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19 papers in the last four weeks, up 19% on the four weeks before. 0.2% of all new papers.

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Latest papers 149

Jun 30, 2026cs.AI

Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing

Large-scale capacitated vehicle routing problems (CVRPs) are commonly addressed using cluster-first route-second (CFRS) approaches that split a routing instance into smaller, computationally tractable subproblems. Existing splitting methods typically rely on fixed partitioning rules, predefined optimization objectives, or learned policies, which may perform inconsistently across instances exhibiting different spatial, demand, and operational characteristics. In this work, we propose an adaptive CFRS system that formulates a decomposition procedure as an iterative decision-making process. Motivated by the recent success of large language models (LLMs) in reasoning and tool selection, the system employs an LLM as a high-level decision maker that analyzes the evolving decomposition state and selectively applies further clustering, balancing, and refinement operators. The proposed algorithm jointly partitions customers and vehicles, enabling capacity-aware clustering while adapting partitioning decisions to the characteristics of each problem. We evaluate the approach on synthetic and benchmark-derived CVRP instances containing up to 500,000 customers. Experimental results demonstrate competitive performance on benchmark-scale instances while exhibiting improved scalability and robust routing quality on substantially larger problems. These results highlight the potential of adaptive, LLM-guided decision support as a practical approach for industrial-scale vehicle routing and large-scale logistics planning.

Oguzhan Karaahmetoglu, Hyong Kim

Carnegie Mellon University · Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA

Vehicle Routing Problem Large Language Model Routing Decomposition

Jun 30, 2026cs.GR

Intrinsic decomposition and editing of 3D Gaussian splats

Intrinsic decomposition which expresses image colors as the product of diffuse albedo and shading, possibly augmented with view-dependent residuals has a long history in image editing as it enables the modification of object colors and textures without altering lighting. We extend intrinsic decomposition to radiance fields represented with Gaussian splatting by proposing solutions to three key aspects of such decomposition. First, we describe how to model the intrinsic decomposition as independent sets of Gaussian primitives, which allows each set to adapt to the characteristics of the layer it represents. Second, we present an optimization procedure guided by data-driven predictions to disentangle multi-view photographs of a scene into the aforementioned intrinsic sets. Finally, we provide an editing workflow where users modify the texture of planar surfaces simply by modifying the albedo of that surface in one image. Capturing this edit within the intrinsic radiance field allows re-rendering of the edited scene with plausible lighting under arbitrary viewpoints.

Alexandre Lanvin, Jeffrey Hu, Simon Lucas +2

Inria, Université Côte d’Azur, France · Cambridge University, United Kingdom

Image Editing Basis Decomposition 3D Generation Decomposition

Jun 30, 2026cs.CR

The Decomposition Is the Fingerprint: Per-Component Identity for Agent Skills

AI agents increasingly acquire and execute skills at runtime: bundles of prompt instructions, executable code, and tool declarations fetched from marketplaces and other agents. Governing them needs a stable notion of skill identity, yet cryptographic hashing is engineered to destroy the very similarity we need, as a one-character edit scrambles the digest. We present a compact, locality-sensitive fingerprint that embeds each component of a skill and projects it to bits with a multi-bank SimHash, giving a fixed 120-byte signature compared in constant time by Hamming distance. Our central claim is that keeping the fingerprint as a per-component triple (prompt, code, tools), rather than a single score, is what makes it useful: the triple recovers skill-family identity through paraphrase, renaming, refactoring, and controlled code translation when another component remains shared, while independent multilingual reimplementation is not recovered; it also localizes which component carries the reuse. We claim lineage, not behavioral equivalence: identity supplies the structural axis of a registry and leaves safety to behavioral verification. The fingerprint reaches an area under the ROC curve (AUC) of 0.974 (95% CI [0.956, 0.994]) over 4,950 pairwise comparisons while using 77x fewer bits than the embedding it approximates, with ranking preserved in expectation and finite-bit concentration; the per-component split turns one number into relationship classification, families, novelty, and a portable "SkillBOM" for a skill registry. On a 906-skill injection benchmark the fingerprint recognizes injected skills as tampered copies of a known base and localizes the change, but recognition is not trust: it remains, by design, an identity signal complementary to behavioral verification rather than a safety verdict.

Hongliang Liu, Yuhao Wu, Tung-Ling Li

Palo Alto Networks

Skills Fingerprint Locality-Sensitive Hashing Artificial Intelligence Agents Decomposition

Jun 30, 2026math.NA

Online TT-ALS for Streaming Tensor Decomposition with Incremental Orthogonalization

Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data. Existing algorithms for computing TT decompositions can be categorized into two main types: conventional batch-based approaches and recursive online methods. In the context of streaming data, batch methods typically achieve higher reconstruction accuracy but often suffer from memory exhaustion, while online methods provide greater computational efficiency. In this work, we introduce Online TT-ALS (Alternating Least Squares), an algorithm that sequentially enforces orthogonality constraints. This approach allows for efficient and exact updates of the core tensor while maintaining high reconstruction accuracy. Theoretically, we prove that enforcing these orthogonal gauge constraints guarantees monotonic decrease of the local objective function and temporal smoothness. Computationally, our deterministic single-sweep update reduces the rank dependence from quadratic to linear, achieving an overall complexity of

\mathcal{O}(I^{n-1} r)

. Experimental results demonstrate that the proposed method outperforms existing online techniques not only in terms of mathematical approximation accuracy but also in human perception-based video quality metrics. Furthermore, compared to recent deep learning-based paradigms, our algebraic approach achieves speedups of several orders of magnitude. Consequently, our method exhibits high computational efficiency and is suitable for low-latency real-time processing applications.

Hiroki Takeda, Yuto Miyatake, Daisuke Furihata

Department of Pure and Applied Mathematics, The University of Osaka, Japan · D3 Center, The University of Osaka, Japan

Tensor Decomposition Reconstruction Fidelity Decomposition

Jun 29, 2026cs.CG

Computing the Integral R2 Indicator by Perspective Mapping and Box Decomposition

The continuous integral R2 indicator is a Pareto-compliant refinement of the classical finite-weight-vector R2 indicator, used in performance assessment, bounded archiving for a-posteriori multi-objective optimization, and skyline selection in databases. This work introduces a bidirectional perspective mapping between continuous integral R2 computation and integration over unions of anchored axis-aligned boxes. After translating the ideal point of a minimization problem to the origin, approximation points become strictly positive loss vectors, and the subgraph of the lower weighted Tchebycheff envelope over the weight simplex maps to the complement of an anchored-box union in reciprocal objective space. The Jacobian gives an absolute R2 formula as a weighted complement volume with density

(x_1+\cdots+x_N)^{-(N+1)}

, while differences of R2 values become finite weighted hypervolume differences. Hence, hypervolume algorithms that emit box decompositions can be reused by replacing ordinary box volumes with closed-form weighted box integrals. For

N

objectives, this gives an output-sensitive overhead

O(2^N M)

for an

M

-box decomposition, or

O(M)

for fixed

N

. Using existing box-decomposition approaches, the integral R2 can be computed in

O(n \log n)

for

N=2,3

, in

O(n^2)

for

N=4

, and in

O\left(n^{\lfloor (N-1)/2\rfloor+1}\right)

for

N\geq4

, with

n

denoting the size of the approximation set. On the lower-bound side, exact value computation has an

Ω(n\log n)

lower bound in the algebraic decision-tree model already in two objectives, this bound lifts to every fixed

N\geq2

, and exact computation is

\#P

-hard when

N

is part of the input. Together, the proposed perspective mapping provides a powerful tool for transferring algorithmic and structural results between anchored-box union and hypervolume theory and integral R2 computation.

Michael T. M. Emmerich

Faculty of Information Technology, University of Jyväskylä, Finland

Integral Multi-Objective Optimization Volume Decomposition Perspective

Jun 29, 2026cs.CV

A Dual-domain Refinement Network with FBP-based Jacobian Learning for Sparse-view Dual-Energy CT Material Decomposition

Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely used in medical imaging. While sparse-view acquisition can lower radiation exposure, it makes DECT material decomposition even more challenging, as the problem is nonlinear and ill-posed. Existing deep unrolling approaches generally do not explicitly incorporate the Jacobian operator induced by the nonlinear forward model, and their sparsity priors are still mainly built on conventional convolutions, which are insufficient for modeling global structural information. This study addresses the challenge of DECT multi-material decomposition in sparse-view settings by representing it as a sparse-regularized nonlinear least-squares problem. To solve it, we propose an iterative dual-domain refinement network (DECT-DRNet). In each iteration, the filtered back-projection (FBP)-based Jacobian approximation module is used first to generate an intermediate material decomposition result. Here, we characterize the forward process of material decomposition using a nonlinear operator, and then construct a theoretically grounded learnable approximation of the adjoint Jacobian operator by integrating the FBP algorithm with a U-Net into the backward process. In addition, to address the limitation of existing deep learning-based decomposition methods in globally suppressing noise and artifacts, we introduce a learnable sparse dual domain regularization term that incorporates Fourier convolutional residual blocks. This refinement block combines geometric feature extraction in the image domain with noise suppression in the frequency domain, allowing the model to capture both global and local features while maintaining structural details. DECT-DRNet demonstrates its ability to achieve more accurate material decomposition under sparse-view conditions.

Qian Liu, Xiaohong Fan, Ke Chen +3

School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education, Xiangtan 411105, China · College of Mathematical Medicine, Zhejiang Normal University, Jinhua 321004, China · Department of Mathematics and Statistics, University of Strathclyde, G1 1XH Glasgow, U.K. +1

Cone-Beam Computed Tomography Deep Unfolding Networks Sparse-View Decomposition Jacobian Regularization

Jun 23, 2026cs.CL

Task Decomposition for Efficient Annotation

High-quality annotations of structured representations are expensive to collect over large corpora. Manual annotation of structure is laborious, and model-based annotation, although cheaper to generate, requires expensive validation and potentially significant supervision to ensure that the annotation quality is strong enough to be useful downstream. In traditional annotation workflows, annotation of each complete example is performed end-to-end by a single annotator. However, structured annotation is complex, and each aspect of the task represents a unique challenge with an associated inferential load for a given annotator. Modern annotation projects can incorporate heterogeneous groups of annotators, including both models and human annotators with varying domain and linguistic expertise. It remains unclear, however, how to redesign annotation tasks in this setting, where efforts are discriminately allocated across heterogeneous annotators with respect to distinct annotation challenges. We propose to decompose annotation tasks into sub-tasks in order to reduce the aggregate inferential load of annotation projects. Inspired by the notion of centers from centering theory, we introduce a formal model of inferential load based on the degrees of freedom in the space of valid annotations. Using this model, we show that identifying these centers (i.e. salient anchor entities realized by annotation sub-tasks) constrains the output space complexity, and decompositions which isolate and advance center identification reduce the aggregate inferential load. We provide guidelines for decomposing complex structured annotation tasks, supported by examples demonstrating improved cost-efficiency from our prior work. Finally, we present a procedure for allocating sub-tasks across annotators to maximize quality under a fixed budget.

Nupoor Gandhi, Emma Strubell

Carnegie Mellon University

Annotations Decomposition Linguistics

Jun 22, 2026q-bio.GN

Privacy-preserving federated tensor decomposition of single-cell immune data: recovering multicellular programs across institutions

Tensor decomposition of donor

\times

cell-type

\times

gene single-cell data recovers \emph{multicellular programs}: coordinated axes of inter-individual transcriptional variation that span cell types and stratify disease. Yet immune single-cell atlases are increasingly multi-institution, multi-ancestry, and governed, so patient cells often cannot be pooled. We present a federated estimator: each site computes a local program subspace, and a coordinator merges these by stacked SVD under federated global-mean centering, provably equivalent (up to truncation) to the centralised decomposition. This centering makes the merge robust to site-label confounding (program AUC

0.957

vs.\

0.861

for naive per-site centering). Only program subspaces leave a site, and aggregation is compatible with secure aggregation. On a 261-donor systemic lupus erythematosus atlas it recovers the canonical interferon program (ISG enrichment AUC

0.998

; case--control separation

0.958

; bootstrap

Δ\text{AUC}=-0.000

, 95% CI

[-0.004,+0.012]

vs.\ centralised), across institution-scale and multi-ancestry partitions, and across three \emph{real} COVID-19 sites (subspace correlation

0.989

). It recovers the program when \emph{no site observes all cell types} (correlation

1.000

, exact by construction), which fixed-feature federated PCA cannot. On an interstitial-lung-disease atlas the recovered program predicts disease better than the best single cell type (AUC

0.96

vs.\

0.91

; gap 95% CI excludes zero) and the advantage survives federation; a liver cohort is consistent (

p=0.005

). Membership-inference shows secure aggregation cuts attack AUC from

0.91

to

0.61

. The method enables cross-institution, cross-ancestry recovery of multicellular immune programs without sharing cells.

Axel Faes, Stephanie M. van den Berg, Maryam Amir Haeri

Data Science Institute, Hasselt University, Belgium · University of Twente, The Netherlands · Learning, Data Analytics and Technology, University of Twente, The Netherlands

Single-Cell Rna Tensor Decomposition Decomposition Institutions

Jun 20, 2026cs.LG

Ranking-and-Selection with Multiple Correct Answers and Non-Answerable Estimates

We study fixed-precision ranking-and-selection in structured settings where the answer may be non-unique and where noisy estimates may temporarily admit no valid answer at all. This phenomenon arises naturally in problems such as multi-fidelity ranking-and-selection and identifying a Condorcet winner from pairwise comparisons. To address this, we propose a unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and an answer-pitfall decomposition that yields a max-max-min characteristic value and a common sampling principle. We introduce ENDS, a general procedure that combines estimation, nomination, pitfall detection, and cost-aware information-directed selection. We instantiate ENDS for various problems by deriving explicit formulas. Extensive numerical experiments show that this unified recipe performs well across a broad range of pure-exploration problems and offers a practical framework and proof-of-concept algorithmic recipe.

Qiaoqiao Wang, Wei You

Dept. of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Hong Kong, China

Selection Bias Ranking Finite-Sample Answer Stochastic Exploration Acceptance+1

Jun 19, 2026cs.LG

Targeted Recovery of Weight-Space Mechanisms From Neural Networks

Parameter decomposition (PD) decomposes neural networks into interpretable computational components that faithfully reflect the original network's operations. However, scaling PD to large models requires vast compute, making it a costly and risky endeavor. Here we propose targeted PD (tPD), which identifies only the components that process specific inputs of interest -- from isolated prompts to large subtasks -- by introducing a high-rank catch-all component that handles all non-target data. We validate tPD on toy models and on transformer language models trained on The Pile, where it recovers reproducible, mechanistically faithful circuits. We extract a CSS-only submodel of a 4-block transformer using 7% of the FLOPs of its published decomposition, and in a 12-block transformer we surgically ablate and rewire memorized sequences, with negligible side effects on other inputs.

Antoine Vigouroux, Lee Sharkey

1MATS · 2Goodfire

Model Weights Neural Network Weight-Space Decomposition Energy-Based Transformer

Jun 18, 2026cs.CL

CREDENCE: Claim Reduction for Decomposition & Enhanced Credibility -- Semantic Metrics and Convergence Analysis

Decomposing compound sentences into atomic, verifiable claims is a prerequisite for reliable automated fact-checking. Prior work has relied on token-overlap (Jaccard) metrics that systematically underestimate decomposition quality for paraphrastic claims, and has lacked formal termination analysis for the repair loop. We present Credence, a revised claim decomposition and evaluation framework addressing both shortcomings. Our contributions are: (1) Semantic-F1: we use BGE-large cosine similarity fidelity metric that resolves Jaccard's penalisation and improves downstream fact-checking accuracy; (2) Convergence theorems: we formally characterise four properties of the repair pipeline, establishing that rule-based repair is monotone and finitely terminating under an oracle parser assumption; LLM-based self-repair is provably non-monotone and requires an early-exit guard; (3) Three evaluation benchmarks spanning social-media, encyclopaedic, and news domains for cross-domain generalisation measurement; (4) Multi-model benchmarking across four decomposer models (3.8B-12B) and a closed API model. Experiments on SocialClaimSplit, WikiSplitBench, and ClaimDecompBench show that Semantic-F1 outperforms Jaccard-F1 by +15-32pp. EPR ranges from 0.94 to 1.00 on SocialClaimSplit and WikiSplitBench, while ClaimDecompBench includes lower base EPR cases (down to 0.824) due to harder news-domain constructions, and rule-repair reduces the Atomicity Violation Rate (AVR) by 47-100% relative to the base model without degrading fidelity.

Phuong Huu Vu Tran, Thuan Duc Mai, Bach Xuan Le

Vietnamese-German University, Ho Chi Minh City, Vietnam · Ho Chi Minh University of Technology, Ho Chi Minh City, Vietnam

Fact-Checking Credibility Entailment Paraphrasing Decomposition Convergence

Jun 17, 2026stat.ML

The Representational Limit of Scalar Interactions: An Interventional Decomposition

Signed pairwise interaction scores fundamentally conflate uniqueness (U), redundancy (R), and synergy (S). We prove this on a minimal 3-way XOR structural causal model: faithful indices such as Shapley-Taylor return zero per pair, whereas projective indices such as Shapley Interaction spread the third-order effect into pair scalars that conflate the three mechanisms. We introduce Stochastic Hi-Fi, a post-hoc, retraining-free predictability decomposition that estimates per-feature U/R/S profiles by interventional masked inference. The estimator provides exact interventional semantics, finite-sample Monte Carlo bounds, strict variance reduction from coupled diamond sampling, and uniform finite-vocabulary convergence. Across tabular SCMs, Stochastic Hi-Fi recovers structure missed by scalar baselines (up to 411x larger interaction-magnitude recovery ratios). It also separates redundant and synergistic heads in the GPT-2 IOI circuit. On NIH ChestX-ray14, Stochastic Hi-Fi matches GradCAM on Pointing Game and improves substantially on Deletion AUC.

Potito Aghilar, Sabino Roccotelli, Stanislao Fidanza +3

Polytechnic University of Bari · University of Bari Aldo Moro

High-Order Correlations Post-Hoc Decomposition Representational Capacity

Jun 17, 2026cs.CR

OpenAnt: LLM-Powered Vulnerability Discovery Through Code Decomposition, Adversarial Verification, and Dynamic Testing

Automated vulnerability discovery in large codebases remains challenging: traditional static analysis produces high false-positive rates, while dynamic approaches such as fuzzing require substantial infrastructure and often target narrow classes of bugs. Recent advances in large language models (LLMs) enable semantic reasoning about program behavior, but applying LLMs to repository-scale security analysis introduces challenges related to context management, cost, and verification. We present OpenAnt, an open-source vulnerability discovery system that integrates static program analysis with LLM-based reasoning in a multi-stage pipeline. OpenAnt introduces three key techniques. First, codebases are decomposed into self-contained analysis units filtered by reachability from external entry points, reducing the analysis surface by up to 97% while preserving attack-relevant code. Second, candidate vulnerabilities undergo adversarial verification through constrained attacker simulation, where the model evaluates exploitability under realistic attacker capabilities. Third, findings are validated through dynamic verification, in which exploit environments are generated automatically, executed in sandboxed containers, and discarded after use. Evaluation on widely used open-source projects including OpenSSL, WordPress, and Flowise shows that this architecture can identify previously unknown vulnerabilities while maintaining manageable analysis cost and substantially reducing false positives. Our results suggest that closed-loop vulnerability discovery pipelines, combining semantic reasoning with exploit validation, provide a practical path toward scalable automated security analysis. OpenAnt is released as open source under the Apache 2.0 license at https://github.com/knostic/OpenAnt.

Nahum Korda, Gadi Evron

Knostic

Program Analysis Decomposition

Jun 16, 2026cs.CL

Compositional Skill Routing for LLM Agents: Decompose, Retrieve, and Compose

LLM agents increasingly rely on external skills -- reusable tool specifications -- but real-world tasks often require composing multiple skills, not just selecting one. We formalize this as the Compositional Skill Routing problem: given a complex user query and a large skill library, decompose the query into atomic sub-tasks, retrieve the appropriate skill for each sub-task, and compose an executable plan. We present SkillWeaver, a decompose-retrieve-compose framework combining an LLM task decomposer, a bi-encoder skill retriever with FAISS indexing, and a dependency-aware DAG planner. To support evaluation, we introduce CompSkillBench, a benchmark of 300 compositional queries over 2,209 real MCP server skills spanning 24 functional categories, sourced from the public MCP ecosystem. Our experiments reveal that task decomposition quality is the primary bottleneck: standard LLM decomposition reaches only 34.2% category recall at the step level. To address this, we propose Iterative Skill-Aware Decomposition (SAD), a retrieval-augmented feedback loop that iteratively aligns decomposition with available skills. SAD improves decomposition accuracy from 51.0% to 67.7% (+32.7%, Wilcoxon p < 10^-6) in a single iteration; DA-conditioned analysis confirms that correct granularity is the prerequisite for effective retrieval (CatR@1 rises from 34% to 41% when DA=1). SkillWeaver reduces context window consumption by over 99%, and transfer experiments confirm generalization (+35.6% relative DA gain even when target categories are absent from the retrieval pool).

Xueping Gao

Alibaba Cloud Hangzhou, China

Large Language Model Agents Weave Decomposition

Jun 14, 2026cs.CR

Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliably

We ask a structural question: given unreliable elementary problem-solvers, what organizations of them solve hard problems reliably, and what are the limits? We develop a

decomposition~algebra

: elementary solvers are morphisms in a stochastic category, and four combinators (sequential composition, parallel ensembling, verification gating, and recursive reduction) generate the space of compound solvers. We equip this algebra with two homomorphisms, a

reliability

valuation into the ordered monoid

([0,1],\le)

and a

cost

valuation into a commutative semiring, and we derive the composition laws that govern how reliability flows through structure. Our central results are (i) a

verification~odds~law

(the result that names this report), showing that a verification gate multiplies the odds of correctness by the verifier's likelihood ratio

Λ

, so that

k

conditionally independent gates yield geometric amplification; (ii) a

reliability~amplification~theorem

, giving target reliability

1-δ

at

O(\log 1/δ)

verification depth whenever

Λ>1

; and (iii) a

threshold~dichotomy

: above the critical parameters reliability can be driven arbitrarily close to one at logarithmic cost, while at or below them no amplification is possible. We then show that

self-organization

is the least fixed point of a monotone improvement operator on the complete lattice of strategies, and that this fixed point equalizes marginal log-odds gain per unit cost. Finally, we prove matching limits: an information ceiling bounds per-gate amplification by a divergence quantity; shared error causes create a strictly positive voting floor, so diversity is

necessary

for unbounded amplification. Reliability, in short, is neither free nor magical: it is bought with independent information, arranged by composition, and bounded by the verifier.

Hidayet Aksu

Algebraic Structures Verification Framework Decomposition Reasoning Errors Hard Betting+1

Jun 14, 2026cs.CV

Fusing Transferred Priors and Physics-based Decomposition for Underwater Image Enhancement

The underwater images are captured within diverse water-medium conditions, leading to complex degradation, including color bias, low contrast, and blur effect. Recently, learning-based methods have demonstrated their potential for underwater image enhancement (UIE). However, most of the previous work focus on the training strategy or network design to make the enhanced result aligned well with the labels in datasets, ignoring that the labels are selected from the enhanced results of previous UIE methods and these pseudo-labels are noisy. Consequently, the performance of their models is not satisfactory to a certain extent. However, collecting the true labels of the underwater images is challenging. In this work, we propose a transfer learning-based UIE that does not require underwater images to have paired noisy or true labels for learning. Instead, the UIE task is first divided into global color correction, haze removal, and background noise suppression following the underwater physics. Then multiple types of prior from other vision tasks are leveraged as cross-domain supervision in each step. In this way, a novel UIE is available via transfer learning, and the physics-aligned UIE decomposition provides theoretical soundness. Qualitative and quantitative experiments demonstrate that our proposal based on physics and priors fusion achieves SOTA performance in the UIE task and effectively boosts downstream vision tasks, significantly outperforming benchmark methods. Project repo: https://github.com/Haru2022/P2-UIE.

Haochen Hu, Yanrui Bin, Zhengyan Zhang +3

The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR

Underwater Image Enhancement Methods Underwater Visual Priors Unpaired Image-To-Image Translation Transfer Learning Decomposition

Jun 12, 2026cs.LG

Decompose Sparsely Where You Should, Absorb Densely Where You Should No

Sparse autoencoders (SAEs) are typically trained to reconstruct the \textbf{entire} residual stream through a sparse dictionary, implicitly assuming that all activation content is amenable to sparse, monosemantic decomposition. We question this assumption and hypothesize that activations contain a low-rank, dense component that is computationally important to the model yet inherently unsuitable for sparse representation, which serves as a major source of the persistent dense latents widely observed in trained SAEs. To test this, we add a small rank-

r

linear bottleneck in parallel with standard SAEs (BatchTopK and Matryoshka), allowing dense structure to be absorbed before sparse reconstruction. On Gemma-2-2B layer 12, a rank-24 bottleneck reduces dense latent count by up to 84% while improving sparse probing and targeted probe perturbation on both architectures at matched sparsity. The absorbed component is (i) \textbf{structurally identifiable} as the top principal components and outlier dimensions; (ii) \textbf{causally necessary}, with removing it raising next-token cross-entropy by 7.5

\times

, far exceeding the 2.8

\times

from removing the geometrically near-identical top-24 PCA directions; and (iii) \textbf{redundantly encoded by sparse dictionaries}, with ablating 787 maximally aligned sparse features raising cross-entropy by only 2.9

\times

and ablating 2,048 topic-aligned features leaving MMLU topic classification virtually unchanged, whereas removing the scaffold drops it from 98.7% to chance. Together, our findings identify a compact, semantically informative and causally important component of residual stream activations (which we term a \textbf{computational scaffold}) that standard sparse dictionaries represent inefficiently, suggesting that the scope of sparsity-based interpretability methods warrants careful re-examination.

Ruixuan Deng, Zehao Jin, Zekun Wang +1

School of Psychology Georgia Institute of Technology · College of Computing Georgia Institute of Technology · School of Interactive Computing Georgia Institute of Technology

Improving Sparse Autoencoders Sparsity Model Activations Sparse Supervision Decomposition Mmlu-Pro

Jun 11, 2026cs.CL

Operads for compositional reasoning in LLMs

Question decomposition, i.e. breaking a complex query into simpler sub-queries whose answers are composed to produce a final answer, is a widely used strategy for improving LLM reasoning, yet it currently lacks a rigorous mathematical foundation. In this paper, we propose operads, mathematical structures that model many-in, one-out operations and compositions thereof, as a natural framework for describing question decomposition. We define the questions operad

Q

, in which operations correspond to question templates and composition corresponds to substitution of sub-answers, and show how QA models can be interpreted as algebras over

Q

. Beyond reframing existing practice, this operadic perspective points toward new methods, in particular a notion of operadic consistency, which measures whether a QA model's answers agree across the partial collapses of a question decomposition tree. Empirical evaluation of operadic consistency is reported in our companion paper (Bottman, Liu, and Richardson, 2026), which finds it strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets and outperforming standard temperature-based self-consistency baselines. We argue that operads are the natural mathematical home for question decomposition, and that invariants such as operadic consistency open new directions for analyzing and improving the reliability of multi-step reasoning.

Nathaniel Bottman, Kyle Richardson

Incubilate, Seattle, USA · Allen Institute for Artificial Intelligence, Seattle, USA

LLM Reasoning Strategies Decomposition

Jun 11, 2026cs.AI

From Verdict to Process: Agentic Reinforcement Learning for Multi-Stage Fact Verification

Recent approaches combining Large Language Models (LLMs) with retrieval-augmented reasoning have shown promise for automated fact verification. To process complex claims, these verification pipelines typically execute multi-stage workflows that coordinate tightly coupled modules, including claim decomposition, evidence gathering, and verdict prediction. However, existing methods optimize individual stages in isolation or rely on fixed heuristics, which limits adaptive coordination among stages and can lead to suboptimal outcomes. In this work, we propose ProFact, an agentic reinforcement learning framework for end-to-end optimization of multi-stage fact verification trajectories. ProFact trains a unified policy to coordinate claim decomposition, evidence seeking, answer generation, and verdict prediction. To address the sparse and delayed supervision provided by final veracity labels, ProFact introduces process-aware rewards that provide stage-level learning signals throughout the verification process. Empirical evaluation shows that ProFact consistently outperforms strong baselines in both verification performance and inference efficiency. These results highlight the effectiveness of process-aware trajectory optimization for multi-stage fact verification.

Rongxin Yang, Shenghong He, Siyuan Zhu +1

School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China

Fact-Checking Reference-Guided Multimodal In-Context Verification Agentic Learning Agentic Reinforcement Learning Data Generation Decomposition

Jun 7, 2026cs.LG

Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.

Stéphane Eilles-Chan Way, Hugo Percot, Quentin Cappart +2

Polytechnique Montréal, Montreal, Canada · Ecole Polytechnique, Palaiseau, France · UCLouvain, Louvain-la-Neuve, Belgium +2

Linear Programming Decentralized Optimization Portfolio Optimization Decomposition Lagrangian Methods Scaling

Jun 5, 2026math.OC

The Proxy Benders Decomposition

Benders decomposition is a fundamental framework for solving large-scale mixed-integer optimization problems with complicating variables that, when fixed, yield significantly easier subproblems. However, classical Benders decomposition repeatedly solves highly similar subproblems and often exhibits zigzagging behavior across iterations, leading to slow convergence in large-scale settings. Motivated by the repetitive structure and parametric nature of Benders subproblems, this paper introduces the proxy Benders decomposition (Proxy-BD), a new decomposition framework in which subproblem optimization is replaced by certified optimization proxies rather than repeated exact solves. The proposed proxy follows a self-supervised predict-project-and-complete mechanism that produces dual-feasible solutions for generating provably valid Benders cuts. The framework preserves the theoretical validity of the decomposition independently of prediction quality through a projection-and-completion certification layer. A formal characterization of proxy-induced cuts is established, and the framework naturally extends to modern decomposition schemes, including branch-and-Benders-cut algorithms. Computational experiments on large-scale facility location and network design problems demonstrate that Proxy-BD substantially reduces the computational effort of subproblems while maintaining near-optimal solution quality. On large-scale uncapacitated facility location instances up to 2000x2000, Proxy-BD achieves median optimality gaps below 0.5%, yields up to 161x median speedups, and reduces the number of generated cuts by more than 240x on the largest instances. The computational gains consistently increase with recourse complexity, indicating that proxy-based inference scales substantially more favorably than repeated exact subproblem optimization in large-scale decomposition settings.

Changkun Guan, El Mehdi Er Raqabi, Mathieu Tanneau +1

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA · Department of Operations and Decision Systems, Université Laval, Quebec, Canada

Mixed-Integer Programming Solvers Decomposition Self-Supervised Learning

Jun 5, 2026cs.CL

SigmaScale: LLM Compression with SVD-based Low-Rank Decomposition and Learned Scaling Matrices

We present SigmaScale, a method for learning auxiliary scaling matrices

S

to aid truncated Singular Value Decomposition (SVD) based Large Language Model (LLM) compression. Instead of deriving scaling matrices analytically, SigmaScale optimizes two sets of vectors that define diagonal row and column scaling transformations under an activation-aware compression loss. We show that learned scaling lowers the effective intrinsic rank of weight matrices, as reflected by reductions in effective-rank entropy, and that this reduction is strongly correlated with compression loss. Experiments on Llama 3.1 8B Instruct and Qwen3-8B show that SigmaScale is competitive with closely related state-of-the-art SVD-based compression methods across perplexity and zero-shot benchmarks. By using learned activation-aware transformations, SigmaScale explores a more flexible route to low-rank LLM compression by adapting to the structure of individual model weights. The advantage observed in specific tasks makes our approach a valid option for applications requiring a reduced LLM-inference computing cost.

Ernests Lavrinovics, Marco Letizia, Roy Janco +3

Department of Computer Science, Aalborg University Copenhagen, Denmark · MaLGa-DIBRIS, University of Genoa, Genoa, Italy · INFN, Sezione di Genova, Genoa, Italy +2

Large Language Model Compression Data Compression Methods Decomposition

Jun 4, 2026cs.IR

Agent-Orchestrated Adaptive RAG: A Comparative Study on Structured and Multi-Hop Retrieval

Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by grounding their responses in external knowledge, but conventional pipelines rely on static, single-step retrieval that limits performance on complex queries. This paper presents an Agent-Orchestrated Adaptive RAG framework that introduces dynamic query decomposition, iterative retrieval, and a bounded self-reflective evaluation loop. We evaluate the system across two complementary datasets: a domain-specific DevOps knowledge base and the multi-hop reasoning benchmark MuSiQue. Using metrics that include overall score, citation accuracy, mean reciprocal rank, and topic coverage, we find that query decomposition yields consistent gains in the structured domain (overall score

+0.04

, MRR

+0.17

on DevOps) but degrades ranking precision on the multi-hop benchmark, while the reflection mechanism improves citation accuracy at a substantial latency cost. These contrasting results show that agentic enhancements are not universally beneficial and must be applied selectively according to query and domain characteristics. Our findings argue for adaptive, cost-aware orchestration rather than uniformly aggressive reasoning pipelines.

Anuj Maharjan, Devinder Kaur, Richard Molyet

Dept. of Electrical Engineering and Computer Science University of Toledo Toledo, OH, USA

Agentic Retrieval-Augmented Generation Systems Decomposition

Jun 3, 2026cs.LG

TD-Grokking: Learning from Zero-Reward Problems by Training-Time Decomposition

Large language models (LLMs) have made remarkable progress in reasoning tasks, largely driven by post-training paradigms, especially reinforcement learning with verifiable rewards (RLVR). However, a critical bottleneck persists: RLVR fails on highly challenging zero-reward problems, where all sampled reasoning trajectories yield uniformly failed outcomes, providing no optimization signal to drive model improvement. Prior efforts to address this limitation, such as dense process supervision, partial reward assignment, or prefix-guided exploration, suffer from inherent task constraints or do not fully equip the policy model with the capabilities necessary to solve the original intractable problems. To address this, we propose TD-Grokking, a training-time decomposition framework for zero-reward problems. It recursively decomposes intractable root problems into self-contained, verifiable subproblems, forming hierarchical trees where solvable leaves provide non-zero rewards. Evaluations on mathematical and medical tasks show that TD-Grokking outperforms vanilla GRPO as well as all baseline approaches. Together with detailed analysis, these results confirm that training-time decomposition effectively converts zero-reward examples into usable training signals, enabling consistent performance gains. Our code and datasets are available at https://anonymous.4open.science/r/TD-Grokking-6567/.

Ningyuan Xi, Hao Xu, Hongsheng Xin +1

Department of Data Science, City University of Hong Kong. · Hong Kong Institute of AI for Science, City University of Hong Kong. · Li Auto Inc.

Training Time Reasoning Skills Grokking Decomposition

Jun 2, 2026cs.CL

Rethinking the Idiomaticity Decomposability Hypothesis: Evidence from Distributional Learning

Idioms can be analysed in terms of their decomposability, the extent to which constituent meanings contribute to the figurative whole. Decomposability is thought to predict syntactic flexibility. Usage-based accounts instead attribute idiom behaviour to distributional experience, such as speaker familiarity and predictability. We examine these views using contextualised language models as controlled distributional learners. We propose a model-internal measure of decomposability and relate it to human ratings, syntactic flexibility, and predictability while tracking idiom learning during pretraining. Model-derived decomposability correlates weakly with human judgments and shows a small but consistent negative relationship with syntactic flexibility. Pretraining analyses show that stabilisation of idiom representations in models is not explained by frequency alone. Instead, surprisal, decomposability, and frequency all contribute, with decomposability showing the strongest training-dependent effect.

Maggie Mi, Golzar Atefi, Atsuki Yamaguchi +3

University of Sheffield · Berliner Hochschule für Technik (BHT) · University of Exeter +1

Idiom Syntactic Structure Language Modeling Decomposition Speaker

Jun 2, 2026cs.CV

TeX-1500: A Paired Real-World LWIR Hyperspectral Dataset and Benchmark for Temperature-Emissivity-Texture Decomposition

Temperature-emissivity-texture (TeX) decomposition seeks to recover object heat state, material spectral response, and visible-like geometric texture from long-wave infrared hyperspectral imaging (LWIR HSI). Existing TeX pipelines are mainly scene-specific inverse solvers, and the lack of paired LWIR HSI-TeX supervision has limited learning-based decomposition. To address this gap, we introduce TeX-1500, a large-scale paired LWIR HSI-TeX dataset and benchmark for supervised HSI-to-TeX decomposition. TeX-1500 contains 1,522 calibrated real-scene pairs from DARPA Invisible Headlights (DARPA IH) pushbroom imagery and our FTIR acquisitions, covering five locations, four seasons, diverse acquisition times, heterogeneous wavelength layouts, and two sensor families. Each sample stores a calibrated valid-band radiance cube, calibrated wavelength positions, and aligned temperature, emissivity, and texture supervision constructed through a consistent restoration and TeX-construction protocol. We further provide TeX-UNet, a simple wavelength-aware baseline that maps calibrated HSI bands and wavelength positions to TeX fields. Experiments on the held-out DARPA IH pushbroom scenes and zero-/few-shot transfer to FTIR scenes show that TeX-1500 provides usable paired supervision and a measurable benchmark for data-driven physical-property-centered thermal perception.

Cheng Dai, Jiale Lin, Hongyi Xu +3

School of Science, Westlake University, Hangzhou 310030, China · School of Engineering, Westlake University, Hangzhou 310030, China

Hyperspectral Image Reflectance Decomposition

Jun 2, 2026cs.CL

Beyond the Literal: Decomposing Pragmatic Intent in Multimodal Meme Understanding

When asked what a meme or sarcastic post means, Large Vision Language Models (LVLMs) tend to describe what the image shows rather than what the author is trying to communicate. Standard instruction tuning entangles a post's literal content with its pragmatic meaning, letting surface-level details contaminate the final response. We reframe meme understanding as a problem of literal-pragmatic decomposition and propose \textbf{Intent Projection}, a framework that separates the two signals at the representation, output, and objective levels within a single LVLM backbone. At the representation level, an orthogonal projection module removes dominant unimodal directions from the fused image-text representation, retaining only the pragmatic residual, while a surface-real affect classifier anchors the decoder with a discrete tag that names the polarity gap. At the output level, the model externalizes a structured reasoning chain, and at the objective level a contrastive reward explicitly penalizes answers that restate the literal description. Across six multimodal benchmarks, Intent Projection consistently outperforms open-source baselines and narrows the gap to proprietary models, with the largest gains on high-divergence posts where literal collapse is most damaging.

Zhengyi Zhao, Shubo Zhang, Zezhong Wang +6

The Chinese University of Hong Kong · Huawei · Central China Normal University +3

Memes Decomposition

Jun 2, 2026cs.LG

Bayesian Tensor Decomposition with Diffusion Model Prior

Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

Zerui Tao, Qibin Zhao

RIKEN Center for Advanced Intelligence Project (AIP), Tokyo, Japan.

Tensor Decomposition Diffusion Priors Low-Rank Structure Bayesian Posterior Decomposition+1

Jun 1, 2026cs.CV

Pave-GRPO: Beyond Instantaneous Guidance through Principled Average Velocity Decomposition

Post-training via Group Relative Policy Optimization (GRPO) has emerged as a powerful paradigm for aligning flow-based generative models with human preferences. However, the iterative denoising nature of flow models incurs substantial costs when generating group rollouts for policy-gradient updates, compelling existing methods to train with extremely few denoising steps. This temporal sparsity severely restricts preference optimization: reward feedback can only reach a handful of stages per trajectory, leaving the vast majority of intermediate denoising steps without direct supervision and thus compromising alignment granularity. To address this, we propose Pave-GRPO, which reformulates the GRPO objective through Principled average velocity decomposition. Rather than generating expensive high-step rollouts, we maintain efficient few-step group sampling but decompose each coarse transition into an equivalent ensemble of finer sub-trajectories spanning multiple intermediate timesteps. This propagates reward feedback to a denser set of temporal stages for more comprehensive preference alignment without additional generation cost. This design offers two benefits: (i) zero-cost horizon expansion: through the direct reuse of piece-wise group samples and their associated rewards, Pave-GRPO significantly broadens the effective optimization scope under fixed sampling budgets; and (ii) comprehensive temporal supervision: by equivalently decomposing an instantaneous velocity target into a multi-timestep ensemble, it distributes reward signals across more intermediate stages of the denoising process, enabling finer-grained and more thorough preference optimization. Extensive experiments validate that Pave-GRPO effectively advances preference alignment across different reward settings, offering comprehensive performance enhancement.

Pengyang Ling, Jiazi Bu, Yujie Zhou +6

University of Science and Technology of China, China · Shanghai Jiao Tong University, China · Fudan University, China +3

Repair-Based Group-Relative Policy Optimization Generative Flow Networks Preference Alignment Geometric Guidance Feedback Mean+1

May 30, 2026cs.LG

LASER: Loss-Aware Singular-value Decomposition and Rank Allocation for Efficient Low-Precision Vision-Language Models

Vision-language models (VLMs) deliver strong multimodal reasoning capabilities, but their large computational cost and high parameter counts make deployment challenging on resource-constrained devices. Low-rank decomposition has emerged as a promising compression technique, yet existing methods often optimize local matrix reconstruction error, rely on uniform or heuristic rank allocation, and focus mainly on attention projections while leaving feed-forward networks underexplored. In this paper, we propose~\textit{LASER} (\textbf{L}oss-\textbf{A}ware \textbf{S}ingular-value d\textbf{E}composition and \textbf{R}ank allocation), a low-rank compression framework for efficient low-precision VLM inference. LASER derives a curvature-weighted SVD objective from a second-order approximation of the model loss and uses Kronecker-factored Fisher information to guide decomposition toward downstream performance rather than reconstruction alone. We further introduce a loss-aware cross-layer rank allocation strategy based on calibration gradients, enabling more effective parameter budgeting across layers. Finally, we extend low-rank compression to FFN layers through a hybrid scheme that combines SVD with quantization. The evaluation results show that LASER achieves more than

2.3\times

decoding speedup over previous work while preserving strong accuracy under low-precision inference.

Haiyu Wang, Yutong Wang, Leshu Li +2

Tandon School of Engineering, New York University · Courant Institute of Mathematical Sciences, New York University · Brookhaven National Laboratory

Large Language Model Compression Low-Rank Structure Singular Value Decomposition Loss Function Decomposition

May 27, 2026math.OC

Manifold-based Algorithms for the Hadamard Decomposition

Given a matrix

X

, and two ranks

r_1

and

r_2

, the Hadamard decomposition (HD) looks for two low-rank matrices,

X_1

of rank

r_1

and

X_2

of rank

r_2

, both of the same size as

X

, such that

X\approx X_1\circ X_2

, where

\circ

is the Hadamard (element-wise) product. In most cases, HD is more expressive than standard low-rank approximations such as the truncated singular value decomposition (TSVD), as it can represent higher-rank matrices with the same number of parameters; this is because the rank of

X_1 \circ X_2

is generically equal to

r_1 r_2

. In this paper, we first present some theoretical insights for HD, in particular a useful reformulation

X\approx WH^\top

where

W

and

H

have

r_1 r_2

columns and belong to certain manifolds. These allow us to develop three new algorithms for computing HD. The first one uses the representation

X\approx X_1\circ X_2

and relies on the Manopt toolbox. The other two rely on the reformulation

X\approx WH^\top

: one is a block projected gradient method, and the other is a manifold-based gradient descent algorithm that does not require projection onto the feasible set. The last two algorithms are particularly effective for handling large sparse data. We also propose new initializations that allow us to improve the accuracy of the HD. We compare our algorithms and initialization strategies with the TSVD and with the state of the art. Numerical results show that the new methods are efficient and competitive on both synthetic and real data.

Nicolas Gillis, Subhayan Saha, Stefano Sicilia +1

Department of Mathematics and Operational Research, University of Mons, Mons, Belgium. · SS is a member of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM).

Randomized Hadamard Transforms Singular Value Decomposition Low-Rank Structure Decomposition

May 27, 2026cs.CV

Bias Leaves a Gradient Trail: Label-Free Bias Identification via Gradient Probes on Concept Decompositions

Vision classifiers can exploit spurious correlations, achieving high in-distribution accuracy yet failing under distribution shift. Existing approaches to bias mitigation and analysis often depend on curated datasets, spurious-attribute or group labels, or retraining, which may be infeasible once a model is deployed or the relevant bias is unknown. We present a bias-label-free, post-hoc method for identifying spurious concepts in frozen vision models, relying only on standard class labels from a held-out audit dataset. For each target class, we collect patches from inputs predicted as that class and apply non-negative matrix factorization to intermediate activations to obtain a bank of interpretable concept vectors. Candidate concepts are then ranked with a bias estimator derived from their interaction with backpropagated gradients on misclassified examples: bias concepts tend to get activated when correcting false negatives and suppressed when correcting false positives. On Colored MNIST and Waterbirds the method recovers concepts aligned with the known spurious cue, and on CelebA it surfaces decision-relevant directions that only partially coincide with the annotated gender attribute; suppressing the top-ranked concepts at inference time improves worst-group accuracy by up to 17.9 percentage points on Waterbirds and 10.4 on CelebA without any retraining or parameter updates. Our method identifies decision-relevant spurious directions that need not coincide with annotated ones, providing both an interpretable auditing tool and an actionable debiasing handle for frozen vision models. Code is available at https://github.com/vitryt/label-free-bias-identification.

Thomas Vitry, Kieran Edgeworth, Stefan Wermter +1

University of Hamburg, Hamburg, Germany · Ecole Normale Superieure de Rennes, Rennes, France

Frozen Vision-Language Models In-Distribution Decomposition

May 27, 2026cs.CL

DecomposeRL: Learning to Ask Useful, Informative, and Diverse Questions for Semi-Supervised, Traceable Claim Verification

Claim verification splits between end-to-end classifiers that are accurate but yields no inspectable traces, and decomposition-based methods produce inspectable traces but lag performance on benchmark datasets. We propose DecomposeRL an accurate claim-verifier that produce inspectable traces. DecomposeRL frames decomposition as an RL policy trained with GRPO and a multi-faceted reward ensemble, enabling both fully supervised and semi-supervised learning from unlabeled claims. DecomposeRL addresses the prohibitive training cost of GRPO with a data-curation funnel that distills 115K fact-verification claims into a compact, learning-signal-dense subset of 5K claims. We show that a DecomposeRL-7B policy trained with full supervision on only ~5K curated claims achieves 86.3 in-domain and 69.8 out-of-domain balanced accuracy across 11 claim-verification benchmarks containing biomedical, political, scientific, and general-domain claims. Despite being 4x smaller, it matches 32B baselines and GPT-4.1-mini, and it further outperforms baselines in a semi-supervised setting with only 10% labeled claims data. Code, data, and models are available at https://dipta007.github.io/DecomposeRL

Shubhashis Roy Dipta, Ankur Padia, Francis Ferraro

Department of Computer Science and Electrical Engineering · University of Maryland Baltimore County · Baltimore, MD 21250 USA

Category-Aware Atomic Claims Verdict Decomposition Traces Semi-Supervised Learning

May 25, 2026cs.LG

Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding

Conditionally positive definite (CPD) kernels are defined with respect to a function class

\mathcal{F}

. It is well known that such a kernel

K

is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method -- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR -- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by

\mathcal{F}

, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by

\mathcal{O}(1/\sqrt{N})

, where

N

is the sample size and the hidden constant depends on the class

\mathcal{F}

and the input distribution. This reduction enables us to analyze conditional KRR in the case where

K

is positive definite and

\mathcal{F}

is given by the first

k

principal eigenfunctions in the Mercer decomposition of

K

. We also consider the setting where

\mathcal{F}

consists of

k

random features from a random feature representation of

K

. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the

\mathcal{F}

-component of the regression function is more pronounced than the residual part.

Rustem Takhanov, Zhenisbek Assylbekov

Department of Mathematics, Nazarbayev University, Astana, Kazakhstan · Nazarbayev University Research Administration, Astana, Kazakhstan · Purdue University Fort Wayne, Indiana, USA.

Kernel Ridge Regression Kernel Method Exponential Family Spectral Decomposition Adaptive Thresholding Decomposition

May 25, 2026cs.LG

Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition

The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical misalignment between their mathematical formulation and the physical reality of molecules. Existing approaches predominantly treat molecules as unstructured point clouds in Cartesian space, overlooking the intrinsic hierarchical mechanics where bond lengths and bond angles are relatively stiff, whereas torsion angles constitute the dominant flexible degrees of freedom. This lack of manifold awareness forces models to relearn fundamental geometric constraints from scratch, often leading to physically implausible intermediate structures. To address this, we propose GO-Flow that aligns generative modeling with molecular geometry via manifold decomposition. Instead of forcing motion through Euclidean space, GO-Flow decomposes the generation process into three physically motivated subspaces: translation space with linear optimal transport, rotation space with geodesic flows on

SO(3)

, and conformation space with entropic optimal transport. This decomposition injects geometric inductive biases and makes the generative paths better aligned with molecular degrees of freedom. When combined with equivariant neural architectures, it encourages rotation-consistent generation and improves geometric validity. Extensive experiments on GEOM-Drugs and GEOM-QM9 demonstrate that GO-Flow achieves state-of-the-art generation quality. Notably, by learning straighter probability paths on the correct manifolds naturally, our method enables high-fidelity sampling with as few as 50 steps, effectively bridging the gap between structural precision and computational efficiency.

Yunqing Liu, Yi Zhou, Wenqi Fan

The Hong Kong Polytechnic University Hong Kong, China

Conformational Ensembles Riemannian Flow Matching Decomposition

May 25, 2026cs.AI

Beyond Query Memorization: Large Language Model Routing with Query Decomposition and Historical Matching

Optimizing the trade-off among predictive performance and computational cost is a central focus in the deployment of Large Language Models (LLMs). Current routing methods primarily rely on direct mapping from queries to models based on surface-level features, making them susceptible to the memorization trap and leading to poor generalizability on out-of-distribution (OOD) data. In this paper, we propose DecoR, a novel routing framework that recasts the routing task as a matching process of sifting similar queries from historical logs, effectively mitigating the memorization trap. To enhance matching accuracy, we introduce a query capability deconstruction method that decouples linguistic surface forms from task-intrinsic requirements, directing matching toward capability dimensions to ground decisions in essential task attributes. Furthermore, we develop CodaSet, a comprehensive benchmark for assessing routing generalization, where experimental results demonstrate that DecoR maintains superior accuracy while substantially lowering inference costs across both in-distribution and OOD settings. All the codes and data are available at https://github.com/lvbotenbest/DecoR.

Bo Lv, Jingbo Sun

Tencent Hunyuan · University of Chinese Academy of Sciences

Large Language Model Routing Memorization Decomposition History

May 24, 2026cs.LG

Factorize to Generalize: Retrieval-Guided Invariant-Dynamic Decomposition for Time Series Forecasting

Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction. However, our empirical analysis reveals a non-trivial limitation of retrieval-based forecasting: retrieval tends to induce more oscillatory predictions, improving performance on highly fluctuating series while degrading accuracy on smoother, trend-dominated ones. This suggests that retrieved information may be fused into prediction without explicitly distinguishing stable temporal structure from instance-specific variations, which can reduce robustness under distribution shifts. We propose a Retrieval-guided Invariant-Dynamic DEcomposition framework for time series forecasting. Rather than using retrieval as auxiliary predictive context, we leverage retrieved sequences as implicit samples from related environments to guide representation decomposition. Specifically, we first construct a retrieval-aware representation via attention-based aggregation, and then introduce a retrieval-guided routing mechanism to decompose it into an invariant component capturing stable shared structure and a dynamic component modeling context-dependent variations. These two components are forecast separately and fused for final prediction, enabling the model to preserve transferable patterns while remaining adaptive to evolving dynamics. We further design training objectives that encourage invariant learning and disentanglement, and provide theoretical insight showing that retrieval aggregation reduces variance and approximates invariant representation learning without explicit environment supervision. Extensive experiments demonstrate that our method consistently improves robustness under distribution shifts and outperforms existing TSFMs and retrieval-based baselines in zero-shot forecasting settings.

Jinjin Chi, Lei Feng, Lulu Zhang +6

College of Computer Science and Technology, Jilin University, Changchun, China · College of Computing and Data Science, Nanyang Technological University, Singapore · City St George’s, University of London, London, United Kingdom +1

Zero-Shot Forecasting Time Series Forecasting Equivariant Learning Decomposition Factor

May 23, 2026cs.CV

Structured Visual Evidence Decomposition for Evidence-Grounded Multimodal Screening of Obstructive Sleep Apnea-Hypopnea Syndrome

Effective pre-polysomnography screening for obstructive sleep apnea-hypopnea syndrome (OSAHS) requires combining clinical risk factors with visible craniofacial and neck cues. Directly prompting general-purpose multimodal foundation models for medical yes/no decisions can yield unstable, poorly calibrated outputs. We propose EviOSAHS, an evidence-grounded multimodal reasoning framework that separates image-only anatomical evidence acquisition from final clinical adjudication. Each frontal facial image is decomposed into seven fixed anatomical queries covering the neck, chin, mouth, face/neck fat, lower jaw, midface, and nose. Visual responses are converted into structured evidence cards recording target anatomy, visibility, risk direction, evidence strength, confidence, and a concise summary. These cards are combined with a cleaned clinical profile only in the final stage, where a large language model performs balanced binary screening adjudication. We evaluated EviOSAHS on a 642-subject cohort, mapping normal subjects to screening-negative and mild, moderate, or severe OSAHS subjects to screening-positive. EviOSAHS achieved 88.47% accuracy, 94.86% sensitivity, 93.74% F1-score, and a 5.14% false-negative rate, outperforming clinical-only prompting, direct multimodal prompting, and naive two-stage pipelines under a unified protocol. Ablations showed that seven-question visual decomposition and balanced final adjudication were critical to the high-sensitivity operating point. A question-level audit of 4,494 visual outputs showed a 100% structured parse rate and 93.88% high-visibility rate. EviOSAHS provides an auditable, high-sensitivity workflow for binary pre-polysomnography OSAHS screening, but should be viewed as a triage assistant rather than a diagnostic system. Prospective validation, external testing, and calibrated operating-point control are needed before clinical deployment.

Chen Zhan, Yingchen Wei, Xiaoyu Tan +2

School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 200438, China · Tencent Youtu Lab, Shanghai 200233, China · ENT Institute and Department of Otorhinolaryngology, Eye & ENT Hospital of Fudan University, Shanghai 200031, China +1

Screening Multimodal Clinical Data Ophthalmology Multimodal Evaluation Sleep Visual Evidence+2

May 22, 2026cs.CV

MuellerPT: Decomposition Driven Pretraining for Dense Learning in Mueller Polarimetry

Mueller matrix imaging provides rich, physically meaningful contrast for biomedical tissue analysis, but supervised learning is hindered by scarce dense annotations and strong domain shifts across specimens and acquisition settings. We introduce MuellerPT, a physics guided pre-training approach that learns transferable dense representations by predicting Lu-Chipman decomposition maps from per-pixel 4x4 Mueller matrices. To scale pre-training, we collected a new large Multispectral Animal Polarimetric Organ dataset (MAP-Org). The pre-trained encoder is adapted with a segmentation head for grey vs. white matter segmentation in lamb brain. A classification head is used for colorectal cancer vs. non-cancer classification. Both segmentation and classification are evaluated across few-shot learning scenarios. In segmentation, MuellerPT improves label efficiency and cross specimen transfer compared to models without pre-training, achieving an absolute DICE gain of over 20% compared to the baseline trained from scratch when using 5% of the training data. In classification, MuellerPT also enhances label efficiency, improving overall accuracy by 8% compared to the baseline when using 1% of the training data. We demonstrate MuellerPT's robustness to domain shift with a qualitative evaluation of its predicted Lu-Chipman maps on an ex vivo human oesophagus sample. These results suggest that predicting Lu-Chipman decomposition is an effective and practical pretext task for robust biomedical inference from Mueller polarimetry and can pave the way for future work on label efficient Mueller imaging.

Adam Tlemsani, Yingdian Li, Maxime Giot +4

Department of Computing, Imperial College London · Hamlyn Centre for Robotic Surgery, Imperial College London · Department of Surgery and Cancer, Imperial College London +2

Multiple Instance Learning Hyperspectral Image Basis Decomposition Decomposition

May 22, 2026cs.LG

Every Component Is a Lookup: One Linear Graph for Interaction, Composition and Attribution

Interpretability methods for transformers are typically built around separate questions: which components interact, how information routes to the output, and which input tokens contribute. Because these methods rely on different assumptions, their answers are difficult to relate. We argue that two architecturally motivated assumptions suffice to address all three questions: attention and MLPs share a key-value form,

φ(S)\,U

, in which

φ(S)

selects over values

U

, and components read from an additive residual stream, the sum of component outputs. Holding these selections at their forward-pass values turns the model into a computational graph, of which component interactions, composition paths, and token attribution are different readouts. We develop Unpack, a backward attribution procedure over this graph, and validate each readout against the corresponding established test: interaction scores predict ablation effects across models from 160M to 6.9B parameters, recovered routes reproduce established circuits down to the key, query, or value branch the circuit specifies, and token attribution passes the same faithfulness test as dedicated attribution methods. The results suggest that these two assumptions suffice for the interpretability questions above. On a task with a known circuit, we find that contribution and causal effect can differ, and that the difference has a recognisable signature: components that matter for the task change their contribution when the task is removed from the input, while components that act like a bias term do not. Code is available at https://github.com/Fun-Cry/unpacklm.

Po-Kai Chen, Aske Plaat, Niki van Stein

Leiden University

Transformer Attention Transformer Architectures Mechanistic Interpretability Decomposition

May 21, 2026cs.LG

Decomposing and Measuring Evaluation Awareness

Frontier language models sometimes recognize that they are under evaluation and adjust their behavior which can undermine validity of benchmark results. Yet the field studies it without a shared foundation, conflating flaws of the evaluation with capabilities of the model, and detection with behavioral response. We ground evaluation awareness in social psychology, decomposing it into an environment component and a model component that separates recognition from propensity. We operationalize the environment component through eight categorized trigger factors, such as placeholder entities and grading-style output formats, and study recognition and behavior through chain-of-thought monitoring. Across nine frontier models and four benchmarks, recognition rates depend on the specific pairing of model and benchmark. Recognition rarely associates with behavioral change, and when it does, the direction depends on the type of evaluation perceived. Models are also more sensitive to safety than capability evaluations, placing safety benchmark validity at greater risk. To study which factors each model is sensitive to and how they interact, we propose \textbf{EvalAwareBench}, a factor-controlled benchmark of 100 paired safety-capability tasks where each of the eight factors can be independently toggled, varying evaluative signals while holding the underlying request fixed. Through EvalAwareBench, we find that no single factor uniformly affects all models, but stacking factors progressively raises evaluation awareness across all of them. Our framework and EvalAwareBench provide the tools to measure, attribute, and mitigate evaluation awareness, building the foundation for future solutions.

Changling Li, Terry Jingchen Zhang, Jie Zhang +4

ETH Zürich · Max Planck Institute for Intelligent Systems · University of Toronto & Vector Institute +3

Safety Benchmarks Frontier Models Agent Behavior Modeling Decomposition

May 21, 2026cs.LG

A Posterior-Predictive Variance Decomposition for Epistemic and Aleatoric Uncertainty in Wind Power Forecasting

Accurate wind power forecasting requires reliable uncertainty quantification, yet most existing methods report a single predictive uncertainty that conflates epistemic and aleatoric sources. This paper applies the law of total variance to the joint setting of heteroscedastic neural network regression and Bayesian posterior approximation, deriving an explicit decomposition of total uncertainty (TU) into aleatoric (AU) and epistemic (EU) components. The resulting estimators are compatible with standard posterior-approximation methods and with

β

-NLL training to regulate the mean--variance learning trade-off. A wind power--specific evaluation framework is proposed to validate disentanglement without access to ground-truth uncertainty labels, comprising three modules: controlled synthetic experiments to verify responses to heteroscedastic noise and distribution shift; data-property--driven validation on a real-world wind turbine SCADA dataset; and dataset-size scaling experiments to examine the predicted asymptotic behavior of EU. Across synthetic and real-world experiments, the decomposed AU and EU components respond in theoretically consistent directions to noise structure, distributional shift, and training-scale variation, supporting the theoretical consistency and operational utility of the proposed decomposition and evaluation protocol.

Yinsong Chen, Samson S. Yu, Kashem M. Muttaqi

School of Engineering, Deakin University, Melbourne, VIC 3216, Australia · ARC Training Centre in Energy Technologies for Future Grids, School of Engineering, University of Wollongong, Wollongong, NSW 2522, Australia

Offshore Wind Turbine Predictive Uncertainty Input Uncertainties Posterior Predictive Distribution Decomposition

May 20, 2026cs.CV

Decomposing Subject-Driven Image Generation via Intermediate Structural Prediction

Subject-driven text-to-image generation still struggles to preserve high-frequency identity details such as logos, patterns, and text. Existing methods typically operate directly in RGB space, which often leads to detail degradation under substantial edits. We propose a two-stage framework that decouples structure from appearance by first predicting a Canny map and then rendering the final image conditioned on both the source appearance and the predicted structure. To improve text handling, we further introduce a fully automatic pipeline that constructs a 100k-pair text-aware dataset with cross-view textual consistency. Experiments, including GPT-4.1-based evaluation and a knowledge distillation study, show clear gains over selected baselines and suggest that intermediate structural prediction is an effective route for high-fidelity subject-driven generation. Our dataset and code will be made publicly available.

Hanzhong Guo, Yizhou Yu

School of Computing and Data Science, The University of Hong Kong

May 18, 2026stat.ML

On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions

We study sample quantiles of distributions indexed by estimated parameters, with a on Value-at-Risk related to linear projections of financial returns that whose underlying probability law is heavy-tailed. In this setting, the projection direction and the empirical quantile threshold are estimated from the data, so the standard Bahadur representation under a fixed distribution does not separate the distinct sources of instability. A canonical starting point is Bahadur's representation, which expresses the sample quantile through the empirical distribution function plus a remainder term \cite{bahadur1966}. Empirical-process theory provides a usable scaffolding through the mechanics of half-spaces, symmetric differences, and Glivenko--Cantelli uniform convergence. They yield stability bounds, but absorb changes in projection direction and changes in quantile threshold into a single symmetric-difference measure. Interestingly, a global uniform-convergence requirement is imposed on what is intrinsically a local quantile-stability problem. This paper introduces a Q-Q orthogonality formulation for separating projection-direction and quantile-threshold effects. The object of interest is the difference between the empirical quantile computed using the estimated projection direction and the population quantile computed at the reference projection direction. We decompose this difference into three terms,

\hat q_α(\hat w)-q_α(w_0)=D_1+D_2+D_3

. Here,

D_1

measures the population quantile movement induced by perturbing the projection direction,

D_2

measures the empirical quantile fluctuation with the projection direction held fixed, and

D_3

is the Bahadur-type remainder.

Choudur Lakshminarayan

School of Business, Stevens Institute of Technology

Quantile Regression Long-Tailed Distribution Conditional-Value-At-Risk Fluctuation-Dissipation Theorem Distributions Projection+1

May 15, 2026cs.CV

Decomposed Vision-Language Alignment for Fine-Grained Open-Vocabulary Segmentation

Open-vocabulary segmentation models often struggle to generalize to unseen combinations of object categories and attributes, because fine-grained descriptions are typically encoded as holistic sentences that entangle multiple semantic units. We propose a Decomposed Vision-Language Alignment framework that explicitly factorizes textual prompts into a concept token and multiple attribute tokens, enabling separate cross-modal interactions for each semantic unit. At the feature level, we introduce a Feature-Gated Cross-Attention module that generates attribute-specific gating maps to fuse information in a multiplicative manner, effectively enforcing compositional semantics. At the scoring level, per-token similarities are aggregated in log-space, producing a stable and interpretable compositional matching. The method can be seamlessly integrated into existing transformer-based segmentation architectures and significantly improves generalization to unseen attribute-category compositions in fine-grained open-vocabulary segmentation benchmarks.

Chenhao Wang, Yingrui Ji, Yu Meng +1

Aerospace Information Research Institute, Chinese Academy of Sciences · University of Chinese Academy of Sciences · Zhejiang University

Open-Vocabulary Segmentation Vision-Language Alignment Cross-Attention Decomposition

May 14, 2026cs.SE

Runtime-Structured Task Decomposition for Agentic Coding Systems

Agentic coding systems increasingly use large language models (LLMs) for software engineering tasks such as debugging, root cause analysis, and code review. However, many existing systems encode task logic, execution flow, and output generation inside monolithic prompts. This design creates brittle behavior, limited debuggability, and high retry costs because failures often require rerunning the full workflow. We present runtime-structured task decomposition, an architectural approach in which task partitioning and execution flow are managed through executable control logic rather than prompt structure alone. LLMs are used only for focused judgment tasks, and outputs are validated against predefined schemas before downstream execution. We evaluate this approach on two software engineering workloads using three configurations: monolithic execution, static decomposition with fixed subtasks and no runtime branching, and runtime-structured decomposition. Each configuration was evaluated across 10 runs. Our results show that decomposition alone does not necessarily reduce retry cost. In the Kubernetes root cause analysis workload, the static decomposition baseline produced a retry cost of 1,632 +/- 145 tokens versus 904 +/- 17 tokens for the monolithic baseline because failures forced reruns of downstream subtasks. A similar pattern appeared in the multi-file debugging workload, where the static baseline consumed 933 tokens compared to 703 tokens for the monolithic system. The runtime-structured approach reran only failed subtasks, reducing retry costs to 436 +/- 132 tokens for root cause analysis and 460 tokens for debugging. Overall, the approach achieved up to 51.7% lower retry cost than monolithic systems and 73.2% lower retry cost than static decomposition baselines, improving efficiency, debuggability, and operational reliability in agentic coding systems.

Shubhi Asthana, Bing Zhang, Chad DeLuca +2

IBM Research · San Jose, California · Zoom +2

Coding Agents Decomposition

May 14, 2026cs.LG

AQKA: Active Quantum Kernel Acquisition Under a Shot Budget

Estimating an

N \times N

quantum kernel from circuit fidelities requires

Θ(N^2 S)

measurement shots, the dominant bottleneck for deployment on near-term hardware. Existing budget-saving methods (Nyström-QKE, ShoFaR, kernel-target alignment) sub-sample \emph{which} entries to measure but allocate shots \emph{uniformly} within their chosen subset, ignoring how much each entry drives the downstream classifier. We close this gap with two contributions. \textbf{First, a complete regime decomposition} for shot-budgeted quantum kernel learning: a principled menu of when each allocator wins. Our method, \emph{AQKA}, dominates the budget-limited regime (

B \lesssim 16 n_{\mathrm{pairs}}

) on sparse-sensitivity KRR, with the gap \emph{growing} from

+8

to

+25

pts over uniform as

N

scales

225{\to}1000

and reaching

+26

--

32

pts on an \texttt{ibm_pittsburgh} (156-qubit Heron) hardware kernel; Nyström-QKE wins at saturating budgets on planted-sparse via low-rank reconstruction; ShoFaR is competitive only at extreme low budgets. \textbf{Second, a closed-form pair-level acquisition theory}:

s_{ij}^{\star} \propto |g_{ij}|\sqrt{K_{ij}(1-K_{ij})}

with explicit gradient

g_{ij}

for KRR (Lemma1, $|β_iα_j+β_jα_i|\sqrt{K_{ij}(1-K_{ij})}$ ) and SVM via the envelope theorem ( $|η_i^*η_j^*|\sqrt{K_{ij}(1-K_{ij})}$ ); a \emph{corrected} sparsity-aware Cauchy--Schwarz rate $ρ\le 2m/N$ matching empirics (vs.\ the naive $m^2/N^2$ ); an explicit-constant plug-in regret bound (Theorem2); and a tighter SVM ceiling

ρ^{\mathrm{SVM}} \le m_{\mathrm{sv}}^2/N^2

. We close with the first multi-seed live online adaptive shot allocation on quantum hardware:

+17.0 \pm 4.8

pts at

N{=}20

on \texttt{ibm_aachen} (

3.5σ

, 5 seeds), with the advantage holding at

N{=}30

at higher budget on \texttt{ibm_berlin} (

+14.0 \pm 8.5

pts, 5 seeds).

Jian Xu, Chao Li, Delu Zeng +2

1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1

Quantum Kernels Kernel Method Token Budget Allocation Sparsity Decomposition

May 14, 2026cs.AI

PyCSP3-Scheduling: A Scheduling Extension for PyCSP3

PyCSP

^3

provides a productive way to build constraint models for solving combinatorial constrained problems and export them to XCSP

^3

, preserving a complete separation between modeling and solving. However, it lacks native support for scheduling abstractions such as interval variables, sequence variables, and resource functions. As a result, scheduling models must be encoded with low-level integer variables and manual channeling constraints, even though PyCSP

^3

already provides global constraints like NoOverlap and Cumulative on integer arrays. We present PyCSP

^3

Scheduling, a library that adds scheduling abstractions to PyCSP

^3

through 53 dedicated constraints and 27 expressions, and compiles them down to standard PyCSP

^3

/XCSP

^3

constraints, maintaining the modeling/solving separation that underpins the PyCSP

^3

ecosystem. On 261 paired instances across 17 model families (5 runs each), both formulations produce identical objectives on all 72 doubly-proved optimal pairs and nearly half of the families (8/17) remain structurally unchanged after compilation; however, runtime performance diverges across families, with clear gains on some (up to 5.8x) and regressions on others due to the overhead of compilation decompositions. Code and benchmarks are available at: https://github.com/sohaibafifi/pycsp3-scheduling

Sohaib Afifi

Univ. Artois, UR 3926, Laboratoire de Génie Informatique et d’Automatique de l’Artois (LGI2A), F-62400 Béthune, France

Job Shop Scheduling Schedule Structural Constraints Decomposition Quantum Chemistry

May 14, 2026cs.CL

Does RAG Know When Retrieval Is Wrong? Diagnosing Context Compliance under Knowledge Conflict

The Context-Compliance Regime in Retrieval-Augmented Generation (RAG) occurs when retrieved context dominates the final answer even when it conflicts with the model's parametric knowledge. Accuracy alone does not reveal how retrieved context causally shapes answers under such conflict. We introduce Context-Driven Decomposition (CDD), a belief-decomposition probe that operates at inference time and serves as an intervention mechanism for controlled retrieval conflict. Across Epi-Scale stress tests, TruthfulQA misconception injection, and cross-model reruns, CDD exposes three patterns. P1: context compliance is measurable in an upper-bound adversarial setting, where Standard RAG reaches 15.0% accuracy on TruthfulQA misconception injection (N=500). P2: adversarial accuracy gains transfer across model families -- CDD improves accuracy on Gemini-2.5-Flash and on Claude Haiku/Sonnet/Opus -- but rationale-answer causal coupling does not transfer. CDD reaches 64.1% mistake-injection causal sensitivity on Gemini-2.5-Flash, while sensitivities for all three Claude variants fall in the [-3%, +7%] range, suggesting that the Claude-side accuracy gains operate through a mechanism distinct from the explicit conflict-resolution trace. P3: explicit conflict decomposition improves robustness under temporal drift and noisy distractors, with CDD reaching 71.3% on temporal shifts and 69.9% on distractor evidence on the full Epi-Scale adversarial benchmark. These three patterns identify context-compliance as a structural axis along which standard RAG can be probed and intervened on, distinct from retrieval-quality or single-method robustness questions, and motivate releasing Epi-Scale for systematic study across model families and retrieval pipelines.

Yihang Chen, Pin Qian, Su Wang +4

1Georgia Institute of Technology · 2Carnegie Mellon University · University of California San Diego

Question-Answering Benchmarks Compliance Decomposition

May 14, 2026cs.CV

ICED: Concept-level Machine Unlearning via Interpretable Concept Decomposition

Machine unlearning in Vision-Language Models (VLMs) is typically performed at the image or instance level, making it difficult to precisely remove target knowledge without affecting unrelated semantics. This issue is especially pronounced since a single image often contains multiple entangled concepts, including both target concepts to be forgotten and contextual information that should be preserved. In this paper, we propose an interpretable concept-level unlearning framework for VLMs, which constructs a compact task-specific concept vocabulary from the forgetting set using a multimodal large language model. In addition to modality alignment, visual representations are decomposed into sparse, nonnegative combinations of semantic concepts, providing an explicit interface for fine-grained knowledge manipulation. Based on this decomposition, our method formulates unlearning as concept-level optimization, where target concepts are selectively suppressed while intra-instance non-target semantics and global cross-modal knowledge are preserved. Extensive experiments across both in-domain and out-of-domain forgetting settings demonstrate that our method enables more comprehensive target forgetting, better preserves non-target knowledge within the same image, and maintains competitive model utility compared with existing VLM unlearning methods.

Shen Lin, Jing Lin, Junhao Dong +2

1Fujian Normal University · 2Nanyang Technological University · University of New South Wales +1

Large Language Model Unlearning Machine Unlearning Cross-Modal Forgetting Decomposition

May 13, 2026quant-ph

Physics Guided Generative Optimization for Trotter Suzuki Decomposition

Trotter Suzuki product formulas are the standard route to Hamiltonian evolution on noisy intermediate-scale quantum (\NISQ{}) hardware, but their accuracy depends on three coupled choices: term grouping, product-formula order, and time-step allocation. Grouping and order are discrete, which makes direct gradient optimization infeasible and forces existing compilers to rely on static heuristics. We describe P-GONE, a method that combines a conditional diffusion model (D3PM + DDPM), a graph neural network (\GNN{}) encoder, and closed-loop REINFORCE fine-tuning to jointly learn grouping, order, and time-step optimization over a mixed discrete-continuous space. Under fidelity-matched conditions (

F \geq 0.95

), the method achieves circuit depth 86 versus 1673 for Qiskit fourth-order (ungrouped, Suzuki-4), about

19.4\times

compression, and 141 for Paulihedral (first-order Trotter), about

1.6\times

compression. At

T=0.90

the method also beats the Qiskit group-commuting teacher (65 vs 103,

1.6\times

compression), though at

T=0.95

the teacher still leads -- a stratified pattern that points toward fidelity-aware fine-tuning. Under a standard depolarizing noise model, the method achieves noisy fidelity roughly

2\times

the Qiskit fourth-order baseline (0.743 vs 0.380). Ablation shows a clear hierarchy: order learning

>

time allocation

>

grouping. Best-of-N sampling (

N=32

is a practical sweet spot) and CFG guidance give flexible fidelity-depth trade-offs at inference. The method works well on structured Hamiltonians (TFIM, Heisenberg), but random Pauli Hamiltonians fail entirely at

T \geq 0.95

-- a boundary that defines where the method applies.

WenBin Yan

University of Colorado Boulder[quant-ph]

Hamiltonian Physics-Guided Machine Learning Decomposition

May 13, 2026cs.LG

What Information Matters? Graph Out-of-Distribution Detection via Tri-Component Information Decomposition

Graph neural networks are widely used for node classification, but they remain vulnerable to out-of-distribution (OOD) shifts in node features and graph structure. Prior work established that methods trained with standard supervised learning (SL) objectives tend to capture spurious signals from either features and/or structure, leaving the model fragile under distributional changes. To address this, we propose TIDE, a novel and effective Tri-Component Information Decomposition framework that explicitly decomposes information into feature-specific, structure-specific and joint components. TIDE aims to preserve only the label-relevant part of the joint information while filtering out spurious feature- and structure-specific information, thereby enhancing the separation between in-distribution (ID) and OOD nodes. Beyond the framework, we provide theoretical and empirical analyses showing that an information bottleneck objective is preferable to standard SL for graph OOD detection, with higher ID confidence and a greater entropy gap between ID and OOD data. Extensive experiments across seven datasets confirm the efficacy of TIDE, achieving up to a 34% improvement in FPR95 over strong baselines while maintaining competitive ID accuracy.

Danny Wang, Ruihong Qiu, Zi Huang

The University of Queensland, Australia.

Out-Of-Distribution Detection Generalist Graph Anomaly Detection Out-Of-Distribution Graph Representation Learning Graph Neural Networks Decomposition

May 12, 2026cs.LG

The Routing and Filtering Structure of Attention

The attention interaction matrix

QK^{\top}

contains two entangled computations: a skew-symmetric component that redistributes information between positions (routing) and a symmetric component that scales mutual relevance (filtering). We decompose 1776 heads across five pretrained transformers and find routing operating at low rank, well below the routing capacity allocated by the weight kernel. We introduce

S

-

D

attention as a diagnostic parameterization that disentangles routing from filtering by construction with guaranteed stability (

\mathrm{Re}(λ) \le 0

) and trains stably without layer normalization. When disentangled and unnormalized, routing self-organizes into a spectral cascade, effective rank

2

at the first layer, expanding with depth across six scales from 7M to 355M parameters. The cascade predicts where attention can be simplified: linearizing the first seven layers of 125M

S

-

D

attention costs

{<}5\%

perplexity, whereas standard attention collapses under the same intervention. The linearizable region widens with depth. Replacing the first four layers with ELU+1 linear attention reaches within

1.4\%

of baseline at full head dimension. Cascade-allocated architectures trade attention parameters for perplexity (

47\%-65\%

fewer attention parameters at

+3.9\%

to

+8.4\%

PPL). The routing-filtering decomposition makes the spectral budget legible; the cascade makes it actionable.

Shafayeth Jamil, Rehan Kapadia

Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles, CA 90089

Kimi Delta Attention Decomposition Spectral

May 12, 2026q-bio.BM

Learning Protein Structure-Function Relationships through Knowledge-guided Representation Decomposition

Proteins encode diverse functions within complex three-dimensional structures, yet most deep learning representations remain highly entangled, obscuring the biophysical signals that underlie function. Here we introduce ProtDiS, a knowledge-guided framework that decomposes pretrained protein micro-environment embeddings into biologically grounded and task-relevant dimensions. Inspired by the information bottleneck principle, ProtDiS learns representations that balance informativeness and compression, yielding structural features that are more specific, independent, and information-efficient, and achieving consistent improvements across twelve downstream tasks, with the largest gains under structure-based splits. Protein- and residue-level analyses further show that ProtDiS differentiates proteins with similar folds but divergent functions and captures fine-grained biophysical signals critical. These findings suggest that knowledge-guided decomposition provides a general and interpretable approach for structuring latent spaces in protein structural modeling. The source code and implementation details are publicly available at https://github.com/AI-HPC-Research-Team/ProtDiS.

Mingqing Wang, Zhiwei Nie, Athanasios V. Vasilakos +2

Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · Pengcheng Laboratory, Shenzhen, China · School of Electronic and Computer Engineering, Peking University, Shenzhen, China +2

Protein Structure Prediction Protein Representation Learning Decomposition Structure-Aware

May 12, 2026cs.CV

PD-4DGS:Progressive Decomposition of 4D Gaussian Splatting for Bandwidth-Adaptive Dynamic Scene Streaming

4D Gaussian Splatting (4DGS) enables high-quality dynamic novel view synthesis, yet current models remain monolithic bitstreams that clients must download in full before any frame can be rendered, causing black-screen waits of tens to hundreds of seconds on mobile bandwidth and leaving 4DGS incompatible with modern adaptive-bitrate delivery. Progressive 3DGS compression alleviates this for static scenes, but it acts only on spatial anchors and cannot partition the temporal deformation networks that dominate dynamic-scene size. We present PD-4DGS, the first framework for progressive compression and on-demand transmission of 4DGS. Hierarchical Deformation Decomposition (HDD) externalises the coarse-to-fine motion hierarchy already latent in 4DGS into three independently transmittable layers -- a static scaffold, a global deformation, and a local refinement -- so that any prefix of the bitstream is already renderable, turning a single training run into a scalable, DASH/HLS-compatible bitstream. A Gaussian-entropy attribute rate-distortion loss together with a temporal mask consistency regulariser shrink the base layer while suppressing low-bitrate flicker; a capacity-weighted rollout schedule, gated online by a learnt activation rate rho, then prevents deformation-network under-training without any per-scene hyperparameter. On the Dycheck iPhone benchmark, PD-4DGS cuts the streamed bitstream by >60% at matched rendering fidelity and reduces first-frame latency from 73--930 s to ~1.7 s on a 2 Mbps link, uniquely enabling true on-demand progressive streaming for 4DGS.

Jiachen Li, Guangzhi Han, Jin Wan +5

Qilu University of Technology

Gaussian Splatting Novel View Synthesis Decomposition Scene Understanding

May 11, 2026cs.RO

A cell-decomposition based path planner for 3D navigation in constrained workspaces

This paper proposes a cell decomposition algorithm for binary occupancy grids that ensures mutual complete visibility from each cell to at least one adjacent cell. This decomposition establishes a simplified framework for verifying path feasibility that can be easily embedded in optimization problems. To illustrate its utility, we formulate both second-order cone programs (SOCP) and their mixed-integer variant (MISOCP) within the proposed framework. Furthermore, we propose the KSP-SOCP method, which combines Yen's k-shortest path algorithm with the SOCP, achieving improved solutions compared to a standard SOCP approach while avoiding the computational burden of MISOCP. The cell decomposition algorithm, KSP-SOCP, and MISOCP approaches were evaluated in 9 city-like workspaces. The decomposition efficiently partitioned each map, enabling both optimization methods to compute feasible paths. The proposed KSP-SOCP achieved time performance comparable to the MISOCP while requiring less memory, making it highly suitable for large-scale problems.

João P. L. Morais, Luciano C. A. Pimenta, Marcelo A. Santos +1

Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil · Department of Management, Information and Production Engineering, University of Bergamo, Dalmine, BG, Italy · Department of Electronic Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

Path Planning Shortest Paths Combinatorial Optimization Workspaces Decomposition Path

May 10, 2026cs.CV

Towards Robust Sequential Decomposition for Complex Image Editing

Recent advances in visual generative models have enabled high-fidelity image editing guided by human instructions. However, these models often struggle with complex instructions involving combinatorial editing operations or inter-step dependencies. This difficulty stems from the limitations of two canonical paradigms: (1) single-turn editing, which attempts to apply all instructed edits in one pass, often fails to parse the complex instruction accurately and causes undesired edits; and (2) sequential editing can decompose the task into simpler steps but suffers from compounding errors introduced by the sequential execution, leading to low-fidelity results. To derive a robust solution for complex image editing, we examine editing behaviors of different paradigms under a unified in-context editing framework, and study how the benefits of sequential decomposition can be balanced against its error-accumulation drawbacks. We further develop a synthetic data pipeline that constructs editing tasks of varying instruction complexity, allowing us to curate a large-scale editing dataset with high-quality decomposed sequences. By finetuning on synthetic data, we discovered that with properly designed editing paradigms, sequential decomposition yields robust improvements even as task complexity increases. Furthermore, the decomposition skills learned from synthetic tasks can transfer to real images by co-training with real-world editing data, demonstrating the promise of sim-to-real generalization for tackling complex image editing across broader domains.

Zilai Zeng, Mingdeng Cao, Zijie Li +5

Brown University · ByteDance Seed · The University of Tokyo

Image Editing Multi-Reference Image Generation Generative Models Synthetic Task Decomposition

May 9, 2026cs.CL

Decomposing and Steering Functional Metacognition in Large Language Models

Large language models (LLMs) increasingly exhibit behaviors suggesting awareness of their evaluation context, often adapting their reasoning strategies in benchmark settings. Prior work has shown that such evaluation awareness can distort performance measurements; however, it remains unclear whether this phenomenon reflects a single behavioral artifact or a deeper internal structure within the model. We propose that LLMs maintain a decomposable space of functional metacognitive states: internal variables encoding factors such as evaluation awareness, self-assessed capability, perceived risk, computational effort allocation, audience expertise adaptation, and intentionality. Through residual stream analysis across multiple reasoning models, we demonstrate that these states are linearly decodable from internal activations and exhibit distinct layer-wise profiles. Moreover, by steering model activations along probe-derived directions, we show that each functional metacognitive state causally modulates reasoning behavior in dissociable ways, affecting verbosity, accuracy, and safety-related responses across tasks. Our findings suggest that benchmark performance reflects not only task competence but also the activation of specific functional metacognitive states. We argue that understandi ng and controlling these internal states is essential for reliable evaluation and deployment of reasoning models, and we provide a mechanistic framework for studying functional m etacognition in artificial systems. Our code and data are publicly available at https://github.com/xlands/meta-cognition.

Yanshi Li, Xueru Bai, Shuman Liu +2

Shopee Singapore, Singapore

Metacognition LLM Reasoning Strategies Model Activations Decomposition

May 9, 2026cs.LG

Deterministic Decomposition of Stochastic Generative Dynamics

Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field

b_t

of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects:

b_t = u_t + d_t

, where

u_t

governs marginal probability transport and

d_t

captures an osmotic effect induced by diffusion and determined by the marginal score. Based on this decomposition, we propose Bridge Matching, a flow-based framework for learning decomposed generative dynamics through both marginal and conditional formulations. In generative modeling experiments, we recombine the learned components as

b_t = u_t + λ_d d_t

, showing that the proposed decomposition enables interpretable and controllable sampling by adjusting the osmotic contribution in probability transport.

Xingyu Song, Yuan Mei, Naoya Takeishi

1The University of Tokyo · 2Zhejiang University · *Visiting student at The University of Tokyo from Zhejiang University.

Stochastic Decomposition

May 9, 2026stat.ML

Core-Halo Decomposition: Decentralizing Large-Scale Fixed-Point Problems

We study solving large-scale fixed-point equation

x^\star=\bar F(x^\star)

with decomposition. Standard strict decomposition assigns each agent a disjoint block and evaluates updates using only owned coordinates. For most operators, however, a block update may depend on variables outside the block. Truncating these dependencies by strict decomposition changes the mean operator and creates structural bias that cannot be removed by more samples, smaller stepsizes, or additional consensus. We therefore propose Core-Halo decomposition, which separates write ownership from read-only evaluation context: each agent updates its own core and reads from an overlapping halo. By aligning the Core-Halo decomposition with the block-dependence structure of

\bar F

, the original fixed-point problem can be implemented faithfully in a decentralized multi-agent system. We further characterize the fundamental obstruction faced by strict decomposition through a Bellman closure condition and a blockwise bias lower bound, showing that local-only updates can alter the original fixed-point operator. Finally, we conduct extensive experiments across a range of application settings, and demonstrate that Core-Halo achieves near-centralized performance while retaining the parallelism benefits of decentralization.

Haixiang, Yang Xu, Jiefu Zhang +4

Purdue University · The University of Hong Kong · Johns Hopkins University

Decentralized Autonomous Organization Fixed-Point Iteration Basis Decomposition Decomposition