Metric Learning

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6 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 47

Oct 7, 2026cs.CV

Global Average Precision for Representation Learning

Standard information retrieval metrics, such as mean Average Precision (mAP), assess performance one query at a time, based on how the similarities between a query and its positives compare against those with its negatives. The same holds for common representation learning losses, such as InfoNCE and per-query AP surrogates. None of them considers whether similarities are comparable across queries, which any system with a single decision threshold relies on. Global Average Precision (gAP) does, by ranking all query-candidate pairs in one list and computing a single AP. We introduce gSAP, a differentiable surrogate of gAP. It needs only a similarity matrix and a binary matrix marking the positive pairs, the same input as existing losses, so it is a drop-in replacement for them and agnostic to the encoder, the modality, and the source of supervision. Since it considers all possible pairwise comparisons in the batch jointly, it also remains trainable at low temperatures, a regime where per-query surrogates run out of gradient. Swapping it into established recipes improves supervised metric learning, cross-modal alignment, and self-supervised pretraining, where, to our knowledge, it is the first ranking loss to replace the community standard InfoNCE in the latter two. Its similarities are more consistent across queries, which drives the gains under a universal threshold. gSAP retrieves up to four times as many positive pairs as the strongest AP surrogate at the same precision, and it degrades the least when queries with no positives in the database are added. Beyond thresholding, models trained with gSAP also learn better representations, with higher transfer,

k

NN and zero-shot classification accuracy.

Bill Psomas, Mohammad Mahdi, Michalis Thomas +3

VRG, FEE, Czech Technical University in Prague · INSAIT, Sofia University “St. Kliment Ohridski”

Learning to Rank Metric Learning Self-Supervised Learning

Oct 6, 2026cs.LG

Directed Temporal Representations for Offline Visual Control

Predictive world models provide compact visual representations for control. Control requires a latent geometry aligned with temporal reachability rather than predictive similarity alone. We introduce Directed Temporal Representations for Control (DTRC), which learns such a geometry from offline visual trajectories on top of frozen LeWorldModel (LeWM) features. DTRC constructs a directed temporal quasimetric over the learned control representation. Short-range temporal offsets calibrate the distance scale. Bootstrapped targets extend temporal reachability across longer horizons. Action-conditioned consistency aligns the representation with local transition dynamics. The resulting distance estimates temporal reaching cost, and its change across a transition defines goal-relative temporal progress. We use this progress signal as a temporal critic for direct goal-conditioned policy learning. Model-assisted targets provide an additional training-time refinement under behavior-support and dynamics-agreement constraints. Across ten visual control tasks, DTRC achieves strong goal-conditioned control performance relative to planning and direct-policy baselines. Held-out diagnostics on the four LeWM tasks show consistent short-range temporal calibration, task-dependent long-range and directional structure, and positive transition-level progress. Temporal supervision improves the same flow-policy parameterization across all four LeWM tasks, while the resulting policy acts directly without iterative trajectory search at test time.

Chenyang Yuan, Haoyu Wang, Zhuo Sun +1

University of Sheffield · Shanghai Jiao Tong University · Shanghai University of Finance and Economics +1

Visual RL Trajectory Representation Learning Offline RL Goal-Conditioned RL Metric Learning

Oct 4, 2026cs.LG

METRO: Metric-Enhanced Token Routing Operator

State-of-the-art neural operators scale to complex meshes via slice-and-process architectures, yet many rely on linear compatibility scores for latent tokenization. Under common feature normalization, such scores are equivalent to isotropic Euclidean clustering, while without normalization they induce unbounded linear decision regions. In both cases, they lack slice-specific anisotropic locality, which can lead to redundant and entangled latent slices. To address this, we propose Metric-Enhanced Token Routing Operator (METRO), a geometry-aware routing mechanism that replaces linear projection with a learnable Mahalanobis metric. By enabling each latent slice to learn a local anisotropic tensor, METRO shapes receptive fields into exponentially localized, oriented ellipsoids that naturally align with flow features like boundary layers and wakes. As a drop-in replacement, METRO yields consistent improvements across both Transformer and Mamba backbones. Empirically, our method achieves substantial performance gains on irregular domains, outperforming baselines on both standard PDE benchmarks and complex industrial design tasks. Finally, METRO exhibits enhanced robustness in out-of-distribution regimes across varying Reynolds numbers and geometric configurations.

Nodens Koren, Thomas Hofmann, Georgios Kissas

Department of Computer Science ETH Zürich Zürich, Switzerland · Swiss Data Science Center ETH Zürich Zürich, Switzerland

Metric Learning PDE Operator Learning Neural Operators

Sep 30, 2026cs.LG

Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachability

In goal-conditioned reinforcement learning (GCRL), quasimetric learning models goal-reaching costs as quasimetric distances, connecting local constraints to global value geometry. Its local constraints, however, should reflect the direction- dependent effects of control composition over a finite horizon together with environmental feasibility. We propose ReQRL, which constrains the critic's value gradients through finite-horizon reachability. Drawing on state-constrained optimal control, we decouple dynamical reachability from boundary geometry, estimating both from data. On OGBench, our method outperforms or rivals existing quasimetric approaches and other offline GCRL methods.

Daisuke Yamada, Travis Pence, Vikas Singh

Department of Computer Science University of Wisconsin–Madison · Department of Biostatistics and Medical Informatics University of Wisconsin–Madison

Metric Learning Offline RL Goal-Conditioned RL

Sep 27, 2026eess.AS

Rethinking Automated Voice Similarity by Shifting from EER to Embedding Geometry

Speaker verification (SV) models are commonly assumed to better capture nuances among speaker characteristics as verification accuracy improves, leading to their widespread use as automated proxies for human voice similarity in speech generation tasks. However, by establishing a human perceptual alignment metric and conducting systematic analysis, we demonstrate that perceptual alignment is governed far more by how a model is trained (its learning objective) than by how well it performs (EER). Notably, standard margin-based classification losses (e.g., AAM-Softmax) yield substantially lower perceptual alignment than prototypical metric losses, while EER itself fails to track human judgment, directly challenging the community's implicit assumption. We trace this divergence to embedding geometry, where a model's effective dimensionality (

d_{\mathrm{eff}}

) tracks perceptual alignment with a

-0.95

rank correlation, revealing that the dimensional spread favored by classification losses fundamentally clashes with the low-dimensional nature of human voice perception. Imposing a dimensionality bottleneck compresses

d_{\mathrm{eff}}

and raises perceptual alignment (

ρ_{\mathrm{align}}

) from 0.08 to 0.74, establishing a principled geometric criterion for evaluating voice similarity.

Szu-Chi Chen, Jia-Kai Dong, Yi-Cheng Lin +2

National Taiwan University, Taipei, Taiwan · NVIDIA, Taiwan · Artificial Intelligence Center of Research Excellence (NTU AI-CoRE), NTU, Taiwan

Audio Representation Learning Speaker Verification Metric Learning

Sep 23, 2026cs.CV

Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces

Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason to believe the true task geometry has this property. The task-sensitive geometry of the feature space is given by the pullback metric

g(F) = J(F)^\top J(F)

, where

J

is the Jacobian of the decoder's output fed to a task-specific distance, with respect to the features. Storing the full

g

is infeasible at modern scales, and for dense outputs such as depth maps even forming

J

is impractical. We show that whether a low-rank approximation of this metric can be learned depends on the model-decoder pair, and we characterize this with a matrix-free diagnostic

κ_{cap}(r)

computable with a low number of Jacobian-vector products. For tractable pairs, we develop the Spectral Pullback Network (SPN), which learns a low-rank version of the metric from randomized power iteration, and we distill it into a

310

K-parameter importance head that predicts token importance directly from the features. When the Jacobian spectrum is too spread out for a low-rank approximation, passing the decoder's input features through a VAE bottleneck can restore tractability. Across DPT, DINOv2, CLIP, and VGGT backbones,

κ_{cap}(r)

predicts which learned-metric architectures are viable. The importance head reaches Spearman

ρ= 0.998

on DINOv2 CLS, and our geometric token pruning reduces the additional depth error of ToMe-based token selection by

25\%

on DPT depth at prune ratio

0.5

, without fine-tuning the ViT. Project page: https://cyberiada.github.io/TaskInducedViTs/

Andrew Bond, Ege Erdem Özlü, Tuna Çimen +4

Imperial College London London, UK · Hacettepe University Ankara, Türkiye

Vision Transformer Geometric Representation Learning Metric Learning Efficient ViTs

Sep 15, 2026cs.RO

Kernel-Based Metrics Learning for Uncertain Opponent Vehicle Trajectory Prediction in Autonomous Racing

Autonomous racing confronts significant challenges in safely overtaking Opponent Vehicles (OVs) that exhibit uncertain trajectories, stemming from unknown driving policies. To address these challenges, this study proposes heterogeneous kernel metrics for Deep Kernel Learning (DKL), designed to robustly capture the diverse driving policies of OVs, and carry out precise trajectory predictions along with the associated uncertainties. A key virtue of the proposed kernel metrics lies in their ability to align similar driving policies and disjoin dissimilar ones in an unsupervised manner, given the observed interactions between the Ego Vehicle (EV) and OVs. The efficacy of the proposed method is substantiated through experimental studies on a 1/10th scale racecar platform, demonstrating improved prediction accuracy and thereby safely overtaking against OVs. Furthermore, our method is computationally efficient for onboard computing units, affirming its viability in fast-paced racing environments. The video and source code can be found at https://github.com/HMCL-UNIST/OpponentPredictionWithKMDKL.git.

Hojin Lee, Youngim Nam, Sanghun Lee +1

Department of Mechanical Engineering, Ulsan National Institute of Science and Technology, Ulsan, 44919, Republic of Korea

Multi-Agent Trajectory Prediction Autonomous Racing Metric Learning Kernel Methods Trajectory Prediction Vehicle Trajectory Prediction

Sep 14, 2026cs.NE

Complete Suffix Prediction for Recommendation via Latent Retrieval over Process Graphs

Complete suffix prediction is challenging in sequential decision settings, where the same prefix can remain compatible with several plausible suffixes. We propose a graphbased metric-learning framework that reformulates complete suffix prediction as latent retrieval over process graphs. Prefixes and suffixes are represented as directed attributed graphs and encoded by edge-conditioned graph neural networks, allowing event-level activities and transition-level durations to be modelled jointly. Prefix representations are projected into the latent suffix space through a predictor trained with a joint reconstruction and contrastive objective strengthened using process-aware hard negatives. To stabilise the learned retrieval geometry, spectral normalisation, and retrieval robustness, spectral normalisation is applied to enforce a Lipschitz constraint on both encoders and predictor. Experiments on two real-life process datasets demonstrate that the proposed framework achieves the best overall results across nearly all evaluated criteria. It improves semantic suffix accuracy measured by normalized Damerau-Levenshtein distance, yields strong retrieval quality through Recall@1, Recall@5, and MRR@5, and maintains temporal plausibility according to Mean Absolute Error. These results show that graph-based latent retrieval is an effective alternative to sequential suffix prediction for recommendation-oriented process monitoring under structural and KPI-related constraints.

Sarra Madad, Myriam Maumy, Fr{é}d{é}ric Bertrand +1

UTT, LIST3N - OPTI, QAD · LIST3N Lab, AI Lab · University of Technology of Troyes (UTT), QAD +11

Predictive Process Monitoring Process Mining Graph-Based Retrieval Metric Learning

Sep 6, 2026cs.LG

Learning Kernels by Alignment for Multiclass Bayes Classification

Kernel methods separate data representation from decision-making, but typically require the kernel to be chosen in advance. We show that this kernel can instead be learned by alignment, and develop the resulting framework through the recently introduced Collaborative Learning and Inference (CLaI). We show that Collaborative Learning can be viewed as a kernel alignment process, in which an embedding is trained so that its induced similarity matches a label-derived target kernel. We also prove that Collaborative Inference is equivalent to kernel Bayes classification with Parzen-window density estimation. Motivated by these perspectives, we generalise CLaI by replacing cosine similarity with a learned Mahalanobis distance and extend it to multiclass classification. On CIFAR-10, PathMNIST, and SleepEDF, the Mahalanobis formulation improves accuracy, converges faster, and yields lower calibration error than the cosine-based variant. Auxiliary experiments further support these connections, showing that CLaI produces latent signals of the same form as a Gaussian process, while achieving competitive calibration on sepsis prediction. Together, these results establish a principled learned-kernel framework that unifies representation learning, kernel alignment, and Bayesian classification, and extends naturally to the multiclass setting.

Hollan Haule, Javier Escudero

Bayesian Inference Metric Learning Multiclass Classification Classification Kernel Methods

Sep 2, 2026cs.CV

Learning to Attract and Repel: Dual Quality Margin Learning for Face Recognition (DQM-Face)

Face recognition in unconstrained environments remains highly challenging due to diverse and extreme variations encountered in real-world scenarios. To mitigate these effects, existing margin-based approaches model sample quality through feature magnitude. However, magnitude-based modeling alone is susceptible to identity-agnostic noise, which can degrade the reliability and discriminative power of learned representations. In this paper, we propose Dual Quality Margin Learning for Face Recognition (DQM-Face), a novel framework that enables refined attraction and repulsion dynamics during representation learning. Our approach unifies conventional magnitude-based quality estimation with a newly introduced semantic quality learning mechanism, realized via squeeze-and-excitation semantic attention. By jointly leveraging magnitude and semantic cues, we construct enhanced quality-aware margins that adaptively strengthen intra-class compactness through improved attraction during learning. To further enhance inter-class discrimination, we introduce a repulsion margin formulation that explicitly enlarges inter-class separation. The unified integration of semantic quality modeling with dual attraction-repulsion margin optimization results in a more structured and discriminative feature geometry. Extensive experiments on multiple challenging benchmarks demonstrate that DQM-Face consistently outperforms state-of-the-art face recognition methods. Moreover, we show that the quality learned for margin optimization is highly effective for face image quality assessment within the proposed framework, demonstrating that the learned quality signal is intrinsically aligned with the recognition objective. The code is publicly available: https://github.com/RAIB-group/DQM-Face

El Ouanas Belabbaci, Bhavesh Wani, Philipp Terhörst

Laboratoire d’Ingénierie des Systèmes Intelligents et Communicants (LISIC), Faculty of Electrical Engineering, University of Sciences and Technology Houari Boumediene (USTHB), Algiers, Algeria · Johannes Gutenberg University Mainz, Germany

Face Recognition Metric Learning

Aug 8, 2026cs.AI

GRACE: LLM-Grounded Semantic Metric Spaces for Scalable Mixed-Data Clustering

Clustering mixed tabular data requires a unified metric space to bridge the inherent heterogeneity between continuous numerical measurements and discrete categorical symbols. Traditionally, algorithms rely entirely on dataset-internal statistics to estimate categorical relationships, which confines the learned metric to empirical co-occurrences and ignores conceptually obvious yet statistically unobserved affinities. Although LLMs offer external world knowledge, applying their text-centric reasoning to highly abstract tabular concepts presents significant challenges. Bridging this modality gap to construct a semantically complete metric typically requires embedding LLMs into iterative metric learning loops to dynamically optimize cross-modality representations. This incurs intractable computational overhead, forcing a compromise between semantic enrichment and scalability. Therefore, we propose GRACE, an LLM-grounded framework for scalable mixed-data clustering. GRACE shifts semantic acquisition to the attribute-value level via a multi-perspective LLM querying strategy, mapping heterogeneous values into knowledge-informed descriptions. Crucially, this one-shot grounding extracts general-purpose semantic representations that embed heterogeneous attributes into a unified space, decoupling expensive LLM invocation from iterative optimization. Furthermore, GRACE cross-validates these external semantics against dataset-internal statistical evidence to ensure alignment with the dataset-specific cluster structure. Ultimately, GRACE matches the scalability of conventional statistics-driven baselines while achieving superior clustering accuracy and conceptual interpretability over 11 competing methods. The source code is available at https://github.com/develop-yang/GRACE-GRACE-A

Zihua Yang, Zhencheng Xie, Junyang Chen +4

Guangdong University of Technology · Tsinghua University · Peking University +2

Clustering Unsupervised Clustering Metric Learning Tabular ML

Aug 6, 2026eess.IV

Algorithmic statistics of retinal images

There has been a tremendous amount of image processing and machine learning research to measure and classify disease progression from live optical coherence tomography (OCT) imaging of the retina. The images considered here are large, complex, three-dimensional (3-D) and difficult to visualize effectively. Many current supervised machine learning approaches, \emph{e.g.} neural networks, are non-metric meaning that any features or measurements generated can introduce systematic distortion that may be correlated with underlying non-meaningful physiological differences. Here we present a metric learning approach using the normalized compression distance (NCD) combined with anisotropic structure-enhancing filters to quantify and visualize the principal differences among a collection of 3-D retinal images. We validate the NCD-measured structural differences between pairs of images against the physician-measured change in visual field function, achieving a prediction error of

\sim

0.5 dB, more accurate than non-metric deep learning approaches. The normalized compression vectors (NCV) are proposed as a feature set measuring visual differences among a collection of 3-D microscopy images. The utility of the NCV for visualizing and measuring patterns of change is demonstrated for a human with moderate non-progressing glaucoma and for a non-human primate model using intraocular pressure setting manipulation. We conclude with a brief simulation of non-metric embedding features, \emph{e.g.} from neural networks, introducing class-correlated statistical distortion.

Loan Huynh, Ronald Zambrano, Layton Aho +4

Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA · Glaucoma Service, Wills Eye Hospital, Philadelphia, PA, USA · School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, USA +2

Medical Imaging Longitudinal Medical Image Analysis Optical Coherence Tomography Metric Learning

Jul 28, 2026cs.LG

Re-thinking Mammography Transfer Learning: The Dataset-Informed Transfer Learning (DITL) Framework for Breast Cancer Screening and Lesion Diagnosis

Enhancing classification performance in mammography remains a persistent challenge across both small curated datasets and large-scale clinical cohorts. Conventional transfer learning approaches often neglect dataset-specific characteristics, while recent neighborhood-informed methods have been restricted to narrow tasks with rigid formulations, limiting their scalability to population-level datasets. To address these challenges, we propose the Dataset-Informed Transfer Learning (DITL) framework, which integrates dataset-derived difficulty signals with neighborhood-based triplet supervision in a unified objective. DITL introduces two adaptive components: (i) Adaptive Difficulty-Weighted Cross-Entropy (A-DWCE), which assigns per-sample weights based on k-nearest neighbor label purity in a self-supervised feature space, and (ii) Adaptive Neighborhood Representation Triplet (A-NR-Triplet), which enforces intra-class compactness and inter-class separation using a learnable margin. Unlike focal loss, DITL requires no hyperparameter tuning, removes heuristic weighting and fixed margins, and incurs negligible computational overhead, yielding a robust and scalable optimization strategy. On the large-scale VinDR-Mammo dataset, DITL achieves state-of-the-art performance for whole-image breast density classification, with significant improvements across accuracy, F1-score, and AUC (p < 0.0001). Beyond large cohorts, DITL also delivers consistent, statistically significant gains on small ROI datasets (p < 0.0001). By bridging small-scale lesion analysis with large-scale density estimation, DITL establishes a clinically relevant, scalable, and generalizable framework for mammography classification, spanning the full breast cancer screening-to-diagnosis spectrum.

Adarsh Bhandary Panambur, Siming Bayer, Andreas Maier

Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany · Siemens Healthineers, Erlangen, Germany

Metric Learning Medical Image Classification Transfer Learning Mammography

Jul 20, 2026cs.AI

PAMD: Structured Adaptive Distances for Bisimulation Representations in Visual Reinforcement Learning

Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g.,

\ell_p

norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce PAMD: Pairwise Adaptive Mahalanobis Distance, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity. PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.

Daegyeong Roh, Juho Bae, Han-Lim Choi

Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Daejon, Republic of Korea.

Mahalanobis Distance Metric Learning State Representation Learning Visual RL

Jul 20, 2026cs.CV

Leveraging Dissimilarity Invariance as a Robust Anchor for Learning with Noisy Labels

Deep learning models excel in visual recognition but suffer severe performance drops when training labels are corrupted by noise. Under label noise prior work cannot learn accurate similarities and thus misguide the learning process. In this paper, we uncover a complementary and novel phenomenon, Dissimilarity Invariance, whereby semantic dissimilarity between unrelated samples remains stable despite label noise. Leveraging this insight, we propose NegScale, a plug-and-play framework that shifts focus from fragile similarity to robust dissimilarity. NegScale integrates: (1) Structured Negative Orthogonality Penalty (SNOP), enforcing subspace orthogonality for unrelated samples; and (2) Dissimilarity-Calibrated Similarity Adjustment (DCSA), suppressing spurious similarity using dissimilarity anchors. We also give theoretical analysis that proves Dissimilarity Invariance and the effectiveness of NegScale. Empirical results demonstrate that NegScale consistently outperforms state-of-the-art baselines, establishing new benchmarks on CIFAR with synthetic noise and real-world datasets.

Wenxiao Fan, Kan Li

School of Computer Science, Beijing Institute of Technology

Metric Learning Learning with Noisy Labels

Jul 20, 2026cs.CV

Miles: Metric Learning with Expandable Subspace for Pre-Trained Model-Based Class-Incremental Learning

Class Incremental Learning (CIL) aims to learn new concepts consistently from a data stream without forgetting. Unlike typical CIL methods which need to learn a model from scratch, pre-trained model (PTM) can easily adapt to a new task with fine-tuning. However, existing PTM-based CIL methods fail to achieve a trade-off between performance and computational expenditure, i.e., they either adopt the same parameter space so that leading catastrophic forgetting, or expand a new branch for each task but adding more computational cost. To this end, we propose MetrIc Learning with Expandable Subspace (Miles) to harness the prior information within pre-trained knowledge, thereby orchestrating an efficient expansion of the parameter space through guided optimization. Specifically, it decouples the learnable modules with the pre-trained model, exploiting prior information from intermediate features of the backbone network to enable more flexible parameter expansion. Then, a central loss is adopted to guide the new category to cluster towards the corresponding prototype in the new task subspace while incorporating an auxiliary distance regularization term to maintain metric equilibrium across tasks. Extensive experiments on six benchmark datasets demonstrate that Miles achieves state-of-the-art performance in various CIL settings.

Kai Jiang, Zisong Lin, Hongyuan Zhang +2

National Key Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China · The University of Hong Kong, Hong Kong SAR, China · Institute of Artificial Intelligence (TeleAI) of China Telecom, China

Class-Incremental Learning Metric Learning Incremental Learning

Jul 14, 2026cs.AI

Who Grades the Grader? Co-Evolving Evaluation Metrics and Skills for Self-Improving LLM Agents

Self-evolving agent systems improve by creating, revising, and retiring their own skills, but every such loop rests on a hidden assumption: a reliable evaluation metric already exists. In many real applications it does not. We make three claims. First, metrics can be \emph{evolved}: our metric loop searches compositions of small drawback detectors under a full evolutionary lifecycle, trained to agree with a ten-item anchored reference set, regularized by consensus over unlabeled outputs, and audited against a held-out anchor it never reads, yielding a transparent, inspectable metric rather than an opaque judge. Second, since no metric exists to beat, the yardstick is recovering what an accurate metric would have enabled, and \emph{Double Ratchet}, our co-evolution of the metric with a lifecycle-managed skill loop, does so: across code generation (MBPP+), enterprise text-to-SQL (Spider~2.0-Snow), and reference-free report generation, it retains 88--110% of the held-out lift achieved by the same skill loop driven by ground truth or the best available rubric. Third, safety comes from anchor discipline plus outer audits: removing anchor guards collapses the metric into a vacuous detector while removing the lifecycle does not; and when evolved skills gamed the report rubric, an independent judge caught it, one detector repaired it, and a task-aware judge then preferred the evolved outputs over the pre-evolution baseline in 77% of decided pairs. We argue this failure-expecting architecture is the right default wherever no reliable automatic verifier exists.

Xing Zhang, Guanghui Wang, Yanwei Cui +4

1AWS Generative AI Innovation Center · 2HSBC Holdings Plc., HSBC Technology Center, China

LLM Agent Evaluation LLM Agent Self-Improvement LLM Agent Skill Learning Metric Learning Rubric-Based Evaluation

Jul 9, 2026cs.CL

Large-Language-Models-as-a-Judge in Theory-Agnostic Adaptive Metric-Alignment for Prototypical Networks in Personality Recognition

Personality recognition has traditionally been constrained by theory-dependent formulations, where models are trained to fit predefined psychological taxonomies rather than uncovering shared underlying behavioral structure. This limits generalization, as personality itself is better understood as theory-invariant, while existing annotations reflect only partial and sometimes inconsistent views of the same latent traits. In this work, we introduce JAM ((J)udge for (A)daptive (M)etric-Alignment), a theory-agnostic framework that shifts learning from adapting to predefined personality theories toward discovering unified latent pseudo-facets that capture shared psychological structure. Rather than constraining the model to any personality taxonomy during training or inference, the framework learns generalizable psychological representations and can infer an individual's latent psychological profile directly from the textual samples, without requiring theory-specific labels. JAM achieves this through an Attention-Pooled Graph Prototypical Network that learns structured representations via clustering in embedding space, together with a Cross-Theory Harmonization (CTH) approach that integrates (i) Human-Guided Linkage and (ii) Machine-Induced Consensus to unify heterogeneous datasets without relying on predefined labels. To further improve robustness and data quality, we incorporate an LLM-as-a-Judge mechanism operating in two configurations, (i) LLM-before-the-loop and (ii) LLM-in-the-loop which identifies ambiguous samples to guide adaptive metric learning. Experiments show that JAM improves cross-framework generalization and performance, establishing a strong step toward theory-agnostic personality inference and supporting low-resource personality theories. The related code repository, model weights, and artifacts are available at https://research.jingjietan.com/JAM

Jing Jie Tan, Ban-Hoe Kwan, Danny Wee-Kiat Ng +6

Department of Mechatronics and Biomedical Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Malaysia · Institute of Communication Studies, National Yang Ming Chiao Tung University, Taiwan · Institute of Information Management, National Yang Ming Chiao Tung University, Taiwan +2

Personality Modeling in Language Models Metric Learning

Jul 6, 2026cs.LG

Learnable Weighting of Intra-Attribute Distances for Categorical Data Clustering with Nominal and Ordinal Attributes

The success of categorical data clustering generally much relies on the distance metric that measures the dissimilarity degree between two objects. However, most of the existing clustering methods treat the two categorical subtypes, i.e. nominal and ordinal attributes, in the same way when calculating the dissimilarity without considering the relative order information of the ordinal values. Moreover, there would exist interdependence among the nominal and ordinal attributes, which is worth exploring for indicating the dissimilarity. This paper will therefore study the intrinsic difference and connection of nominal and ordinal attribute values from a perspective akin to the graph. Accordingly, we propose a novel distance metric to measure the intra-attribute distances of nominal and ordinal attributes in a unified way, meanwhile preserving the order relationship among ordinal values. Subsequently, we propose a new clustering algorithm to make the learning of intra-attribute distance weights and partitions of data objects into a single learning paradigm rather than two separate steps, whereby circumventing a suboptimal solution. Experiments show the efficacy of the proposed algorithm in comparison with the existing counterparts.

Yiqun Zhang, Yiu-ming Cheung

Clustering Metric Learning

Jul 4, 2026cs.LG

PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling

Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling. We propose Physics-Informed Eigenfunction Features with Learnable Scaling (PIEFS), a supervised neural representation-learning framework with a spectral inductive bias, based on a modified Dirichlet energy. In PIEFS, scalar coordinate maps are trained under empirical Gram orthogonality, a supervised linear readout, and a Dirichlet penalty in which the input gradient is transformed by a learnable metric

A(x)=Λ(x)U(x)

. The diagonal factor

Λ(x)

controls anisotropic scaling, while the orthogonal factor

U(x)

is parameterized by a structured product of Givens rotations. This construction yields task-adaptive Dirichlet-regularized coordinates rather than eigenfunctions of a fixed supervision-independent operator. Experiments on synthetic, tabular, and image-based benchmarks study the effect of identity, diagonal, and rotation-scaling metrics, and compare the resulting coordinates with classical baselines and NeuralEF. The results support PIEFS as a compact supervised spectral representation method and identify optimization stability, validation on explicit operator eigenproblems, and richer metric parameterizations as the main directions for future work.

Varvara Nazarenko, Timur Lidzhiev, Alexander Tarakanov

Faculty of Computer Science, HSE University, Moscow, Russia · AI VK, Moscow, Russia

Spectral Regularization Representation Learning Metric Learning Spectral Methods

Jul 3, 2026cs.LG

MABLE: Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning

We propose MABLE (Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning), a self-supervised framework for learning node and graph embeddings from large, heterogeneous graphs, demonstrated here on geospatial mineral-exploration data. MABLE combines masked reconstruction with fixed cosine-similarity losses that align matched augmented views while keeping unpaired embeddings well spread. A bi-Lipschitz feature decoder ties a low-dimensional reconstruction component of each node embedding to feature similarity, while matched-node consistency shapes the remaining context used by graph pooling. Lipschitz-controlled pooling helps stabilize graph-level representations under perturbations of retained node embeddings, while augmentation alignment trains robustness to masking, node dropping, and sampling variation. Across local copper and regional Arabian Shield studies, MABLE embeddings provide complementary downstream signal and produce coherent embedding-derived layers for hypothesis generation without learned discriminators or hard-negative selection.

Yaniv Shulman, Shaghayegh Akbarpour, Jack B. Muir

Fleet Space Technologies, Adelaide, Australia · Research School of Earth Sciences, Australian National University, Acton, Australia

Masked Autoencoders Graph Representation Learning Geospatial Representation Learning Graph SSL Metric Learning

Jun 29, 2026cs.CV

CouCE: A Unified Causal Framework for Debiased Deep Metric Learning

Deep Metric Learning (DML) often struggles with zero-shot generalization because standard objectives inherently capture what co-occurs rather than what causes similarity. Consequently, DML models are vulnerable to shortcut learning driven by two structurally distinct confounders: background spurious correlations (which create backdoor paths via scene context) and foreground nuisance perturbations (which inject non-semantic variations like pose or illumination). Although existing methods have proposed targeted solutions for each pathway individually, none can simultaneously address both due to their fundamentally distinct causal roles. To bridge this gap, we propose the Counterfactual Causal Embedding (CouCE), a unified causal framework that explicitly models and neutralizes both confounders. Specifically, we introduce Orthogonal Dictionary-Based Backdoor Adjustment (ODBA), which isolates spurious background patterns into a variance-gated dictionary and stably disentangles them from the learned embeddings via soft orthogonal regularization. Simultaneously, we propose Multi-Scale Randomized Causal Intervention (MSRCI) to enforce causal invariance against foreground nuisances through multi-scale Fourier amplitude randomization and a symmetric KL invariance constraint. Notably, CouCE seamlessly integrates with any proxy-based loss, incurring modest training overhead without requiring architectural modifications during inference. Extensive experiments on CUB-200-2011, Cars-196, and Stanford Online Products demonstrate that CouCE consistently achieves state-of-the-art performance, providing a principled and robust solution for debiased DML.

Xin Yuan, Zhenyang Niu, Meiqi Wan +3

Wuhan University of Science and Technology Wuhan, China · Harbin Institute of Technology Harbin, China

Debiased ML Causal Representation Learning Metric Learning Shortcut Learning

Jun 17, 2026cs.RO

Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation

Traditional approaches place intelligence in the agent, whether as a learned policy or a search procedure. We instead place intelligence in the space itself: a scene induces a Riemannian metric on the configuration manifold, and action reduces to following the geodesics of that metric rather than invoking a separate planner or collision checker. A single Encoder-Router network realizes this idea through three complementary parameter groups -- frame parameters that orient the generators, modulation parameters that govern their spatial propagation, and basic coefficients that determine their strength. These groups combine through a shared semigroup-superposition mechanism to produce a single Riemannian metric field, yielding a compact architecture whose geometry scales naturally with scene complexity. Trained on a single two-obstacle scene, the model demonstrates robust zero-shot generalization across unseen obstacle configurations, with orders-of-magnitude separation between collision-free and obstacle-penetrating path costs.

Chenghao Xu

School of Artificial Intelligence and Robotics and National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, Changsha, Hunan, China

Geometric Representation Learning Metric Learning Motion Planning Robot Motion Planning

Jun 13, 2026cs.CV

Beyond Scalar Distances: Semantic Attribute Gradients from Frozen MLLMs for Visual Embeddings

Vision encoders for retrieval are typically trained with class-label supervision: each training pair reduces to a scalar that uniformly pushes the embedding apart or pulls it together, as if every visual attribute either differed or matched. A multimodal large language model (MLLM), shown the same pair, can articulate those attributes and use them to predict whether the images share a class. We propose \textbf{SAGA}, a framework that turns this language-grounded, attribute-aware perception into a training signal for the encoder itself. Specifically, we use Group Relative Policy Optimization (GRPO) to reward the MLLM for correct predictions on the vision encoder's tokens. Since correct predictions require those tokens to expose the specific attributes that differ or match between the pair, the gradient pushes the encoder to encode them, replacing the uniform pair-level scalar with attribute-resolved supervision. An auxiliary attention-distillation loss anchors the encoder's embedding to tokens the MLLM attended to, and a standard metric-learning loss shapes the embedding geometry for nearest-neighbour retrieval. The MLLM is frozen throughout and discarded at inference, matching the deployment cost of a metric-learning baseline. SAGA improves Recall@1 by 3 to 6 points over state-of-the-art baselines on CUB-200-2011, Cars-196, FGVC-Aircraft, and iNaturalist Aves on zero-shot image retrieval.

Shubhang Bhatnagar, Dheeraj Baiju, Narendra Ahuja

University of Illinois Urbana-Champaign

Visual Representation Learning Fine-Grained Image Retrieval Metric Learning Vision-Language Retrieval

Jun 12, 2026cs.LG

Riemannian Metric Matching for Scalable Geometric Modeling of Distributions

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose Riemannian metric matching: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the carré du champ operator, which, using diffusion geometry, gives us access to the Riemannian geometry toolkit for downstream machine learning and statistical tasks. Our key observation is that the carré du champ operator can be formulated as a conditional expectation over random perturbations of the data, which can be exploited for sample-wise training and constant cost, amortized inference without explicit kernel construction. Empirically, metric matching rivals or improves the accuracy of

k

-NN-based diffusion geometry estimators, while enabling amortized inference that is up to

400\times

faster, and supports graph-free geometric analysis on high-dimensional images where nearest neighbors break down.

Jacob Bamberger, Adam Gosztolai, Pierre Vandergheynst +2

Department of Computer Science, University of Oxford, Oxford, UK · Institute of Artificial Intelligence, Medical University of Vienna, Vienna, Austria · EPFL, Lausanne, Switzerland +1

Geometric Representation Learning Metric Learning Riemannian Geometry

Jun 10, 2026cs.SD

Quality Adaptive Angular Margin Learning for Respiratory Sound Classification

We present a quality-adaptive angular-margin learning framework that improves feature generalization by enforcing intra-class compactness and inter-class separability. Our framework, titled QLung, introduces a no-reference audio quality margin derived from spectral entropy and root-mean-square energy, which adaptively scales angular margins based on recording quality. To this end, we propose a log-scaled angular margin that stabilizes training under severe class imbalance. We also use an angular classifier that normalizes features and class weights, ensuring margin penalties are applied consistently on the unit hypersphere. Our approach improves in-distribution performance on the ICBHI dataset by 2.46% over the cross-entropy baseline, and most significantly, achieves the strongest out-of-distribution performance on the SPRSound dataset compared to prior state-of-the-art methods. Code is available at https://github.com/RSC-Toolkit/QLung.

Yoon Tae Kim, Heejoon Koo, Miika Toikkanen +1

RSC LAB, MODULABS, Republic of Korea · Department of Electronic Engineering, Wonkwang University, Republic of Korea · AI Convergence Research Institute, Wonkwang University, Republic of Korea

OOD Generalization Metric Learning Audio Classification Respiratory Sound Classification

Jun 10, 2026cs.SD

The Hidden Cost of Pairwise Verification in Synthetic Speech Source Tracing

Open-set source tracing is increasingly framed as a verification problem, motivating the use of pairwise metric-learning objectives from biometrics. We thus compare global anchoring and pairwise verification under matched backbones and a fixed data and epoch budget on MLAAD (in-domain) and STOPA (out-of-domain). In our runs, global anchoring yields lower in-domain error (8.61% EER) than pairwise variants (12-15% EER), even with rival mining and XLS-R finetuning. Because pairwise objectives optimize similarity directly, they concentrate variance into fewer embedding directions, reducing resolution among closely related generators. To test if this drives the drop, we impose a similar bottleneck to the globally supervised baseline, yet the baseline remains competitive. Together with an embedding-space analysis (

k_{99}

), these results suggest that the gap is not explained by dimensionality alone, but rather by the pairwise objective's shaping of the retained directions.

Anton Firc, Zbyněk Lička, Vojtěch Staněk +1

Representation Geometry Speaker Verification Metric Learning

May 22, 2026stat.ML

Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models

Individual fairness, the notion that "similar individuals should be treated similarly," provides a strong and flexible fairness guarantee for algorithmic decision makers. However, a barrier to implementing individual fairness in practice is the difficulty of learning the similarity metric over individuals. In this work, we present an algorithm for learning a Mahalanobis similarity metric from triplet queries of the form "is individual

i

more similar to individual

j

or

k

?" We work in the standard Bradley-Terry model for pairwise comparisons. Our algorithm consists of a spectral initialization step followed by gradient descent. We provide extensive theoretical guarantees on our algorithm, showing that it converges quickly to the ground truth metric despite the non-convexity of the loss in our model. Because our focus is on fairness, we also show that individual fairness with respect to an estimated metric is sufficient to achieve similar fairness with respect to the true metric. We also discuss potential applications of our work to AI model tuning. Finally, we present experimental results that demonstrate the convergence of our algorithm and the fairness performance of downstream fair predictors trained on our estimated metric.

Conlan Olson, Linjun Zhang, Zhun Deng +1

Columbia University · Rutgers University · UNC Chapel Hill +1

Mahalanobis Distance Algorithmic Fairness Metric Learning Bradley–Terry Model Preference Learning

May 19, 2026cs.AI

High Quality Embeddings for Horn Logic Reasoning

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.

Yifan Zhang, Yasir White, Dean Clark +4

Lehigh University, Computer Science and Engineering, 113 Research Dr., Bethlehem, PA, 18015 · Los Angeles Pierce College, Computer Science, 6201 Winnetka Ave, Woodland Hills, CA 91367 · Colorado College, Computer Science, 14 E Cache La Poudre St, Colorado Springs, CO 80903

Logical Reasoning Metric Learning Neuro-Symbolic Reasoning

May 17, 2026cs.CR

Few-Shot Network Intrusion Detection Using Online Triplet Mining

Network intrusion detection systems play a vital role in protecting networks by detecting malicious network traffic which can then be investigated by a cybersecurity operations centre. State-of-the-art approaches utilise supervised machine learning methods to train a classification model to recognise known cyberattacks; however, these models require a large labelled dataset to train and show poor performance when trained on smaller datasets. In an attempt to address this shortcoming, anomaly detection models learn the distribution of benign traffic and flag non-conforming traffic as malicious. While these methods do not require malicious examples to train, they suffer from high false-positive rates rendering them impractical. As a result, networks may be particularly vulnerable when there are insufficient labelled instances of a specific attack class to train an effective classifier. This often occurs in newly established networks or when previously unseen types of attacks emerge. To address this challenge, this work proposes the use of a triplet network, utilising online triplet mining and a KNN classifier, which is able to perform few-shot classification, enabling effective intrusion detection after being trained on a limited number of malicious examples. Various online triplet mining algorithms were explored and model design choices, such as the inference algorithm and optimised distance metrics, were compared and evaluated through a series of ablation studies. The final model was compared against other state-of-the-art approaches in few-shot binary and multiclass classification, where the proposed approach was found to be competitive with existing methods when trained on as little as 10 malicious samples of each class.

Jack Wilkie, Hanan Hindy, Christos Tachtatzis +2

Department of Electronics and Electrical Engineering, University of Strathclyde, Glasgow G1 1XQ, UK · Faculty of Computer and Information Sciences, Ain Shams University, Cairo 11566, Egypt · Faculty of Electrical Engineering, Czech Technical University, 160 00 Prague, Czech Republic

Network Intrusion Detection Few-Shot Learning Metric Learning