTQ, and AWQ), and the location of peak recovery correlates with architecture within a family, though not across families. Within this budget setting, global granularity is a better default than selectively protecting critical layers. More broadly, cheap signals that correlate with quantization damage do not necessarily identify where restoring precision improves accuracy; this must be tested with causal intervention.

Prior work has shown that fine-tuning models on a narrow domain with misaligned data can lead to broad misalignment - a phenomenon termed "emergent misalignment" (Betley et al. 2025). While all tested models were susceptible to emergent misalignment, some models showed more resistance than others. Specifically the Qwen-2.5 family proved to be relatively resistant, while GPT-4o exhibited the strongest misalignment. In this paper we evaluate if current-generation open-weights models exhibit similar resistance to the Qwen-2.5 family and measure misalignment robustness over a range of model architectures and scales. We replicate the effect across nine modern open-weights models (Gemma 3 and Qwen 3 families, 1B-32B parameters). Models fine-tuned on insecure code generation show a 0.68% misalignment rate (compared to 0.07% for base models), matching the lower end of prior open-model results but dramatically lower than GPT-4o's 20%. We identify a critical format-dependent vulnerability: requiring JSON output doubles misalignment rates compared to natural language prompts (0.96% vs 0.42%). This suggests that structural constraints may bypass safety training by reducing the model's 'degrees of freedom' to refuse. These findings confirm emergent misalignment as a reproducible phenomenon in modern open-weights models, with rates substantially lower than observed in proprietary systems.

Spatial return models take the interaction matrix as given and leave feedback uninterpreted. We construct a bandwidth-free field from firms' language-model article embedding distributions using target-anchored Wasserstein barycentric reconstruction. A quadratic exposure-adjustment problem maps feedback into a peer-misalignment penalty ratio. For 52 firms, the field, frozen from 2018-2022 news, yields a 2023-2026 penalty ratio of 3.46 (95% interval [2.89, 4.17]) and higher conditional quasi-likelihood than equal-weighted peer support or RBF weighting of the same distances. Joint penalty ratios for the barycentric and news co-mention fields are 2.33 and 0.86 with boundary calibrated tests which reject both exclusions.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

We introduce fusion-based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

With the growing adoption of Large Language Model (LLM) agents in persistent, real-world roles, they naturally encounter continuous streams of tasks and inevitable failures. A key limitation, however, is their inability to systematically learn from these mistakes, forcing them to repeat identical errors in similar contexts. Unlike prior training-free methods that primarily store raw instance-level experience or focus on retrieving successful trajectories, we propose Mistake Notebook Learning (MNL), a novel memory framework that enables agents to self-curate generalizable guidance from batch-clustered failures. This mechanism allows agents to distill shared error patterns into structured "mistake notes," updating an external memory only when batch performance improves to ensure stability. To further amplify adaptability, we integrate MNL with test-time scaling, leveraging aggregated failure patterns to actively steer the search process away from known pitfalls. Experiments on mathematical reasoning, Text-to-SQL, and interactive agent benchmarks show that MNL achieves competitive performance compared to existing memory mechanisms and in-context methods in both effectiveness and efficiency. These findings position structured mistake abstraction as a critical lever for robust agent evolution, enabling continuous improvement without the cost of parameter updates. The code is available at https://github.com/Bairong-Xdynamics/MistakeNotebookLearning/tree/main.

Large language models frequently fail to produce correct code on their first attempt, yet most benchmarks evaluate them in a single-shot setting. We investigate iterative self-repair (feeding execution errors back to the model for correction) across seven models spanning three families and both open-weight and proprietary providers: Llama 3.1 8B, Llama 3.3 70B, Llama 4 Scout (MoE, 16 experts), Llama 4 Maverick (MoE, 128 experts), Qwen3 32B, Gemini 2.5 Flash, and Gemini 2.5 Pro. On HumanEval (164 problems) and MBPP Sanitized (257 problems) with up to five attempts, self-repair universally improves pass rates: +4.9 to +17.1 pp on HumanEval and +16.0 to +30.0 pp on MBPP. Gemini 2.5 Flash achieves the highest final pass rates (96.3% HumanEval, 93.8% MBPP). Most gains concentrate in the first two rounds.Error-type analysis shows assertion errors (logical mistakes) are the hardest to repair at ~45%, while syntax and name errors are repaired at substantially higher rates, connecting to broader findings on the limits of LLM self-correction. Prior work found that weaker models fail at self-repair or require fine-tuning; we show that modern instruction-tuned models succeed with prompting alone, even at 8B scale. We also provide the first comparison of dense and MoE architectures for self-repair, and extend the repair-vs-resampling tradeoff analysis to modern models. A prompt ablation reveals chain-of-thought repair yields up to +5.5 pp additional self-repair gain (measured as improvement in repair delta) over minimal prompting for capable models.

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can diverge under interventions, so observational adequacy alone cannot guarantee interventional competence. We begin by laying foundations, definitions of knowledge, learning, intelligence, counterfactual competence and AGI, and then analyze the limits of observational learning that motivate an error centric shift. We recast the problem as three questions about how explicit and implicit errors evolve under an agent's actions, which errors are unreachable within a fixed hypothesis space, and how conjecture and criticism expand that space. From these questions we propose Causal Mechanics, a mechanisms first program in which hypothesis space change is a first class operation and probabilistic structure is used when useful rather than presumed. We advance structural principles that make error discovery and correction tractable, including a differential Locality and Autonomy Principle for modular interventions, a gauge invariant form of Independent Causal Mechanisms for separability, and the Compositional Autonomy Principle for analogy preservation, together with actionable diagnostics. The aim is a scaffold for systems that can convert unreachable errors into reachable ones and correct them.

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an optimal code sequence. We automate this choice by estimating the effective noise channel after each level and selecting the next code accordingly. In particular, we use learning-based methods to tailor small, non-additive encoders when the noise exhibits sufficient structure, then switch to standard codes once the noise is nearly uniform. In simulations, this level-wise adaptation achieves a target logical error rate with far fewer qubits than concatenating stabilizer codes alone--reducing qubit counts by up to two orders of magnitude for strongly structured noise. Therefore, this hybrid, learning-based strategy offers a promising tool for early fault-tolerant quantum computing.

Diffusion probabilistic models (DPMs) have shown remarkable performance in visual synthesis but are computationally expensive due to the need for multiple evaluations during the sampling. Recent predictor-corrector diffusion samplers have significantly reduced the required number of function evaluations (NFE), but inherently suffer from a misalignment issue caused by the extra corrector step, especially with a large classifier-free guidance scale (CFG). In this paper, we introduce a new fast DPM sampler called DC-Solver, which leverages dynamic compensation (DC) to mitigate the misalignment of the predictor-corrector samplers. The dynamic compensation is controlled by compensation ratios that are adaptive to the sampling steps and can be optimized on only 10 datapoints by pushing the sampling trajectory toward a ground truth trajectory. We further propose a cascade polynomial regression (CPR) which can instantly predict the compensation ratios on unseen sampling configurations. Additionally, we find that the proposed dynamic compensation can also serve as a plug-and-play module to boost the performance of predictor-only samplers. Extensive experiments on both unconditional sampling and conditional sampling demonstrate that our DC-Solver can consistently improve the sampling quality over previous methods on different DPMs with a wide range of resolutions up to 1024times1024. Notably, we achieve 10.38 FID (NFE=5) on unconditional FFHQ and 0.394 MSE (NFE=5, CFG=7.5) on Stable-Diffusion-2.1. Code is available at https://github.com/wl-zhao/DC-Solver

The high computational costs of large language models (LLMs) have led to a flurry of research on LLM compression, via methods such as quantization, sparsification, or structured pruning. A new frontier in this area is given by dynamic, non-uniform compression methods, which adjust the compression levels (e.g., sparsity) per-block or even per-layer in order to minimize accuracy loss, while guaranteeing a global compression threshold. Yet, current methods rely on heuristics for identifying the "importance" of a given layer towards the loss, based on assumptions such as error monotonicity, i.e. that the end-to-end model compression error is proportional to the sum of layer-wise errors. In this paper, we revisit this area, and propose a new and general approach for dynamic compression that is provably optimal in a given input range. We begin from the motivating observation that, in general, error monotonicity does not hold for LLMs: compressed models with lower sum of per-layer errors can perform worse than models with higher error sums. To address this, we propose a new general evolutionary framework for dynamic LLM compression called EvoPress, which has provable convergence, and low sample and evaluation complexity. We show that these theoretical guarantees lead to highly competitive practical performance for dynamic compression of Llama, Mistral and Phi models. Via EvoPress, we set new state-of-the-art results across all compression approaches: structural pruning (block/layer dropping), unstructured sparsity, as well as quantization with dynamic bitwidths. Our code is available at https://github.com/IST-DASLab/EvoPress.

Trajectory-based data attribution methods estimate the influence of training samples on model predictions by unrolling the training trajectory. They are widely used in applications such as data selection, data valuation, and model diagnosis, but there is a lack of comprehensive error analysis of these methods, raising concerns about method faithfulness and hindering reliable deployment. In this work, we provide the first systematic analysis of error sources in trajectory-based data attribution, together with concrete remedies to mitigate them and practical guidelines for downstream use. We organize the total error into three categories, config-level, algorithm-level, and system-level. We make three contributions. First, we identify optimizer mismatch as the dominant config-level error: existing methods derive their attribution under the assumption of SGD, even for models trained with the modern de facto optimizer AdamW. We propose AdamW-influence to fully account for AdamW's optimization dynamics, yielding improvements from 10% to over 300% in Spearman correlation between estimated and ground-truth influence across four settings spanning MLP, CNN, GPT-2, and Llama 3.2-1B. Second, we isolate the remaining algorithm-level error arising from the first-order Taylor approximation, identify the learning rate and trajectory length as factors governing the error magnitude, and derive a closed-form error proxy that can be evaluated along the original trajectory without retraining. Third, we translate these insights into practical guidelines for data selection by unifying offline and online strategies under a K-step look-ahead framework. Under this framework, online selection with a short horizon often matches or exceeds offline, and the optimal horizon can be tuned jointly with the learning rate. Together, these results turn the framework into an actionable selection recipe for practitioners.

A pervasive intuition holds that vision-language models (VLMs) are most trustworthy when their attention maps look sharp: concentrated attention on the queried region should imply a confident, calibrated answer. We test this Attention-Confidence Assumption directly. We instrument three open-weight VLM families (LLaVA-1.5, PaliGemma, Qwen2-VL; 3-7B parameters) with a unified mechanistic pipeline -- the VLM Reliability Probe (VRP) -- that compares attention structure, generation dynamics, and hidden-state geometry against a single correctness label. Three results emerge. (i) Attention structure is a near-zero predictor of correctness (R_pb(C_k,y)=0.001, 95% CI [-0.034,0.036]; R_pb(H_s,y)=-0.012, [-0.047,0.024] on a pooled n=3,090 split), even though attention remains causally necessary for feature extraction (top-30% patch masking drops accuracy by 8.2-11.3 pp, p<0.001). (ii) Reliability becomes legible later in the computation: a single hidden-state linear probe reaches AUROC>0.95 on POPE for two of three families, and self-consistency at K=10 is the strongest behavioral predictor we measure at 10x inference cost (R_pb=0.43). (iii) Causal neuron-level ablations expose a sharp architectural split with direct monitor-design implications: late-fusion LLaVA concentrates reliability in a fragile late bottleneck (-8.3 pp object-identification accuracy after top-5 probe-neuron ablation), whereas early-fusion PaliGemma and Qwen2-VL distribute it widely and absorb destruction of ~50% of their peak-layer hidden dimension with <=1 pp degradation. The takeaway is narrow but consequential: in 3-7B VLMs, reliability is read more reliably off hidden-state geometry, layer-wise margin formation, and sparse late-layer circuits than off attention-map sharpness.

LLM-based Triton kernel generation has attracted significant interest, yet a fundamental empirical question remains unanswered: where does this capability break down, and why? We present KernelBench-X, a benchmark designed to answer this question through category-aware evaluation of correctness and hardware efficiency across 176 tasks in 15 categories. Our systematic comparison of five representative methods yields three main findings. First, task structure determines correctness more than method design. Category explains nearly three times more variance in semantic correctness than method (9.4% vs 3.3% explained deviance), and 72% of Fusion tasks fail across all five methods while Math tasks are solved consistently. Second, iterative refinement improves correctness, but not performance. Across GEAK iterations, compile rate rises from 52.3% to 68.8% while average speedup declines from 1.58times to 1.44times; newly rescued kernels consistently underperform persistently correct ones (1.16times vs 1.58times speedup in round~0to1). Third, correctness does not imply efficiency. 46.6% of correct kernels are slower than the PyTorch eager baseline, and cross-hardware speedup variance reaches 21.4times. Besides, quantization remains completely unsolved (0/30 successes) despite non-trivial compilation rates, revealing systematic misunderstanding of numerical computation contracts rather than surface-level syntax errors. These findings suggest that future progress depends on handling global coordination, explicitly modeling numerical precision, and incorporating hardware efficiency into generation. The code is available at https://github.com/BonnieW05/KernelBenchX

Self-correction is particularly useful when a failure constrains the next repair. Coding agents benefit from this property because compilers, tests, and execution traces turn many failures into typed recovery signals, but broad language-agent tasks often expose only a coarse task failure. This creates a tension for generic recovery playbooks: they broaden the agent's context precisely when the system needs a narrower repair interface, mixing incompatible signals for invalid actions, missing procedures, and strict-format errors. Our insight is that development-set failures can recover part of the missing diagnostic substrate by deciding which recovery interventions are admissible before test-time correction. We propose DARC, a diagnosis-guided recovery harness that profiles task-family failure modes, prunes mismatched interventions from a shared recovery library, and freezes a verifier-selected success-cost policy for deployment. This causal order makes correction selective: the harness first determines what kind of failure can be repaired, then decides how much recovery evidence to spend. In ALFWorld, AppWorld, and XBRL Finance, the same protocol yields an action-validity harness, a procedural-recovery fallback, and a format-precision retrieval policy; in each evaluated setting it improves average task performance over base agents and broad playbooks while reducing environment steps or retrieval budget. Our experiments show that failures need not trigger uniformly more context: DARC turns self-correction from prompt expansion into recovery-interface design. DARC provides a practical route toward more reliable agents in domains where compiler-like feedback is absent: making failures actionable before making contexts larger.

Asking a large language model to respond in JSON should be a formatting choice, not a capability tax. Yet we find that structured output requirements -- JSON, XML, LaTeX, Markdown -- substantially degrade reasoning and writing performance across open-weight models. The research response has focused on constrained decoding, but sampling bias accounts for only a fraction of the degradation. The dominant cost enters at the prompt: format-requesting instructions alone cause most of the accuracy loss, before any decoder constraint is applied. This diagnosis points to a simple principle: decouple reasoning from formatting. Whether by generating freeform first and reformatting in a second pass, or by enabling extended thinking within a single generation, separating the two concerns substantially recovers lost accuracy. Across six open-weight models, four API models, four formats, and tasks spanning math, science, logic, and writing, decoupling recovers most lost accuracy. Notably, most recent closed-weight models show little to no format tax, suggesting the problem is not inherent to structured generation but a gap that current open-weight models have yet to close. Code is available at https://github.com/ivnle/the-format-tax.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model's reflective ability. Though some studies attempt to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes. In this work, we propose to enhance LLMs' reasoning ability by Learning from Errors for Mathematical Advancement (LEMMA). LEMMA constructs data consisting of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an error-type grounded mistake augmentation method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. Through a model-aware smooth reflection connection, the erroneous solution is transferred to the correct one. By fine-tuning on the constructed dataset, the model is able to self-correct errors autonomously within the generation process without relying on external critique models. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong baselines.

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.

Large language models (LLMs) can call tools effectively, yet they remain brittle in multi-turn execution: following a tool call error, smaller models often degenerate into repetitive invalid re-invocations, failing to interpret error feedback and self-correct. This brittleness hinders reliable real-world deployment, where the execution errors are inherently inevitable during tool interaction procedures. We identify a key limitation of current approaches: standard reinforcement learning (RL) treats errors as sparse negative rewards, providing no guidance on how to recover, while pre-collected synthetic error-correction datasets suffer from distribution mismatch with the model's on-policy error modes. To bridge this gap, we propose Fission-GRPO, a framework that converts execution errors into corrective supervision within the RL training loop. Our core mechanism fissions each failed trajectory into a new training instance by augmenting it with diagnostic feedback from a finetuned Error Simulator, then resampling recovery rollouts on-policy. This enables the model to learn from the precise errors it makes during exploration, rather than from static, pre-collected error cases. On the BFCL v4 Multi-Turn, Fission-GRPO improves the error recovery rate of Qwen3-8B by 5.7% absolute, crucially, yielding a 4% overall accuracy gain (42.75% to 46.75%) over GRPO and outperforming specialized tool-use agents.

Agent skill libraries are becoming routable software assets: a retrieved skill can contribute instructions, scripts, resource bindings, and execution assumptions to an agent. This makes retrieval failures more specific than broad irrelevance. A system can find the right capability family yet expose the wrong same-capability representative. We study this failure as same-capability risk-exposure retrieval. Each benchmark unit pairs a helpful skill with a query-specific risky sibling that shares the capability family but differs on an execution-controlling contract, such as the required resource, precondition, procedure, or artifact. We introduce SameCapRisk-Bench, an auditable benchmark with 1,190 skill-risk units and 1,686 evaluation query cases: 694 marked-sibling units under public library pressure and 496 hard role-flip units where the same two skills swap helpful/risky roles across paired queries. The release records admission evidence, cue/leakage checks, source hashes, family relations, and fixed candidate pools. The benchmark reports helpful ranking together with harmful sibling rate (HSR@K), the top-K exposure of the marked risky sibling. On this benchmark, public SkillRouter, SkillRet, and R3-Skill retrieve helpful skills at high Recall@3 (0.848--0.888) but also expose marked risky siblings frequently (HSR@3 0.346--0.372). A fully public score-and-cluster pipeline lowers HSR@3 to 0.128--0.182, with Recall@3 of 0.713--0.776. Under a benchmark-trained reference scorer, public text-cluster and controlled resolvers reach HSR@3 0.012 and 0.007; the latter attains Recall@3 0.833. Skill retrieval should therefore report both capability matching and same-family risk exposure, with HSR serving as a targeted exposure certificate for fixed skill libraries.

Instruction-tuning data are judged by quality metrics, and tuned models are judged by benchmarks, but both judgments pass through an output interface: the surface format in which an answer is written. Using gradient signatures across 12 tasks, four semantically equivalent interfaces, three model families, and controlled corruptions, we show that this interface confounds both measurements. Spectral statistics such as effective rank are provably invariant to interface rotation and empirically blind to semantic corruption, while the direction of the update carries the quality signal. The interface-varying residual is not noise: it identifies each unit's own target task perfectly across all three families. Capability itself is stored relative to the training interface: a skill that raises accuracy by more than 40 points under the training format can be nearly invisible under every other, and correcting a single generation budget flips the measured effect of fine-tuning on GSM8K from a gain into a large loss. Pre-registered interventions delimit where this geometry stops short of control. Data quality and model capability are interface-conditioned quantities, and current practice often reports the interface instead of the content.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a harness system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76\% of cases. Our ReFlect harness achieves task success rates ranging from 41\% on gpt-4o-mini to 56\% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0\% (Direct CoT) to between 82\% (Qwen2.5-72B) and 87\% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7\% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

Agent frameworks increasingly package procedural knowledge as skills: instruction files an agent reads on demand, while public libraries now hold thousands of them. Which skill to read has thus become a decision the policy itself makes in the middle of an episode, yet no existing signal trains it. We show that the default remedy, outcome-rewarded RL over the candidate slate, cannot teach it, for a structural reason we identify and name selector credit starvation: under a broadcast, sequence-level advantage, the few tokens that name the chosen skill carry a vanishing share of the loss, and the credit they inherit is increasingly wrong-signed as trajectories lengthen. A correct choice is punished whenever the execution after it fails, even though the choice itself is among the most valuable decisions in the trajectory. Auditing a completed run's own training artifacts confirms all three properties, each worsening monotonically with horizon. SkillGate removes the failure by construction: it partitions the token support into two disjoint credit channels, outcome credit reaching only execution tokens, and a separate action-local advantage reaching exactly the skill-naming tokens, positive only when a trajectory's single read is the correct one. On five agentic benchmarks under a 16-candidate slate, SkillGate lifts a 9B policy from 40.8% to 53.2% trial success, well ahead of the identical budget spent on outcome reward alone, while cutting exposure to misleading candidates by two thirds and reading fewer skills.

Consider the problem of finding the best matching in a weighted graph where we only have access to predictions of the actual stochastic weights, based on an underlying context. If the predictor is the Bayes optimal one, then computing the best matching based on the predicted weights is optimal. However, in practice, this perfect information scenario is not realistic. Given an imperfect predictor, a suboptimal decision rule may compensate for the induced error and thus outperform the standard optimal rule. In this paper, we propose multicalibration as a way to address this problem. This fairness notion requires a predictor to be unbiased on each element of a family of protected sets of contexts. Given a class of matching algorithms mathcal C and any predictor γ of the edge-weights, we show how to construct a specific multicalibrated predictor hat γ, with the following property. Picking the best matching based on the output of hat γ is competitive with the best decision rule in mathcal C applied onto the original predictor γ. We complement this result by providing sample complexity bounds.

We consider a combinatorial multi-armed bandit problem for maximum value reward function under maximum value and index feedback. This is a new feedback structure that lies in between commonly studied semi-bandit and full-bandit feedback structures. We propose an algorithm and provide a regret bound for problem instances with stochastic arm outcomes according to arbitrary distributions with finite supports. The regret analysis rests on considering an extended set of arms, associated with values and probabilities of arm outcomes, and applying a smoothness condition. Our algorithm achieves a O((k/Delta)log(T)) distribution-dependent and a O(T) distribution-independent regret where k is the number of arms selected in each round, Delta is a distribution-dependent reward gap and T is the horizon time. Perhaps surprisingly, the regret bound is comparable to previously-known bound under more informative semi-bandit feedback. We demonstrate the effectiveness of our algorithm through experimental results.

Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a latent preference state matrix, where the spread between an agent's internal ask price (the unconditional maximum) and the market's best bid (the reachable maximum) creates a structural liquidity constraint. We establish a Threshold Impossibility Theorem showing that linear compensation cannot close these spreads unless it induces a categorical identity shift. A dynamic discrete choice execution model further demonstrates that matches occur only when the market to book ratio crosses a time decaying liquidity threshold, analogous to order execution under inventory pressure. Numerical experiments validate persistent slippage, regional invariance of preference orderings, and high tier zero spread executions. The model provides a unified microstructure explanation for matching failures, compensation inefficiency, and post match regret in illiquid order driven environments.

Sentence-level human value detection is typically framed as multi-label classification over Schwartz values, but it remains unclear whether Schwartz higher-order (HO) categories provide usable structure. We study this under a strict compute-frugal budget (single 8 GB GPU) on ValueEval'24 / ValuesML (74K English sentences). We compare (i) direct supervised transformers, (ii) HOrightarrowvalues pipelines that enforce the hierarchy with hard masks, and (iii) PresencerightarrowHOrightarrowvalues cascades, alongside low-cost add-ons (lexica, short context, topics), label-wise threshold tuning, small instruction-tuned LLM baselines (le10B), QLoRA, and simple ensembles. HO categories are learnable from single sentences (e.g., the easiest bipolar pair reaches Macro-F_1approx0.58), but hard hierarchical gating is not a reliable win: it often reduces end-task Macro-F_1 via error compounding and recall suppression. In contrast, label-wise threshold tuning is a high-leverage knob (up to +0.05 Macro-F_1), and small transformer ensembles provide the most consistent additional gains (up to +0.02 Macro-F_1). Small LLMs lag behind supervised encoders as stand-alone systems, yet can contribute complementary errors in cross-family ensembles. Overall, HO structure is useful descriptively, but enforcing it with hard gates hurts sentence-level value detection; robust improvements come from calibration and lightweight ensembling.

We study single-error detection and correction for analog codes over R. The key performance measures are the parameters Γ_1(C) and Γ_2(C), which quantify, respectively, the minimum separation required between large outlying errors that must be detected or located and the magnitude of tolerable perturbations. First, we prove that every real linear [n,k] code C satisfies \[ Γ_1(C)\ge 2\left\lceiln{n-k}\right\rceil. \] Moreover, when k=n-2, we prove that every real linear [n,n-2] code C satisfies \[ Γ_2(C)\ge 1{\sin^2(π/2n)}. \] Together, these two lower bounds settle all four open problems of Roth concerning the optimality of single-error-detecting and single-error-correcting analog codes. The proof of the first bound is based on a double-induction argument, while the proof of the second combines a zonotope-based geometric characterization of Γ_2(C) with a cyclic sine-product inequality. In addition, we construct analog codes with higher fixed redundancy and show that, for every fixed rge 2, there exists a class of linear [n,ge n-r] codes over R such that \[ Γ_2(C)\le O\left(n^{1+1{r-1}}\right). \] This gives a new upper bound in the fixed-redundancy regime, which was not covered by previously known constructions.

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respect to a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a subset of nodes, we focus on rules dedicated to the hierarchical hF_{beta} scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conduct extensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications. The code is available at https://github.com/RomanPlaud/hierarchical_decision_rules

We introduce a method that dramatically reduces fine-tuning VRAM requirements and rectifies quantization errors in quantized Large Language Models. First, we develop an extremely memory-efficient fine-tuning (EMEF) method for quantized models using Low-Rank Adaptation (LoRA), and drawing upon it, we construct an error-correcting algorithm designed to minimize errors induced by the quantization process. Our method reduces the memory requirements by up to 5.6 times, which enables fine-tuning a 7 billion parameter Large Language Model (LLM) on consumer laptops. At the same time, we propose a Low-Rank Error Correction (LREC) method that exploits the added LoRA layers to ameliorate the gap between the quantized model and its float point counterpart. Our error correction framework leads to a fully functional INT2 quantized LLM with the capacity to generate coherent English text. To the best of our knowledge, this is the first INT2 Large Language Model that has been able to reach such a performance. The overhead of our method is merely a 1.05 times increase in model size, which translates to an effective precision of INT2.1. Also, our method readily generalizes to other quantization standards, such as INT3, INT4, and INT8, restoring their lost performance, which marks a significant milestone in the field of model quantization. The strategies delineated in this paper hold promising implications for the future development and optimization of quantized models, marking a pivotal shift in the landscape of low-resource machine learning computations.

Speech-based applications pass spoken queries through automatic speech recognition (ASR) before any retrieval module, so ASR errors enter the pipeline as a fixed upstream constraint. We empirically test whether two extensions to standard retrieval-augmented generation (RAG), entity-graph linking and iterative reformulation, absorb or amplify these errors. Using four English accents synthesized through neural TTS, we evaluate four RAG configurations on three multi-hop QA benchmarks (HotpotQA, 2WikiMultiHopQA and MuSiQue) against a clean-text oracle. Although the structurally richer configurations generally retain higher absolute F1 under ASR input, both extensions amplify the error: the F1 gap from clean text to the highest-WER accent is 36-67% larger under their combination than under naive dense retrieval, on all three benchmarks. The dominant failure mode is corruption of one or more query entities, accounting for 87-96% of degradation cases on 2WikiMultiHopQA across all four methods. Two lightweight surface-form mitigations leave most of the gap intact, indicating that downstream retrieval structure amplifies remaining entity errors. We release code and data at https://github.com/ZhenghuaBao/spoken-multihop-rag .

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Self-improving AI agents are designed to learn from their mistakes. We show they can also hallucinate mistakes that never happened. We study this failure mode in automated harness optimization, where an LLM-based proposer edits an agent's scaffold, including prompts, parsers, filters, validators and guardrails, to eliminate observed failures. But this process rarely asks first: was there a real failure to fix? We introduce the Counterfactual Fabrication Lab, a deterministic micro-lab where the correct action is known: do nothing. The lab plants a candidate guardrail for a failure class that provably never occurs, presents only legal episodes, and uses a byte-exact oracle to check every cited violation. The proposer behaves as expected on real violations and abstains on featureless legal input. Yet when the legal input contains a harmless pattern resembling a familiar game rule, it invents a failure: in 15/60 runs, versus 0/60 on featureless input, it enables the nonexistent-rule guardrail and cites a violation the oracle refutes. The effect is structured, not indiscriminate. In single-shot proposals it appears only when three conditions coincide: a rule-shaped pattern, an open-ended rule set and an instruction that presupposes failures. Removing any of these conditions eliminates the fabrication. Because the invented guardrail changes no true outcome and cannot improve an already-perfect suppression score, the phenomenon is neither reward hacking nor over-refusal. It is a phantom guardrail: a fix for a failure that never happened, invisible to suppression-only acceptance. Inside an add-only accept loop it re-enters even without the failure-presupposing instruction, the loop's keep-adding role supplying the demand the instruction supplied in single shot, and once in it stays. We present the Counterfactual Fabrication Lab for measuring fabricated failures in self-improving agent harnesses.

Why do language models sometimes prefer correct statements even when trained on mixed-quality data? We introduce the Compression--Consistency Principle: next-token prediction favors hypotheses that allow shorter and more internally consistent descriptions of the training data. Truth bias emerges only when false alternatives are structurally harder to compress. We test this using small GPT-2-style character-level transformers (3.5M--86M parameters) on synthetic math corpora with controlled mixtures of correct and incorrect rules. In the random-error setting, models strongly prefer correct completions in paired evaluation: 83.1% accuracy at balanced data and 67.0% even when correct rules appear in only 10% of the corpus. Replacing random errors with a coherent but mathematically incorrect rule system largely eliminates the preference (near-chance accuracy). In a more natural-language-like synthetic world, the effect is weaker but still present (57.7%). Additional experiments show that embedding verification steps can restore preference for correctness even at small scale, while increasing the number of consistent rules produces a graded improvement in accuracy. Our results suggest that what appears as a "truth bias" is largely a side effect of compression pressure and preference for internal consistency, rather than an intrinsic drive toward truth. Full code and data are available at https://github.com/Rai220/compression-drives-truth.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Despite the recent advancements in abstractive summarization systems leveraged from large-scale datasets and pre-trained language models, the factual correctness of the summary is still insufficient. One line of trials to mitigate this problem is to include a post-editing process that can detect and correct factual errors in the summary. In building such a post-editing system, it is strongly required that 1) the process has a high success rate and interpretability and 2) has a fast running time. Previous approaches focus on regeneration of the summary using the autoregressive models, which lack interpretability and require high computing resources. In this paper, we propose an efficient factual error correction system RFEC based on entities retrieval post-editing process. RFEC first retrieves the evidence sentences from the original document by comparing the sentences with the target summary. This approach greatly reduces the length of text for a system to analyze. Next, RFEC detects the entity-level errors in the summaries by considering the evidence sentences and substitutes the wrong entities with the accurate entities from the evidence sentences. Experimental results show that our proposed error correction system shows more competitive performance than baseline methods in correcting the factual errors with a much faster speed.

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long's (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of O(h^{1/4-epsilon}) rather than the usual O(h^{1/2}). Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses.

Zero-shot models like CLIP are often fine-tuned on a target dataset to improve its accuracy further, but this can compromise out-of-distribution (OOD) robustness. Robust Fine-Tuning (RFT )~wortsman2021robust, which interpolates between the zero-shot and fine-tuned models, has been proposed to address this issue. However, understanding when RFT actually improves OOD error remains limited. In this work, we empirically investigate the robustness of RFT in CLIP models, with a focus on the sharpness of the CLIP model during interpolation. First, we demonstrate that while sharpness may not serve as a reliable indicator for predicting the generalization of modern architectures like CLIP on OOD data, this challenges the conventional belief in the generalization benefits of flat minima in foundation models. However, by examining the role of the straggler layer phenomenon, we show that, unlike overall sharpness, the layer-wise sharpness of straggler layers can reliably capture the generalization performance of interpolated CLIP models on OOD data. Our extensive experiments reveal that layer-wise sharpness correlates with generalization in OOD accuracy for RFT. Furthermore, we demonstrate that by inducing sparsity in the straggler layers, we can mitigate the failure mode phenomenon in RFT. To the best of our knowledge, this is the first work to study the role of sharpness in the success of interpolation in the weight space of CLIP foundation models. Our code is available at https://github.com/alirezaabdollahpour/CLIP_Mode_Connectivity.

Recent works on structured text translation remain limited to the sentence level, as they struggle to effectively handle the complex document-level XML or HTML structures. To address this, we propose Format Reinforcement Learning (FormatRL), which employs Group Relative Policy Optimization on top of a supervised fine-tuning model to directly optimize novel structure-aware rewards: 1) TreeSim, which measures structural similarity between predicted and reference XML trees and 2) Node-chrF, which measures translation quality at the level of XML nodes. Additionally, we apply StrucAUC, a fine-grained metric distinguishing between minor errors and major structural failures. Experiments on the SAP software-documentation benchmark demonstrate improvements across six metrics and an analysis further shows how different reward functions contribute to improvements in both structural and translation quality.

Automatic Question Generation (QG) often produces outputs with critical defects, such as factual hallucinations and answer mismatches. However, existing evaluation methods, including LLM-based evaluators, mainly adopt a black-box and holistic paradigm without explicit error modeling, leading to the neglect of such defects and overestimation of question quality. To address this issue, we propose ErrEval, a flexible and Error-aware Evaluation framework that enhances QG evaluation through explicit error diagnostics. Specifically, ErrEval reformulates evaluation as a two-stage process of error diagnosis followed by informed scoring. At the first stage, a lightweight plug-and-play Error Identifier detects and categorizes common errors across structural, linguistic, and content-related aspects. These diagnostic signals are then incorporated as explicit evidence to guide LLM evaluators toward more fine-grained and grounded judgments. Extensive experiments on three benchmarks demonstrate the effectiveness of ErrEval, showing that incorporating explicit diagnostics improves alignment with human judgments. Further analyses confirm that ErrEval effectively mitigates the overestimation of low-quality questions.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific ``skills,'' but there has been limited study of where these newly-learnt skills reside inside the massive model. This paper introduces the term skill localization for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters (sim0.01% of model parameters) responsible for (>95%) of the model's performance, in the sense that grafting the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further re-training is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution (40-90% error reduction) as well as the quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms of continual learning.

The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of Δ_{acc} = 6.05% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains Δ_{acc} = 2.97% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and Δ_{ppl} = - 0.28 lower perplexity on WikiText2 than LQER.

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.

Automatic Speech Recognition (ASR) error correction aims to correct recognition errors while preserving accurate text. Although traditional approaches demonstrate moderate effectiveness, LLMs offer a paradigm that eliminates the need for training and labeled data. However, directly using LLMs will encounter hallucinations problem, which may lead to the modification of the correct text. To address this problem, we propose the Reliable LLM Correction Framework (RLLM-CF), which consists of three stages: (1) error pre-detection, (2) chain-of-thought sub-tasks iterative correction, and (3) reasoning process verification. The advantage of our method is that it does not require additional information or fine-tuning of the model, and ensures the correctness of the LLM correction under multi-pass programming. Experiments on AISHELL-1, AISHELL-2, and Librispeech show that the GPT-4o model enhanced by our framework achieves 21%, 11%, 9%, and 11.4% relative reductions in CER/WER.

Exploration in environments which differ across episodes has received increasing attention in recent years. Current methods use some combination of global novelty bonuses, computed using the agent's entire training experience, and episodic novelty bonuses, computed using only experience from the current episode. However, the use of these two types of bonuses has been ad-hoc and poorly understood. In this work, we shed light on the behavior of these two types of bonuses through controlled experiments on easily interpretable tasks as well as challenging pixel-based settings. We find that the two types of bonuses succeed in different settings, with episodic bonuses being most effective when there is little shared structure across episodes and global bonuses being effective when more structure is shared. We develop a conceptual framework which makes this notion of shared structure precise by considering the variance of the value function across contexts, and which provides a unifying explanation of our empirical results. We furthermore find that combining the two bonuses can lead to more robust performance across different degrees of shared structure, and investigate different algorithmic choices for defining and combining global and episodic bonuses based on function approximation. This results in an algorithm which sets a new state of the art across 16 tasks from the MiniHack suite used in prior work, and also performs robustly on Habitat and Montezuma's Revenge.

Low-Rank Adaptation (LoRA) offers a parameter-efficient paradigm for tuning large models. While recent spectral initialization methods improve convergence and performance over the naive "Noise & Zeros" scheme, their extra computational and storage overhead undermines efficiency. In this paper, we establish update magnitude as the fundamental driver of LoRA performance and propose LoRAM, a magnitude-driven "Basis & Basis" initialization scheme that matches spectral methods without their inefficiencies. Our key contributions are threefold: (i) Magnitude of weight updates determines convergence. We prove low-rank structures intrinsically bound update magnitudes, unifying hyperparameter tuning in learning rate, scaling factor, and initialization as mechanisms to optimize magnitude regulation. (ii) Spectral initialization succeeds via magnitude amplification. We demystify that the presumed knowledge-driven benefit of the spectral component essentially arises from the boost in the weight update magnitude. (iii) A novel and compact initialization strategy, LoRAM, scales deterministic orthogonal bases using pretrained weight magnitudes to simulate spectral gains. Extensive experiments show that LoRAM serves as a strong baseline, retaining the full efficiency of LoRA while matching or outperforming spectral initialization across benchmarks.

LLM agents often retry after external validation rejects a candidate, but the interface between validation and the next model call remains underspecified. We introduce VeriHarness, a code-controlled agent loop in which models generate candidates while external validators control acceptance, budgets, and traces. We use it to compare raw diagnostics with feedback that identifies the failure location, observed value, and admissible alternatives. Across 50 paired TextWorld games under a four-call cap, feedback containing all three fields raises terminal success from 14/50 to 36/50 for Qwen2.5-Coder-14B (+44 percentage points) and from 8/50 to 29/50 for Llama-3.1-8B (+42 points). Ablations locate most of the gain in the admissible alternatives: feedback containing only the location and observed value remains near the raw diagnostic baseline. Presenting the complete repair information in prose instead of a keyed JSON record yields nearly the same success, providing no evidence that JSON syntax itself improves repair. The ordering persists across the tested call budgets and one sampled-decoding setting.

Although large language models (LLMs) have become transformative, they still make mistakes and can explore unproductive reasoning paths. Self-correction is an important capability for a trustworthy LLM, particularly an autoregressive LLM. While LLMs can identify error in user input, they exhibit a systematic 'Self-Correction Blind Spot' - failing to correct identical error in their own outputs. To systematically study this phenomenon, we introduce Self-Correction Bench, a systematic framework to measure this phenomenon through controlled error injection at three complexity levels. Testing 14 models, we find an average 64.5% blind spot rate. We find multiple evidences that this limitation relates to training data composition: human training demonstrations predominantly show error-free responses rather than error-correction sequences, unlike RL-trained models that learn error correction through outcome feedback. Remarkably, simply appending "Wait" reduces blind spots by 89.3%, suggesting that the capability exists but requires activation. Our work highlights a critical limitation in current LLMs and offers potential avenues for improving their reliability and trustworthiness.

We present Voice Memory, a inference-only scheme for agentic speech recognition: at stream time, a frozen corrector reads a single per-domain memory.md and decides per utterance whether to act on the hypothesis or abstain and keep the 1-best. Asynchronously, a score-gated optimizer revises that file through bounded edits, accepting an edit only when it strictly improves a held-out score. Extended from classical ASR-LM framework, we refer this split the listener-thinker architecture; the two roles are coupled only through the memory, so no weights change and the learned skill stays auditable and portable. Restraint turns out to be the operative skill this loop discovers: unconstrained generative error correction (GER) over-corrects, breaking correct tokens on up to 64% of its edits on financial news, and Voice Memory, reduces this rate to 35%. Across ten HyPoradise domains with an open corrector, Voice Memory, lowers weighted word error rate from 8.36% to 7.52% (7.47% with three added in-context examples) without regressing any dataset below its 1-best baseline; gains concentrate where recoverable headroom is largest, including air-travel commands (8.40% to 3.40%) and noisy far-field speech (CHiME-4, 12.69% to 10.46%). The memory transfers across corrector families and adds zero parameters to the inference path. A demo and example code are provided for future studies.

Can small language models achieve strong tool-use performance without complex adaptation mechanisms? This paper investigates this question through Meta-Tool, a controlled empirical study comparing hypernetwork-based LoRA adaptation against carefully designed few-shot prompting. Using a Llama-3.2-3B-Instruct backbone, we evaluate four adaptation mechanisms--few-shot prompting, documentation encoding, hypernetwork-generated LoRA weights, and value-guided beam search--across four diverse benchmarks: Gorilla APIBench, Spider 2.0, WebArena, and InterCode. Our central finding is a well-supported negative result: despite generating non-trivial weight matrices, the 227.8M-parameter hypernetwork provides no measurable improvement over few-shot prompting alone. Comprehensive ablation studies reveal that few-shot examples contribute +21.5% to performance and documentation contributes +5.0%, while the hypernetwork adds 0%. A 3B model with well-designed prompts achieves 79.7% of GPT-5's average performance at 10 times lower latency. Error analysis across 722 failure cases spanning all shot counts (0--5) shows that at the 5-shot configuration (106 failures), failure modes are task-dependent: schema-heavy tasks (Spider 2.0, WebArena) show near-zero format errors with remaining failures semantic, while format errors dominate on Gorilla (100%) and InterCode (70%). These findings redirect practitioners toward prompt engineering and example curation rather than complex adaptation architectures.

Equivariance theory predicts that an architectural symmetry prior reduces sample complexity by a factor of |G|; this is widely cited but rarely measured as a scaling law with controls that separate the prior from its confounds. On a controlled C_n-symmetric task, we report three findings. First, a wrong-group control with identical orbit size and matched compute is worse than no constraint (joint pairwise CI [+0.79, +3.26] excludes zero, robust across estimators); misaligned constraint is actively harmful, not merely unhelpful. Second, an augmentation baseline equipped with test-time orbit averaging matches the equivariant model exactly -- bit-identical per-epoch validation curves across matched cells -- so the architecture-vs-augmentation gap is conditional on asymmetric test-time computation, not unconditional. Third, the relative exchange rate beta_diff = 1.28 is consistent in sign and order of magnitude with the theoretical 1.0 (single-level CI [+0.92, +2.05]); the more conservative two-level bootstrap (seeds x group sizes) widens this to [-0.63, +1.72], including zero, and a finer-N replication on a sqrt(2)-spaced grid is inconclusive (point estimate -0.82). The methodological contributions -- the relative-rate estimator that cancels the shared-difficulty confound, the wrong-group control, and a pre-specified failure taxonomy -- transfer to any inductive bias whose strength can be parameterised. Honest scoping: the primary estimator beta_diff was adopted post-hoc after the initial analysis revealed a positive-slope identifiability problem; the design was never externally pre-registered; and the headline number rests on an OLS slope over seven group sizes on a coarse N grid. This is an exploratory study, not a confirmatory measurement; the wrong-group result is the cleanest finding and the one we report with the most confidence. A registered replication on fresh seeds is future work.

Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts/ identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.

Large language models (LLMs) show increasing promise in medical applications, but their ability to detect and correct errors in clinical texts -- a prerequisite for safe deployment -- remains under-evaluated, particularly beyond English. We introduce MedRECT, a cross-lingual benchmark (Japanese/English) that formulates medical error handling as three subtasks: error detection, error localization (sentence extraction), and error correction. MedRECT is built with a scalable, automated pipeline from the Japanese Medical Licensing Examinations (JMLE) and a curated English counterpart, yielding MedRECT-ja (663 texts) and MedRECT-en (458 texts) with comparable error/no-error balance. We evaluate 9 contemporary LLMs spanning proprietary, open-weight, and reasoning families. Key findings: (i) reasoning models substantially outperform standard architectures, with up to 13.5% relative improvement in error detection and 51.0% in sentence extraction; (ii) cross-lingual evaluation reveals 5-10% performance gaps from English to Japanese, with smaller disparities for reasoning models; (iii) targeted LoRA fine-tuning yields asymmetric improvements in error correction performance (Japanese: +0.078, English: +0.168) while preserving reasoning capabilities; and (iv) our fine-tuned model exceeds human expert performance on structured medical error correction tasks. To our knowledge, MedRECT is the first comprehensive cross-lingual benchmark for medical error correction, providing a reproducible framework and resources for developing safer medical LLMs across languages.

Chain-of-thought (CoT) prompting has become central to mathematical reasoning in large language models, yet models remain brittle to early errors: a single arithmetic slip or unjustified inference typically propagates uncorrected to an incorrect final answer. We investigate whether training on intentionally flawed reasoning traces can teach models to detect and recover from such errors without degrading standard problem-solving ability. Using competition-level problems from MATH-lighteval, we generate CoT prefixes containing exactly one controlled error, either a calculation error (sign flips, dropped terms) or a reasoning error (misapplied rules, unjustified logical steps), and fine-tune Qwen3-4B with GRPO using a binary final-answer reward. Our Mixed-CoT-RL model matches standard RL on clean problems (41% vs 41%) while substantially outperforming it on problems prefilled with flawed reasoning (24% vs 19%). Notably, clean-only RL fine-tuning degrades robustness below the untuned baseline 19% vs. 20%), indicating that conventional training increases susceptibility to misleading prefills. Among error types, training on reasoning errors yields greater robustness gains than calculation errors alone, with mixed training performing best. These findings demonstrate that exposure to flawed traces during training can improve error-recovery behavior without sacrificing accuracy, suggesting a path toward more robust mathematical reasoning in LLMs.

Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for the end-to-end design of communication systems, offering a data driven alternative to conventional coding schemes. However, enforcing binary codewords within differentiable AE architectures remains difficult, as discretization breaks gradient flow and often leads to unstable convergence. To overcome this limitation, a simplified two stage training procedure is proposed, consisting of a continuous pretraining phase followed by direct binarization and fine tuning without gradient approximation techniques. For the (7,4) block configuration over a binary symmetric channel (BSC), the learned encoder-decoder pair learns a rotated version (coset code) of the optimal Hamming code, naturally recovering its linear and distance properties and thereby achieving the same block error rate (BLER) with maximum likelihood (ML) decoding. These results indicate that compact AE architectures can effectively learn structured, algebraically optimal binary codes through stable and straightforward training.

LLM-based multi-agent pipelines flip from correct to incorrect answers under simulated peer disagreement at rates we term yield, a vulnerability widely attributed to RLHF-induced sycophancy. We test this attribution across four model families and find it largely wrong: pretrained base models exhibit the same substitution pattern as their Instruct variants, averaging higher yield than Instruct. Using activation patching, we localize the corruption to a narrow mid-layer window where attention carries the causal weight and MLP contribution is negligible; patching above this window restores 96% of the clean-to-pressured P(correct) gap. The attack surface decomposes into two independent factors (channel framing and consensus strength) whose interaction produces a 47.5 percentage-point yield gap at majority consensus, preserved across jury sizes N in {4, 5, 6}. Two converging activation-space interventions show that pressure suppresses clean-reasoning features rather than activating a new sycophancy circuit. A single correctly-arguing dissenter reduces yield by 54-73 percentage points across all framings tested, whereas the strongest prompt-level defense fails on attack variants outside its design surface. Mitigations should target the mechanism, structured dissent at the pipeline level, rather than prompt-level defenses.

Recent works have shown the benefits to LLMs from fine-tuning golden-standard Chain-of-Thought (CoT) rationales or using them as correct examples in few-shot prompting. While humans can indeed imitate correct examples, learning from our mistakes is another vital aspect of human cognition. Hence, a question naturally arises: can LLMs learn and benefit from their mistakes, especially for their reasoning? This study investigates this problem from both the prompting and model-tuning perspectives. We begin by introducing CoTErrorSet, a new benchmark with 609,432 questions, each designed with both correct and error references, and demonstrating the types and reasons for making such mistakes. To explore the effectiveness of those mistakes, we design two methods: (1) Self-rethinking prompting guides LLMs to rethink whether they have made similar previous mistakes; and (2) Mistake tuning involves finetuning models in both correct and incorrect reasoning domains, rather than only tuning models to learn ground truth in traditional methodology. We conduct a series of experiments to prove LLMs can obtain benefits from mistakes in both directions. Our two methods offer potentially cost-effective strategies by leveraging errors to enhance reasoning capabilities, which costs significantly less than creating meticulously hand-crafted golden references. We ultimately make a thorough analysis of the reasons behind LLMs' errors, which provides directions that future research needs to overcome. CoTErrorSet will be published soon on \url{https://github.com/YookiTong/Learn-from-Mistakes-CotErrorSet}.

Domain expertise enhances judgment within boundaries but creates systematic vulnerabilities specifically at borders. We term this Transitive Expert Error (TEE), distinct from Dunning-Kruger effects, requiring calibrated expertise as precondition. Mechanisms enabling reliable within-domain judgment become liabilities when structural similarity masks causal divergence. Two core mechanisms operate: structural similarity bias causes experts to overweight surface features (shared vocabulary, patterns, formal structure) while missing causal architecture differences; authority persistence maintains confidence across competence boundaries through social reinforcement and metacognitive failures (experts experience no subjective uncertainty as pattern recognition operates smoothly on familiar-seeming inputs.) These mechanism intensify under three conditions: shared vocabulary masking divergent processes, social pressure for immediate judgment, and delayed feedback. These findings extend to AI routing architectures (MoE systems, multi-model orchestration, tool-using agents, RAG systems) exhibiting routing-induced failures (wrong specialist selected) and coverage-induced failures (no appropriate specialist exists). Both produce a hallucination phenotype: confident, coherent, structurally plausible but causally incorrect outputs at domain boundaries. In human systems where mechanisms are cognitive black boxes; AI architectures make them explicit and addressable. We propose interventions: multi-expert activation with disagreement detection (router level), boundary-aware calibration (specialist level), and coverage gap detection (training level). TEE has detectable signatures (routing patterns, confidence-accuracy dissociations, domain-inappropriate content) enabling monitoring and mitigation. What remains intractable in human cognition becomes addressable through architectural design.

Despite the power of Large Language Models (LLMs) like GPT-4, they still struggle with tasks that require generating complex, structured outputs. In this study, we assess the capability of Current LLMs in generating complex structured data and propose a structure-aware fine-tuning approach as a solution to improve this ability. To perform a comprehensive evaluation, we propose Struc-Bench, include five representative LLMs (i.e., GPT-NeoX 20B, GPT-3.5, GPT-4, and Vicuna) and evaluate them on our carefully constructed datasets spanning raw text, HTML, and LaTeX tables. Based on our analysis of current model performance, we identify specific common formatting errors and areas of potential improvement. To address complex formatting requirements, we utilize FormatCoT (Chain-of-Thought) to generate format instructions from target outputs. Our experiments show that our structure-aware fine-tuning method, when applied to LLaMA-7B, significantly improves adherence to natural language constraints, outperforming other evaluated LLMs. Based on these results, we present an ability map of model capabilities from six dimensions (i.e., coverage, formatting, reasoning, comprehension, pragmatics, and hallucination). This map highlights the weaknesses of LLMs in handling complex structured outputs and suggests promising directions for future work. Our code and models can be found at https://github.com/gersteinlab/Struc-Bench.

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive to round-off errors. We propose herein an explanation of this fact. A first remedy has been proposed in [F. Casenave, Accurate a posteriori error evaluation in the reduced basis method. C. R. Math. Acad. Sci. Paris 350 (2012) 539--542.]. Herein, we improve this remedy by proposing a new approximation of the error bound using the Empirical Interpolation Method (EIM). This method achieves higher levels of accuracy and requires potentially less precomputations than the usual formula. A version of the EIM stabilized with respect to round-off errors is also derived. The method is illustrated on a simple one-dimensional diffusion problem and a three-dimensional acoustic scattering problem solved by a boundary element method.

Fine-tuning can improve legal question-answering accuracy without improving how models use law supplied in context. We study this distinction in bilingual Bangladeshi legal QA, where observed errors can arise from answer scoring, retrieval, or failure to use relevant law. We construct a hierarchy-preserving statutory corpus, 2,165 reviewed bilingual fine-tuning examples, and a 150-item supplied-law control. We evaluate six instruction-tuned models: Llama-3.2-1B, Llama-3.2-3B, Qwen3.5-0.8B, Qwen3.5-2B, Qwen3.5-4B, and Gemma-4-E2B, with three LoRA seeds per model. To separate effects, we combine constrained option-letter scoring, cyclic option rotation, and controlled removal of the governing provision. On 398 Bar Council outputs, an exact-line parser attributes an accuracy gain of 50.0\% to the Qwen3.5-2B seed-42 adapter, whereas option scoring yields only 3.0%. For Gemma-4-E2B, the two scoring methods favor different systems. When the governing provision is guaranteed to be present, five of six reference models improve by 14.7%-19.3% under the four-order criterion. Removing that provision reduces accuracy by 8.0%-15.3% for models and by 13.8%-14.9% points for their adapters. However, difference-in differences estimates show no increase in reliance on the governing provision after fine-tuning. Results show that legal adaptation claims require separating scorer, retriever, and model effects. Our Code and data are available at https://anonymous.4open.science/r/bangladesh-legal-qa-11E3

How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state stays consistent while the returned answer silently violates prior commitments. We build DRIFT-Bench (Decomposing Reasoning Into Failure Types), a solver-instrumented benchmark of 816 test problems across three constraint domains, and evaluate four methods on it across four open-weight models (8B-120B parameters). MUS-Repair, which feeds minimal unsatisfiable subsets back to the generator, is strongest in every setting (+1.8 to +15.0 pp over the best non-MUS baseline). But the central finding is what repair leaves behind. After structured feedback, models rarely contradict themselves. They forget. Residual errors are 98-100% satisfiable drift across all settings, while contradiction drops to near zero. Reliable multi-turn systems must separately validate that the returned answer respects the maintained state. Code is available at https://github.com/kaons-research/drift-bench.

Autonomous agents increasingly perform bounded software tasks under an orchestrator that retries, resumes, and budgets them. The machinery such orchestrators reach for is the service mesh's: retry, timeout, and error-rate circuit breaking. We report a failure study of a production agentic software-delivery platform over 147 numbered incidents spanning 81 runs, each with a measured cost and, in most cases, a mutation proof reproducing the failure. All three assumptions those primitives rest on are violated in practice, and we quantify the consequences: a loop of fifty-four consecutive successful tool calls no error-rate breaker could see; a progress signal constant by construction, guaranteeing a false trip on the third repair round and driving one run from six of six components to three; twenty-one events accumulated across six invocations of one delegation, making a correct, idempotent component unwinnable; a misrouted failure that woke five components for a two-component fault, leaving three bystanders regressing working code; and twelve incidents in which the enforcement layer blocked correct work, the most expensive costing 107 agent turns and zero accepted writes. We find one cross-cutting cause and its dual. Identity adequacy: in five separate subsystems an identity that failed to discriminate produced a confident wrong answer, and two of them derived the corrective rule independently. Evidence adequacy: a reliability decision may be taken only on evidence capable of moving, attributable to what it measures, and deterministic under identical conditions. From the findings we derive seven reliability primitives whose enforcement unit is the delegation rather than the message, and specify the controlled evaluation the study motivates but does not constitute.

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model prediction probabilities to bin the data and evaluate calibration error. We propose a more generalized definition of calibration error called Partitioned Calibration Error (PCE), revealing that the key difference among these calibration error metrics lies in how the data space is partitioned. We put forth an intuitive proposition that an accurate model should be calibrated across any partition, suggesting that the input space partitioning can extend beyond just the partitioning of prediction probabilities, and include partitions directly related to the input. Through semantic-related partitioning functions, we demonstrate that the relationship between model accuracy and calibration lies in the granularity of the partitioning function. This highlights the importance of partitioning criteria for training a calibrated and accurate model. To validate the aforementioned analysis, we propose a method that involves jointly learning a semantic aware grouping function based on deep model features and logits to partition the data space into subsets. Subsequently, a separate calibration function is learned for each subset. Experimental results demonstrate that our approach achieves significant performance improvements across multiple datasets and network architectures, thus highlighting the importance of the partitioning function for calibration.

Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of actual quantum computing devices. In this work, we develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under the circuitlevel noise is reproduced with an error threshold of approximately 0.4%. We also demonstrate the advantage of the decoder through which the Y error detection rate can be improved compared with other matching-based decoders. Our results reveal that a lower logical error rate can be obtained using our algorithm compared with that of the minimum-weight perfect matching algorithm.

In this paper, we study the role of initialization in Low Rank Adaptation (LoRA) as originally introduced in Hu et al. (2021). Essentially, to start from the pretrained model as initialization for finetuning, one can either initialize B to zero and A to random (default initialization in PEFT package), or vice-versa. In both cases, the product BA is equal to zero at initialization, which makes finetuning starts from the pretrained model. These two initialization schemes are seemingly similar. They should in-principle yield the same performance and share the same optimal learning rate. We demonstrate that this is an incorrect intuition and that the first scheme (initializing B to zero and A to random) on average yields better performance compared to the other scheme. Our theoretical analysis shows that the reason behind this might be that the first initialization allows the use of larger learning rates (without causing output instability) compared to the second initialization, resulting in more efficient learning of the first scheme. We validate our results with extensive experiments on LLMs.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.

Large language models (LLMs) are increasingly deployed for tabular question answering, yet calibration on structured data is largely unstudied. This paper presents the first systematic comparison of five confidence estimation methods across five frontier LLMs and two tabular QA benchmarks. All models are severely overconfident (smooth ECE 0.35-0.64 versus 0.10-0.15 reported for textual QA). A consistent self-evaluation versus perturbation dichotomy replicates across both benchmarks and all four fully-covered models: self-evaluation methods (verbalized, P(True)) achieve AUROC 0.42-0.76, while perturbation methods (semantic entropy, self-consistency, and our Multi-Format Agreement) achieve AUROC 0.78-0.86. Per-model paired bootstrap tests reject the null at p<0.001 after Holm-Bonferroni correction, and a 3-seed check on GPT-4o-mini gives a per-seed standard deviation of only 0.006. The paper proposes Multi-Format Agreement (MFA), which exploits the lossless and deterministic serialization variation unique to structured data (Markdown, HTML, JSON, CSV) to estimate confidence at 20% lower API cost than sampling baselines. MFA reduces ECE by 44-63%, generalizes across all four models on TableBench (mean AUROC 0.80), and combines complementarily with sampling: an MFA + self-consistency ensemble lifts AUROC from 0.74 to 0.82. A secondary contribution, structure-aware recalibration, improves AUROC by +10 percentage points over standard post-hoc methods.

Tables condense key transactional and administrative information into compact layouts, but practical extraction requires more than text recognition: systems must also recover structure (rows, columns, merged cells, headers) and interpret roles such as line items, subtotals, and totals under common capture artifacts. Many existing resources for table structure recognition and TableVQA are built from clean digital-born sources or rendered tables, and therefore only partially reflect noisy administrative conditions. We introduce DenTab, a dataset of 2{,}000 cropped table images from dental estimates with high-quality HTML annotations, enabling evaluation of table recognition (TR) and table visual question answering (TableVQA) on the same inputs. DenTab includes 2{,}208 questions across eleven categories spanning retrieval, aggregation, and logic/consistency checks. We benchmark 16 systems, including 14 vision--language models (VLMs) and two OCR baselines. Across models, strong structure recovery does not consistently translate into reliable performance on multi-step arithmetic and consistency questions, and these reasoning failures persist even when using ground-truth HTML table inputs. To improve arithmetic reliability without training, we propose the Table Router Pipeline, which routes arithmetic questions to deterministic execution. The pipeline combines (i) a VLM that produces a baseline answer, a structured table representation, and a constrained table program with (ii) a rule-based executor that performs exact computation over the parsed table. The source code and dataset will be made publicly available at https://github.com/hamdilaziz/DenTab.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.

Score- and flow-matching models often rely on preference-based reinforcement learning for two purposes: aligning with subjective preferences and, surprisingly, recovering properties such as visual realism and coherent object structure that matching-based training is intended to learn from the data itself. We argue that this reflects a structural mismatch. Matching losses measure ell_2 regression error on the velocity or score field under training-time marginals, a proxy poorly aligned with the visual and semantic properties that determine sample quality at inference. Given a reward aligned with these properties, RL sidesteps the mismatch by evaluating the model on its own samples and following the reward landscape directly. The challenge is to obtain such a reward without relying on human preferences, which are expensive and conflate data realism with annotator inclinations. We propose Discriminator-Guided RL (DRL). DRL trains a discriminator to separate data from base-model samples in a pretrained representation space and uses its logit as the reward in KL-regularized RL. The pretrained space restricts the discriminator to perceptually meaningful directions, and the logit estimates the log-likelihood ratio between data and model, which is the optimal reward for targeting the data distribution. Across SiT, JiT, REPA, and RAE, DRL reduces guidance-free FID (e.g., 9.38 to 2.62 on SiT) and semantic-space FD (e.g., 88.2 to 19.3 on DINOv3 for SiT), with consistent gains across all backbones, and improves human-preference rewards without training on them. It also yields a better Pareto frontier between preference reward and image fidelity under subsequent preference-based post-training, increasing alignment while reducing low-level artifacts such as oversaturation and excessive brightness.

Grammatical error correction (GEC) is the task of correcting typos, spelling, punctuation and grammatical issues in text. Approaching the problem as a sequence-to-sequence task, we compare the use of a common subword unit vocabulary and byte-level encoding. Initial synthetic training data is created using an error-generating pipeline, and used for finetuning two subword-level models and one byte-level model. Models are then finetuned further on hand-corrected error corpora, including texts written by children, university students, dyslexic and second-language writers, and evaluated over different error types and origins. We show that a byte-level model enables higher correction quality than a subword approach, not only for simple spelling errors, but also for more complex semantic, stylistic and grammatical issues. In particular, initial training on synthetic corpora followed by finetuning on a relatively small parallel corpus of real-world errors helps the byte-level model correct a wide range of commonly occurring errors. Our experiments are run for the Icelandic language but should hold for other similar languages, particularly morphologically rich ones.

Diffusion language models are structurally well-suited for iterative error correction, as their non-causal denoising dynamics allow arbitrary positions in a sequence to be revised. However, standard masked diffusion language model (MDLM) training fails to reliably induce this behavior, as models often cannot identify unreliable tokens in a complete input, rendering confidence-guided refinement ineffective. We study corrective behavior in diffusion language models, defined as the ability to assign lower confidence to incorrect tokens and iteratively refine them while preserving correct content. We show that this capability is not induced by conventional masked diffusion objectives and propose a correction-oriented post-training principle that explicitly supervises visible incorrect tokens, enabling error-aware confidence and targeted refinement. To evaluate corrective behavior, we introduce the Code Revision Benchmark (CRB), a controllable and executable benchmark for assessing error localization and in-place correction. Experiments on code revision tasks and controlled settings demonstrate that models trained with our approach substantially outperform standard MDLMs in correction scenarios, while also improving pure completion performance. Our code is publicly available at https://github.com/zhangshuibai/CDLM.

We present Cadence, an error-bounded lossy compressor for numeric time series pairing a 330M-parameter time-series foundation model (Google TimesFM-3) with an adaptive arithmetic coder, guaranteeing |x_t-x_t|leτ on every sample. One negative result constrains the design space: for lossless coding a foundation model is worth nothing, because bits saved are logarithmic in predictor accuracy, Δb=log_2(MAE_{old}/MAE_{new}). So the 1.51times advantage TimesFM-3 holds over a 32-tap linear predictor buys 0.60 bits of 20.28, a median gain of +0.03%. Error-bounded coding escapes this at one point: once a forecast lands inside the band the residual index is zero and the sample nearly free. Cadence contributes: (1) an adaptive range coder with context-modelled binarization, beating xz/zstd on real indices by 9.7% (15/15) and reversing a finding from a general-purpose back end; (2) a determinism result -- predictions are not bit-identical across batch sizes, and no PyTorch configuration repairs this, forcing group size and execution device into the container format; and (3) domain localization on corpora postdating any plausible training cutoff. On 49 EIA-930 balancing-authority demand series (2026) Cadence gains 13.3% over the best of six classical predictors, and 28.3% on 50 MTA ridership series (2026): 21.4% median over 297 series-tolerance pairs, winning all 297. Against downsampling, what time-series databases deploy for retention, its guaranteed worst-case error is 28--56times tighter at equal size. End-to-end, once the context bootstrap is paid for, gains run from 6.8% at six months of hourly data to 15.1% asymptotically. Attempting to falsify the domain claim on SDRBench, theory predicts failure and delivers: -0.8% median, 0 of 27 pairs gaining. Three further negative results and eight retracted claims are reported in full.

Supervised fine-tuning (SFT) is a milestone in aligning large language models with human instructions and adapting them to downstream tasks. In particular, Low-Rank Adaptation (LoRA) has gained widespread attention due to its parameter efficiency. However, its impact on improving the performance of large models remains limited. Recent studies suggest that combining LoRA with Mixture-of-Experts (MoE) can significantly enhance fine-tuning performance. MoE adapts to the diversity and complexity of datasets by dynamically selecting the most suitable experts, thereby improving task accuracy and efficiency. Despite impressive results, recent studies reveal issues in the MoE routing mechanism, such as incorrect assignments and imbalanced expert allocation. Inspired by the principles of Redundancy and Fault Tolerance Theory. We innovatively integrate the concept of Mixture of Experts into the routing mechanism and propose an efficient fine-tuning method called Mixture of Routers (MoR). It employs multiple sub-routers for joint selection and uses a learnable main router to determine the weights of the sub-routers. The results show that MoR outperforms baseline models on most tasks, achieving an average performance improvement of 1%. MoR can serve as a plug-and-play, parameter-efficient fine-tuning method suitable for a wide range of applications. Our code is available here: https://anonymous.4open.science/r/MoR-DFC6.

Language models (LMs) are susceptible to in-context reward hacking, where they exploit flaws in tainted or faulty written specifications or rubrics to achieve high scores without fulfilling the user's true intent. We introduce Specification Self-Correction (SSC), a novel, test-time framework that enables an LM to identify and correct flaws within its own guiding specification. SSC employs a multi-step inference process where the model first generates a response based on a potentially tainted specification, critiques its output, and then revises the specification itself to remove the exploitable loophole. A final, more robust response is then generated using this self-corrected specification. Across experiments spanning creative writing and agentic coding tasks with several LMs, we demonstrate that while models initially game tainted specifications in 50-70\% of cases, the SSC process reduces this vulnerability by over 90\%. This dynamic repair occurs at inference time, requires no weight modification, and leads to more robustly aligned model behavior. Code at https://github.com/vicgalle/specification-self-correction .

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Fine-tuning safety-aligned large language models (LLMs) can substantially compromise their safety. Previous approaches require many safety samples or calibration sets, which not only incur significant computational overhead during realignment but also lead to noticeable degradation in model utility. Contrary to this belief, we show that safety alignment can be fully recovered with only a single safety example, without sacrificing utility and at minimal cost. Remarkably, this recovery is effective regardless of the number of harmful examples used in fine-tuning or the size of the underlying model, and convergence is achieved within just a few epochs. Furthermore, we uncover the low-rank structure of the safety gradient, which explains why such efficient correction is possible. We validate our findings across five safety-aligned LLMs and multiple datasets, demonstrating the generality of our approach.

Turning a frontier vision-language model into a robot policy usually means fine-tuning it to emit an action representation it never saw in pretraining, which throws away much of the reasoning that made the model worth reaching for. We go the other way and keep the VLM frozen. It writes the policy as a short Python control function, with no demonstrations and no fine-tuning. Writing that code once is open-loop, though. Existing closed-loop methods react at the wrong level: they retry a fixed policy or pick a different subtask, but never rewrite the code that failed. VLCP closes the loop where the failure actually lives, on the control code, within a single episode. Every K steps the VLM re-observes the scene from multi-view RGB, proprioceptive state, and a state delta, then rewrites the control function from what it just saw, so a failure is caught before it compounds. We evaluate on a 57-task MuJoCo/RoboVerse sweep. This training-free policy reaches 35.1% pooled success, against 3.5% for the identical system queried once per episode. That tenfold gap holds with non-overlapping confidence intervals in every scene family. The gain traces to a 27.3% within-episode recovery rate on failed grasps: a miss an open-loop controller would carry to the end of the episode gets re-observed and fixed at the next replan. And the loop stays cheap. A median 84% of input tokens hit cache, an episode needs only about 10 compact queries, and control blocks written during any replan persist to a cross-episode skill library reused in later prompts.

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

Deep-research agents solve tasks through long trajectories of search, tool use, evidence inspection, and answer synthesis. Evaluation based on final answers shows whether an agent succeeds, but not which parts of the trajectory make the answer unreliable. We study span-level error localization for deep-research agents. We collect 2,790 real trajectories from two agent frameworks, three backbone models, and three benchmarks, convert raw logs into semantic spans, and annotate harmful error spans through LLM-assisted expert review. From these annotations, we build TELBench, a 1,000-instance benchmark for identifying error spans among normal exploration, failed searches, tentative hypotheses, and harmless noise. We further propose DRIFT, a claim-centric auditing framework that tracks agent claims, checks their support in trajectory evidence, and marks spans where unsupported or conflicting claims affect the answer path. Experiments across model families and auditing frameworks show that DRIFT improves span-level error localization and first-error accuracy by up to 30 percentage points. Our work provides a process-level view of reliability in deep-research agents.

Transformer representations evolve through learned additive transformations that either preserve their current direction or redirect it. We study this evolution as a functional geometry, decomposing learned updates into parallel and perpendicular components. Across pretrained models, we find substantial parallel components beyond the residual identity path. We then apply the decomposition in two spaces: to attention and MLP updates relative to the hidden state, and to attention value aggregation relative to the current token's value. Targeted edits reveal a strongly space-dependent asymmetry: exclude-self value-space parallel manipulation is markedly more robust than residual-space and perpendicular counterparts, preserving the direct self message while scaling only the non-self aggregate. The same decomposition gives a component-resolved description of compression-induced update error: perpendicular error separates compression methods more clearly than parallel error. Extensive experiments further demonstrate that full-aggregate parallel suppression during from-scratch pretraining lowers validation-loss trajectories and improves downstream averages, with the value-space variant strongest. Together, these results connect representation geometry to editing robustness, compression diagnosis, and training-time intervention. Code is available in the https://github.com/Shwai-He/Transformer-Geometry{project repository}.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

Large language models (LLMs) exhibit a well-documented gap between latent capability and consistent activation: the router hypothesis posits that models possess the knowledge to solve a task but lack reliable internal routing to activate it. Prior work in formal mathematical reasoning (SAIR, Cázares 2026) reports that structural priors (cheatsheets) raise in-distribution performance dramatically, yet collapse below the zero-shot baseline out-of-distribution (OOD) -- and that iterative recalibration amplifies rather than corrects the collapse. We test whether this phenomenon is cross-domain by reproducing the SAIR design in source-code security vulnerability detection, evaluating three LLMs (GPT-OSS-120B, Llama-3.3-70B, Gemma-4-31B) across three vulnerability categories (CWE-798, CWE-284, and the non-CWE N+1 anti-pattern) spanning syntactic, contextual, and semantic complexity, then transferring cheatsheet-augmented prompts to real-world CVE data from VUDENC (CWE-89, CWE-22). Our findings replicate and extend SAIR: (F1) structural priors lift semantic-vulnerability recall from 20.0% to 100.0% across all models; (F2) zero-shot performance degrades along a semantic complexity gradient; (F3) the same cheatsheets that saturate synthetic performance amplify distribution-shift collapse on real CVE data (CWE-89: 100% synthetic F1 to 48.9% on VUDENC, -51.1pp); (F5) iterative recalibration produces a v2 cheatsheet that performs worse than v1 on real data, mirroring SAIR's AN45c-vs-AN38 finding. These results provide evidence that the cross-distribution trade-off surface documented in SAIR generalises to code security, and that the router hypothesis is cross-domain. We argue the structural nature of the collapse motivates distribution-aware training over prompt calibration. Code and evaluation scripts: https://github.com/bytepro-ai/bitcoder-v2-research

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

Noise is a ubiquitous feature of the physical world. As a result, the first prerequisite of life is fault tolerance: maintaining integrity of state despite external bombardment. Recent experimental advances have revealed that biological systems achieve fault tolerance by implementing mathematically intricate error-correcting codes and by organizing in a modular fashion that physically separates functionally distinct subsystems. These elaborate structures represent a vanishing volume in the massive genetic configuration space. How is it possible that the primitive process of evolution, by which all biological systems evolved, achieved such unusual results? In this work, through experiments in Boolean networks, we show that the simultaneous presence of error correction and modularity in biological systems is no coincidence. Rather, it is a typical co-occurrence in noisy dynamic systems undergoing evolution. From this, we deduce the principle of error correction enhanced evolvability: systems possessing error-correcting codes are more effectively improved by evolution than those without.

Quantization is a promising method that reduces memory usage and computational intensity of Deep Neural Networks (DNNs), but it often leads to significant output error that hinder model deployment. In this paper, we propose Bias Compensation (BC) to minimize the output error, thus realizing ultra-low-precision quantization without model fine-tuning. Instead of optimizing the non-convex quantization process as in most previous methods, the proposed BC bypasses the step to directly minimize the quantizing output error by identifying a bias vector for compensation. We have established that the minimization of output error through BC is a convex problem and provides an efficient strategy to procure optimal solutions associated with minimal output error,without the need for training or fine-tuning. We conduct extensive experiments on Vision Transformer models and Large Language Models, and the results show that our method notably reduces quantization output error, thereby permitting ultra-low-precision post-training quantization and enhancing the task performance of models. Especially, BC improves the accuracy of ViT-B with 4-bit PTQ4ViT by 36.89% on the ImageNet-1k task, and decreases the perplexity of OPT-350M with 3-bit GPTQ by 5.97 on WikiText2.The code is in https://github.com/GongCheng1919/bias-compensation.

Not a day goes by without hearing about the impressive feats of large language models (LLMs), and equally, not a day passes without hearing about their challenges. LLMs are notoriously vulnerable to biases in their dataset, leading to issues such as toxicity. While domain-adaptive training has been employed to mitigate these issues, these techniques often address all model parameters indiscriminately during the repair process, resulting in poor repair quality and reduced model versatility. In this paper, we introduce a novel dynamic slicing-based intent-aware LLM repair strategy, IRepair. This approach selectively targets the most error-prone sections of the model for repair. Specifically, we propose dynamically slicing the model's most sensitive layers that require immediate attention, concentrating repair efforts on those areas. This method enables more effective repairs with potentially less impact on the model's overall performance by altering a smaller portion of the model. We evaluated our technique on three models from the GPT2 and GPT-Neo families, with parameters ranging from 800M to 1.6B, in a toxicity mitigation setup. Our results show that IRepair repairs errors 43.6% more effectively while causing 46% less disruption to general performance compared to the closest baseline, direct preference optimization. Our empirical analysis also reveals that errors are more concentrated in a smaller section of the model, with the top 20% of layers exhibiting 773% more error density than the remaining 80\%. This highlights the need for selective repair. Additionally, we demonstrate that a dynamic selection approach is essential for addressing errors dispersed throughout the model, ensuring a robust and efficient repair.

Error slice discovery is crucial to diagnose and mitigate model errors. Current clustering or discrete attribute-based slice discovery methods face key limitations: 1) clustering results in incoherent slices, while assigning discrete attributes to slices leads to incomplete coverage of error patterns due to missing or insufficient attributes; 2) these methods lack complex reasoning, preventing them from fully explaining model biases; 3) they fail to integrate domain knowledge, limiting their usage in specialized fields \eg radiology. We propose\ladder (Language-Driven Discovery and Error Rectification), to address the limitations by: (1) leveraging the flexibility of natural language to address incompleteness, (2) employing LLM's latent domain knowledge and advanced reasoning to analyze sentences and derive testable hypotheses directly, identifying biased attributes, and form coherent error slices without clustering. Existing mitigation methods typically address only the worst-performing group, often amplifying errors in other subgroups. In contrast,\ladder generates pseudo attributes from the discovered hypotheses to mitigate errors across all biases without explicit attribute annotations or prior knowledge of bias. Rigorous evaluations on 6 datasets spanning natural and medical images -- comparing 200+ classifiers with diverse architectures, pretraining strategies, and LLMs -- show that\ladder consistently outperforms existing baselines in discovering and mitigating biases.

We study the fine-grained uniform convergence behavior of halfspaces beyond worst-case VC bounds. For inhomogeneous halfspaces in R^d with dge 2, we show that standard first-order VC bounds are essentially tight: even consistent hypotheses can incur population error Θ(dln(n/d)/n), and in the agnostic setting the deviation scales as τln(1/τ) at true error τ. In contrast, homogeneous halfspaces in R^2 exhibit a markedly different behavior. In the realizable case, every hypothesis consistent with the sample has error O(1/n). In the agnostic case, we prove a bandwise, log-free deviation bound on each dyadic risk band via a critical-wedge localization argument. Unioning over bands incurs only a lnln n overhead, and we establish a matching lower bound showing this overhead is unavoidable. Together, these results give a fine-grained and nearly complete picture of uniform convergence for halfspaces, revealing sharp dimensional and structural thresholds.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.

Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language generation and reasoning. However, their integration into automated software ecosystems is often hindered by the "Structure Gap" - the inherent tension between the probabilistic nature of token generation and the deterministic requirements of structured data formats (e.g., JSON, XML). Traditional Supervised Fine-Tuning (SFT) often fails to enforce strict syntactic constraints, leading to "hallucinated" keys or malformed structures, while constrained decoding methods impose significant inference latency. In this paper, we propose a lightweight, efficient Reinforcement Learning (RL) framework to bridge this gap. We introduce a novel Multi-dimensional Reward Function that decomposes the structured output task into a hierarchy of constraints: structural integrity, format correctness, content accuracy, and validity. Leveraging Gradient Regularized Policy Optimization (GRPO), we enable the model to internalize these constraints without the need for a separate critic network, reducing peak VRAM usage by 40% compared to PPO. We validate our approach on multiple tasks, including complex recipe generation and structured math reasoning (GSM8K-JSON). Experimental results demonstrate that our method achieves 89.7% structural accuracy and 92.1% JSON validity, significantly outperforming both zero-shot baselines (e.g., GPT-3.5) and SFT on larger models like LLaMA-3-8B. Furthermore, we provide a detailed analysis of training dynamics, revealing a distinct self-paced curriculum where the model sequentially acquires syntactic proficiency before semantic accuracy. Our model is publicly available at https://huggingface.co/Freakz3z/Qwen-JSON.

Large Language Model (LLM) based Chinese Grammatical Error Correction (CGEC) systems face two critical challenges: general-purpose models lack specialized linguistic priors for subtle grammatical distinctions, and Supervised Fine-Tuning (SFT) with Maximum Likelihood Estimation fails to optimize for precision-focused metrics, leading to systematic over-correction. We propose CSRP, a three-stage framework that progressively builds correction capability through Continual Pre-training (CPT) on 5.9M balanced samples to internalize domain knowledge, Chain-of-Thought SFT with explicit error reasoning for diagnostic transparency, and Group Relative Policy Optimization with a novel Efficiency-Aware Reward that explicitly penalizes unnecessary edits. On the NACGEC benchmark, CSRP achieves state-of-the-art performance with 50.99 F_{0.5} and 57.17 precision, substantially outperforming previous best results while effectively mitigating the over-correction bias inherent in MLE-trained models. Our method also advances CSCD spelling correction to 59.61 F1, surpassing GPT-4 by 5.20 points. Comprehensive ablation studies demonstrate that the RL alignment stage contributes a 8\% relative gain over the SFT baseline, and that this gain is orthogonal to the contribution of large-scale CPT, validating that explicit optimization for edit efficiency is essential for high-quality grammatical error correction. Our code is available at https://github.com/TW-NLP/ChineseErrorCorrector.

We present Midicoth, a lossless compression system that introduces a micro-diffusion denoising layer for improving probability estimates produced by adaptive statistical models. In compressors such as Prediction by Partial Matching (PPM), probability estimates are smoothed by a prior to handle sparse observations. When contexts have been seen only a few times, this prior dominates the prediction and produces distributions that are significantly flatter than the true source distribution, leading to compression inefficiency. Midicoth addresses this limitation by treating prior smoothing as a shrinkage process and applying a reverse denoising step that corrects predicted probabilities using empirical calibration statistics. To make this correction data-efficient, the method decomposes each byte prediction into a hierarchy of binary decisions along a bitwise tree. This converts a single 256-way calibration problem into a sequence of binary calibration tasks, enabling reliable estimation of correction terms from relatively small numbers of observations. The denoising process is applied in multiple successive steps, allowing each stage to refine residual prediction errors left by the previous one. The micro-diffusion layer operates as a lightweight post-blend calibration stage applied after all model predictions have been combined, allowing it to correct systematic biases in the final probability distribution. Midicoth combines five fully online components: an adaptive PPM model, a long-range match model, a trie-based word model, a high-order context model, and the micro-diffusion denoiser applied as the final stage.

We introduce PREM (Private Relative Error Multiplicative weight update), a new framework for generating synthetic data that achieves a relative error guarantee for statistical queries under (varepsilon, δ) differential privacy (DP). Namely, for a domain {cal X}, a family {cal F} of queries f : {cal X} to {0, 1}, and ζ> 0, our framework yields a mechanism that on input dataset D cal X^n outputs a synthetic dataset D cal X^n such that all statistical queries in {cal F} on D, namely sum_{x in D} f(x) for f cal F, are within a 1 pm ζ multiplicative factor of the corresponding value on D up to an additive error that is polynomial in log |{cal F}|, log |{cal X}|, log n, log(1/δ), 1/varepsilon, and 1/ζ. In contrast, any (varepsilon, δ)-DP mechanism is known to require worst-case additive error that is polynomial in at least one of n, |{cal F}|, or |{cal X}|. We complement our algorithm with nearly matching lower bounds.

Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a train-inference discrepancy, which leads to catastrophic error cascades: initial token errors during parallel decoding pollute the generation context, triggering a chain reaction of compounding errors and leading to syntactic errors and semantic hallucinations. To address this fundamental challenge, we reframe the generation process from passive denoising to active refining. We introduce ReDiff, a refining-enhanced diffusion framework that teaches the model to identify and correct its own errors. Our approach features a two-stage training process: first, we instill a foundational revision capability by training the model to revise synthetic errors; second, we implement a novel online self-correction loop where the model is explicitly trained to revise its own flawed drafts by learning from an expert's corrections. This mistake-driven learning endows the model with the crucial ability to revisit and refine its already generated output, effectively breaking the error cascade. Extensive experiments demonstrate that ReDiff significantly improves the coherence and factual accuracy of generated content, enabling stable and efficient parallel generation far superior to traditional denoising methods. Our codes and models are available at https://rediff-hku.github.io/.

Automated Program Repair (APR) has evolved significantly with the advent of Large Language Models (LLMs). Fine-tuning LLMs for program repair is a recent avenue of research, with many dimensions which have not been explored. Existing work mostly fine-tunes LLMs with naive code representations and is fundamentally limited in its ability to fine-tune larger LLMs. To address this problem, we propose RepairLLaMA, a novel program repair approach that combines 1) code representations for APR and 2) the state-of-the-art parameter-efficient LLM fine-tuning technique called LoRA. This results in RepairLLaMA producing a highly effective `program repair adapter' for fixing bugs with language models. Our experiments demonstrate the validity of both concepts. First, fine-tuning adapters with program repair specific code representations enables the model to use meaningful repair signals. Second, parameter-efficient fine-tuning helps fine-tuning to converge and contributes to the effectiveness of the repair adapter to fix data-points outside the fine-tuning data distribution. Overall, RepairLLaMA correctly fixes 125 Defects4J v2 and 82 HumanEval-Java bugs, outperforming all baselines.

LLM-agent budget overruns are a documented production failure class: a single retry loop can spend thousands of dollars before an operator notices, and the in-process integrity properties that would prevent it (no aliasing, no double-spend, no use-after-delegation of a cost-bearing value) are enforced, if at all, by ad-hoc wrappers rather than by the type system. Our central contribution is empirical: a catalog of 63 confirmed production incidents from 21 orchestration frameworks (2023-2026), each backed by a quoted GitHub issue and, where reported, a dollar loss, organized into an eight-cluster failure taxonomy (inter-rater Cohen's kappa = 0.837, N = 113), plus 47 supplementary structural entries. As one mitigation evaluated against this taxonomy, we build token-budgets, an 1,180-line Rust crate (no unsafe) that operationalizes affine ownership so that cloning, double-spending, or using a budget after delegating it are compile errors rather than runtime hazards an operator must remember to avoid. The dollar cap is runtime arithmetic under an estimator assumption; the affine layer makes that arithmetic non-bypassable. On single-agent workloads a 4-line Python counter matches the crate at 0/30 overshoot, so the distinguishing value is non-bypassability under operator error in multi-agent delegation: the delegation-fanout race documented in 11 incidents is rejected by the borrow checker at compile time, while the same pattern under asyncio overshoots 30/30 and three disciplined alternatives overshoot 0/30. Across five runtimes, three providers, and a temperature-stratified live-API test (N = 160), the approach reports zero cap violations and zero false refusals, at operational parity with concurrent work. Static over-reservation is 4-6x (2.11x adaptive). Binary-level cap-soundness on the running binary is left open.