Daily Papers

We present AMB3R, a multi-view feed-forward model for dense 3D reconstruction on a metric-scale that addresses diverse 3D vision tasks. The key idea is to leverage a sparse, yet compact, volumetric scene representation as our backend, enabling geometric reasoning with spatial compactness. Although trained solely for multi-view reconstruction, we demonstrate that AMB3R can be seamlessly extended to uncalibrated visual odometry (online) or large-scale structure from motion without the need for task-specific fine-tuning or test-time optimization. Compared to prior pointmap-based models, our approach achieves state-of-the-art performance in camera pose, depth, and metric-scale estimation, 3D reconstruction, and even surpasses optimization-based SLAM and SfM methods with dense reconstruction priors on common benchmarks.

We introduce Any6D, a model-free framework for 6D object pose estimation that requires only a single RGB-D anchor image to estimate both the 6D pose and size of unknown objects in novel scenes. Unlike existing methods that rely on textured 3D models or multiple viewpoints, Any6D leverages a joint object alignment process to enhance 2D-3D alignment and metric scale estimation for improved pose accuracy. Our approach integrates a render-and-compare strategy to generate and refine pose hypotheses, enabling robust performance in scenarios with occlusions, non-overlapping views, diverse lighting conditions, and large cross-environment variations. We evaluate our method on five challenging datasets: REAL275, Toyota-Light, HO3D, YCBINEOAT, and LM-O, demonstrating its effectiveness in significantly outperforming state-of-the-art methods for novel object pose estimation. Project page: https://taeyeop.com/any6d

Spatial understanding of the physical world from 2D visual inputs hinges on two complementary forms of geometric knowledge: holistic 3D structural perception and fine-grained metric scale estimation. Existing multimodal large language models (MLLMs) typically address only one facet, ingesting either depth maps or point clouds as additional model inputs, which incurs substantial computational overhead and inherits the generalization limitations of upstream prediction models. We propose GAMSI, a dual-pathway Geometry-Aware MLLM for Spatial Intelligence that takes only RGB images as input while internalizing both forms of geometric prior within a unified autoregressive backbone. Specifically, we introduce Metric-Structure Decoupled Queries (MSDQ) which employ two groups of learnable queries to respectively extract dense metric signals and sparse structural cues from the shared visual context, with a task-decoupled attention mask further preventing the two pathways from contaminating each other. Building on this, an Expert-Guided Visual Grounding (EVG) module projects the aggregated cues back to frame-level visual features and aligns them with vision foundation models, which serve purely as training-time supervision, rather than as model inputs. We further build a multi-task spatial instruction-tuning dataset (MTS) comprising 152{,}776 samples spanning 13 task types and three visual modalities, consolidated from six public datasets. Trained with a two-stage curriculum, GAMSI achieves state-of-the-art performance on seven spatial intelligence benchmarks.

Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.

Monocular depth estimation is scale-ambiguous, and thus requires scale supervision to produce metric predictions. Even so, the resulting models will be geometry-specific, with learned scales that cannot be directly transferred across domains. Because of that, recent works focus instead on relative depth, eschewing scale in favor of improved up-to-scale zero-shot transfer. In this work we introduce ZeroDepth, a novel monocular depth estimation framework capable of predicting metric scale for arbitrary test images from different domains and camera parameters. This is achieved by (i) the use of input-level geometric embeddings that enable the network to learn a scale prior over objects; and (ii) decoupling the encoder and decoder stages, via a variational latent representation that is conditioned on single frame information. We evaluated ZeroDepth targeting both outdoor (KITTI, DDAD, nuScenes) and indoor (NYUv2) benchmarks, and achieved a new state-of-the-art in both settings using the same pre-trained model, outperforming methods that train on in-domain data and require test-time scaling to produce metric estimates.

Long-sequence streaming 3D reconstruction remains a significant open challenge. Existing autoregressive models often fail when processing long sequences. They typically anchor poses to the first frame, which leads to attention decay, scale drift, and extrapolation errors. We introduce LongStream, a novel gauge-decoupled streaming visual geometry model for metric-scale scene reconstruction across thousands of frames. Our approach is threefold. First, we discard the first-frame anchor and predict keyframe-relative poses. This reformulates long-range extrapolation into a constant-difficulty local task. Second, we introduce orthogonal scale learning. This method fully disentangles geometry from scale estimation to suppress drift. Finally, we solve Transformer cache issues such as attention-sink reliance and long-term KV-cache contamination. We propose cache-consistent training combined with periodic cache refresh. This approach suppresses attention degradation over ultra-long sequences and reduces the gap between training and inference. Experiments show LongStream achieves state-of-the-art performance. It delivers stable, metric-scale reconstruction over kilometer-scale sequences at 18 FPS. Project Page: https://3dagentworld.github.io/longstream/

Heatmap representations have formed the basis of human pose estimation systems for many years, and their extension to 3D has been a fruitful line of recent research. This includes 2.5D volumetric heatmaps, whose X and Y axes correspond to image space and Z to metric depth around the subject. To obtain metric-scale predictions, 2.5D methods need a separate post-processing step to resolve scale ambiguity. Further, they cannot localize body joints outside the image boundaries, leading to incomplete estimates for truncated images. To address these limitations, we propose metric-scale truncation-robust (MeTRo) volumetric heatmaps, whose dimensions are all defined in metric 3D space, instead of being aligned with image space. This reinterpretation of heatmap dimensions allows us to directly estimate complete, metric-scale poses without test-time knowledge of distance or relying on anthropometric heuristics, such as bone lengths. To further demonstrate the utility our representation, we present a differentiable combination of our 3D metric-scale heatmaps with 2D image-space ones to estimate absolute 3D pose (our MeTRAbs architecture). We find that supervision via absolute pose loss is crucial for accurate non-root-relative localization. Using a ResNet-50 backbone without further learned layers, we obtain state-of-the-art results on Human3.6M, MPI-INF-3DHP and MuPoTS-3D. Our code will be made publicly available to facilitate further research.

Advances in deep learning recognition have led to accurate object detection with 2D images. However, these 2D perception methods are insufficient for complete 3D world information. Concurrently, advanced 3D shape estimation approaches focus on the shape itself, without considering metric scale. These methods cannot determine the accurate location and orientation of objects. To tackle this problem, we propose a framework that jointly estimates a metric scale shape and pose from a single RGB image. Our framework has two branches: the Metric Scale Object Shape branch (MSOS) and the Normalized Object Coordinate Space branch (NOCS). The MSOS branch estimates the metric scale shape observed in the camera coordinates. The NOCS branch predicts the normalized object coordinate space (NOCS) map and performs similarity transformation with the rendered depth map from a predicted metric scale mesh to obtain 6d pose and size. Additionally, we introduce the Normalized Object Center Estimation (NOCE) to estimate the geometrically aligned distance from the camera to the object center. We validated our method on both synthetic and real-world datasets to evaluate category-level object pose and shape.

We propose MoGe-2, an advanced open-domain geometry estimation model that recovers a metric scale 3D point map of a scene from a single image. Our method builds upon the recent monocular geometry estimation approach, MoGe, which predicts affine-invariant point maps with unknown scales. We explore effective strategies to extend MoGe for metric geometry prediction without compromising the relative geometry accuracy provided by the affine-invariant point representation. Additionally, we discover that noise and errors in real data diminish fine-grained detail in the predicted geometry. We address this by developing a unified data refinement approach that filters and completes real data from different sources using sharp synthetic labels, significantly enhancing the granularity of the reconstructed geometry while maintaining the overall accuracy. We train our model on a large corpus of mixed datasets and conducted comprehensive evaluations, demonstrating its superior performance in achieving accurate relative geometry, precise metric scale, and fine-grained detail recovery -- capabilities that no previous methods have simultaneously achieved.

We present X-lens, a compact feed-forward model for metric depth estimation from a variable number of calibrated fisheye and pinhole views. To support real-time downstream perception, X-lens is built around a geometry-aware heterogeneous camera formulation with two key components. Learnable calibration tokens provide a coarse alignment between fisheye and pinhole projective spaces, while a Jacobian-parameterized distortion bias injected into cross-attention models local projection changes and promotes cross-camera consistency, enabling robust generalization with only 0.04B parameters and up to 41 FPS. The model predicts dense depth together with a global metric scale, avoiding auxiliary reconstruction targets that increase computation and optimization complexity. To learn such cross-camera generalization at scale and depth, X-lens is trained on multiple public datasets and OmniScene, our newly released large-scale synthetic dataset containing approximately 266K synchronized six-view frames, 1.7M individual images, and 103 indoor and outdoor scenes. Extensive experiments on both real-world and synthetic indoor and outdoor datasets demonstrate superior heterogeneous-camera metric depth accuracy, reducing AbsRel by 25.4\% on OmniScene-Full over the strongest baseline while using 88.9\% fewer parameters, with competitive performance on conventional fisheye-only and pinhole-only settings.

This paper introduces PatchRefiner, an advanced framework for metric single image depth estimation aimed at high-resolution real-domain inputs. While depth estimation is crucial for applications such as autonomous driving, 3D generative modeling, and 3D reconstruction, achieving accurate high-resolution depth in real-world scenarios is challenging due to the constraints of existing architectures and the scarcity of detailed real-world depth data. PatchRefiner adopts a tile-based methodology, reconceptualizing high-resolution depth estimation as a refinement process, which results in notable performance enhancements. Utilizing a pseudo-labeling strategy that leverages synthetic data, PatchRefiner incorporates a Detail and Scale Disentangling (DSD) loss to enhance detail capture while maintaining scale accuracy, thus facilitating the effective transfer of knowledge from synthetic to real-world data. Our extensive evaluations demonstrate PatchRefiner's superior performance, significantly outperforming existing benchmarks on the Unreal4KStereo dataset by 18.1% in terms of the root mean squared error (RMSE) and showing marked improvements in detail accuracy and consistent scale estimation on diverse real-world datasets like CityScape, ScanNet++, and ETH3D.

Monocular depth estimation (MDE) has been widely adopted in the perception systems of autonomous vehicles and mobile robots. However, existing approaches often struggle to maintain temporal consistency in depth estimation across consecutive frames. This inconsistency not only causes jitter but can also lead to estimation failures when the depth range changes abruptly. To address these challenges, this paper proposes a consistency-aware monocular depth estimation framework that leverages wheel odometry from a mobile robot to achieve stable and coherent depth predictions over time. Specifically, we estimate camera pose and sparse depth from triangulation using optical flow between consecutive frames. The sparse depth estimates are used to update a recursive Bayesian estimate of the metric scale, which is then applied to rescale the relative depth predicted by a pre-trained depth estimation foundation model. The proposed method is evaluated on the KITTI, TartanAir, MS2, and our own dataset, demonstrating robust and accurate depth estimation performance.

Monocular depth estimation can be broadly categorized into two directions: relative depth estimation, which predicts normalized or inverse depth without absolute scale, and metric depth estimation, which aims to recover depth with real-world scale. While relative methods are flexible and data-efficient, their lack of metric scale limits their utility in downstream tasks. A promising solution is to infer absolute scale from textual descriptions. However, such language-based recovery is highly sensitive to natural language ambiguity, as the same image may be described differently across perspectives and styles. To address this, we introduce VGLD (Visually-Guided Linguistic Disambiguation), a framework that incorporates high-level visual semantics to resolve ambiguity in textual inputs. By jointly encoding both image and text, VGLD predicts a set of global linear transformation parameters that align relative depth maps with metric scale. This visually grounded disambiguation improves the stability and accuracy of scale estimation. We evaluate VGLD on representative models, including MiDaS and DepthAnything, using standard indoor (NYUv2) and outdoor (KITTI) benchmarks. Results show that VGLD significantly mitigates scale estimation bias caused by inconsistent or ambiguous language, achieving robust and accurate metric predictions. Moreover, when trained on multiple datasets, VGLD functions as a universal and lightweight alignment module, maintaining strong performance even in zero-shot settings. Code will be released upon acceptance.

Monocular geometry estimation has recently achieved impressive performance across diverse scenes. However, state-of-the-art models still face notable distortion in local 3D structure, especially in fine details, like thin structures and small objects. We attribute this limitation to an architectural mismatch: most current models decode 3D geometry within a 2D parameterization, where feature interactions are governed by image-plane proximity rather than true 3D spatial relationships. This inadvertently mixes features from geometrically distant surfaces, resulting in over-smoothed geometry particularly around thin or elongated structure. In this paper, we propose MoGe-3, a fine-detail monocular geometry estimation model with Self-Guided Sparse 3D Refinement (SSR) that lifts monocular geometry modeling from 2D image space to 3D space for high-fidelity metric-scale point maps. MoGe-3 lifts the coarse point map from a foundation base model onto a sparse voxel shell and refines it via SSR. The SSR employs sparse convolutions that aggregate features based on 3D spatial locality, avoiding feature mixing across depth discontinuities. Extensive experiments on diverse datasets demonstrate that MoGe-3 significantly outperforms existing approaches in recovering fine detailed 3D geometry across both quantitative metrics and qualitative visualizations. Project page: https://qft-333.github.io/moge3page/

Trajectory planning in unstructured environments is a fundamental and challenging capability for mobile robots. Traditional modular pipelines suffer from latency and cascading errors across perception, localization, mapping, and planning modules. Recent end-to-end learning methods map raw visual observations directly to control signals or trajectories, promising greater performance and efficiency in open-world settings. However, most prior end-to-end approaches still rely on separate localization modules that depend on accurate sensor extrinsic calibration for self-state estimation, thereby limiting generalization across embodiments and environments. We introduce LoGoPlanner, a localization-grounded, end-to-end navigation framework that addresses these limitations by: (1) finetuning a long-horizon visual-geometry backbone to ground predictions with absolute metric scale, thereby providing implicit state estimation for accurate localization; (2) reconstructing surrounding scene geometry from historical observations to supply dense, fine-grained environmental awareness for reliable obstacle avoidance; and (3) conditioning the policy on implicit geometry bootstrapped by the aforementioned auxiliary tasks, thereby reducing error propagation.We evaluate LoGoPlanner in both simulation and real-world settings, where its fully end-to-end design reduces cumulative error while metric-aware geometry memory enhances planning consistency and obstacle avoidance, leading to more than a 27.3\% improvement over oracle-localization baselines and strong generalization across embodiments and environments. The code and models have been made publicly available on the https://steinate.github.io/logoplanner.github.io/{project page}.

Learning model-free object pose estimation for unseen instances remains a fundamental challenge in 3D vision. Existing methods typically fall into two disjoint paradigms: category-level approaches predict absolute poses in a canonical space but rely on predefined taxonomies, while relative pose methods estimate cross-view transformations but cannot recover single-view absolute pose. In this work, we propose Object Pose Transformer (), a unified feed-forward framework that bridges these paradigms through task factorization within a single model. jointly predicts depth, point maps, camera parameters, and normalized object coordinates (NOCS) from RGB inputs, enabling both category-level absolute SA(3) pose and unseen-object relative SE(3) pose. Our approach leverages contrastive object-centric latent embeddings for canonicalization without requiring semantic labels at inference time, and uses point maps as a camera-space representation to enable multi-view relative geometric reasoning. Through cross-frame feature interaction and shared object embeddings, our model leverages relative geometric consistency across views to improve absolute pose estimation, reducing ambiguity in single-view predictions. Furthermore, is camera-agnostic, learning camera intrinsics on-the-fly and supporting optional depth input for metric-scale recovery, while remaining fully functional in RGB-only settings. Extensive experiments on diverse benchmarks (NOCS, HouseCat6D, Omni6DPose, Toyota-Light) demonstrate state-of-the-art performance in both absolute and relative pose estimation tasks within a single unified architecture.

Estimating the 6D pose of arbitrary unseen objects from a single reference image is critical for robotics operating in the long-tail of real-world instances. However, this setting is notoriously challenging: 3D models are rarely available, single-view reconstructions lack metric scale, and domain gaps between generated models and real-world images undermine robustness. We propose OnePoseViaGen, a pipeline that tackles these challenges through two key components. First, a coarse-to-fine alignment module jointly refines scale and pose by combining multi-view feature matching with render-and-compare refinement. Second, a text-guided generative domain randomization strategy diversifies textures, enabling effective fine-tuning of pose estimators with synthetic data. Together, these steps allow high-fidelity single-view 3D generation to support reliable one-shot 6D pose estimation. On challenging benchmarks (YCBInEOAT, Toyota-Light, LM-O), OnePoseViaGen achieves state-of-the-art performance far surpassing prior approaches. We further demonstrate robust dexterous grasping with a real robot hand, validating the practicality of our method in real-world manipulation. Project page: https://gzwsama.github.io/OnePoseviaGen.github.io/

We present StereoWorld, a camera-conditioned stereo world model that jointly learns appearance and binocular geometry for end-to-end stereo video generation.Unlike monocular RGB or RGBD approaches, StereoWorld operates exclusively within the RGB modality, while simultaneously grounding geometry directly from disparity. To efficiently achieve consistent stereo generation, our approach introduces two key designs: (1) a unified camera-frame RoPE that augments latent tokens with camera-aware rotary positional encoding, enabling relative, view- and time-consistent conditioning while preserving pretrained video priors via a stable attention initialization; and (2) a stereo-aware attention decomposition that factors full 4D attention into 3D intra-view attention plus horizontal row attention, leveraging the epipolar prior to capture disparity-aligned correspondences with substantially lower compute. Across benchmarks, StereoWorld improves stereo consistency, disparity accuracy, and camera-motion fidelity over strong monocular-then-convert pipelines, achieving more than 3x faster generation with an additional 5% gain in viewpoint consistency. Beyond benchmarks, StereoWorld enables end-to-end binocular VR rendering without depth estimation or inpainting, enhances embodied policy learning through metric-scale depth grounding, and is compatible with long-video distillation for extended interactive stereo synthesis.

Recent geometric foundation models (e.g., Metric3D, Depth Anything and UniDepth) have substantially improved monocular depth estimation (MDE) in both cross-scene generalization and metric-scale prediction, yet these gains have not translated to tiny models. We bridge this gap with DepthART (Depth Anything Rethought for Tiny Models), which is a compact MDE model for on-device deployment across diverse scenes. We first identify two capacity-driven bottlenecks in tiny models: (i) overfitting to dataset-specific distribution bias and (ii) unstable metric adaptation under camera shift, where full fine-tuning easily damages transferable geometry. Accordingly, DepthART combines two simple but effective strategies: a bias-resistant data sampling scheme to reduce distribution bias under the same training budget, and a camera-conditioned fine-tuning protocol that freezes the distilled encoder and adjusts metric scale conditioned on intrinsics while better preserving cross-dataset generalization. Across datasets, DepthART consistently surpasses previous tiny baselines in both zero-shot generalization and metric accuracy (e.g., zero-shot δ_1=0.964 for DepthART-S on NYUD v2), and in some cases approaches heavy models. We further provide a scalable model family, with DepthART-S reaching 347/245 FPS (strict FP32) on an RTX A6000 at 224^2/448^2, 102 FPS (TF32) on a Orin NX 8GB, and over 15 FPS (FP32) on a Jetson Nano 4GB.

Estimating depth from a single image is a challenging visual task. Compared to relative depth estimation, metric depth estimation attracts more attention due to its practical physical significance and critical applications in real-life scenarios. However, existing metric depth estimation methods are typically trained on specific datasets with similar scenes, facing challenges in generalizing across scenes with significant scale variations. To address this challenge, we propose a novel monocular depth estimation method called ScaleDepth. Our method decomposes metric depth into scene scale and relative depth, and predicts them through a semantic-aware scale prediction (SASP) module and an adaptive relative depth estimation (ARDE) module, respectively. The proposed ScaleDepth enjoys several merits. First, the SASP module can implicitly combine structural and semantic features of the images to predict precise scene scales. Second, the ARDE module can adaptively estimate the relative depth distribution of each image within a normalized depth space. Third, our method achieves metric depth estimation for both indoor and outdoor scenes in a unified framework, without the need for setting the depth range or fine-tuning model. Extensive experiments demonstrate that our method attains state-of-the-art performance across indoor, outdoor, unconstrained, and unseen scenes. Project page: https://ruijiezhu94.github.io/ScaleDepth

Recovering metric depth from a single image remains a fundamental challenge in computer vision, requiring both scene understanding and accurate scaling. While deep learning has advanced monocular depth estimation, current models often struggle with unfamiliar scenes and layouts, particularly in zero-shot scenarios and when predicting scale-ergodic metric depth. We present MetricGold, a novel approach that harnesses generative diffusion model's rich priors to improve metric depth estimation. Building upon recent advances in MariGold, DDVM and Depth Anything V2 respectively, our method combines latent diffusion, log-scaled metric depth representation, and synthetic data training. MetricGold achieves efficient training on a single RTX 3090 within two days using photo-realistic synthetic data from HyperSIM, VirtualKitti, and TartanAir. Our experiments demonstrate robust generalization across diverse datasets, producing sharper and higher quality metric depth estimates compared to existing approaches.

Recent years have seen a significant increase in demand for robotic solutions in unstructured natural environments, alongside growing interest in bridging 2D and 3D scene understanding. However, existing robotics datasets are predominantly captured in structured urban environments, making them inadequate for addressing the challenges posed by complex, unstructured natural settings. To address this gap, we propose WildCross, a cross-modal benchmark for place recognition and metric depth estimation in large-scale natural environments. WildCross comprises over 476K sequential RGB frames with semi-dense depth and surface normal annotations, each aligned with accurate 6DoF poses and synchronized dense lidar submaps. We conduct comprehensive experiments on visual, lidar, and cross-modal place recognition, as well as metric depth estimation, demonstrating the value of WildCross as a challenging benchmark for multi-modal robotic perception tasks. We provide access to the code repository and dataset at https://csiro-robotics.github.io/WildCross.

This work presents a generalizable framework to transfer relative depth to metric depth. Current monocular depth estimation methods are mainly divided into metric depth estimation (MMDE) and relative depth estimation (MRDE). MMDEs estimate depth in metric scale but are often limited to a specific domain. MRDEs generalize well across different domains, but with uncertain scales which hinders downstream applications. To this end, we aim to build up a framework to solve scale uncertainty and transfer relative depth to metric depth. Previous methods used language as input and estimated two factors for conducting rescaling. Our approach, TR2M, utilizes both text description and image as inputs and estimates two rescale maps to transfer relative depth to metric depth at pixel level. Features from two modalities are fused with a cross-modality attention module to better capture scale information. A strategy is designed to construct and filter confident pseudo metric depth for more comprehensive supervision. We also develop scale-oriented contrastive learning to utilize depth distribution as guidance to enforce the model learning about intrinsic knowledge aligning with the scale distribution. TR2M only exploits a small number of trainable parameters to train on datasets in various domains and experiments not only demonstrate TR2M's great performance in seen datasets but also reveal superior zero-shot capabilities on five unseen datasets. We show the huge potential in pixel-wise transferring relative depth to metric depth with language assistance. (Code is available at: https://github.com/BeileiCui/TR2M)

We introduce Metric3D v2, a geometric foundation model for zero-shot metric depth and surface normal estimation from a single image, which is crucial for metric 3D recovery. While depth and normal are geometrically related and highly complimentary, they present distinct challenges. SoTA monocular depth methods achieve zero-shot generalization by learning affine-invariant depths, which cannot recover real-world metrics. Meanwhile, SoTA normal estimation methods have limited zero-shot performance due to the lack of large-scale labeled data. To tackle these issues, we propose solutions for both metric depth estimation and surface normal estimation. For metric depth estimation, we show that the key to a zero-shot single-view model lies in resolving the metric ambiguity from various camera models and large-scale data training. We propose a canonical camera space transformation module, which explicitly addresses the ambiguity problem and can be effortlessly plugged into existing monocular models. For surface normal estimation, we propose a joint depth-normal optimization module to distill diverse data knowledge from metric depth, enabling normal estimators to learn beyond normal labels. Equipped with these modules, our depth-normal models can be stably trained with over 16 million of images from thousands of camera models with different-type annotations, resulting in zero-shot generalization to in-the-wild images with unseen camera settings. Our method enables the accurate recovery of metric 3D structures on randomly collected internet images, paving the way for plausible single-image metrology. Our project page is at https://JUGGHM.github.io/Metric3Dv2.

We present Pumpire, a unified benchmark for evaluating metric point-pair distance estimation capability of both image- and video-level 3D foundation models, with or without depth priors. In contrast to previous approaches that normally evaluate depth and camera intrinsics separately or evaluate point-clouds with geometric similarity metrics, which cannot directly reflect models' point-to-point distance estimation capability, Pumpire directly assesses point-to-point distances from the reconstructed geometry. To this end, we collect a large-scale and diverse dataset (pumpire-6k) comprising 100 real-world scenes, each annotated with physically measured point-pair distances and containing 64 frames, for a total of 6,400 frames. Building on this dataset, we establish a holistic evaluation protocol that covers both image- and video-level 3D foundation models and enables direct assessment of point-pair distance errors and cross-setting comparison. We conduct extensive experiments across 29 baseline configurations of representative 3D foundation models and provide a comprehensive analysis of the results. By offering this benchmark, we target the more fundamental ability to perceive and estimate physical scale in the reconstructed 3D space, which prior evaluation protocols have largely overlooked. The project page can be found at https://pumpire.github.io/

Gaze estimation is a fundamental task in many applications of computer vision, human computer interaction and robotics. Many state-of-the-art methods are trained and tested on custom datasets, making comparison across methods challenging. Furthermore, existing gaze estimation datasets have limited head pose and gaze variations, and the evaluations are conducted using different protocols and metrics. In this paper, we propose a new gaze estimation dataset called ETH-XGaze, consisting of over one million high-resolution images of varying gaze under extreme head poses. We collect this dataset from 110 participants with a custom hardware setup including 18 digital SLR cameras and adjustable illumination conditions, and a calibrated system to record ground truth gaze targets. We show that our dataset can significantly improve the robustness of gaze estimation methods across different head poses and gaze angles. Additionally, we define a standardized experimental protocol and evaluation metric on ETH-XGaze, to better unify gaze estimation research going forward. The dataset and benchmark website are available at https://ait.ethz.ch/projects/2020/ETH-XGaze

This paper presents a vision-only autonomous flight system for small UAVs operating in controlled indoor environments. The system combines semantic segmentation with monocular depth estimation to enable obstacle avoidance, scene exploration, and autonomous safe landing operations without requiring GPS or expensive sensors such as LiDAR. A key innovation is an adaptive scale factor algorithm that converts non-metric monocular depth predictions into accurate metric distance measurements by leveraging semantic ground plane detection and camera intrinsic parameters, achieving a mean distance error of 14.4 cm. The approach uses a knowledge distillation framework where a color-based Support Vector Machine (SVM) teacher generates training data for a lightweight U-Net student network (1.6M parameters) capable of real-time semantic segmentation. For more complex environments, the SVM teacher can be replaced with a state-of-the-art segmentation model. Testing was conducted in a controlled 5x4 meter laboratory environment with eight cardboard obstacles simulating urban structures. Extensive validation across 30 flight tests in a real-world environment and 100 flight tests in a digital-twin environment demonstrates that the combined segmentation and depth approach increases the distance traveled during surveillance and reduces mission time while maintaining 100% success rates. The system is further optimized through end-to-end learning, where a compact student neural network learns complete flight policies from demonstration data generated by our best-performing method, achieving an 87.5% autonomous mission success rate. This work advances practical vision-based drone navigation in structured environments, demonstrating solutions for metric depth estimation and computational efficiency challenges that enable deployment on resource-constrained platforms.

While current high-resolution depth estimation methods achieve strong results, they often suffer from computational inefficiencies due to reliance on heavyweight models and multiple inference steps, increasing inference time. To address this, we introduce PatchRefiner V2 (PRV2), which replaces heavy refiner models with lightweight encoders. This reduces model size and inference time but introduces noisy features. To overcome this, we propose a Coarse-to-Fine (C2F) module with a Guided Denoising Unit for refining and denoising the refiner features and a Noisy Pretraining strategy to pretrain the refiner branch to fully exploit the potential of the lightweight refiner branch. Additionally, we introduce a Scale-and-Shift Invariant Gradient Matching (SSIGM) loss to enhance synthetic-to-real domain transfer. PRV2 outperforms state-of-the-art depth estimation methods on UnrealStereo4K in both accuracy and speed, using fewer parameters and faster inference. It also shows improved depth boundary delineation on real-world datasets like CityScape, ScanNet++, and KITTI, demonstrating its versatility across domains.

We propose Intrinsic Quality (IQ), a validation-free metric designed to estimate the inherent potential of face recognition (FR) datasets to produce high-performance models without the need for full-scale training. IQ integrates two components: (i) a Neighbor-Consistency Score that quantifies local identity label agreement via nearest neighbors, and (ii) Global Representation Subspace Complexity (Effective Rank, ER), which captures the underlying embedding geometry and dataset diversity. IQ allows for rapid evaluation using lightweight proxy models or data subsets, facilitating dataset diagnosis and curation prior to resource-intensive full-scale training. We describe an experimental protocol tailored to clean, noisy, and mixed-quality FR datasets, and outline evaluation methodologies to validate IQ's predictive power for downstream performance.

This paper presents a novel self-supervised two-frame multi-camera metric depth estimation network, termed M{^2}Depth, which is designed to predict reliable scale-aware surrounding depth in autonomous driving. Unlike the previous works that use multi-view images from a single time-step or multiple time-step images from a single camera, M{^2}Depth takes temporally adjacent two-frame images from multiple cameras as inputs and produces high-quality surrounding depth. We first construct cost volumes in spatial and temporal domains individually and propose a spatial-temporal fusion module that integrates the spatial-temporal information to yield a strong volume presentation. We additionally combine the neural prior from SAM features with internal features to reduce the ambiguity between foreground and background and strengthen the depth edges. Extensive experimental results on nuScenes and DDAD benchmarks show M{^2}Depth achieves state-of-the-art performance. More results can be found in https://heiheishuang.xyz/M2Depth .

While methods for monocular depth estimation have made significant strides on standard benchmarks, zero-shot metric depth estimation remains unsolved. Challenges include the joint modeling of indoor and outdoor scenes, which often exhibit significantly different distributions of RGB and depth, and the depth-scale ambiguity due to unknown camera intrinsics. Recent work has proposed specialized multi-head architectures for jointly modeling indoor and outdoor scenes. In contrast, we advocate a generic, task-agnostic diffusion model, with several advancements such as log-scale depth parameterization to enable joint modeling of indoor and outdoor scenes, conditioning on the field-of-view (FOV) to handle scale ambiguity and synthetically augmenting FOV during training to generalize beyond the limited camera intrinsics in training datasets. Furthermore, by employing a more diverse training mixture than is common, and an efficient diffusion parameterization, our method, DMD (Diffusion for Metric Depth) achieves a 25\% reduction in relative error (REL) on zero-shot indoor and 33\% reduction on zero-shot outdoor datasets over the current SOTA using only a small number of denoising steps. For an overview see https://diffusion-vision.github.io/dmd

We present a foundation model for zero-shot metric monocular depth estimation. Our model, Depth Pro, synthesizes high-resolution depth maps with unparalleled sharpness and high-frequency details. The predictions are metric, with absolute scale, without relying on the availability of metadata such as camera intrinsics. And the model is fast, producing a 2.25-megapixel depth map in 0.3 seconds on a standard GPU. These characteristics are enabled by a number of technical contributions, including an efficient multi-scale vision transformer for dense prediction, a training protocol that combines real and synthetic datasets to achieve high metric accuracy alongside fine boundary tracing, dedicated evaluation metrics for boundary accuracy in estimated depth maps, and state-of-the-art focal length estimation from a single image. Extensive experiments analyze specific design choices and demonstrate that Depth Pro outperforms prior work along multiple dimensions. We release code and weights at https://github.com/apple/ml-depth-pro

Underwater stereo depth estimation provides accurate 3D geometry for robotics tasks such as navigation, inspection, and mapping, offering metric depth from low-cost passive cameras while avoiding the scale ambiguity of monocular methods. However, existing approaches face two critical challenges: (i) parameter-efficiently adapting large vision foundation encoders to the underwater domain without extensive labeled data, and (ii) tightly fusing globally coherent but scale-ambiguous monocular priors with locally metric yet photometrically fragile stereo correspondences. To address these challenges, we propose StereoAdapter, a parameter-efficient self-supervised framework that integrates a LoRA-adapted monocular foundation encoder with a recurrent stereo refinement module. We further introduce dynamic LoRA adaptation for efficient rank selection and pre-training on the synthetic UW-StereoDepth-40K dataset to enhance robustness under diverse underwater conditions. Comprehensive evaluations on both simulated and real-world benchmarks show improvements of 6.11% on TartanAir and 5.12% on SQUID compared to state-of-the-art methods, while real-world deployment with the BlueROV2 robot further demonstrates the consistent robustness of our approach. Code: https://github.com/AIGeeksGroup/StereoAdapter. Website: https://aigeeksgroup.github.io/StereoAdapter.

Geometry estimation from perspective images has greatly advanced, maturing to the point where off-the-shelf foundation models are able to reconstruct 3D scene structure not only from multi-view imagery, but even from a single view. A natural extension is 3D reconstruction from panoramas, with the exciting prospect of recovering a full 360-degree scene from a single panoramic image. In this work, we introduce PaGeR (Panoramic Geometry Reconstruction), a framework to lift powerful 3D foundation models designed for perspective imagery to the panorama domain. Our strategy is to start from a pre-trained transformer for 3D reconstruction and turn it into a unified high-performance model that predicts scale-invariant depth, metric depth, surface normals, and sky masks from both perspective and omnidirectional images, in a single forward pass. By keeping architectural changes to a minimum and mixing perspective and panoramic images during training, PaGeR retains the rich 3D prior of the underlying foundation model while learning to also estimate geometrically consistent 360-degree scenes from single panoramas. We extensively test our method in both indoor and outdoor environments and find that it delivers state-of-the-art performance and excellent zero-shot performance across a wide range of scenes.

Estimating accurate and temporally consistent 3D human geometry from videos is a challenging problem in computer vision. Existing methods, primarily optimized for single images, often suffer from temporal inconsistencies and fail to capture fine-grained dynamic details. To address these limitations, we present GeoMan, a novel architecture designed to produce accurate and temporally consistent depth and normal estimations from monocular human videos. GeoMan addresses two key challenges: the scarcity of high-quality 4D training data and the need for metric depth estimation to accurately model human size. To overcome the first challenge, GeoMan employs an image-based model to estimate depth and normals for the first frame of a video, which then conditions a video diffusion model, reframing video geometry estimation task as an image-to-video generation problem. This design offloads the heavy lifting of geometric estimation to the image model and simplifies the video model's role to focus on intricate details while using priors learned from large-scale video datasets. Consequently, GeoMan improves temporal consistency and generalizability while requiring minimal 4D training data. To address the challenge of accurate human size estimation, we introduce a root-relative depth representation that retains critical human-scale details and is easier to be estimated from monocular inputs, overcoming the limitations of traditional affine-invariant and metric depth representations. GeoMan achieves state-of-the-art performance in both qualitative and quantitative evaluations, demonstrating its effectiveness in overcoming longstanding challenges in 3D human geometry estimation from videos.

Camera-controlled video generation has achieved remarkable progress in recent years. However, existing video-to-video re-rendering methods primarily rely on Supervised Fine-Tuning using synthetic datasets. At present, there is an extreme scarcity of synchronized, multi-view real-world video data. Consequently, the prevailing paradigm often exhibits limited generalization when processing out-of-distribution real-world videos, with models struggling to accurately adhere to physical scales and camera trajectories. To bridge this gap, we propose Geo-Align, the first Reinforcement Learning framework specifically designed for camera-controlled video re-rendering. Built upon a pretrained model, we optimize the model through a scale-aware perceptual reward mechanism. Specifically, we introduce a metric 3D estimator to extract precise camera trajectories from generated videos, explicitly penalizing deviations in rotation and translation. Furthermore, we meticulously designed a data pipeline strategy based on real-world conditioning videos and target camera trajectories derived from synthetic data, eliminating the reliance on paired data. Extensive experiments demonstrate that Geo-Align consistently outperforms existing supervised learning baselines in both precise camera controllability and visual fidelity, indicating the effectiveness of our method.

The SCARED dataset is a widely used benchmark for endoscopic depth estimation, offering ground-truth 3D reconstructions captured with a structured light sensor. However, the depth maps for non-keyframe images rely on robot kinematics that introduce substantial pose errors, limiting the reliably labeled portion of the dataset to 35 keyframes. We present SCARED-C, a corrected version of the SCARED dataset that expands the number of reliable RGB-D pairs from 35 to 17,135. Our pipeline applies COLMAP, a Structure-from-Motion system, to re-estimate camera poses for all frames, followed by a scale recovery step that aligns the resulting reconstructions to metric space using the ground-truth keyframe depth maps. We validate the corrected poses through (1) stereo disparity evaluation and (2) monocular depth estimation experiments. The corrected dataset and code are publicly released to the community.

We introduce Princeton365, a large-scale diverse dataset of 365 videos with accurate camera pose. Our dataset bridges the gap between accuracy and data diversity in current SLAM benchmarks by introducing a novel ground truth collection framework that leverages calibration boards and a 360-camera. We collect indoor, outdoor, and object scanning videos with synchronized monocular and stereo RGB video outputs as well as IMU. We further propose a new scene scale-aware evaluation metric for SLAM based on the the optical flow induced by the camera pose estimation error. In contrast to the current metrics, our new metric allows for comparison between the performance of SLAM methods across scenes as opposed to existing metrics such as Average Trajectory Error (ATE), allowing researchers to analyze the failure modes of their methods. We also propose a challenging Novel View Synthesis benchmark that covers cases not covered by current NVS benchmarks, such as fully non-Lambertian scenes with 360-degree camera trajectories. Please visit https://princeton365.cs.princeton.edu for the dataset, code, videos, and submission.

While ubiquitous wearable sensors capture a wealth of behavioral and physiological information, effectively transforming these signals into personalized health insights is challenging. Specifically, converting low-level sensor data into representations capable of characterizing higher-level states is difficult due to high phenotypic diversity and variation in individual baseline health, physiology, and lifestyle factors. Moreover, collecting wearable data paired with health outcome annotations is laborious and expensive, and retrospective annotation remains practically unfeasible, contributing to a scarcity of data with high-quality labels. To overcome these limitations, we propose a foundation model for wearable health that is pretrained on more than one trillion minutes of unlabeled sensor signals drawn from a large cohort of five million participants. We demonstrate that the joint scaling of model capacity and pretraining data volume leads to systematic improvements in performance, as evaluated on a diverse set of 35 health prediction tasks, spanning cardiovascular, metabolic, sleep, and mental health, as well as lifestyle choices and demographic factors. We find that this population scale representation unlocks label-efficient few-shot learning and generative capabilities for robust daily metric estimation. To further leverage this learned representation, we deploy a classroom of LLM agents to autonomously search the space of downstream predictive heads built on the model embeddings, showing broad performance improvements that increase with LLM model capacity. Finally, we show how integrating these downstream predictors into a Personal Health Agent can support model responses that are more relevant, contextually aware, and safe, and we validate this via 1,860 ratings from a cohort of clinicians.

Monocular depth foundation models have demonstrated remarkable generalization capabilities across diverse environments. However, they continue to struggle with metric depth estimation in diverse environments. This limitation stems from the inherent scale ambiguity of single-view inference, leading to misaligned scale predictions even when the relative geometry is accurate. Conversely, recent multi-view foundation models leverage cross-view cues to learn robust scene-level geometry and consistent scale. Yet, these benefits typically vanish during single-image inference, as the absence of explicit geometric constraints causes performance to degrade. To bridge this gap, we propose a novel framework that transfers the scale-aware geometric priors of multi-view models into monocular depth foundation models. Specifically, we introduce an Epipolar Distillation (EpiDistill), an approach utilizing Rectified Stereo Tokens, which enables the single-view prediction model to retain epipolar attention patterns and maintain geometric consistency without requiring multi-view inputs at inference. Experimental results demonstrate that our method significantly improves zero-shot metric depth estimation, particularly on challenging datasets like ETH3D and DIODE where scale alignment is critical. Furthermore, our approach is model-agnostic, consistently boosting the performance of state-of-the-art ViT-based models, including UniDepthV2 and DepthPro.

Real-world applications like video gaming and virtual reality often demand the ability to model 3D scenes that users can explore along custom camera trajectories. While significant progress has been made in generating 3D objects from text or images, creating long-range, 3D-consistent, explorable 3D scenes remains a complex and challenging problem. In this work, we present Voyager, a novel video diffusion framework that generates world-consistent 3D point-cloud sequences from a single image with user-defined camera path. Unlike existing approaches, Voyager achieves end-to-end scene generation and reconstruction with inherent consistency across frames, eliminating the need for 3D reconstruction pipelines (e.g., structure-from-motion or multi-view stereo). Our method integrates three key components: 1) World-Consistent Video Diffusion: A unified architecture that jointly generates aligned RGB and depth video sequences, conditioned on existing world observation to ensure global coherence 2) Long-Range World Exploration: An efficient world cache with point culling and an auto-regressive inference with smooth video sampling for iterative scene extension with context-aware consistency, and 3) Scalable Data Engine: A video reconstruction pipeline that automates camera pose estimation and metric depth prediction for arbitrary videos, enabling large-scale, diverse training data curation without manual 3D annotations. Collectively, these designs result in a clear improvement over existing methods in visual quality and geometric accuracy, with versatile applications.

We present ORB-SLAM2 a complete SLAM system for monocular, stereo and RGB-D cameras, including map reuse, loop closing and relocalization capabilities. The system works in real-time on standard CPUs in a wide variety of environments from small hand-held indoors sequences, to drones flying in industrial environments and cars driving around a city. Our back-end based on bundle adjustment with monocular and stereo observations allows for accurate trajectory estimation with metric scale. Our system includes a lightweight localization mode that leverages visual odometry tracks for unmapped regions and matches to map points that allow for zero-drift localization. The evaluation on 29 popular public sequences shows that our method achieves state-of-the-art accuracy, being in most cases the most accurate SLAM solution. We publish the source code, not only for the benefit of the SLAM community, but with the aim of being an out-of-the-box SLAM solution for researchers in other fields.

Multimodal Large Language Models (MLLMs) excel at 2D semantic understanding but lack intrinsic 3D awareness, resulting in representations that fail to maintain geometric and spatial consistency across video frames. Given the scarcity of large-scale 3D data, we present GeoVR, a novel framework that learns geometric representations using purely 2D video sequences. This approach effectively restructures the semantic latent space within MLLMs to unlock spatial intelligence. Rather than employing superficial feature mixing, GeoVR reshapes the internal representations of the MLLM by distilling geometry knowledge from pre-trained 3D foundation models. This is accomplished through a multi-objective learning strategy driven by four complementary geometric targets: (1) estimating inter-frame camera poses to embed varying viewpoint dynamics, (2) regressing dense depth maps to anchor physical distances, (3) predicting a metric scale factor for real-world calibration, and (4) distilling multi-scale 3D features to align the intermediate feature space. Guided by these explicit physical and geometric constraints, the model's internal representations naturally develop strong 3D awareness. Extensive experiments on spatial reasoning benchmarks demonstrate that GeoVR achieves state-of-the-art performance, establishing a new paradigm for endowing foundation models with spatial intelligence.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Many advanced Large Language Model (LLM) applications require long-context processing, but the self-attention module becomes a bottleneck during the prefilling stage of inference due to its quadratic time complexity with respect to sequence length. Existing sparse attention methods accelerate attention computation by skipping less significant regions of the attention map. However, these approaches typically perform coarse-grained inspection of the attention map, rendering considerable loss in model accuracy. In this paper, we propose SALE, a fine-grained sparse attention method that accelerates the long-context prefilling stage of LLM with negligible loss in model accuracy. SALE achieves fast and accurate fine-grained attention weight estimation through 4-bit quantized query-key products, followed by block-sparse attention to accelerate prefilling computations. For importance evaluation for query-key pairs, we adopt our Relative Attention Score metric, which offers significantly higher efficiency within our framework. We implement a custom CUDA kernel optimized for our approach for hardware efficiency, reducing the additional overhead to approximately 11% of the full attention latency. Notably, SALE requires no parameter training and can be seamlessly integrated into existing systems with trivial code modifications. Experiments on long-context benchmarks demonstrate that our method outperforms existing approaches in accuracy-efficiency trade-offs, achieving at least 3.36x speedups on Llama-3.1-8B for sequences longer than 64K while maintaining model quality.

Scaling has powered recent advances in vision foundation models, yet extending this paradigm to metric depth estimation remains challenging due to heterogeneous sensor noise, camera-dependent biases, and metric ambiguity in noisy cross-source 3D data. We introduce Metric Anything, a simple and scalable pretraining framework that learns metric depth from noisy, diverse 3D sources without manually engineered prompts, camera-specific modeling, or task-specific architectures. Central to our approach is the Sparse Metric Prompt, created by randomly masking depth maps, which serves as a universal interface that decouples spatial reasoning from sensor and camera biases. Using about 20M image-depth pairs spanning reconstructed, captured, and rendered 3D data across 10000 camera models, we demonstrate-for the first time-a clear scaling trend in the metric depth track. The pretrained model excels at prompt-driven tasks such as depth completion, super-resolution and Radar-camera fusion, while its distilled prompt-free student achieves state-of-the-art results on monocular depth estimation, camera intrinsics recovery, single/multi-view metric 3D reconstruction, and VLA planning. We also show that using pretrained ViT of Metric Anything as a visual encoder significantly boosts Multimodal Large Language Model capabilities in spatial intelligence. These results show that metric depth estimation can benefit from the same scaling laws that drive modern foundation models, establishing a new path toward scalable and efficient real-world metric perception. We open-source MetricAnything at http://metric-anything.github.io/metric-anything-io/ to support community research.

Counterfactual analysis is widely used to study evidence use in vision-language models, but its diagnostic value is limited on well-posed tasks: when several cues independently support the same answer, removing one may not change the prediction. We propose monocular metric object-size estimation as an ill-posed diagnostic setting for evidence selection: because physical size cannot be determined from a single uncalibrated image, models must rely on imperfect cues category priors, target appearance, local context, apparent image size, and scene geometry. We assemble Metric VQA (10{,}813 dimension queries from Objectron and 331 tape-measured in-the-wild scenes) and evaluate 12 open-weight VLMs (3--397\,B parameters) with counterfactual analysis decomposing six visual and language evidence channels. Even the largest VLMs tested (Qwen3-VL-235B, Qwen3.5-397B, InternVL3.5-241B) trail a text-only frontier LLM on the in-the-wild split. The diagnostic analysis shows: target identity is the most load-bearing cue, target pixels and local context help only some models, apparent size shifts predictions without a directional readout, and global scene geometry is largely unused. We analyze LoRA fine-tuning as an actionable intervention specific to metric estimation: while the task is learnable, the models do not learn to leverage scene geometry.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Evaluating the quality of search, ranking and RAG systems traditionally requires a significant number of human relevance annotations. In recent times, several deployed systems have explored the usage of Large Language Models (LLMs) as automated judges for this task while their inherent biases prevent direct use for metric estimation. We present a statistical framework extending Prediction-Powered Inference (PPI) that combines minimal human annotations with LLM judgments to produce reliable estimates of metrics which require sub-instance annotations. Our method requires as few as 100 human-annotated queries and 10,000 unlabeled examples, reducing annotation requirements significantly compared to traditional approaches. We formulate our proposed framework (PRECISE) for inference of relevance uplift for an LLM-based query reformulation application, extending PPI to sub-instance annotations at the query-document level. By reformulating the metric-integration space, we reduced the computational complexity from O(2^|C|) to O(2^K), where |C| represents corpus size (in order of millions). Detailed experiments across prominent retrieval datasets demonstrate that our method reduces the variance of estimates for the business-critical Precision@K metric, while effectively correcting for LLM bias in low-resource settings.

Recent advances in multimodal foundation models, exemplified by GPT-6 Astra, raise the prospect of general-purpose embodied reasoning and planning. Using Internet videos for embodied pretraining calls for reliable physical-scale annotations. Yet visual geometry foundation models often recover scene structure and camera motion without reliable metric scale. We show that uncertain size priors of familiar objects can jointly constrain a reconstruction's shared scale. Building on this insight, we present UniMetric, a universal and training-free metric scale recovery framework for geometry foundation models, without additional sensors or task-specific metric supervision. Specifically, Metric Prior Acquisition elicits object height intervals from a vision-language model. Semantic-Geometric Alignment measures reconstructed object heights along the estimated support-surface normal in each frame and converts the priors into scale intervals. Global Scale Recovery reconciles these intervals through a convex objective, yielding a jointly feasible scale when they overlap and a unique compromise otherwise. The estimated sequence-level scale is applied uniformly to reconstructed points and camera translations. Controlled experiments with real VLM priors show that combining observations improves scale accuracy with exact relative object heights. To evaluate metric accuracy on GFM reconstructions without ground-truth scale alignment, we introduce MetricBench, covering twelve embodied, driving, and roadside subsets with sensor-derived ground truth. Across nine geometry foundation models, UniMetric reduces mean depth Abs Rel, reconstruction Chamfer distance, and trajectory error by 54.2%, 83.8%, and 65.6%, respectively, improving every model on all three tasks at the suite level. We release the UniMetric code and MetricBench data.

Prompts play a critical role in unleashing the power of language and vision foundation models for specific tasks. For the first time, we introduce prompting into depth foundation models, creating a new paradigm for metric depth estimation termed Prompt Depth Anything. Specifically, we use a low-cost LiDAR as the prompt to guide the Depth Anything model for accurate metric depth output, achieving up to 4K resolution. Our approach centers on a concise prompt fusion design that integrates the LiDAR at multiple scales within the depth decoder. To address training challenges posed by limited datasets containing both LiDAR depth and precise GT depth, we propose a scalable data pipeline that includes synthetic data LiDAR simulation and real data pseudo GT depth generation. Our approach sets new state-of-the-arts on the ARKitScenes and ScanNet++ datasets and benefits downstream applications, including 3D reconstruction and generalized robotic grasping.

Based on the Manhattan World assumption, most existing indoor layout estimation schemes focus on recovering layouts from vertically compressed 1D sequences. However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability. To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. To compensate for the potential errors in pre-segmentation, we further leverage triple attention to reconstruct the disentangled sequences for better performance. Experiments on four popular benchmarks demonstrate our superiority over existing SoTA solutions, especially on the 3DIoU metric. The code is available at https://github.com/zhijieshen-bjtu/DOPNet.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

Accurately predicting watch time is crucial for optimizing recommendations and user experience in short video platforms. However, existing methods that estimate a single average watch time often fail to capture the inherent uncertainty in user engagement patterns. In this paper, we propose Conditional Quantile Estimation (CQE) to model the entire conditional distribution of watch time. Using quantile regression, CQE characterizes the complex watch-time distribution for each user-video pair, providing a flexible and comprehensive approach to understanding user behavior. We further design multiple strategies to combine the quantile estimates, adapting to different recommendation scenarios and user preferences. Extensive offline experiments and online A/B tests demonstrate the superiority of CQE in watch-time prediction and user engagement modeling. Specifically, deploying CQE online on a large-scale platform with hundreds of millions of daily active users has led to substantial gains in key evaluation metrics, including active days, engagement time, and video views. These results highlight the practical impact of our proposed approach in enhancing the user experience and overall performance of the short video recommendation system. The code will be released https://github.com/justopit/CQE.

We survey the large language model (LLM) serving area to understand the intricate dynamics between cost-efficiency and accuracy, which is magnified by the growing need for longer contextual understanding when deploying models at a massive scale. Our findings reveal that works in this space optimize along three distinct but conflicting goals: improving serving context length (C), improving serving accuracy (A), and improving serving performance (P). Drawing inspiration from the CAP theorem in databases, we propose a CAP principle for LLM serving, which suggests that any optimization can improve at most two of these three goals simultaneously. Our survey categorizes existing works within this framework. We find the definition and continuity of user-perceived measurement metrics are crucial in determining whether a goal has been met, akin to prior CAP databases in the wild. We recognize the CAP principle for LLM serving as a guiding principle, rather than a formal theorem, to inform designers of the inherent and dynamic trade-offs in serving models. As serving accuracy and performance have been extensively studied, this survey focuses on works that extend serving context length and address the resulting challenges.

Obtaining large pre-trained models that can be fine-tuned to new tasks with limited annotated samples has remained an open challenge for medical imaging data. While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images. To bridge this gap, we introduce LVM-Med, the first family of deep networks trained on large-scale medical datasets. We have collected approximately 1.3 million medical images from 55 publicly available datasets, covering a large number of organs and modalities such as CT, MRI, X-ray, and Ultrasound. We benchmark several state-of-the-art self-supervised algorithms on this dataset and propose a novel self-supervised contrastive learning algorithm using a graph-matching formulation. The proposed approach makes three contributions: (i) it integrates prior pair-wise image similarity metrics based on local and global information; (ii) it captures the structural constraints of feature embeddings through a loss function constructed via a combinatorial graph-matching objective; and (iii) it can be trained efficiently end-to-end using modern gradient-estimation techniques for black-box solvers. We thoroughly evaluate the proposed LVM-Med on 15 downstream medical tasks ranging from segmentation and classification to object detection, and both for the in and out-of-distribution settings. LVM-Med empirically outperforms a number of state-of-the-art supervised, self-supervised, and foundation models. For challenging tasks such as Brain Tumor Classification or Diabetic Retinopathy Grading, LVM-Med improves previous vision-language models trained on 1 billion masks by 6-7% while using only a ResNet-50.

Super-resolution (SR) techniques have made major advances in reconstructing high-resolution images from low-resolution inputs. The increased resolution provides visual enhancement and utility for monitoring tasks. In particular, SR has been increasingly developed for satellite-based Earth observation, with applications in urban planning, agriculture, ecology, and disaster response. However, existing SR studies and benchmarks typically use fidelity metrics such as PSNR or SSIM, whereas the true utility of super-resolved images lies in supporting downstream tasks such as land cover classification, biomass estimation, and change detection. To bridge this gap, we introduce GeoSR-Bench, a downstream task-integrated SR benchmark dataset to evaluate SR models beyond fidelity metrics. GeoSR-Bench comprises spatially co-located, temporally aligned, and quality-controlled image pairs from about 36,000 locations across diverse land covers, spanning resolutions from 500m to 0.6m. To the best of our knowledge, GeoSR-Bench is the first SR benchmark that directly connects improved image resolution from SR models with downstream Earth monitoring tasks, including land cover segmentation, infrastructure mapping, and biophysical variable estimation. Using GeoSR-Bench, we benchmark GAN, transformer, neural operator, and diffusion-based SR models on perceptual quality and downstream task performance. We conduct experiments with 270 settings, covering 2 cross-platform SR tasks, 9 SR models, 3 downstream task models, and 5 downstream tasks for each SR task. The results show that improvements in traditional SR metrics often do not correlate with gains in task performance, and the correlations can be negative, indicating that these metrics provide limited guidance for selecting superior models for downstream tasks. This reveals the need to integrate downstream tasks into SR model development and evaluation.

Machine vision systems (MVS) are intrinsically vulnerable to performance degradation under adverse visual conditions. To address this, we propose a machine-centric image quality assessment (MIQA) framework that quantifies the impact of image degradations on MVS performance. We establish an MIQA paradigm encompassing the end-to-end assessment workflow. To support this, we construct a machine-centric image quality database (MIQD-2.5M), comprising 2.5 million samples that capture distinctive degradation responses in both consistency and accuracy metrics, spanning 75 vision models, 250 degradation types, and three representative vision tasks. We further propose a region-aware MIQA (RA-MIQA) model to evaluate MVS visual quality through fine-grained spatial degradation analysis. Extensive experiments benchmark the proposed RA-MIQA against seven human visual system (HVS)-based IQA metrics and five retrained classical backbones. Results demonstrate RA-MIQA's superior performance in multiple dimensions, e.g., achieving SRCC gains of 13.56% on consistency and 13.37% on accuracy for image classification, while also revealing task-specific degradation sensitivities. Critically, HVS-based metrics prove inadequate for MVS quality prediction, while even specialized MIQA models struggle with background degradations, accuracy-oriented estimation, and subtle distortions. This study can advance MVS reliability and establish foundations for machine-centric image processing and optimization. The model and code are available at: https://github.com/XiaoqiWang/MIQA.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach accurately predicts the loss of a model of size N trained with D tokens and a specific domain weight vector h. We validate the universality of these scaling laws by demonstrating their predictive power in three distinct and large-scale settings: large language model (LLM), native multimodal model (NMM), and large vision models (LVM) pretraining. We further show that these scaling laws can extrapolate to new data mixtures and across scales: their parameters can be accurately estimated using a few small-scale training runs, and used to estimate the performance at larger scales and unseen domain weights. The scaling laws allow to derive the optimal domain weights for any target domain under a given training budget (N,D), providing a principled alternative to costly trial-and-error methods.

Face reconstruction and tracking is a building block of numerous applications in AR/VR, human-machine interaction, as well as medical applications. Most of these applications rely on a metrically correct prediction of the shape, especially, when the reconstructed subject is put into a metrical context (i.e., when there is a reference object of known size). A metrical reconstruction is also needed for any application that measures distances and dimensions of the subject (e.g., to virtually fit a glasses frame). State-of-the-art methods for face reconstruction from a single image are trained on large 2D image datasets in a self-supervised fashion. However, due to the nature of a perspective projection they are not able to reconstruct the actual face dimensions, and even predicting the average human face outperforms some of these methods in a metrical sense. To learn the actual shape of a face, we argue for a supervised training scheme. Since there exists no large-scale 3D dataset for this task, we annotated and unified small- and medium-scale databases. The resulting unified dataset is still a medium-scale dataset with more than 2k identities and training purely on it would lead to overfitting. To this end, we take advantage of a face recognition network pretrained on a large-scale 2D image dataset, which provides distinct features for different faces and is robust to expression, illumination, and camera changes. Using these features, we train our face shape estimator in a supervised fashion, inheriting the robustness and generalization of the face recognition network. Our method, which we call MICA (MetrIC fAce), outperforms the state-of-the-art reconstruction methods by a large margin, both on current non-metric benchmarks as well as on our metric benchmarks (15% and 24% lower average error on NoW, respectively).

Evaluation metrics are central to binary target segmentation because they determine how progress is measured, compared, and interpreted. In this paper, target denotes the task-defined positive region to be segmented rather than a generic foreground object. It may be salient, camouflaged, transparent, glass-like, mirror-like, shadow-like, lesion-like, or defined by other application-specific semantics. We treat existing metrics as compositions of modular design choices rather than isolated formulas. The proposed framework decomposes each metric into five stages covering prediction representation, target extraction, target matching, score computation, and metric reporting. We use this framework to analyze representative metrics and show how newer metrics address specific limits in earlier protocols. The stage choices keep each metric's assumptions visible. We then discuss the design space opened by the framework and its implications for task-aware evaluation protocols. Reference code is available at https://github.com/lartpang/PySODMetrics.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

There is extensive interest in metric learning methods for image retrieval. Many metric learning loss functions focus on learning a correct ranking of training samples, but strongly overfit semantically inconsistent labels and require a large amount of data. To address these shortcomings, we propose a new metric learning method, called contextual loss, which optimizes contextual similarity in addition to cosine similarity. Our contextual loss implicitly enforces semantic consistency among neighbors while converging to the correct ranking. We empirically show that the proposed loss is more robust to label noise, and is less prone to overfitting even when a large portion of train data is withheld. Extensive experiments demonstrate that our method achieves a new state-of-the-art across four image retrieval benchmarks and multiple different evaluation settings. Code is available at: https://github.com/Chris210634/metric-learning-using-contextual-similarity

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship -- an anchor point x is similar to a set of positive points Y, and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15% points, while converging three times as fast as other triplet-based losses.

"What cannot be measured cannot be improved" while likely never uttered by Lord Kelvin, summarizes effectively the driving force behind this work. This paper presents a detailed discussion of automated metrics for evaluating structured 3D reconstructions. Pitfalls of each metric are discussed, and an analysis through the lens of expert 3D modelers' preferences is presented. A set of systematic "unit tests" are proposed to empirically verify desirable properties, and context aware recommendations regarding which metric to use depending on application are provided. Finally, a learned metric distilled from human expert judgments is proposed and analyzed. The source code is available at https://github.com/s23dr/wireframe-metrics-iccv2025

A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis and on geometric regularity such as intrinsic dimension, curvature, and reach. Progress requires insight into data-manifold geometry and suitable benchmarks, yet existing options are polarized: analytic manifolds with known geometry but limited applicability, or real-world datasets where geometry is only coarsely estimable. We introduce a benchmarking framework for studying data geometry. We repurpose and extend dSprites and COIL-20 with additional transformation dimensions and dense, axis-aligned sampling, and pair them with finite-difference estimators that recover curvature, reach, and volume at near-ground-truth accuracy in a regime where general-purpose estimators are unreliable or difficult to deploy. The framework is intended as a controlled testbed, useful as a calibration environment for geometric estimators and a sandbox for probing theoretical assumptions. To illustrate its use, we present two application studies, namely assessing the scaling behavior of the bounds of Genovese et al. and Fefferman et al., and tracking the layer-wise geometry of a β-VAE, highlighting the behavior of current bounds and the value of controlled benchmarks for guiding and validating future theory. A reference implementation is available at https://github.com/koulakis/manifold-microscope.

Geolocating images of a ground-level scene entails estimating the location on Earth where the picture was taken, in absence of GPS or other location metadata. Typically, methods are evaluated by measuring the Great Circle Distance (GCD) between a predicted location and ground truth. However, this measurement is limited because it only evaluates a single point, not estimates of regions or score heatmaps. This is especially important in applications to rural, wilderness and under-sampled areas, where finding the exact location may not be possible, and when used in aggregate systems that progressively narrow down locations. In this paper, we introduce a novel metric, Recall vs Area (RvA), which measures the accuracy of estimated distributions of locations. RvA treats image geolocation results similarly to document retrieval, measuring recall as a function of area: For a ranked list of (possibly non-contiguous) predicted regions, we measure the accumulated area required for the region to contain the ground truth coordinate. This produces a curve similar to a precision-recall curve, where "precision" is replaced by square kilometers area, allowing evaluation of performance for different downstream search area budgets. Following directly from this view of the problem, we then examine a simple ensembling approach to global-scale image geolocation, which incorporates information from multiple sources to help address domain shift, and can readily incorporate multiple models, attribute predictors, and data sources. We study its effectiveness by combining the geolocation models GeoEstimation and the current SOTA GeoCLIP, with attribute predictors based on ORNL LandScan and ESA-CCI Land Cover. We find significant improvements in image geolocation for areas that are under-represented in the training set, particularly non-urban areas, on both Im2GPS3k and Street View images.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

Scene graph generation has emerged as a prominent research field in computer vision, witnessing significant advancements in the recent years. However, despite these strides, precise and thorough definitions for the metrics used to evaluate scene graph generation models are lacking. In this paper, we address this gap in the literature by providing a review and precise definition of commonly used metrics in scene graph generation. Our comprehensive examination clarifies the underlying principles of these metrics and can serve as a reference or introduction to scene graph metrics. Furthermore, to facilitate the usage of these metrics, we introduce a standalone Python package called SGBench that efficiently implements all defined metrics, ensuring their accessibility to the research community. Additionally, we present a scene graph benchmarking web service, that enables researchers to compare scene graph generation methods and increase visibility of new methods in a central place. All of our code can be found at https://lorjul.github.io/sgbench/.

Large Language Models (LLMs) obey consistent scaling laws -- empirical power-law fits that predict how loss decreases with compute, data, and parameters. While predictive, these laws are descriptive rather than prescriptive: they characterize typical training, not optimal training. Surprisingly few works have successfully challenged the data-efficiency bounds implied by these laws -- which is our primary focus. To that end, we introduce the Geodesic Hypothesis, positing that token sequences trace geodesics on a smooth semantic manifold and are therefore locally linear. Building on this principle, we propose a novel Semantic Tube Prediction (STP) task, a JEPA-style regularizer that confines hidden-state trajectories to a tubular neighborhood of the geodesic. STP generalizes JEPA to language without requiring explicit multi-view augmentations. We show this constraint improves signal-to-noise ratio, and consequently preserves diversity by preventing trajectory collisions during inference. Empirically, STP allows LLMs to match baseline accuracy with 16times less training data on the NL-RX-SYNTH dataset, directly violating the data term of Chinchilla-style scaling laws and demonstrating that principled geometric priors can surpass brute-force scaling. Code is available at https://github.com/galilai-group/llm-jepa#stp.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

In many industries, predicting metric outcomes of large systems is a fundamental problem, driven largely by traditional tabular regression. However, such methods struggle on complex systems data in the wild such as configuration files or system logs, where feature engineering is often infeasible. We propose text-to-text regression as a general, scalable alternative. For predicting resource efficiency on Borg, Google's massive compute cluster scheduling system, a 60M parameter encoder-decoder, trained from random initialization, achieves up to a near perfect 0.99 (0.9 average) rank correlation across the entire fleet, and 100x lower MSE than tabular approaches. The model also easily adapts to new tasks in only 500 few-shot examples and captures the densities of complex outcome distributions. Ablation studies highlight the importance of using encoders, increasing sequence length, and the model's inherent uncertainty quantification. These findings pave the way for universal simulators of real-world outcomes.

Because large language models are expensive to pretrain on different datasets, using smaller-scale experiments to decide on data is crucial for reducing costs. Which benchmarks and methods of making decisions from observed performance at small scale most accurately predict the datasets that yield the best large models? To empower open exploration of this question, we release models, data, and evaluations in DataDecide -- the most extensive open suite of models over differences in data and scale. We conduct controlled pretraining experiments across 25 corpora with differing sources, deduplication, and filtering up to 100B tokens, model sizes up to 1B parameters, and 3 random seeds. We find that the ranking of models at a single, small size (e.g., 150M parameters) is a strong baseline for predicting best models at our larger target scale (1B) (~80% of com parisons correct). No scaling law methods among 8 baselines exceed the compute-decision frontier of single-scale predictions, but DataDecide can measure improvement in future scaling laws. We also identify that using continuous likelihood metrics as proxies in small experiments makes benchmarks including MMLU, ARC, HellaSwag, MBPP, and HumanEval >80% predictable at the target 1B scale with just 0.01% of the compute.

Accurately converting pixel measurements into absolute real-world dimensions remains a fundamental challenge in computer vision, limiting progress in applications such as biomedicine, forensics, nutritional analysis, and e-commerce. We introduce RulerNet, a deep learning framework that robustly infers scale in the wild by reformulating ruler reading as a unified keypoint detection problem and representing rulers with geometric progression parameters that compactly approximate the non-uniform spacing induced by perspective transformations. Unlike traditional methods that rely on handcrafted thresholds or rigid, ruler-specific pipelines, RulerNet directly localizes centimeter markings using a mark-visibility-based annotation and training strategy that remains valid under mark-preserving transformations, enabling strong generalization across diverse ruler types and imaging conditions while mitigating data scarcity. Additionally, we introduce a scalable synthetic data generation pipeline that combines graphics-based ruler creation with ControlNet-enhanced realism, significantly expanding training diversity and improving model performance. Extensive experiments on both our datasets and public benchmarks demonstrate that RulerNet achieves accurate, consistent, and efficient scale estimation under challenging real-world conditions. Integration into a medical analysis pipeline further demonstrates its practical utility for scale-aware measurement. These results suggest that RulerNet can serve as a generalizable measurement component and be readily integrated with other vision modules, such as segmentation, monocular depth estimation, and diagnostic workflows, for automated analysis in medical and other domains. An online demo is provided. The project page is at https://github.com/ymp5078/RulerNet.

We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

With PRECISE, we extended Prediction-Powered Inference to produce bias-corrected estimates of ranking evaluation metrics by combining a small human-labeled set with a large LLM-judged set. PPI is provably unbiased regardless of the LLM judge's error profile. We make it applicable to hierarchical metrics like Precision@K, where annotations are per-document but the metric is per-query, by reducing the output-space computation from O(2^|C|) to O(2^K). On the ESCI benchmark, augmenting 30 human annotations with Claude 3 Sonnet judgments reduces the standard error of Precision@4 estimates from 4.45 to 3.50 (a 21% relative reduction). In a production system, our framework correctly identified the best of three system variants from 100 human labels and 2 hours of domain-expert annotation; A/B testing confirmed this ranking with +407 bps in daily sales.

We present UniScale, a unified, scale-aware multi-view 3D reconstruction framework for robotic applications that flexibly integrates geometric priors through a modular, semantically informed design. In vision-based robotic navigation, the accurate extraction of environmental structure from raw image sequences is critical for downstream tasks. UniScale addresses this challenge with a single feed-forward network that jointly estimates camera intrinsics and extrinsics, scale-invariant depth and point maps, and the metric scale of a scene from multi-view images, while optionally incorporating auxiliary geometric priors when available. By combining global contextual reasoning with camera-aware feature representations, UniScale is able to recover the metric-scale of the scene. In robotic settings where camera intrinsics are known, they can be easily incorporated to improve performance, with additional gains obtained when camera poses are also available. This co-design enables robust, metric-aware 3D reconstruction within a single unified model. Importantly, UniScale does not require training from scratch, and leverages world priors exhibited in pre-existing models without geometric encoding strategies, making it particularly suitable for resource-constrained robotic teams. We evaluate UniScale on multiple benchmarks, demonstrating strong generalization and consistent performance across diverse environments. We will release our implementation upon acceptance.

This work explores the visual explanation for deep metric learning and its applications. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not as well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decomposing the final activation. Instead of only providing the overall activation map of each image, we propose to generate point-to-point activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed to a large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval. The source code is available at https://github.com/Jeff-Zilence/Explain_Metric_Learning.

Evaluating an AI system requires disaggregated assessment, as performance varies across domains such as benchmark task types or conversation types in deployed agents. Exhaustive testing is expensive, so evaluation rests on a sample of labeled units. We treat the evaluation set as a finite population and seek accurate point and interval estimates of each domain mean. Direct estimators, including prediction-powered inference (PPI), use only a domain's own labels and are imprecise where labels are few. Small area estimation addresses this problem, and we build on it to develop an integrated workflow for estimation and validation. For estimation, we propose prediction-powered smoothing (PP-S), a Bayesian model fit to each domain's prediction-powered estimate, with an extension that borrows strength across a reporting taxonomy (PP-TS). For validation, we derive a new, approximately unbiased design-based cross-validation score for choosing among direct and smoothed estimators. We study a curated benchmark with verifiable grading and deployed agent traffic graded by humans, each with every outcome observed. In both, the proposed estimators improve on the direct estimators in point and interval estimation, with near-nominal coverage. At the same sampling budget, our score selects as well as an independent validation sample does and estimates the selected estimator's error far more accurately.

Recent work reported that simple Bayesian optimization (BO) methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates why. We identify underlying challenges that arise in high-dimensional BO and explain why recent methods succeed. Our empirical analysis shows that vanishing gradients caused by Gaussian process (GP) initialization schemes play a major role in the failures of high-dimensional Bayesian optimization (HDBO) and that methods that promote local search behaviors are better suited for the task. We find that maximum likelihood estimation (MLE) of GP length scales suffices for state-of-the-art performance. Based on this, we propose a simple variant of MLE called MSR that leverages these findings to achieve state-of-the-art performance on a comprehensive set of real-world applications. We present targeted experiments to illustrate and confirm our findings.

Deep Metric Learning (DML) methods aim at learning an embedding space in which distances are closely related to the inherent semantic similarity of the inputs. Previous studies have shown that popular benchmark datasets often contain numerous wrong labels, and DML methods are susceptible to them. Intending to study the effect of realistic noise, we create an ontology of the classes in a dataset and use it to simulate semantically coherent labeling mistakes. To train robust DML models, we propose ProcSim, a simple framework that assigns a confidence score to each sample using the normalized distance to its class representative. The experimental results show that the proposed method achieves state-of-the-art performance on the DML benchmark datasets injected with uniform and the proposed semantically coherent noise.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

In studies of transferable learning, scaling laws are obtained for various important foundation models to predict their properties and performance at larger scales. We show here how scaling law derivation can also be used for model and dataset comparison, allowing to decide which procedure is to be preferred for pre-training. For the first time, full scaling laws based on dense measurements across a wide span of model and samples seen scales are derived for two important language-vision learning procedures, CLIP and MaMMUT, that use either contrastive only or contrastive and captioning text generative loss. Ensuring sufficient prediction accuracy for held out points, we use derived scaling laws to compare both models, obtaining evidence for MaMMUT's stronger improvement with scale and better sample efficiency than standard CLIP. To strengthen validity of the comparison, we show scaling laws for various downstream tasks, classification, retrieval, and segmentation, and for different open datasets, DataComp, DFN and Re-LAION, observing consistently the same trends. We show that comparison can also be performed when deriving scaling laws with a constant learning rate schedule, reducing compute cost. Accurate derivation of scaling laws provides thus means to perform model and dataset comparison across scale spans, avoiding misleading conclusions based on measurements from single reference scales only, paving the road for systematic comparison and improvement of open foundation models and datasets for their creation. We release all the pre-trained models with their intermediate checkpoints, including openMaMMUT-L/14, which achieves 80.3% zero-shot ImageNet-1k accuracy, trained on 12.8B samples from DataComp-1.4B. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/scaling-laws-for-comparison.

Deep Metric Learning (DML) has long attracted the attention of the machine learning community as a key objective. Existing solutions concentrate on fine-tuning the pre-trained models on conventional image datasets. As a result of the success of recent pre-trained models trained from larger-scale datasets, it is challenging to adapt the model to the DML tasks in the local data domain while retaining the previously gained knowledge. In this paper, we investigate parameter-efficient methods for fine-tuning the pre-trained model for DML tasks. In particular, we propose a novel and effective framework based on learning Visual Prompts (VPT) in the pre-trained Vision Transformers (ViT). Based on the conventional proxy-based DML paradigm, we augment the proxy by incorporating the semantic information from the input image and the ViT, in which we optimize the visual prompts for each class. We demonstrate that our new approximations with semantic information are superior to representative capabilities, thereby improving metric learning performance. We conduct extensive experiments to demonstrate that our proposed framework is effective and efficient by evaluating popular DML benchmarks. In particular, we demonstrate that our fine-tuning method achieves comparable or even better performance than recent state-of-the-art full fine-tuning works of DML while tuning only a small percentage of total parameters.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the perceptual scale of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured perceptual scale corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the perceptual scale is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of perceptual scale is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

Deep metric learning objectives (e.g., triplet loss) require storing and comparing high-dimensional embeddings, making the per-batch loss buffer scale as O(Scdot D), where S is the number of samples in a batch and D is the feature dimension, thus limiting training on memory-constrained hardware. We propose Shadow Loss, a proxy-free, parameter-free objective that measures similarity via scalar projections onto the anchor direction, reducing the loss-specific buffer from O(Scdot D) to O(S) while preserving the triplet structure. We analyze gradients, provide a Lipschitz continuity bound, and show that Shadow Loss penalizes trivial collapse for stable optimization. Across fine-grained retrieval (CUB-200, CARS196), large-scale product retrieval (Stanford Online Products, In-Shop Clothes), and standard/medical benchmarks (CIFAR-10/100, Tiny-ImageNet, HAM-10K, ODIR-5K), Shadow Loss consistently outperforms recent objectives (Triplet, Soft-Margin Triplet, Angular Triplet, SoftTriple, Multi-Similarity). It also converges in approx 1.5-2times fewer epochs under identical backbones and mining. Furthermore, it improves representation separability as measured by higher silhouette scores. The design is architecture-agnostic and vectorized for efficient implementation. By decoupling discriminative power from embedding dimensionality and reusing batch dot-products, Shadow Loss enables memory-linear training and faster convergence, making deep metric learning practical on both edge and large-scale systems.

Evaluating large language models at scale remains a practical bottleneck for many organizations. While existing evaluation frameworks work well for thousands of examples, they struggle when datasets grow to hundreds of thousands or millions of samples. This scale is common when assessing model behavior across diverse domains or conducting comprehensive regression testing. We present Spark-LLM-Eval, a distributed evaluation framework built natively on Apache Spark. The system treats evaluation as a data-parallel problem, partitioningexamplesacrossexecutorsandaggregatingresultswithproperstatistical accounting. Beyond raw throughput, we emphasize statistical rigor: every reported metric includes bootstrap confidence intervals, and model comparisons come with appropriate significance tests (paired t-tests, McNemar's test, or Wilcoxon signed-rank, depending on the metric type). The framework also addresses the cost problem inherent in LLM evaluation through content-addressable response caching backed by Delta Lake, which allows iterating on metric definitions without re-running inference. We describe the system architecture, the statistical methodology, and report benchmark results showing linear scaling with cluster size. The framework and all evaluation code are available as open source.

Modern image generation and editing systems can produce photorealistic, prompt-aligned images, but still often render familiar objects at implausible relative sizes. To measure this failure mode, we introduce GenScale, a benchmark and evaluation protocol for real-world relative object scale in image generation and editing. GenScale contains 900 image-level entries and 1,643 pairwise anchor-target scale relations across common-object generation, human-product generation with metric dimensions, and scale correction from failed generations. We further design a human-calibrated ordinal judge for scalable pairwise scale evaluation. Last but not the least, we introduce Rescale, a model-agnostic post-processing agent for localized scale correction without modifying the source generator. Experiments reveal that state-of-the-art image generators and editors cannot reliably observe relative scale yet, while Rescale consistently improves scale plausibility across generated and edited images. Together, GenScale establishes relative object scale as a distinct, measurable, and actionable capability for image generation systems.

Vision-language models (VLMs) are trained for thousands of GPU hours on carefully curated web datasets. In recent times, data curation has gained prominence with several works developing strategies to retain 'high-quality' subsets of 'raw' scraped data. For instance, the LAION public dataset retained only 10% of the total crawled data. However, these strategies are typically developed agnostic of the available compute for training. In this paper, we first demonstrate that making filtering decisions independent of training compute is often suboptimal: the limited high-quality data rapidly loses its utility when repeated, eventually requiring the inclusion of 'unseen' but 'lower-quality' data. To address this quality-quantity tradeoff (QQT), we introduce neural scaling laws that account for the non-homogeneous nature of web data, an angle ignored in existing literature. Our scaling laws (i) characterize the differing 'utility' of various quality subsets of web data; (ii) account for how utility diminishes for a data point at its 'nth' repetition; and (iii) formulate the mutual interaction of various data pools when combined, enabling the estimation of model performance on a combination of multiple data pools without ever jointly training on them. Our key message is that data curation cannot be agnostic of the total compute that a model will be trained for. Our scaling laws allow us to curate the best possible pool for achieving top performance on Datacomp at various compute budgets, carving out a pareto-frontier for data curation. Code is available at https://github.com/locuslab/scaling_laws_data_filtering.

Domain reweighting is an emerging research area aimed at adjusting the relative weights of different data sources to improve the effectiveness and efficiency of LLM pre-training. We show that data mixtures that perform well at smaller scales may not retain their advantage at larger scales, challenging the existing practice of determining competitive mixtures in small-scale experiments and directly applying them at much larger scales. To address this, we propose AutoScale, a two-stage, scale-aware data composition framework. First, AutoScale fits a parametric model that predicts the model's loss under different data compositions, then uses it to find an approximate best allocation at smaller, more manageable budgets. Next, leveraging a novel theoretical analysis of how optimal compositions evolve with scale, AutoScale extrapolates that composition to larger budgets without further retraining. Empirically, AutoScale accelerates convergence and improves downstream performance. For instance, when pre-training GPT-2 Large, it achieves a 28% faster perplexity reduction than baselines and up to a 38% speed-up over unweighted training, while yielding best-average results on various downstream tasks. Overall, our findings illustrate how domain importance shifts with training scale, underscoring the need for scale-dependent data curation in LLM training. Our code is open-sourced.

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre training compute budget, what downstream accuracy is attainable with contemporary post training practice, and how stable is that mapping as the field evolves? Using large scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries, high conditional quantiles of benchmark scores as a function of log pre training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task dependent saturation and to probe contamination related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near full data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus 2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries shift across time.

This paper tackles the problem of depth estimation from a single image. Existing work either focuses on generalization performance disregarding metric scale, i.e. relative depth estimation, or state-of-the-art results on specific datasets, i.e. metric depth estimation. We propose the first approach that combines both worlds, leading to a model with excellent generalization performance while maintaining metric scale. Our flagship model, ZoeD-M12-NK, is pre-trained on 12 datasets using relative depth and fine-tuned on two datasets using metric depth. We use a lightweight head with a novel bin adjustment design called metric bins module for each domain. During inference, each input image is automatically routed to the appropriate head using a latent classifier. Our framework admits multiple configurations depending on the datasets used for relative depth pre-training and metric fine-tuning. Without pre-training, we can already significantly improve the state of the art (SOTA) on the NYU Depth v2 indoor dataset. Pre-training on twelve datasets and fine-tuning on the NYU Depth v2 indoor dataset, we can further improve SOTA for a total of 21% in terms of relative absolute error (REL). Finally, ZoeD-M12-NK is the first model that can jointly train on multiple datasets (NYU Depth v2 and KITTI) without a significant drop in performance and achieve unprecedented zero-shot generalization performance to eight unseen datasets from both indoor and outdoor domains. The code and pre-trained models are publicly available at https://github.com/isl-org/ZoeDepth .

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score. Because it does not differentiate the fidelity and diversity aspects of the generated images, recent papers have introduced variants of precision and recall metrics to diagnose those properties separately. In this paper, we show that even the latest version of the precision and recall metrics are not reliable yet. For example, they fail to detect the match between two identical distributions, they are not robust against outliers, and the evaluation hyperparameters are selected arbitrarily. We propose density and coverage metrics that solve the above issues. We analytically and experimentally show that density and coverage provide more interpretable and reliable signals for practitioners than the existing metrics. Code: https://github.com/clovaai/generative-evaluation-prdc.

Correctness of instance segmentation constitutes counting the number of objects, correctly localizing all predictions and classifying each localized prediction. Average Precision is the de-facto metric used to measure all these constituents of segmentation. However, this metric does not penalize duplicate predictions in the high-recall range, and cannot distinguish instances that are localized correctly but categorized incorrectly. This weakness has inadvertently led to network designs that achieve significant gains in AP but also introduce a large number of false positives. We therefore cannot rely on AP to choose a model that provides an optimal tradeoff between false positives and high recall. To resolve this dilemma, we review alternative metrics in the literature and propose two new measures to explicitly measure the amount of both spatial and categorical duplicate predictions. We also propose a Semantic Sorting and NMS module to remove these duplicates based on a pixel occupancy matching scheme. Experiments show that modern segmentation networks have significant gains in AP, but also contain a considerable amount of duplicates. Our Semantic Sorting and NMS can be added as a plug-and-play module to mitigate hedged predictions and preserve AP.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

Scaling laws are well studied for language models and first-stage retrieval, but not for reranking. We present the first systematic study of scaling laws for cross-encoder rerankers across pointwise, pairwise, and listwise objectives. Across model size and training exposure, ranking quality follows predictable power laws, enabling larger rerankers to be forecast from smaller runs. Using models up to 150M parameters, we forecast 400M and 1B rerankers on MSMARCO-dev and TREC DL. Beyond forecasting, we derive compute-allocation rules from the fitted joint scaling law and compare them with equal-compute checkpoints, showing that retrieval metrics often favor data-heavy scaling, though the recommendation depends on the training objective. The forecasts are accurate and typically conservative, making them useful for planning expensive large-model training. These results provide practical scaling principles for industrial reranking systems, and we will release code and evaluation protocols.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Designing metrics for evaluating instance segmentation revolves around comprehensively considering object detection and segmentation accuracy. However, other important properties, such as sensitivity, continuity, and equality, are overlooked in the current study. In this paper, we reveal that most existing metrics have a limited resolution of segmentation quality. They are only conditionally sensitive to the change of masks or false predictions. For certain metrics, the score can change drastically in a narrow range which could provide a misleading indication of the quality gap between results. Therefore, we propose a new metric called sortedAP, which strictly decreases with both object- and pixel-level imperfections and has an uninterrupted penalization scale over the entire domain. We provide the evaluation toolkit and experiment code at https://www.github.com/looooongChen/sortedAP.

We study the online min-cost perfect matching with delay (MPMD) problem where m requests arrive in a metric space of n points. In MPMD, an algorithm can choose to match a request or to delay, and the objective is to minimise the sum of connection and delay costs. The connection cost of a match is the distance between the locations of two matched requests in the metric, and the increase of the delay cost is a function of the set of unmatched requests at every moment. In this paper, we study two different types of delay functions, size-based (MPMD-Size) and convex delays (MPMD-Convex). The study of MPMD-Size was initiated by Deryckere and Umboh (APPROX/RANDOM 2023) where the instantaneous delay increment is a non-negative monotone function of the number of unmatched requests. Our bounds are in terms of n, as opposed to Deryckere and Umboh's bounds that depend on m. Our results settle the deterministic competitive ratio (up to constants). At the heart of these results is a succinct encoding scheme of MPMD-Size on a given n-point metric as a metrical task system problem on a 2^{n-1}-point metric. We also consider MPMD-Convex proposed by Liu et al. (ISAAC 2018) where the delay cost incurred by each request is a uniform convex delay function of the time difference between its arrival time and the moment that it is matched by the algorithm. They focused on delay functions f that are unbounded, non-decreasing, continuous, and satisfy f(0)=f'(0)=0, and showed that the deterministic competitive ratio is Ω(n) for n-point uniform metrics. We show that, surprisingly, when f is a non-negative, monotone polynomial with f'(0)>0, there is an O(1)-competitive deterministic algorithm for uniform metrics. Our result completes our understanding of MPMD-Convex on uniform metrics for a broad class of functions.

Large, pretrained models are commonly finetuned with imagery that is heavily augmented to mimic different conditions and scales, with the resulting models used for various tasks with imagery from a range of spatial scales. Such models overlook scale-specific information in the data for scale-dependent domains, such as remote sensing. In this paper, we present Scale-MAE, a pretraining method that explicitly learns relationships between data at different, known scales throughout the pretraining process. Scale-MAE pretrains a network by masking an input image at a known input scale, where the area of the Earth covered by the image determines the scale of the ViT positional encoding, not the image resolution. Scale-MAE encodes the masked image with a standard ViT backbone, and then decodes the masked image through a bandpass filter to reconstruct low/high frequency images at lower/higher scales. We find that tasking the network with reconstructing both low/high frequency images leads to robust multiscale representations for remote sensing imagery. Scale-MAE achieves an average of a 2.4 - 5.6% non-parametric kNN classification improvement across eight remote sensing datasets compared to current state-of-the-art and obtains a 0.9 mIoU to 1.7 mIoU improvement on the SpaceNet building segmentation transfer task for a range of evaluation scales.