Daily Papers

The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.

Large Language Models (LLMs) can adopt distinct personas to tune their semantics, expertise, and perspective to different users and tasks. Precise control over these traits is critical to ensure safety and reliability in model behavior. Existing methods like activation steering and prompt-based persona induction reduce a persona to a single dominant direction, missing the finer, nested traits that emerge only once that dominant signal is factored out. We introduce modulation as a setting where the persona context is already embedded in the content being manipulated, requiring control methods to amplify or suppress a trait already present rather than inject it from scratch. PaSS is an inference-time control paradigm that models personas as multi-dimensional subspaces in a model's latent space without supervised contrastive examples. The persona subspaces are extracted via iterative concept erasure and applied to modulate persona-guided generation without retraining. To extract this subspace, we use Iterative Nullspace Projections (INLP) to linearly and iteratively isolate persona-specific directions. We causally evaluate six personas against diverse tasks like MATH-500, TinyAlpaca, GSM8K, and IFEval, showing that discriminative, iterative subspace extraction captures diverse traits underlying a given persona, enabling stronger and larger modulation than single-direction additive methods, while maintaining content fidelity. We further study individual peeled directions within each subspace to uncover the distinct aspects of persona behavior they encode. Overall, we show that persona subspaces offer a controllable, interpretable, and generalizable framework for modulating LLM behavior without sacrificing task performance.

Arditi et al. (2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) -- nullspace projection and counterfactual flipping -- on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP interventions land in qualitatively different regions of activation space: nullspace projection collapses transformed activations between the harmful and harmless clusters, while counterfactual flipping moves them into the opposite cluster, suggesting that the model encodes the absence of a concept differently from its opposite -- an intriguing distinction that warrants further investigation in future work.

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law s^*=R/c that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where R is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.

Recent work has shown pre-trained language models capture social biases from the large amounts of text they are trained on. This has attracted attention to developing techniques that mitigate such biases. In this work, we perform an empirical survey of five recently proposed bias mitigation techniques: Counterfactual Data Augmentation (CDA), Dropout, Iterative Nullspace Projection, Self-Debias, and SentenceDebias. We quantify the effectiveness of each technique using three intrinsic bias benchmarks while also measuring the impact of these techniques on a model's language modeling ability, as well as its performance on downstream NLU tasks. We experimentally find that: (1) Self-Debias is the strongest debiasing technique, obtaining improved scores on all bias benchmarks; (2) Current debiasing techniques perform less consistently when mitigating non-gender biases; And (3) improvements on bias benchmarks such as StereoSet and CrowS-Pairs by using debiasing strategies are often accompanied by a decrease in language modeling ability, making it difficult to determine whether the bias mitigation was effective.

A faithful and interpretable explanation of an AI model's behavior and internal structure is a high-level explanation that is human-intelligible but also consistent with the known, but often opaque low-level causal details of the model. We argue that the theory of causal abstraction provides the mathematical foundations for the desired kinds of model explanations. In causal abstraction analysis, we use interventions on model-internal states to rigorously assess whether an interpretable high-level causal model is a faithful description of an AI model. Our contributions in this area are: (1) We generalize causal abstraction to cyclic causal structures and typed high-level variables. (2) We show how multi-source interchange interventions can be used to conduct causal abstraction analyses. (3) We define a notion of approximate causal abstraction that allows us to assess the degree to which a high-level causal model is a causal abstraction of a lower-level one. (4) We prove constructive causal abstraction can be decomposed into three operations we refer to as marginalization, variable-merge, and value-merge. (5) We formalize the XAI methods of LIME, causal effect estimation, causal mediation analysis, iterated nullspace projection, and circuit-based explanations as special cases of causal abstraction analysis.

Text-based causal inference increasingly employs textual data as proxies for unobserved confounders, yet this approach introduces a previously undertheorized source of bias: treatment leakage. Treatment leakage occurs when text intended to capture confounding information also contains signals predictive of treatment status, thereby inducing post-treatment bias in causal estimates. Critically, this problem can arise even when documents precede treatment assignment, as authors may employ future-referencing language that anticipates subsequent interventions. Despite growing recognition of this issue, no systematic methods exist for identifying and mitigating treatment leakage in text-as-confounder applications. This paper addresses this gap through three contributions. First, we provide formal statistical and set-theoretic definitions of treatment leakage that clarify when and why bias occurs. Second, we propose four text distillation methods -- similarity-based passage removal, distant supervision classification, salient feature removal, and iterative nullspace projection -- designed to eliminate treatment-predictive content while preserving confounder information. Third, we validate these methods through simulations using synthetic text and an empirical application examining International Monetary Fund structural adjustment programs and child mortality. Our findings indicate that moderate distillation optimally balances bias reduction against confounder retention, whereas overly stringent approaches degrade estimate precision.

The rapid evolution of Vision-Language Models (VLMs) has catalyzed unprecedented capabilities in artificial intelligence; however, this continuous modal expansion has inadvertently exposed a vastly broadened and unconstrained adversarial attack surface. Current multimodal jailbreak strategies primarily focus on surface-level pixel perturbations and typographic attacks or harmful images; however, they fail to engage with the complex semantic structures intrinsic to visual data. This leaves the vast semantic attack surface of original, natural images largely unscrutinized. Driven by the need to expose these deep-seated semantic vulnerabilities, we introduce MemJack, a MEMory-augmented multi-agent JAilbreak attaCK framework that explicitly leverages visual semantics to orchestrate automated jailbreak attacks. MemJack employs coordinated multi-agent cooperation to dynamically map visual entities to malicious intents, generate adversarial prompts via multi-angle visual-semantic camouflage, and utilize an Iterative Nullspace Projection (INLP) geometric filter to bypass premature latent space refusals. By accumulating and transferring successful strategies through a persistent Multimodal Experience Memory, MemJack maintains highly coherent extended multi-turn jailbreak attack interactions across different images, thereby improving the attack success rate (ASR) on new images. Extensive empirical evaluations across full, unmodified COCO val2017 images demonstrate that MemJack achieves a 71.48\% ASR against Qwen3-VL-Plus, scaling to 90\% under extended budgets. Furthermore, to catalyze future defensive alignment research, we will release MemJack-Bench, a comprehensive dataset comprising over 113,000 interactive multimodal jailbreak attack trajectories, establishing a vital foundation for developing inherently robust VLMs.

Vision-Language Models (VLMs) are known to inherit and amplify societal biases from their web-scale training data with Indian being particularly misrepresented. Existing fairness-aware datasets have significantly improved demographic balance across global race and gender groups, yet they continue to treat Indian as a single monolithic category. The oversimplification ignores the vast intra-national diversity across 28 states and 8 Union Territories of India and leads to representational and geographical bias. To address the limitation, we present IndicFairFace, a novel and balanced face dataset comprising 14,400 images representing geographical diversity of India. Images were sourced ethically from Wikimedia Commons and open-license web repositories and uniformly balanced across states and gender. Using IndicFairFace, we quantify intra-national geographical bias in prominent CLIP-based VLMs and reduce it using post-hoc Iterative Nullspace Projection debiasing approach. We also show that the adopted debiasing approach does not adversely impact the existing embedding space as the average drop in retrieval accuracy on benchmark datasets is less than 1.5 percent. Our work establishes IndicFairFace as the first benchmark to study geographical bias in VLMs for the Indian context.

Code agents must both reason over long-horizon repository state and obey strict tool-use protocols. In paired Instruct/Thinking checkpoints, these capabilities are complementary but misaligned. The Instruct model is concise and tool-disciplined, whereas the Thinking model offers stronger planning and recovery behavior but often over-deliberates and degrades agent performance. We present CRANE (Constrained Reasoning Injection for Code Agents via Nullspace Editing), a training-free parameter-editing method that treats the Thinking-Instruct delta as a directional pool of candidate reasoning edits for the Instruct backbone. CRANE combines magnitude thresholding to denoise the delta, a Conservative Taylor Gate to retain edits that are jointly beneficial for reasoning transfer and tool-use preservation, and Graduated Sigmoidal Projection to suppress format-critical update directions. By merging paired Instruct and Thinking checkpoints, CRANE delivers strong gains over either individual model while preserving Instruct-level efficiency: on Roo-Eval it achieves pass1 of 66.2% (+19.5%) for Qwen3-30B-A3B and 81.5% (+8.7%) for Qwen3-Next-80B-A3B; on SWE-bench-Verified it resolves up to 14 additional instances at both scales (122/500 and 180/500); and on Terminal-Bench v2 it improves pass1/pass5 by up to 2.3%/7.8%, reaching 7.6%/17.9% and 14.8%/30.3%, respectively, consistently outperforming alternative merging strategies across all three benchmarks.

Existing post-training quantization methods for large language models (LLMs) offer remarkable success. However, the increasingly marginal performance gains suggest that existing quantization strategies are insufficient to support the development of more compressed models. To inspire new directions for future research, this paper introduces the concept of null space into LLMs quantization. We argue that the quantization error can be effectively alleviated by constraining the post-quantization weight perturbation to lie within the null space of input activations. To prove this idea, we propose a plug-and-play null space projection module for existing milestone PTQ baselines named Q2N. Specifically, we first design an efficient and accurate null space projection approximation method tailored to the characteristics of LLMs. Subsequently, we theoretically derive a closed-form solution for an equivalent vector of the obtained projection matrix, which satisfies practical inference condition while avoiding additional memory overhead. Extensive experiments are conducted on various state-of-the-art LLMs (LLaMA3, DeepSeek, Qwen3) and baselines, demonstrating the effectiveness of both our Q2N and the perspective of null space optimization for LLMs quantization. We view this paper the first step to further alleviate the quantization error based on the insights of null space, hoping it inspiring future researchers to design more advanced quantization methods. Codes are available at https://github.com/zjq0455/q2n.

Ensuring the safe and reliable deployment of large language models (LLMs) remains a fundamental challenge. Existing safety alignment approaches either incur high computational cost or unintentionally disrupt the model's core knowledge, leading to degraded fluency and factual accuracy on benign tasks. This reveals a persistent trade-off between safety and utility. We propose DNAlign, a lightweight alignment framework that integrates control-theoretic optimization with null-space projection. By treating the LLM as a dynamic system, the proposed framework introduces controllable perturbations to steer generation toward safe behavior. A key component is the projection module, which restricts these perturbations to the harmful-related subspace derived from neutral hidden states, thereby preserving general knowledge and response quality. A value function trained on human preference data adaptively optimizes the control signals to align with human safety preferences. Extensive evaluations across multiple LLM backbones demonstrate that our framework consistently reduces harmful outputs while maintaining fluency, coherence, and factual utility. It achieves superior overall performance compared to prior alignment baselines without sacrificing generation diversity. These results indicate that the proposed framework provides an effective and practically deployable solution for safe LLM alignment. Code is available at https://anonymous.4open.science/r/DNAlign.

Sophisticated instrumentation for AI systems might have indicators that signal misalignment from human values, not unlike a "check engine" light in cars. One such indicator of misalignment is deceptiveness in generated responses. Future AI instrumentation may have the ability to detect when an LLM generates deceptive responses while reasoning about seemingly plausible but incorrect answers to factual questions. In this work, we demonstrate that linear probes on LLMs internal activations can detect deception in their responses with extremely high accuracy. Our probes reach a maximum of greater than 90% accuracy in distinguishing between deceptive and non-deceptive arguments generated by llama and qwen models ranging from 1.5B to 14B parameters, including their DeepSeek-r1 finetuned variants. We observe that probes on smaller models (1.5B) achieve chance accuracy at detecting deception, while larger models (greater than 7B) reach 70-80%, with their reasoning counterparts exceeding 90%. The layer-wise probe accuracy follows a three-stage pattern across layers: near-random (50%) in early layers, peaking in middle layers, and slightly declining in later layers. Furthermore, using an iterative null space projection approach, we find multitudes of linear directions that encode deception, ranging from 20 in Qwen 3B to nearly 100 in DeepSeek 7B and Qwen 14B models.

Traditional Text-based Person Search (TPS) is typically limited to matching static appearance attributes, severely neglecting dynamic action information. The Text-based Person Anomaly Search (TPAS) task bridges this gap, requiring models to locate micro-level specific abnormal behaviors while matching macro-level appearance of pedestrians. However, current TPAS methods face fundamental limitations: external explicit pose estimators are fragile in unconstrained surveillance scenarios, and implicit learning encounters visual decoupling failure under pixel-level entanglement, causing dominant appearance information to easily swallow and contaminate subtle action features. Furthermore, performing contrastive optimization on hard negative samples (``same appearance, different actions'') in conventional Euclidean spaces induces severe shortcut learning. To address these, we propose the Lightweight Action Inversion and Riemannian rectification network (LightAIR). First, it introduces textual semantic priors as anchors via a lightweight action inversion operator to extract pure action features, thereby overcoming visual-inherent coupling. Subsequently, it employs orthogonal null-space projection to constrain appearance features within the orthogonal complement space of action features, guaranteeing strict forward decoupling. Finally, we designed a gradient rectification module that computes the Riemannian gradient to constrain the backpropagation trajectory, forcing the gradient flow to update strictly along the tangent space that preserves decoupling properties, thereby cutting off harmful shortcuts. Extensive experiments on the widely used TPAS and TIPR datasets demonstrate that LightAIR significantly outperforms existing state-of-the-art methods. Codes are available at https://github.com/rainy-london/LightAIR

Standard unlearning evaluations measure behavioral suppression in full precision, immediately after training, despite every deployed language model being quantized first. Recent work has shown that 4-bit post-training quantization can reverse machine unlearning; we show this is not a tuning artefact but a systematic dual failure: gradient-based methods that achieve meaningful forgetting lose it under compression, while methods that survive quantization barely change the model. Both failures trace to the same root cause: across all baselines, per-parameter updates lie 47-828x below the NF4 quantization bin width; updates diffused across billions of parameters cannot clear quantization bin boundaries, a consequence we formalize as a sparsity-permanence tradeoff. We present MANSU (Mechanistic-Aligned Null-Space Unlearning), which resolves both modes by combining causal circuit attribution to isolate the minimal forget-set subgraph, circuit-restricted null-space projection with a diagonal-Fisher retain bound, and a per-parameter magnitude floor guaranteeing quantization survival by construction. We additionally introduce Circuit Attribution Divergence (CAD), a mechanistic verification metric distinguishing structural erasure from behavioral suppression, a distinction existing metrics cannot make. Across multiple model families and hazard benchmarks, MANSU is the first method to jointly satisfy all four properties with margin on each (meaningful forgetting, retain preservation, non-positive PTQ gap, and structural erasure), while gradient-based baselines recover up to +0.05 accuracy under compression.

Large language models (LLMs) acquire a large amount of knowledge through pre-training on vast and diverse corpora. While this endows LLMs with strong capabilities in generation and reasoning, it amplifies risks associated with sensitive, copyrighted, or harmful content in training data. LLM unlearning, which aims to remove specific knowledge encoded within models, is a promising technique to reduce these risks. However, existing LLM unlearning methods often force LLMs to generate random or incoherent answers due to their inability to alter the encoded knowledge precisely. To achieve effective unlearning at the knowledge level of LLMs, we propose Knowledge Unlearning by Deviating representAtion (KUDA). We first utilize causal tracing to locate specific layers for target knowledge storage. We then design a new unlearning objective that induces the model's representations to deviate from its original position in the phase of knowledge removal, thus disrupting the ability to associate with the target knowledge. To resolve the optimization conflicts between forgetting and retention, we employ a relaxation null-space projection mechanism to mitigate the disruption to the representation space of retaining knowledge. Extensive experiments on representative benchmarks, WMDP and MUSE, demonstrate that KUDA outperforms most existing baselines by effectively balancing knowledge removal and model utility retention.

High memory demands of generative language models have drawn attention to quantization, which reduces computational cost, memory usage, and latency by mapping model weights to lower-precision integers. Approaches such as GPTQ effectively minimize input-weight product errors during quantization; however, recent empirical studies show that they can increase biased outputs and degrade performance on fairness benchmarks, and it remains unclear which specific weights cause this issue. In this work, we draw new links between quantization and model fairness by adding explicit group-fairness constraints to the quantization objective and introduce Fair-GPTQ, the first quantization method explicitly designed to reduce unfairness in large language models. The added constraints guide the learning of the rounding operation toward less-biased text generation for protected groups. Specifically, we focus on stereotype generation involving occupational bias and discriminatory language spanning gender, race, and religion. Fair-GPTQ has minimal impact on performance, preserving at least 90% of baseline accuracy on zero-shot benchmarks, reduces unfairness relative to a half-precision model, and retains the memory and speed benefits of 4-bit quantization. We also compare the performance of Fair-GPTQ with existing debiasing methods and find that it achieves performance on par with the iterative null-space projection debiasing approach on racial-stereotype benchmarks. Overall, the results validate our theoretical solution to the quantization problem with a group-bias term, highlight its applicability for reducing group bias at quantization time in generative models, and demonstrate that our approach can further be used to analyze channel- and weight-level contributions to fairness during quantization.

We present Brainstacks, a modular architecture for continual multi-domain fine-tuning of large language models that packages domain expertise as frozen adapter stacks composing additively on a shared frozen base at inference. Five interlocking components: (1) MoE-LoRA with Shazeer-style noisy top-2 routing across all seven transformer projections under QLoRA 4-bit quantization with rsLoRA scaling; (2) an inner loop performing residual boosting by freezing trained stacks and adding new ones; (3) an outer loop training sequential domain-specific stacks with curriculum-ordered dependencies; (4) null-space projection via randomized SVD constraining new stacks to subspaces orthogonal to prior directions, achieving zero forgetting in isolation; (5) an outcome-based sigmoid meta-router trained on empirically discovered domain-combination targets that selectively weights stacks, enabling cross-domain composition. Two boundary experiments: (6) PSN pretraining on a randomly initialized model; (7) per-domain RL (DPO/GRPO) validating compatibility with post-SFT alignment. Validated on TinyLlama-1.1B (4 domains, 9 stacks) and Gemma 3 12B IT (5 domains, 10 stacks), MoE-LoRA achieves 2.5x faster convergence than parameter-matched single LoRA, residual boosting breaks through the single-stack ceiling, and the routed system recovers generation quality destroyed by ungated stack accumulation. The central finding: the outcome-based router discovers that domain stacks encode transferable cognitive primitives (instruction-following clarity, numerical reasoning, procedural logic, chain-of-thought structure) rather than domain-specific knowledge, with medical prompts routing to chat+math stacks in 97% of cases despite zero medical data in those stacks.

Catastrophic forgetting is a critical chanllenge for incremental object detection (IOD). Most existing methods treat the detector monolithically, relying on instance replay or knowledge distillation without analyzing component-specific forgetting. Through dissection of Faster R-CNN, we reveal a key insight: Catastrophic forgetting is predominantly localized to the RoI Head classifier, while regressors retain robustness across incremental stages. This finding challenges conventional assumptions, motivating us to develop a framework termed NSGP-RePRE. Regional Prototype Replay (RePRE) mitigates classifier forgetting via replay of two types of prototypes: coarse prototypes represent class-wise semantic centers of RoI features, while fine-grained prototypes model intra-class variations. Null Space Gradient Projection (NSGP) is further introduced to eliminate prototype-feature misalignment by updating the feature extractor in directions orthogonal to subspace of old inputs via gradient projection, aligning RePRE with incremental learning dynamics. Our simple yet effective design allows NSGP-RePRE to achieve state-of-the-art performance on the Pascal VOC and MS COCO datasets under various settings. Our work not only advances IOD methodology but also provide pivotal insights for catastrophic forgetting mitigation in IOD. Code is available at https://github.com/fanrena/NSGP-RePRE{https://github.com/fanrena/NSGP-RePRE} .

Arbitrary slice super-resolution reconstructs isotropic volumes from anisotropic clinical acquisitions by synthesizing intermediate slices at arbitrary scales. However, treating this ill-posed inverse problem as unconstrained residual-based regression risks hallucinating anatomically implausible structures or altering the originally observed data. To address both concerns, this paper presents the Dual-Prior Null-space Learning (DP-NSL) framework, which reformulates the task as a constrained recovery process guided by two complementary priors. A Measurement-Consistent Projection (MCP) enforces a Deterministic Observation Prior: the reconstruction undergoes an exact orthogonal projection that reproduces every acquired slice with zero error, confining all learned details to the unobservable null space. Within this null space, a Mixture-of-Splines (MoS) module imposes a Geometric Continuity Prior by dynamically mixing B-spline experts of different analytic orders, allowing each anatomical region to be modeled with a content-aware level of continuity. To promote spatial coherence, a Local Spatial Consistency Decoder (LSCD) further injects local inductive bias. Experiments on three CT and one MRI benchmark show that DP-NSL outperforms existing approaches while strictly preserving measurement consistency. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

All classifiers, including state-of-the-art vision models, possess invariants, partially rooted in the geometry of their linear mappings. These invariants, which reside in the null-space of the classifier, induce equivalent sets of inputs that map to identical outputs. The semantic content of these invariants remains vague, as existing approaches struggle to provide human-interpretable information. To address this gap, we present Semantic Interpretation of the Null-space Geometry (SING), a method that constructs equivalent images, with respect to the network, and assigns semantic interpretations to the available variations. We use a mapping from network features to multi-modal vision language models. This allows us to obtain natural language descriptions and visual examples of the induced semantic shifts. SING can be applied to a single image, uncovering local invariants, or to sets of images, allowing a breadth of statistical analysis at the class and model levels. For example, our method reveals that ResNet50 leaks relevant semantic attributes to the null space, whereas DinoViT, a ViT pretrained with self-supervised DINO, is superior in maintaining class semantics across the invariant space.

Benchmark contamination is diagnosed with n-gram overlap, likelihood-based membership inference, or canary strings, and each needs something usually unavailable: the training corpus, a well-chosen test statistic, or foresight at release. A recent alternative reads it off a linear probe on internal activations. We show the natural way to do this does not work, specify one that survives measurement, then find that the correction making it work carries more variance than the null it is tested against. The protocol reports a zero-sum contrast on the depth profile of probe accuracy, recentred on a level-matched placebo baseline, tested against a label-permutation null, with the reference set twice the size of the suspect set. Each choice replaces a simpler alternative we rejected on measurement. Reporting the level of excess separability rather than its shape makes the false positive rate track the size of the analyst's own control set, 0.03 to 0.99 under a true null. Contrasting against a flat depth profile rejects a true null 0.72 of the time when surface decodability rises with depth, and loses all power when it falls. On real transformers the protocol fails a test the simulations did not pose. The recentring subtracts an estimate, and the permutation null holds it fixed. Re-estimated across split seeds on four audits of contaminated checkpoints, its standard deviation is 1.30 to 1.56 times the null's own in every arm: what is subtracted to remove a bias is more variable than what it corrects. The one nominally significant result, p = 0.0075, becomes 0.0745 once that variance is propagated, and no verdict is issued. The simulations missed this because their surface key is the covariate driving item variation; on real text it is a proxy, and degrading key quality in simulation reproduces it. We add a companion measurement and a widened null. No arm shows contamination.

Neural posterior estimation (NPE), a type of amortized variational inference, is a computationally efficient means of constructing probabilistic catalogs of light sources from astronomical images. To date, NPE has not been used to perform inference in models with spatially varying covariates. However, ground-based astronomical images have spatially varying sky backgrounds and point spread functions (PSFs), and accounting for this variation is essential for constructing accurate catalogs of imaged light sources. In this work, we introduce a method of performing NPE with spatially varying backgrounds and PSFs. In this method, we generate synthetic catalogs and semi-synthetic images for these catalogs using randomly sampled PSF and background estimates from existing surveys. Using this data, we train a neural network, which takes an astronomical image and representations of its background and PSF as input, to output a probabilistic catalog. Our experiments with Sloan Digital Sky Survey data demonstrate the effectiveness of NPE in the presence of spatially varying backgrounds and PSFs for light source detection, star/galaxy separation, and flux measurement.

Large language model unlearning aims to suppress designated undesirable knowledge while preserving benign capabilities. Many unlearning objectives focus on suppressing undesired answers, while recent target-guided variants specify replacement behavior but still leave update locality largely unconstrained. This paper introduces Null-Space Constrained Response-Specified Unlearning (NSRU), a projection-constrained low-rank framework for controlled LLM unlearning. NSRU uses an explicitly structured safe target response to specify the desired behavior for each forget query, while suppressing the original undesired content. To localize adaptation, NSRU estimates per-module retain subspaces from benign hidden representations and uses an orthogonal-projected low-rank parameterization to confine LoRA updates to the null space of the retain subspace. The resulting objective jointly optimizes safe-target learning, undesired-response suppression, and retention preservation under this constrained parameterization. We provide a local first-order analysis showing that the projected update reduces retain-side perturbations while preserving editable directions for shaping forget-query behavior. Experiments on TOFU show that NSRU effectively suppresses extractable forget-set knowledge while improving retain QA performance, model utility, and safe-target alignment over representative baselines. On WMDP, NSRU keeps hazardous-domain accuracy near the random-choice region while preserving broad and domain-adjacent MMLU utility. Ablation studies support the complementary roles of safe-target supervision, undesired-response suppression, retention loss, and null-space projected updates, while sensitivity and robustness analyses indicate stable behavior across the tested hyperparameter and prompt variations.

Large language models (LLMs) often exhibit hallucinations due to incorrect or outdated knowledge. Hence, model editing methods have emerged to enable targeted knowledge updates. To achieve this, a prevailing paradigm is the locating-then-editing approach, which first locates influential parameters and then edits them by introducing a perturbation. While effective, current studies have demonstrated that this perturbation inevitably disrupt the originally preserved knowledge within LLMs, especially in sequential editing scenarios. To address this, we introduce AlphaEdit, a novel solution that projects perturbation onto the null space of the preserved knowledge before applying it to the parameters. We theoretically prove that this projection ensures the output of post-edited LLMs remains unchanged when queried about the preserved knowledge, thereby mitigating the issue of disruption. Extensive experiments on various LLMs, including LLaMA3, GPT2-XL, and GPT-J, show that AlphaEdit boosts the performance of most locating-then-editing methods by an average of 36.4% with a single line of additional code for projection solely. Our code is available at: https://github.com/jianghoucheng/AlphaEdit.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

We introduce Post-Optimization Model Edit (POME), a new algorithm that enhances the performance of fine-tuned large language models using only their pretrained and fine-tuned checkpoints, without requiring extra data or further optimization. The core idea is to apply a muon-style projection to ΔW, the difference between the fine-tuned and pretrained weights. This projection uses truncated singular value decomposition (SVD) to equalize the influence of dominant update directions and prune small singular values, which often represent noise. As a simple post-processing step, POME is completely decoupled from the training pipeline. It requires zero modifications and imposes no overhead, making it universally compatible with any optimizer or distributed framework. POME delivers consistent gains, boosting average performance by +2.5\% on GSM8K and +1.0\% on code generation. Its broad applicability -- from 7B foundation models to 72B RLHF-instructed models -- establishes it as a practical, zero-cost enhancement for any fine-tuning pipeline. Code is available at https://github.com/NUS-HPC-AI-Lab/POME.

Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces. However, we reveal that existing learnable projection mechanisms cannot ensure stable and balanced assignments from observation points to latent tokens, causing some latent tokens to be over-assigned while others remain underutilized. This limitation further restricts the design of hierarchical architectures, as assignment imbalance is continuously inherited and amplified across latent spaces, eventually causing severe token collapse in deeper spaces. To address these issues, we propose MoNo (Multiscale Optimal Transport Neural Operator), a progressive multiscale neural operator that efficiently solves PDEs on general geometries through stable latent-space construction. At its core is CoTAP (Cross-scale Optimal Transport Assignment and Projection), a novel latent-space construction method that formulates cross-space assignment between adjacent spaces as an entropy-regularized optimal transport problem, thereby constructing balanced bidirectional projections and stable latent spaces. CoTAP also ensures stable information transfer across multiple latent spaces, further enabling multiscale architectures on general geometries, which in turn support more efficient learning of long-range physical interactions. Extensive experiments demonstrate that MoNo outperforms existing state-of-the-art neural operators in both prediction performance and computational efficiency. Code is available at https://github.com/ZijiangY1116/MoNo.

We study the inverse adjoint problem for a perturbative bosonic outgoing map. Within the polynomial bosonic canonical-commutation-relation (CCR) algebra, we prove a constructive integrability theorem: order-by-order preservation of the CCRs is sufficient to reconstruct recursively a formal self-adjoint generator whose exponential implements the outgoing map by adjoint conjugation. At each order, the Baker--Campbell--Hausdorff contribution determined by previously reconstructed generators is subtracted from the outgoing coefficient, and the remaining homogeneous CCR conditions determine the next generator explicitly. We apply the construction to graviton scattering in the null-surface formulation (NSF), specialized to the flat solution-space sector with Minkowski metric, null generators, affine parameter, and cone measure. The NSF outgoing map preserves the Ashtekar radiative CCRs through (δa_3), corresponding to order (\varepsilon^2). At this order, the scalar CCR sector uniquely selects the symmetric ordering (c=1) for the nontrivial interacting kernel. The associated linear contraction, generated by the same cubic kernel, cancels the double-contraction contribution from ([δa_2,δa_2^\dagger]). The theorem then reconstructs the self-adjoint generators (δT_1) and (δT_2), providing a formal perturbative unitary implementation. The resulting canonical organization also separates the direct (2\to2) contribution into irreducible-loop, one-particle-reducible, and factorized sectors.

Galaxy clusters selected based on overdensities of galaxies in photometric surveys provide the largest cluster samples. Yet modeling the selection function of such samples is complicated by non-cluster members projected along the line of sight (projection effects) and the potential detection of unvirialized objects (contamination). We empirically constrain the magnitude of these effects by cross-matching galaxy clusters selected in the Dark Energy survey data with the \rdmpr, algorithm with significant detections in three South Pole Telescope surveys (SZ, pol-ECS, pol-500d). For matched clusters, we augment the \rdmpr,catalog by the SPT detection significance. For unmatched objects we use the SPT detection threshold as an upper limit on the SZe signature. Using a Bayesian population model applied to the collected multi-wavelength data, we explore various physically motivated models to describe the relationship between observed richness and halo mass. Our analysis reveals the limitations of a simple lognormal scatter model in describing the data. We rule out significant contamination by unvirialized objects at the high-richness end of the sample. While dedicated simulations offer a well-fitting calibration of projection effects, our findings suggest the presence of redshift-dependent trends that these simulations may not have captured. Our findings highlight that modeling the selection function of optically detected clusters remains a complicated challenge, requiring a combination of simulation and data-driven approaches.

Text-guided diffusion models have become a popular tool in image synthesis, known for producing high-quality and diverse images. However, their application to editing real images often encounters hurdles primarily due to the text condition deteriorating the reconstruction quality and subsequently affecting editing fidelity. Null-text Inversion (NTI) has made strides in this area, but it fails to capture spatial context and requires computationally intensive per-timestep optimization. Addressing these challenges, we present Noise Map Guidance (NMG), an inversion method rich in a spatial context, tailored for real-image editing. Significantly, NMG achieves this without necessitating optimization, yet preserves the editing quality. Our empirical investigations highlight NMG's adaptability across various editing techniques and its robustness to variants of DDIM inversions.

In this work, we investigate the optical signatures of black holes surrounded by a generalized cloud of strings, described by the Letelier--Alencar spacetime. We first analyze null geodesics, showing that the string parameters can either increase or decrease the photon sphere radius and the critical impact parameter relative to their Schwarzschild values. Since the spacetime is not asymptotically flat, the critical impact parameter does not directly coincide with the physical shadow radius. We use this distinction to derive constraints on the model parameters from the shadow radius bounds of Sgr A* and M87*. In the weak-field regime, we calculate the light deflection angle using both the Gauss--Bonnet method and a perturbative expansion of the null geodesic equations, obtaining consistent results that contain a contribution from the asymptotically conical geometry in addition to the local gravitational deflection. We also examine the Shapiro time delay and identify a distance dependent contribution associated with the non Minkowskian asymptotic background. Finally, we study the optical appearance of geometrically and optically thin accretion disks and construct celestial sphere images through backward ray tracing. The transfer functions and lensing images show that the generalized cloud of strings modifies the null geodesic mapping in a nonuniform manner rather than producing a simple rescaling of the Schwarzschild image. In particular, configurations with a smaller shadow may still produce an outward displacement of the main Einstein ring image, demonstrating that different optical observables probe distinct aspects of photon propagation in this geometry.

Novel view synthesis (NVS) enables to generate new images of a scene or convert a set of 2D images into a comprehensive 3D model. In the context of Space Domain Awareness, since space is becoming increasingly congested, NVS can accurately map space objects and debris, improving the safety and efficiency of space operations. Similarly, in Rendezvous and Proximity Operations missions, 3D models can provide details about a target object's shape, size, and orientation, allowing for better planning and prediction of the target's behavior. In this work, we explore the generalization abilities of these reconstruction techniques, aiming to avoid the necessity of retraining for each new scene, by presenting a novel approach to 3D spacecraft reconstruction from single-view images, DreamSat, by fine-tuning the Zero123 XL, a state-of-the-art single-view reconstruction model, on a high-quality dataset of 190 high-quality spacecraft models and integrating it into the DreamGaussian framework. We demonstrate consistent improvements in reconstruction quality across multiple metrics, including Contrastive Language-Image Pretraining (CLIP) score (+0.33%), Peak Signal-to-Noise Ratio (PSNR) (+2.53%), Structural Similarity Index (SSIM) (+2.38%), and Learned Perceptual Image Patch Similarity (LPIPS) (+0.16%) on a test set of 30 previously unseen spacecraft images. Our method addresses the lack of domain-specific 3D reconstruction tools in the space industry by leveraging state-of-the-art diffusion models and 3D Gaussian splatting techniques. This approach maintains the efficiency of the DreamGaussian framework while enhancing the accuracy and detail of spacecraft reconstructions. The code for this work can be accessed on GitHub (https://github.com/ARCLab-MIT/space-nvs).

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Generating complete 3D assets from sparse, unposed images requires preserving observed geometry while completing unseen regions. Joint reconstruction and generation offers a way to address both goals: reconstruction recovers the geometry observed in the input images, while generation contributes learned shape priors. However, combining camera-relative reconstruction with canonical-space generation introduces a coordinate mismatch that makes direct geometric interaction more difficult. Moreover, conditioning each 3D location on all views without accounting for their relevance may mix useful geometric evidence with unrelated image content, hindering local detail recovery. We present UniForge3D, which jointly models reconstruction and generation in a shared anchor-guided space, resolving their coordinate mismatch. This space follows the anchor view's azimuth while keeping the object upright. The two branches exchange features bidirectionally to predict per-view point maps and a complete sparse voxel structure. We further condition point-map prediction on the generated structure to establish pixel-to-voxel correspondences and select the most informative input view for each voxel. Features from the selected views then guide detailed shape generation, helping preserve observed geometric details. Our method achieves state-of-the-art appearance and geometry results on Toys4K and GSO, generating complete 3D assets with improved fidelity. Project webpage: https://xishuxishu.github.io/uniforge3d-project/

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function varepsilon(z,z) on the conformal sphere at future null infinity (mathscr I^+) but are independent of the retarded time. The value of varepsilon at past null infinity (mathscr I^-) is determined from that on mathscr I^+ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The varepsilonneq constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

We introduce ProLoRA, enabling zero-shot adaptation of parameter-efficient fine-tuning in text-to-image diffusion models. ProLoRA transfers pre-trained low-rank adjustments (e.g., LoRA) from a source to a target model without additional training data. This overcomes the limitations of traditional methods that require retraining when switching base models, often challenging due to data constraints. ProLoRA achieves this via projection of source adjustments into the target model's weight space, leveraging subspace and null space similarities and selectively targeting aligned layers. Evaluations on established text-to-image models demonstrate successful knowledge transfer and comparable performance without retraining.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

Simulations are the best approximation to experimental laboratories in astrophysics and cosmology. However, the complexity, richness, and large size of their outputs severely limit the interpretability of their predictions. We describe a new, unbiased, and machine learning based approach to obtaining useful scientific insights from a broad range of simulations. The method can be used on today's largest simulations and will be essential to solve the extreme data exploration and analysis challenges posed by the Exascale era. Furthermore, this concept is so flexible, that it will also enable explorative access to observed data. Our concept is based on applying nonlinear dimensionality reduction to learn compact representations of the data in a low-dimensional space. The simulation data is projected onto this space for interactive inspection, visual interpretation, sample selection, and local analysis. We present a prototype using a rotational invariant hyperspherical variational convolutional autoencoder, utilizing a power distribution in the latent space, and trained on galaxies from IllustrisTNG simulation. Thereby, we obtain a natural Hubble tuning fork like similarity space that can be visualized interactively on the surface of a sphere by exploiting the power of HiPS tilings in Aladin Lite.

Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises: Frequency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and Orthogonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at https://github.com/sonhm3029/FreqOrtho-SR{sonhm3029/FreqOrtho-SR}.

This paper presents a systematic cataloging of the generators of celestial symmetries on phase space. Starting from the celestial OPEs, we first show how to extract a representation of the general-spin analog of the wedge subalgebra of w_{1+infty} on the phase space of massless matter fields of arbitrary helicity. These generators can be expressed as light-sheet operators that are quadratic in the matter fields at future or past null infinity. We next show how to extend these symmetries beyond the wedge. Doing so requires us to augment the quadratic operators with: 1) linear terms corresponding to primary descendants of the negative helicity gauge fields the matter modes couple to, and 2) a tower of higher-particle composite operator contributions. These modes can be realized as light-ray operators supported on generators of null infinity, but local on the celestial sphere. Finally, we construct a representation of the celestial symmetries that captures how the positive helicity gauge fields transform. We close by discussing how these celestial symmetries inform our choice of detector operators.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling A(phi) and chameleon/Vainshtein screening, we map cosmological responses {mu(z,k),Sigma(z,k)} inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials Phi_N. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with |gamma-1|simfewtimes 10^{-6}, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization {V(phi),A(phi)}. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters gamma,beta; and dot G/G) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, |gamma-1|lesssim (2-5)times 10^{-6} (Ka-/X-band or optical Shapiro), eta_{EEP}sim (1--10)times 10^{-17} (drag-free AIS), |dot G/G|sim(3-5)times10^{-15},yr^{-1} (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and (3-10)times improved ULDM-coupling reach from clocks. For a conformal benchmark, mu_{ lin,0}=0.10 implies chisimeq mu_{lin,0/2} and a Sun thin shell Delta R/Rlesssim (1/3chi)|gamma-1|/2=2.4times 10^{-3} at |gamma-1|=5times 10^{-6}; Vainshtein screening at 1 AU yields |gamma-1|lesssim 10^{-11}, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

The shadow of an abstract simplicial complex K with vertices in R^N is a subset of R^N defined as the union of the convex hulls of simplices of K. The Vietoris--Rips complex of a metric space (S,d) at scale β is an abstract simplicial complex whose each k-simplex corresponds to (k+1) points of S within diameter β. In case Ssubsetmathbb R^2 and d(a,b)=|a-b| the standard Euclidean metric, the natural shadow projection of the Vietoris--Rips complex is already proved by Chambers et al. to induce isomorphisms on π_0 and π_1. We extend the result beyond the standard Euclidean distance on Ssubsetmathbb R^N to a family of path-based metrics, d^varepsilon_{S}. From the pairwise Euclidean distances of points in S, we introduce a family (parametrized by varepsilon) of path-based Vietoris--Rips complexes R^varepsilon_β(S) for a scale β>0. If SsubsetR^2 is Hausdorff-close to a planar Euclidean graph G, we provide quantitative bounds on scales β,varepsilon for the shadow projection map of the Vietoris--Rips complex of (S,d^varepsilon_S) at scale β to induce π_1-isomorphism. This paper first studies the homotopy-type recovery of Gsubsetmathbb R^N using the abstract Vietoris--Rips complex of a Hausdorff-close sample S under the d^varepsilon_S metric. Then, our result on the π_1-isomorphism induced by the shadow projection lends itself to providing also a geometrically close embedding for the reconstruction. Based on the length of the shortest loop and large-scale distortion of the embedding of G, we quantify the choice of a suitable sample density varepsilon and a scale β at which the shadow of R^varepsilon_β(S) is homotopy-equivalent and Hausdorff-close to G.

We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the structure of Busemann functions. We introduce a projection based variant of the proximal point algorithm, termed the Busemann hybrid projection proximal point algorithm, which replaces Euclidean hyperplanes with horospheres defined via convex Busemann functions. The algorithm performs projections in closed form using the gradients of these functions, resulting in a geometrically intrinsic scheme that requires no tangent space linear solves. We allow for inexact subgradient evaluations and prove global convergence under controlled inexactness, with a relative error level strictly below one. We establish a Fejér type descent and sublinear complexity with a rate proportional to the inverse square root of the iteration count, and show that the exact variant coincides with the classical Riemannian proximal point algorithm. The framework clarifies the role of Busemann based subdifferentials in optimization on spaces of nonpositive curvature.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

We consider the image transmission problem over a noisy wireless channel via deep learning-based joint source-channel coding (DeepJSCC) along with a denoising diffusion probabilistic model (DDPM) at the receiver. Specifically, we are interested in the perception-distortion trade-off in the practical finite block length regime, in which separate source and channel coding can be highly suboptimal. We introduce a novel scheme that utilizes the range-null space decomposition of the target image. We transmit the range-space of the image after encoding and employ DDPM to progressively refine its null space contents. Through extensive experiments, we demonstrate significant improvements in distortion and perceptual quality of reconstructed images compared to standard DeepJSCC and the state-of-the-art generative learning-based method. We will publicly share our source code to facilitate further research and reproducibility.

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

The Q/U Imaging ExperimenT (QUIET) employs coherent receivers at 43GHz and 95GHz, operating on the Chajnantor plateau in the Atacama Desert in Chile, to measure the anisotropy in the polarization of the CMB. QUIET primarily targets the B modes from primordial gravitational waves. The combination of these frequencies gives sensitivity to foreground contributions from diffuse Galactic synchrotron radiation. Between 2008 October and 2010 December, >10,000hours of data were collected, first with the 19-element 43GHz array (3458hours) and then with the 90-element 95GHz array. Each array observes the same four fields, selected for low foregrounds, together covering ~1000deg^2. This paper reports initial results from the 43GHz receiver which has an array sensitivity to CMB fluctuations of 69uK sqrt(s). The data were extensively studied with a large suite of null tests before the power spectra, determined with two independent pipelines, were examined. Analysis choices, including data selection, were modified until the null tests passed. Cross correlating maps with different telescope pointings is used to eliminate a bias. This paper reports the EE, BB and EB power spectra in the multipole range ell=25-475. With the exception of the lowest multipole bin for one of the fields, where a polarized foreground, consistent with Galactic synchrotron radiation, is detected with 3sigma significance, the E-mode spectrum is consistent with the LCDM model, confirming the only previous detection of the first acoustic peak. The B-mode spectrum is consistent with zero, leading to a measurement of the tensor-to-scalar ratio of r=0.35+1.06-0.87. The combination of a new time-stream double-demodulation technique, Mizuguchi-Dragone optics, natural sky rotation, and frequent boresight rotation leads to the lowest level of systematic contamination in the B-mode power so far reported, below the level of r=0.1

Vision Language Models (VLMs) have demonstrated remarkable performance in open-world zero-shot visual recognition. However, their potential in space-related applications remains largely unexplored. In the space domain, accurate manual annotation is particularly challenging due to factors such as low visibility, illumination variations, and object blending with planetary backgrounds. Developing methods that can detect and segment spacecraft and orbital targets without requiring extensive manual labeling is therefore of critical importance. In this work, we propose an annotation-free detection and segmentation pipeline for space targets using VLMs. Our approach begins by automatically generating pseudo-labels for a small subset of unlabeled real data with a pre-trained VLM. These pseudo-labels are then leveraged in a teacher-student label distillation framework to train lightweight models. Despite the inherent noise in the pseudo-labels, the distillation process leads to substantial performance gains over direct zero-shot VLM inference. Experimental evaluations on the SPARK-2024, SPEED+, and TANGO datasets on segmentation tasks demonstrate consistent improvements in average precision (AP) by up to 10 points. Code and models are available at https://github.com/giddyyupp/annotation-free-spacecraft-segmentation.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

Continuous physical fields represent a large fraction of data under scientific investigation. Their multiscale structures are central to discovery, yet useful coordinates are not known in advance. Standard self-supervised methods define context and targets in fixed image coordinates, posing a predictive task misaligned with fields organized across a continuous scale hierarchy. We introduce ScaleAware-JEPA, a framework that constructs dense, label-free latent coordinates for continuous scalar fields. Constrained Diffusion Decomposition (CDD) separates each field into pixel-registered scale components and provides the scale coordinates that define the masking geometry. The resulting JEPA objective predicts hidden structure with a context footprint tied to the diffusion scale of each component rather than to an arbitrary patch size. Across MHD turbulence, interstellar molecular gas and urban nighttime-light structure, the learned geometry maps back to coherent morphology, forming dense structural atlases without labels or predefined segmentation rules. By tying latent prediction to the scale hierarchy of a field, ScaleAware-JEPA constructs latent coordinates through which complex physical patterns can be inspected before their relevant structures have been prescribed. Code is available at https://github.com/gxli/SA-JEPA.

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

The mean Hawking flux does not determine how quantum stress fluctuations perturb a black-hole geometry. That information resides in field correlations, including vacuum contributions absent from the outgoing luminosity. Here we connect the complete exterior Unruh Wightman function to a finite-band stochastic reconstruction of Schwarzschild geometry. We retain the incoming vacuum and both outgoing frequency branches, form the connected stress covariance before angular projection, and propagate its monopole through a density-driven radial response. A shared Gaussian reconstruction then resolves how the value and derivative of the lapse control different geometric observables. For the specified covariance and noise amplitude, 2,200 realizations give relative widths of 0.0185 for the local horizon radius and 0.0483 for the surface-gravity temperature parameter, consistently across histograms and reconstruction checks. Covariance derivatives explain this unequal sensitivity. The construction separates the quantum-state input from the gravitational closure and spatial sampling assumptions, providing a reproducible finite-resolution description of how Hawking-field correlations affect horizon positions and surface-gravity statistics.

Recent text-guided diffusion models provide powerful image generation capabilities. Currently, a massive effort is given to enable the modification of these images using text only as means to offer intuitive and versatile editing. To edit a real image using these state-of-the-art tools, one must first invert the image with a meaningful text prompt into the pretrained model's domain. In this paper, we introduce an accurate inversion technique and thus facilitate an intuitive text-based modification of the image. Our proposed inversion consists of two novel key components: (i) Pivotal inversion for diffusion models. While current methods aim at mapping random noise samples to a single input image, we use a single pivotal noise vector for each timestamp and optimize around it. We demonstrate that a direct inversion is inadequate on its own, but does provide a good anchor for our optimization. (ii) NULL-text optimization, where we only modify the unconditional textual embedding that is used for classifier-free guidance, rather than the input text embedding. This allows for keeping both the model weights and the conditional embedding intact and hence enables applying prompt-based editing while avoiding the cumbersome tuning of the model's weights. Our Null-text inversion, based on the publicly available Stable Diffusion model, is extensively evaluated on a variety of images and prompt editing, showing high-fidelity editing of real images.

We present a method for 3D reconstruction only using calibrated multi-view surface azimuth maps. Our method, multi-view azimuth stereo, is effective for textureless or specular surfaces, which are difficult for conventional multi-view stereo methods. We introduce the concept of tangent space consistency: Multi-view azimuth observations of a surface point should be lifted to the same tangent space. Leveraging this consistency, we recover the shape by optimizing a neural implicit surface representation. Our method harnesses the robust azimuth estimation capabilities of photometric stereo methods or polarization imaging while bypassing potentially complex zenith angle estimation. Experiments using azimuth maps from various sources validate the accurate shape recovery with our method, even without zenith angles.

Existing single-view 3D generative models typically adopt multiview diffusion priors to reconstruct object surfaces, yet they remain prone to inter-view inconsistencies and are unable to faithfully represent complex internal structure or nontrivial topologies. In particular, we encode geometry information by projecting it onto a bounding sphere and unwrapping it into a compact and structural multi-layer 2D Spherical Projection (SP) representation. Operating solely in the image domain, SPGen offers three key advantages simultaneously: (1) Consistency. The injective SP mapping encodes surface geometry with a single viewpoint which naturally eliminates view inconsistency and ambiguity; (2) Flexibility. Multi-layer SP maps represent nested internal structures and support direct lifting to watertight or open 3D surfaces; (3) Efficiency. The image-domain formulation allows the direct inheritance of powerful 2D diffusion priors and enables efficient finetuning with limited computational resources. Extensive experiments demonstrate that SPGen significantly outperforms existing baselines in geometric quality and computational efficiency.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Machine learning models that are overfitted/overtrained are more vulnerable to knowledge leakage, which poses a risk to privacy. Suppose we download or receive a model from a third-party collaborator without knowing its training accuracy. How can we determine if it has been overfitted or overtrained on its training data? It's possible that the model was intentionally over-trained to make it vulnerable during testing. While an overfitted or overtrained model may perform well on testing data and even some generalization tests, we can't be sure it's not over-fitted. Conducting a comprehensive generalization test is also expensive. The goal of this paper is to address these issues and ensure the privacy and generalization of our method using only testing data. To achieve this, we analyze the null space in the last layer of neural networks, which enables us to quantify overfitting without access to training data or knowledge of the accuracy of those data. We evaluated our approach on various architectures and datasets and observed a distinct pattern in the angle of null space when models are overfitted. Furthermore, we show that models with poor generalization exhibit specific characteristics in this space. Our work represents the first attempt to quantify overfitting without access to training data or knowing any knowledge about the training samples.

Let λ_{mathbb K}(m) denote the maximal absolute projection constant among m-dimensional Banach spaces over mathbb K=mathbb R or mathbb C. Its exact value is known only in a few cases, and determining it remains a challenging problem. In this note, we investigate several structured vector configurations that naturally arise in this context. We first recall the connection between maximal projection constants and tight frames, then consider biangular tight frames, and show that their relative and quasimaximal projection constants coincide. A particularly interesting example is provided by the midpoints of the edges of a regular simplex, which yield natural lower bounds for λ_{mathbb R}(m). Numerical evidence suggests that these bounds may be sharp in dimensions 6 and 8. We also discuss weighted spherical (2,2)-designs with a small number of vectors and their connection with maximal projection constants. Examples in dimensions 4 and 5 indicate that the sign patterns of their Gram matrices may play an important role. These observations lead us to formulate several conjectures concerning maximal absolute projection constants and the vector configurations associated with them.

The observation of the shadow of the supermassive black hole M87^{*} by the Event Horizon Telescope (EHT) is sensitive to the spacetime geometry near the circular photon orbit and beyond, and it thus has the potential to test general relativity in the strong field regime. Obstacles to this program, however, include degeneracies between putative deviations from general relativity and both the description of the accretion flow and the uncertainties on "calibration parameters", such as e.g. the mass and spin of the black hole. In this work, we introduce a formalism, based on a principal component analysis, capable of reconstructing the black hole metric (i.e. the "signal") in an agnostic way, while subtracting the "foreground" due to the uncertainties in the calibration parameters and the modelling of the accretion flow. We apply our technique to simulated mock data for spherically symmetric black holes surrounded by a thick accretion disk. We show that separation of signal and foreground may be possible with next generation EHT-like experiments.

Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for arbitrary linear IR problems, including but not limited to image super-resolution, colorization, inpainting, compressed sensing, and deblurring. DDNM only needs a pre-trained off-the-shelf diffusion model as the generative prior, without any extra training or network modifications. By refining only the null-space contents during the reverse diffusion process, we can yield diverse results satisfying both data consistency and realness. We further propose an enhanced and robust version, dubbed DDNM+, to support noisy restoration and improve restoration quality for hard tasks. Our experiments on several IR tasks reveal that DDNM outperforms other state-of-the-art zero-shot IR methods. We also demonstrate that DDNM+ can solve complex real-world applications, e.g., old photo restoration.

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of the scene with one-time inference due to the memory inefficiency and heavy overhead from distance calculation and sorting involved in commonly used farthest point sampling, KNN, and ball query algorithms for local feature aggregation. To mitigate these issues in scene flow learning, we regularize raw points to a dense format by storing 3D coordinates in 2D grids. Unlike the sampling operation commonly used in existing works, the dense 2D representation 1) preserves most points in the given scene, 2) brings in a significant boost of efficiency, and 3) eliminates the density gap between points and pixels, allowing us to perform effective feature fusion. We also present a novel warping projection technique to alleviate the information loss problem resulting from the fact that multiple points could be mapped into one grid during projection when computing cost volume. Sufficient experiments demonstrate the efficiency and effectiveness of our method, outperforming the prior-arts on the FlyingThings3D and KITTI dataset.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

Most Bundle Adjustment (BA) solvers like the Levenberg-Marquardt algorithm require a good initialization. Instead, initialization-free BA remains a largely uncharted territory. The under-explored Variable Projection algorithm (VarPro) exhibits a wide convergence basin even without initialization. Coupled with object space error formulation, recent works have shown its ability to solve small-scale initialization-free bundle adjustment problem. To make such initialization-free BA approaches scalable, we introduce Power Variable Projection (PoVar), extending a recent inverse expansion method based on power series. Importantly, we link the power series expansion to Riemannian manifold optimization. This projective framework is crucial to solve large-scale bundle adjustment problems without initialization. Using the real-world BAL dataset, we experimentally demonstrate that our solver achieves state-of-the-art results in terms of speed and accuracy. To our knowledge, this work is the first to address the scalability of BA without initialization opening new venues for initialization-free structure-from-motion.

As orbital populations grow, conjunction screening must search more object pairs for potential collision risks. Existing pipelines use early-stage filters, such as an apsis filter, to eliminate pairs whose orbital altitude ranges cannot produce a close approach. However, these filters apply the same fixed threshold to every object, making the screening unnecessarily conservative for well-constrained objects while potentially insufficient for objects with greater orbit-prediction uncertainty. In this work, we present an uncertainty-aware conjunction screening method that replaces a single fixed apsis threshold with object-specific thresholds derived from propagated radial uncertainty. The resulting thresholds vary across both objects and prediction time, becoming narrower when propagated uncertainty is small and wider when uncertainty grows. We pair this adaptive screening rule with a binary-search altitude sweep that makes resulting heterogeneous intervals efficient to evaluate at catalog scale with log-linear search complexity. We evaluate the method on 33,791 objects from the Space-Track General Perturbations (GP) catalog using the preceding eight public ephemeris snapshots and a seven-day prediction horizon. The adaptive sieve retains 162.8 million candidate pairs, reducing the candidate set by 28.78% relative to a fixed 50 km apsis threshold and by 71.48% relative to brute-force all-pairs screening. It retains all close approaches identified in two independently propagated reference sets. At the largest tested catalog size, the binary-search sweep is 27 times faster than exhaustive interval evaluation while returning the same candidate set. These results demonstrate that uncertainty-aware screening can substantially reduce the candidate burden passed to downstream conjunction analysis, providing a scalable path toward managing increasingly large and heterogeneous orbital populations.

The Q/U Imaging ExperimenT (QUIET) has observed the cosmic microwave background (CMB) at 43 and 95GHz. The 43-GHz results have been published in QUIET Collaboration et al. (2011), and here we report the measurement of CMB polarization power spectra using the 95-GHz data. This data set comprises 5337 hours of observations recorded by an array of 84 polarized coherent receivers with a total array sensitivity of 87 uK sqrt(s). Four low-foreground fields were observed, covering a total of ~1000 square degrees with an effective angular resolution of 12.8', allowing for constraints on primordial gravitational waves and high-signal-to-noise measurements of the E-modes across three acoustic peaks. The data reduction was performed using two independent analysis pipelines, one based on a pseudo-Cl (PCL) cross-correlation approach, and the other on a maximum-likelihood (ML) approach. All data selection criteria and filters were modified until a predefined set of null tests had been satisfied before inspecting any non-null power spectrum. The results derived by the two pipelines are in good agreement. We characterize the EE, EB and BB power spectra between l=25 and 975 and find that the EE spectrum is consistent with LCDM, while the BB power spectrum is consistent with zero. Based on these measurements, we constrain the tensor-to-scalar ratio to r=1.1+0.9-0.8 (r<2.8 at 95% C.L.) as derived by the ML pipeline, and r=1.2+0.9-0.8 (r<2.7 at 95% C.L.) as derived by the PCL pipeline. In one of the fields, we find a correlation with the dust component of the Planck Sky Model, though the corresponding excess power is small compared to statistical errors. Finally, we derive limits on all known systematic errors, and demonstrate that these correspond to a tensor-to-scalar ratio smaller than r=0.01, the lowest level yet reported in the literature.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

We introduce an Extended Textual Conditioning space in text-to-image models, referred to as P+. This space consists of multiple textual conditions, derived from per-layer prompts, each corresponding to a layer of the denoising U-net of the diffusion model. We show that the extended space provides greater disentangling and control over image synthesis. We further introduce Extended Textual Inversion (XTI), where the images are inverted into P+, and represented by per-layer tokens. We show that XTI is more expressive and precise, and converges faster than the original Textual Inversion (TI) space. The extended inversion method does not involve any noticeable trade-off between reconstruction and editability and induces more regular inversions. We conduct a series of extensive experiments to analyze and understand the properties of the new space, and to showcase the effectiveness of our method for personalizing text-to-image models. Furthermore, we utilize the unique properties of this space to achieve previously unattainable results in object-style mixing using text-to-image models. Project page: https://prompt-plus.github.io

A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close it is to being invariant under the Koopman operator. The notion of invariance proximity provides a tight upper bound on the worst-case relative prediction error of the finite-dimensional model. However, its direct calculation is computationally challenging. This paper leverages the geometric structure behind the definition of invariance proximity to provide a closed-form expression in terms of Jordan principal angles on general inner product spaces. Unveiling this connection allows us to exploit specific isomorphisms to circumvent the computational challenges associated with spaces of functions and enables the use of existing efficient numerical routines to compute invariance proximity.

Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.

Mirror Stars are a generic prediction of dissipative dark matter models, including minimal atomic dark matter and twin baryons in the Mirror Twin Higgs. Mirror Stars capture regular atoms from the interstellar medium through highly suppressed kinetic mixing interactions between the regular and the dark photon. This results in the accumulation of a "nugget", which draws heat from the mirror star core and emits distinctive X-ray and optical signals. In this work, we solve the stellar structure equations of optically thick nuggets across a wide range of the effective mirror star parameter space, and characterize their emission spectra using stellar atmosphere models. This complements an earlier analysis of lower-mass optically thin nuggets. We find that optically thick mirror star nuggets occupy distinct regions of the (stellar surface temperature, luminosity, surface gravity) space, and can be distinguished from regular stars in both HR diagrams and temperature-surface-gravity diagrams using astrometric and spectroscopic stellar catalogues. Our detailed predictions, which are publicly available, now give for the first time a general picture of mirror star signals in the optical and IR to enable realistic mirror star searches using existing catalogues and new telescope observations.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Dense retrieval powers retrieval-augmented generation, semantic search, and question answering, yet the theoretical basis for choosing between shared and dual query-document projections remains unclear. We introduce a bias-variance theory for low-rank bilinear scoring. Shared projections induce positive-semidefinite operators, whereas dual projections realize arbitrary low-rank operators. We derive their exact approximation gap and prove a local Gaussian boundary: dual has lower risk exactly when squared directional signal exceeds the estimation cost of its additional degrees of freedom. This boundary motivates the Cross-fitted Asymmetry Risk Selector (CARS), which estimates reproducible directional signal from training pairs; its Gaussian counterpart admits exact selection-power and regret formulas. Guided by the theory, we run retrieval experiments across multiple datasets and embedding models. The mean Dual-minus-Shared NDCG@10 advantage more than doubles as query rotation increases from 0 degrees to 90 degrees. In the rank-sample-size grids, Shared wins 13 of 16 cells at n=32, whereas Dual wins all 32 cells at n=1024 and n=2048. Consistent with this shift, all 168 comparable operator-risk curves move toward Dual as training data grow. Compared to the two fixed-geometry baselines, CARS reduces held-out regret by 49-96% and achieves 90.1% mean geometry-selection accuracy.

A commonly observed failure mode of Neural Radiance Field (NeRF) is fitting incorrect geometries when given an insufficient number of input views. One potential reason is that standard volumetric rendering does not enforce the constraint that most of a scene's geometry consist of empty space and opaque surfaces. We formalize the above assumption through DS-NeRF (Depth-supervised Neural Radiance Fields), a loss for learning radiance fields that takes advantage of readily-available depth supervision. We leverage the fact that current NeRF pipelines require images with known camera poses that are typically estimated by running structure-from-motion (SFM). Crucially, SFM also produces sparse 3D points that can be used as "free" depth supervision during training: we add a loss to encourage the distribution of a ray's terminating depth matches a given 3D keypoint, incorporating depth uncertainty. DS-NeRF can render better images given fewer training views while training 2-3x faster. Further, we show that our loss is compatible with other recently proposed NeRF methods, demonstrating that depth is a cheap and easily digestible supervisory signal. And finally, we find that DS-NeRF can support other types of depth supervision such as scanned depth sensors and RGB-D reconstruction outputs.

We study the production of QCD axion dark matter (DM) via vacuum and kinetic misalignment mechanisms during an extended reheating period after the end of slow-roll inflation. With pre-inflationary Peccei-Quinn breaking and considering a monomial inflaton potential during reheating, we classify our study into three different perturbative reheating scenarios in which the inflaton decays into (i) a pair of Standard Model (SM)-like bosons, (ii) a pair of SM-like fermions, or (iii) exclusively into a pair of heavy right-handed neutrinos, which eventually decays into the SM final states after dominating the energy density of the Universe for an intermediate epoch. For each of these reheating scenarios, we study the details of QCD axion relic separately via vacuum and kinetic misalignment mechanisms. For different combinations of reheating, monomial inflaton potential and misalignment mechanisms, we identify the parameter space consistent with the observed DM relic density while satisfying other cosmological and laboratory constraints. We also check the scope of probing the currently allowed parameter space at axion-detection and gravitational wave (GW) experiments.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g-2)_μ at the SU(3) flavor-symmetric point m_π=m_Ksimeq 420,MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain a_μ^{rm hlbl} = (65.4pm 4.9 pm 6.6)times 10^{-11}, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

We study two-Higgs-doublet models, extensions of the Standard Model (SM) containing two Higgs doublets rather than one. Tree-level Higgs-mediated interactions that change quark or lepton flavor are conventionally suppressed by a discrete Z_2 symmetry. Motivated by string compactifications, we instead impose a non-invertible Fibonacci selection rule at a matching scale Λ for that purpose. This rule also forbids the independent mass parameter that normally allows the additional Higgs particles to become arbitrarily heavy, while renormalization-group evolution regenerates it below Λ. An allowed Z_2-breaking quartic interaction simultaneously avoids stable cosmological domain walls. In the exact alignment limit, requiring perturbative unitarity and boundedness from below up to the matching scale bounds the masses of the three non-SM Higgs states; for Λ=10^{19},GeV, they lie below about 150,GeV. The scanned parameter space predicts a suppressed Higgs diphoton signal strength within the projected reach of the HL-LHC. This illustrates how a stringy non-invertible selection rule can leave testable signatures in Higgs physics.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

We present the first linear polarization measurements from the 2015 long-duration balloon flight of SPIDER, an experiment designed to map the polarization of the cosmic microwave background (CMB) on degree angular scales. Results from these measurements include maps and angular power spectra from observations of 4.8% of the sky at 95 and 150 GHz, along with the results of internal consistency tests on these data. While the polarized CMB anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is also detected with high significance; Galactic synchrotron emission is found to be negligible in the SPIDER bands. We employ two independent foreground-removal techniques in order to explore the sensitivity of the cosmological result to the assumptions made by each. The primary method uses a dust template derived from Planck data to subtract the Galactic dust signal. A second approach, employing a joint analysis of SPIDER and Planck data in the harmonic domain, assumes a modified-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the template amplitude and r parameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio from Feldman-Cousins and Bayesian constructions, finding r<0.11 and r<0.19, respectively. Roughly half the uncertainty in r derives from noise associated with the template subtraction. New data at 280 GHz from SPIDER's second flight will complement the Planck polarization maps, providing powerful measurements of the polarized Galactic dust emission.

The all-sky 408 MHz map of Haslam et al. is one the most important total-power radio surveys. It has been widely used to study diffuse synchrotron radiation from our Galaxy and as a template to remove foregrounds in cosmic microwave background data. However, there are a number of issues associated with it that must be dealt with, including large-scale striations and contamination from extragalactic radio sources. We have re-evaluated and re-processed the rawest data available to produce a new and improved 408 MHz all-sky map. We first quantify the positional accuracy (approx 7 arcmin) and effective beam (56.0pm1.0 arcmin) of the four individual surveys from which it was assembled. Large-scale striations associated with 1/f noise in the scan direction are reduced to a level ll 1 K using a Fourier-based filtering technique. The most important improvement results from the removal of extragalactic sources. We have used an iterative combination of two techniques -- two-dimensional Gaussian fitting and minimum curvature spline surface inpainting -- to remove the brightest sources (gtrsim 2 Jy), which provides a significant improvement over previous versions of the map. We quantify the impact with power spectra and a template fitting analysis of foregrounds to the WMAP data. The new map is publicly available and is recommended as the template of choice for large-scale diffuse Galactic synchrotron emission. We also provide a higher resolution map with small-scale fluctuations added, assuming a power-law angular power spectrum down to the pixel scale (1.7 arcmin). This should prove useful in simulations used for studying the feasibility of detecting HI fluctuations from the Epoch of Reionization.

Representation alignment (REPA) accelerates diffusion transformer training, but its alignment targets are almost exclusively semantic encoders such as DINOv2 and CLIP. Recent analysis points to spatial structure, not global semantics, as the carrier of the alignment effect, yet dense-prediction foundation models trained to predict that structure remain overlooked as REPA targets. In pixel-space diffusion, SAM2, Depth Anything v2, and Metric3D v2 each outperform the DINOv2-only GenEval baseline, with the two geometric teachers leading the segmentation teacher. A flat sum of all four teachers, however, lands below the best single geometric teacher, as semantic and geometric gradients compete for one denoiser projection. We introduce PixelDense, which routes DINOv2 and SAM2 through a semantic projection stream, routes Depth Anything v2 and Metric3D v2 through a geometric projection stream, and adds a weight-space orthogonality penalty that keeps the two streams in disjoint subspaces. All four teachers are frozen during training and dropped at inference. Applied to PixelGen and DeCo with a single recipe, PixelDense improves GenEval, DPG-Bench, and HPS v2.1, raises PixelGen-XXL's GenEval Overall from 0.7927 to 0.8093, and beats every single-teacher and unfactored multi-teacher variant. In partial-noise reconstruction, independent panoptic, depth, and surface-normal probes show up to 53.1% PQ gain and 36.0% depth AbsRel reduction at τ=0.5 across COCO and Flickr30K. From random initialization, PixelDense also reaches the baseline's peak GenEval 1.23x faster. In SDEdit editing on PIE-Bench, PixelDense keeps more of the source background and layout at every edit strength, raising background PSNR by up to 2.2 dB.

Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode semantic intent indirectly through geometric constraints or model updates, limiting interpretability and flexibility. We introduce LLM-augmented semantic steering, which enables analysts to express semantic intent by grouping a small set of example documents within the projection. A large language model externalizes this intent as natural-language representations and selectively extends it to related documents; the resulting semantic information is then incorporated into document representations via text augmentation or embedding-level blending, without retraining the underlying models. A case study illustrates how the same corpus can be reorganized from different semantic perspectives, while simulation-based evaluation shows that semantic steering improves global and local alignment with target semantic structures using only minimal interaction. Embedding-level blending further enables continuous and controllable steering of projection layouts. These results position projection spaces as intent-dependent semantic workspaces that can be reshaped through explicit, interpretable, language-mediated interaction.

Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives -- as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to small perturbations of noise to the field than baseline parameter inference networks.

Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.

We use NuSTAR observations of the Galactic Center to search for X-ray lines from the radiative decay of sterile neutrino dark matter. Finding no evidence of unknown lines, we set limits on the sterile neutrino mass and mixing angle. In most of the mass range 10-50 keV, these are now the strongest limits, at some masses improving upon previous limits by a factor of ~10. In the neutrino minimal standard model framework, where additional constraints from dark matter production and structure formation apply, the allowed parameter space is reduced by more than half. Future NuSTAR observations may be able to cover much of the remaining parameter space.

Residual connections are the de facto mechanism for training deep neural networks stably. Geodesic Normalization (GeoNorm) recasts them on a Riemannian manifold, orthogonalizing each layer output against the current hidden state and applying the resulting update through the Riemannian exponential map. Every hidden state thus keeps a constant ell_{2}-norm, confining the residual stream to a hypersphere. The exponential map, however, is only one member of a broad family of retraction maps. We show that on the hypersphere this entire family collapses to a single scalar design choice. What distinguishes one retraction from another is only how the magnitude of an update is converted into a rotation angle within the plane spanned by the hidden state and the update. This view places Euclidean residual connections and GeoNorm in one framework. Instantiating it with the metric projection retraction and the Cayley retraction yields Proj-SpheretNorm and Cay-SpheretNorm, which are exactly norm-preserving yet require only algebraic operations. Both prove to be members of a one-parameter family of angular retractions, p-SpheretNorm, whose rotation angle saturates rather than growing without bound. The two methods above are recovered exactly at p = 1 and p = 2, while the identity map and GeoNorm arise only as limits at either end. On nanoGPT, all three methods outperform existing lightweight deep connection schemes, and the best validation loss is attained at finite p, indicating that the exponential map is not the preferred retraction for spherical residual streams but merely one end of a spectrum.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory .

Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that highly noisy diffusion states contain no more information than small, downsampled images - raising the question of why they must be processed at full resolution. To address this, we fuse scale spaces into the diffusion process by formulating a family of diffusion models with generalized linear degradations and practical implementations. Using downsampling as the degradation yields our proposed Scale Space Diffusion. To support Scale Space Diffusion, we introduce Flexi-UNet, a UNet variant that performs resolution-preserving and resolution-increasing denoising using only the necessary parts of the network. We evaluate our framework on CelebA and ImageNet and analyze its scaling behavior across resolutions and network depths. Our project website ( https://prateksha.github.io/projects/scale-space-diffusion/ ) is available publicly.

A universal class of light-ray operators formed from null integrals of the stress tensor is constructed in generic interacting Lorentzian conformal field theories in four spacetime dimensions. This class of light-ray operators generates the wedge algebra of {rm w}_{1+infty}, which was recently identified among the asymptotic symmetries of asymptotically flat spacetimes. In four-dimensional conformal field theories with an additional spin-one conserved current, a second universal class of light-ray operators is constructed and shown to generate the ''S algebra,'' the gauge-theoretic analog of {rm w}_{1+infty}. Finally, a precise relation is established between the one-point functions of these light-ray operators in scalar states and the universal soft factors in the infinite tower of soft graviton theorems. The results presented in this paper will be accompanied by detailed calculations and proofs in a longer forthcoming work.

Continual learning aims to avoid catastrophic forgetting and effectively leverage learned experiences to master new knowledge. Existing gradient projection approaches impose hard constraints on the optimization space for new tasks to minimize interference, which simultaneously hinders forward knowledge transfer. To address this issue, recent methods reuse frozen parameters with a growing network, resulting in high computational costs. Thus, it remains a challenge whether we can improve forward knowledge transfer for gradient projection approaches using a fixed network architecture. In this work, we propose the Restricted Orthogonal Gradient prOjection (ROGO) framework. The basic idea is to adopt a restricted orthogonal constraint allowing parameters optimized in the direction oblique to the whole frozen space to facilitate forward knowledge transfer while consolidating previous knowledge. Our framework requires neither data buffers nor extra parameters. Extensive experiments have demonstrated the superiority of our framework over several strong baselines. We also provide theoretical guarantees for our relaxing strategy.

Monitoring deforestation-driven carbon emissions requires both spatially explicit and temporally continuous estimates of aboveground biomass density (AGBD) with calibrated uncertainty. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides reliable LIDAR-derived AGBD, but its orbital sampling causes irregular spatiotemporal coverage, and occasional operational interruptions, including a 13-month hibernation from March 2023 to April 2024, leave extended gaps in the observational record. Prior work has used machine learning approaches to fill GEDI's spatial gaps using satellite-derived features, but temporal interpolation of biomass through unobserved periods, particularly across active disturbance events, remains largely unaddressed. Moreover, standard ensemble methods for biomass mapping have been shown to produce systematically miscalibrated prediction intervals. To address these gaps, we extend the Attentive Neural Process (ANP) framework, previously applied to spatial biomass interpolation, to jointly sparse spatiotemporal settings using geospatial foundation model embeddings. We treat space and time symmetrically, empirically validating a form of space-for-time substitution in which observations from nearby locations at other times inform predictions at held-out periods. Our results demonstrate that the ANP produces well-calibrated uncertainty estimates across disturbance regimes, supporting its use in Measurement, Reporting, and Verification (MRV) applications that require reliable uncertainty quantification for forest carbon accounting.

Modern one-step diffusion models achieve impressive quality through distribution-based timestep distillation. Yet, they rely on a critical assumption: Teacher and Student must inhabit the same latent space. This Shared-Space constraint prevents knowledge transfer from modern high-capacity Teachers (e.g., SD 3.5 and Flux) into compact, deployment-friendly Students such as SD 1.5, whose latent resolution and VAE parameterization differ from the Teacher. We formalize this overlooked regime as Cross-Space Distillation, where Teacher and Student differ in both latent resolution and VAE space. To enable distillation under this mismatch, we introduce the Bridge, a lightweight latent interface that maps Student latents into the Teacher space without modifying the Student backbone. Bridge combines a frozen Student VAE decoder as a spatial prior with a compact learnable projector, and is trained with latent reconstruction and attention fidelity objectives for stable Teacher-space alignment. Across diverse modern Teachers, Bridge enables substantial gains for compact one-step Students; for example, it improves SD 1.5 from 5.4 to 9.4 HPSv3 while preserving one-step inference, low latency, and broad ecosystem compatibility. These results show that heterogeneous large Teachers can be distilled into efficient, deployable backbones through a lightweight latent-space interface.

For any {rm E}-rigid presentation e, we construct an orthogonal projection functor to {rm rep}(e^perp) left adjoint to the natural embedding. We establish a bijection between presentations in {rm rep}(e^perp) and presentations compatible with e. For quivers with potentials, we show that {rm rep}(e^perp) forms a module category of another quiver with potential. We derive mutation formulas for the delta-vectors of positive and negative complements and the dimension vectors of simple modules in {rm rep}(e^perp), enabling an algorithm to find the projected quiver with potential. Additionally, we introduce a modified projection for quivers with potentials that preserves general presentations. For applications to cluster algebras, we establish a connection to the stabilization functors.

We propose a new method to determine the shape of the gravitational potential of the dark matter (DM) halo of the Milky Way (MW) with the galactocentric tangential velocities of a sample of hypervelocity stars (HVSs). We compute the trajectories of different samples of HVSs in a MW where the baryon distribution is axisymmetric and the DM potential either is spherical or is spheroidal or triaxial with radial-dependent axis ratios. We determine the shape of the DM potential with the distribution of the latitudinal velocity |v_{vartheta}| in axisymmetric Galactic potentials, or with the distribution of |v_{vartheta}| and of a function bar v_{varphi} of the azimuthal velocity in non-axisymmetric Galactic potentials. We recover the correct shape of the DM potential by comparing the distribution of |v_{vartheta}| and bar v_{varphi} against the corresponding distributions of mock samples of HVSs that traveled in DM halos of different shapes. We use the largest possible sample of sim 800 HVSs of 4~M_odot ejected with the Hills mechanism at a rate sim 10^{-4} yr^{-1}, currently outgoing, and located at more than 10 kpc from the Galactic center. In our ideal case of galactocentric velocities with null uncertainties and no observational limitations, our method recovers the correct shape of the DM potential with a success rate Sgtrsim 89% in axisymmetric Galactic potentials, and S > 96% in the explored non-axisymmetric cases. The unsuccessful cases yield axis ratios of the DM potential that are off by pm 0.1. The success rate decreases with decreasing sample size: for example, for a spherical DM halo, S drops from sim 98% to sim 38% when the sample size decreases from sim 800 to sim 40 HVSs. A robust determination of the shape of the DM potential thus requires the measure of the galactocentric velocity of a few hundred genuine HVSs.

The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be found by considering the classical counterparts of a quantum theory. For example, conservation laws in a quantum theory often stem from conservation laws of the corresponding classical theory. In order to construct such laws, this thesis is concerned with the interplay between symmetries and conservation laws of classical field theories and their application to asymptotically flat spacetimes. This work begins with an explanation of symmetries in field theories with a focus on variational symmetries and their associated conservation laws. Boundary conditions for general relativity are then formulated on three-dimensional asymptotically flat spacetimes at null infinity using the method of conformal completion. Conserved quantities related to asymptotic symmetry transformations are derived and their properties are studied. This is done in a manifestly coordinate independent manner. In a separate step a coordinate system is introduced, such that the results can be compared to existing literature. Next, asymptotically flat spacetimes which contain both future as well as past null infinity are considered. Asymptotic symmetries occurring at these disjoint regions of three-dimensional asymptotically flat spacetimes are linked and the corresponding conserved quantities are matched. Finally, it is shown how asymptotic symmetries lead to the notion of distinct Minkowski spaces that can be differentiated by conserved quantities.

We present the results from four stellar occultations by (486958) Arrokoth, the flyby target of the New Horizons extended mission. Three of the four efforts led to positive detections of the body, and all constrained the presence of rings and other debris, finding none. Twenty-five mobile stations were deployed for 2017 June 3 and augmented by fixed telescopes. There were no positive detections from this effort. The event on 2017 July 10 was observed by SOFIA with one very short chord. Twenty-four deployed stations on 2017 July 17 resulted in five chords that clearly showed a complicated shape consistent with a contact binary with rough dimensions of 20 by 30 km for the overall outline. A visible albedo of 10% was derived from these data. Twenty-two systems were deployed for the fourth event on 2018 Aug 4 and resulted in two chords. The combination of the occultation data and the flyby results provides a significant refinement of the rotation period, now estimated to be 15.9380 pm 0.0005 hours. The occultation data also provided high-precision astrometric constraints on the position of the object that were crucial for supporting the navigation for the New Horizons flyby. This work demonstrates an effective method for obtaining detailed size and shape information and probing for rings and dust on distant Kuiper Belt objects as well as being an important source of positional data that can aid in spacecraft navigation that is particularly useful for small and distant bodies.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z to 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.

Diffusion models excel at 2D outpainting, but extending them to 360^circ panoramic completion from unposed perspective images is challenging due to the geometric and topological mismatch between perspective projections and spherical panoramas. We present Gimbal360, a principled framework that explicitly bridges perspective observations and spherical panoramas. We introduce a Canonical Viewing Space that regularizes projective geometry and provides a consistent intermediate representation between the two domains. To anchor in-the-wild inputs to this space, we propose a Differentiable Auto-Leveling module that stabilizes feature orientation without requiring camera parameters at inference. Panoramic generation also introduces a topological challenge. Standard generative architectures assume a bounded Euclidean image plane, while Equirectangular Projection (ERP) panoramas exhibit intrinsic S^1 periodicity. Euclidean operations therefore break boundary continuity. We address this mismatch by enforcing topological equivariance in the latent space to preserve seamless periodic structure. To support this formulation, we introduce Horizon360, a curated large-scale dataset of gravity-aligned panoramic environments. Extensive experiments show that explicitly standardizing geometric and topological priors enables Gimbal360 to achieve state-of-the-art performance in structurally consistent 360^circ scene completion.

Spacecraft deployed in outer space are routinely subjected to various forms of damage due to exposure to hazardous environments. In addition, there are significant risks to the subsequent process of in-space repairs through human extravehicular activity or robotic manipulation, incurring substantial operational costs. Recent developments in image segmentation could enable the development of reliable and cost-effective autonomous inspection systems. While these models often require large amounts of training data to achieve satisfactory results, publicly available annotated spacecraft segmentation data are very scarce. Here, we present a new dataset of nearly 64k annotated spacecraft images that was created using real spacecraft models, superimposed on a mixture of real and synthetic backgrounds generated using NASA's TTALOS pipeline. To mimic camera distortions and noise in real-world image acquisition, we also added different types of noise and distortion to the images. Finally, we finetuned YOLOv8 and YOLOv11 segmentation models to generate performance benchmarks for the dataset under well-defined hardware and inference time constraints to mimic real-world image segmentation challenges for real-time onboard applications in space on NASA's inspector spacecraft. The resulting models, when tested under these constraints, achieved a Dice score of 0.92, Hausdorff distance of 0.69, and an inference time of about 0.5 second. The dataset and models for performance benchmark are available at https://github.com/RiceD2KLab/SWiM.

Activation steering methods are widely used to control large language model (LLM) behavior and are often interpreted as revealing meaningful internal representations. This interpretation assumes that steering directions are identifiable and uniquely recoverable from input-output behavior. We show that, under white-box single-layer access, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we find that orthogonal perturbations achieve near-equivalent efficacy with negligible effect sizes across multiple models and traits, with pre-trained semantic classifiers confirming equivalence at the output level. We estimate null-space dimensionality via SVD of activation covariance matrices and validate that equivalence holds robustly throughout the operationally relevant steering range. Critically, we show that non-identifiability is a robust geometric property that persists across diverse prompt distributions. These findings reveal fundamental interpretability limits and highlight the need for structural constraints beyond behavioral testing to enable reliable alignment interventions.

We present a method for joint inference of cosmological parameters and convergence maps from weak lensing observations, targeting the full posterior conditioned on the observed shear field. Our approach uses implicit inference with diffusion models, learning the joint distribution from simulations, without the need to have an explicit and differentiable forward model for gradient-based MCMC sampling. We introduce a transformer-based architecture that operates in pixel space and treats cosmological parameters as additional tokens in a unified sequence, enabling efficient multimodal processing within a single network. At inference time, the trained model generates posterior samples of joint convergence maps and cosmological parameters conditioned on observed noisy shear fields. We demonstrate the method on simulated weak lensing data generated from log-normal fields in a wcdm cosmology. The model accurately reconstructs convergence maps and recovers cosmological posteriors that agree with traditional MCMC, while remaining well calibrated across the prior, with a MIRA calibration score of 0.635 pm 0.017 on the joint posterior (where 0.667 is optimal). The inferred fields reproduce the correct two-point statistics as well as non-Gaussian statistics such as the one-point distribution. This work establishes diffusion-based implicit inference as a viable route toward full field-level cosmological analyses, paving the way for applications to more realistic, non-differentiable simulators.

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

A key aspect of text-to-image personalization methods is the manner in which the target concept is represented within the generative process. This choice greatly affects the visual fidelity, downstream editability, and disk space needed to store the learned concept. In this paper, we explore a new text-conditioning space that is dependent on both the denoising process timestep (time) and the denoising U-Net layers (space) and showcase its compelling properties. A single concept in the space-time representation is composed of hundreds of vectors, one for each combination of time and space, making this space challenging to optimize directly. Instead, we propose to implicitly represent a concept in this space by optimizing a small neural mapper that receives the current time and space parameters and outputs the matching token embedding. In doing so, the entire personalized concept is represented by the parameters of the learned mapper, resulting in a compact, yet expressive, representation. Similarly to other personalization methods, the output of our neural mapper resides in the input space of the text encoder. We observe that one can significantly improve the convergence and visual fidelity of the concept by introducing a textual bypass, where our neural mapper additionally outputs a residual that is added to the output of the text encoder. Finally, we show how one can impose an importance-based ordering over our implicit representation, providing users control over the reconstruction and editability of the learned concept using a single trained model. We demonstrate the effectiveness of our approach over a range of concepts and prompts, showing our method's ability to generate high-quality and controllable compositions without fine-tuning any parameters of the generative model itself.

Classifier-free Guidance (CFG) is widely adopted in text-to-speech (TTS) systems to enhance generation quality and conditioning fidelity by interpolating between conditioned and unconditioned predictions. A common unconditional technique is to use an empty representation, in the form of a fixed null vector. In this work, we propose replacing this representation with a learnable unconditional embedding, optimized to represent a meaningful unconditional state. Objective and subjective evaluations demonstrate that learnable null embeddings consistently outperform fixed null embeddings across speaker similarity, speech stability, and expressiveness, while exhibiting greater robustness to larger guidance scales. We further show that learning a distinct unconditional embedding for each of the TTS conditioning modalities allows fine-grained control over speaker and text guidance, showcasing the trade-off between similarity and quality, and stability and expressiveness in the generated speech.

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator that combines a Lasso pilot estimate of the regression function with a bias correction term based on the weighted residuals of the Lasso regression. The weights depend on estimates of the missingness probabilities (propensity scores) and solve a convex optimization program that trades off bias and variance optimally. Provided that the propensity scores can be pointwise consistently estimated at in-sample data points, our proposed estimator for the regression function is asymptotically normal and semiparametrically efficient among all asymptotically linear estimators. Furthermore, the proposed estimator retains its asymptotic properties even if the propensity scores are estimated by modern machine learning techniques. We validate the finite-sample performance of the proposed estimator through comparative simulation studies and the real-world problem of inferring the stellar masses of galaxies in the Sloan Digital Sky Survey.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

We use the extrapolate dictionary to revisit the spectrum of operators in Celestial CFT. Under the Celestial CFT map, each state in the 4D Hilbert space should map to one in the 2D Hilbert space. This implies that, beyond the familiar single particle states/operators, there should be multiparticle operators appearing in the celestial OPE. We extend the existing flat-space dictionary by constructing composite primaries from both Carrollian and Celestial perspectives. In the process, we demonstrate some subtleties in deriving the Poincaré primary condition from the Carrollian limit, clarify the compatibility of principal series representations with highest weight representations and unitarity in Celestial CFT, and discuss how the celestial OPE block expansion emerges from a 2D CFT standpoint.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H_0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and ΛCDM-dependent baryon acoustic oscillation observations. The inferred H_0 values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are H_0= 66 pm 6, km,s^{-1},Mpc^{-1}, H_0= 67 pm 10, km,s^{-1},Mpc^{-1} and H_0= 69 pm 6, km,s^{-1},Mpc^{-1}, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln R=12.17pm 0.02.

Existing Neural Radiance Fields (NeRF) methods suffer from the existence of reflective objects, often resulting in blurry or distorted rendering. Instead of calculating a single radiance field, we propose a multi-space neural radiance field (MS-NeRF) that represents the scene using a group of feature fields in parallel sub-spaces, which leads to a better understanding of the neural network toward the existence of reflective and refractive objects. Our multi-space scheme works as an enhancement to existing NeRF methods, with only small computational overheads needed for training and inferring the extra-space outputs. We demonstrate the superiority and compatibility of our approach using three representative NeRF-based models, i.e., NeRF, Mip-NeRF, and Mip-NeRF 360. Comparisons are performed on a novelly constructed dataset consisting of 25 synthetic scenes and 7 real captured scenes with complex reflection and refraction, all having 360-degree viewpoints. Extensive experiments show that our approach significantly outperforms the existing single-space NeRF methods for rendering high-quality scenes concerned with complex light paths through mirror-like objects. Our code and dataset will be publicly available at https://zx-yin.github.io/msnerf.

Non-line-of-sight (NLOS) imaging is conducted to infer invisible scenes from indirect light on visible objects. The neural transient field (NeTF) was proposed for representing scenes as neural radiance fields in NLOS scenes. We propose NLOS neural implicit surface (NLOS-NeuS), which extends the NeTF to neural implicit surfaces with a signed distance function (SDF) for reconstructing three-dimensional surfaces in NLOS scenes. We introduce two constraints as loss functions for correctly learning an SDF to avoid non-zero level-set surfaces. We also introduce a lower bound constraint of an SDF based on the geometry of the first-returning photons. The experimental results indicate that these constraints are essential for learning a correct SDF in NLOS scenes. Compared with previous methods with discretized representation, NLOS-NeuS with the neural continuous representation enables us to reconstruct smooth surfaces while preserving fine details in NLOS scenes. To the best of our knowledge, this is the first study on neural implicit surfaces with volume rendering in NLOS scenes.