Decomposition

Follow this topic Ask about this topic

Momentum

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

Jul 6Week of Sep 21

Latest papers 149

Oct 1, 2026cs.CV

EvenSplat: Coupled 2D-3D Decomposition for Gaussian Splatting under Exposure and Illumination Variation

A surface photographed under even light presents nearly the same appearance from every angle; the same surface under uneven light does not. Exposure changes between views, illumination varies within a single image, and locally strong light sources leave one region bright and its neighbor in shadow. Multi-view reconstruction methods such as 3D Gaussian Splatting treat these lighting artifacts as if they were properties of the scene, entangling capture-specific illumination with the geometry and color they recover. We present EvenSplat, a framework that separates the two. EvenSplat couples an image-space illumination decomposition with an illumination field carried by the Gaussians, so that the same explanation of the lighting is shared between the two-dimensional and three-dimensional views of the scene; a camera-response network and a local exposure-compensation module absorb the global and residual differences that remain across training images. Through extensive experiments across multiple datasets and diverse forms of uneven illumination (cross-view exposure, spatial illumination variation, and high-contrast lighting) on both real-world captured and simulated benchmarks, EvenSplat generally outperforms state-of-the-art methods, particularly under high-contrast illumination.

Tongyu Wu, Jacob Edwards, Ziteng Cui +2

Xi’an Jiaotong University · University of East Anglia · University of Tokyo

Gaussian Splatting Illumination Variations Intrinsic Image Decomposition Exposure Decomposition

Oct 1, 2026cs.LG

Rethinking the Information Bottleneck: Structured Decomposition under Label-Induced Partitions

Standard information bottleneck (IB) regularization constrains representations via a single scalar I(Z;X), implicitlytreating all information as homogeneous. However, a single global compression control couples label-relevant structurewith residual within-condition variation, rather than regulating their allocation independently, allowing nuisanceinformation to persist in learned representations. For example, in medical imaging applications, residual variation oftenstems from acquisition conditions, background factors, or subject-specific appearance. This issue becomes particularlypronounced in data-limited settings, where models tend to overfit such variation, hindering generalization. While existingregularization methods can stabilize training, control capacity, or shape representation geometry, they do not explicitlyseparate nuisance-like variation from task-supporting structure. To address this limitation, we revisit IB from a structuredperspective based on a label-induced partition, where condition-level structure and within-condition information playdistinct roles. This leads to a dual-bottleneck formulation: a standard KL term controls global information capacity, while aconditional KL term targets within-condition information. We show that the conditional KL admits an exact decompositioninto a within-condition information term and a prior-mismatch term, explaining its alignment with the design objective.With a simplex-structured conditional prior, the method provides controllable latent geometry and integrates seamlesslyinto existing pipelines. Experiments on classification and segmentation show the clearest gains in low-data classificationand consistent improvements across dense prediction benchmarks.

Jingyao Zhang, Yuxuan Li, Lu Han +2

School of Computer Science, The University of Sydney Sydney, NSW 2006, Australia

Information Bottleneck Representation Learning Discriminative Congruence Transform Bottlenecks Partitioning Decomposition

Sep 30, 2026cs.LG

Learning the identity: a case study of how SGD selects among functional decompositions

One might think that learning the identity function with a deep linear residual network is trivial - the path along residual connections already implements the identity, and so the network need only drive its weights to zero. However, this zero-weight solution is just one point on an entire manifold of population-loss minimizers, each corresponding to a different decomposition of the identity across the network's layers. Although the population loss does not distinguish among these solutions, stochastic gradient descent (SGD) reproducibly favors particular ones. For instance, under anisotropic label noise, the learned layers exhibit a noise-dependent spectrum; even with weight decay, SGD does not generally recover the zero-weight solution. Changing only the parametrization, while leaving the set of realizable functions unchanged, yields different behavior: factoring each weight matrix as a product of two matrices causes the weights to collapse to zero, even without explicit weight decay. While perhaps mysterious and unintuitive at first, these phenomena can be understood through the lens of entropic loss, which augments the population loss with a term proportional to the expected squared norm of the minibatch gradient (Ziyin et al., 2025). On the identity manifold, the population loss is constant, while the entropic term distinguishes among these decompositions. We characterize its minimizers analytically and use them to derive predictions for the structure of solutions favored by SGD. Networks trained with SGD closely match these predictions. Overall, the identity learning task studied here serves as a clean and simple case study of how the lens of entropic loss can clarify why SGD favors particular decompositions of the same input-output function.

Andy Arditi, Weian Xie, David Bau +1

Northeastern University · Massachusetts Institute of Technology

Stochastic Gradient Descent Anisotropic Loss Landscapes Weight Decay Residual Networks Decomposition Case Study

Sep 30, 2026stat.ME

Heteroskedastic Canonical Polyadic Tensor Decomposition

When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

Kyle Ritscher, Carlos Llosa-Vite

Computer Science Research Institute, Sandia National Laboratories, Albuquerque, NM · Department of Statistics & Data Science, University of California, Los Angeles, CA

Tensor Decomposition Low-Rank Structure Decomposition Online Conformal Prediction

Sep 30, 2026cs.RO

Identifiable Decomposition of Submovements in Human Hand Trajectories

Voluntary movements have long been hypothesised to be comprised of discrete primitives called submovements, as a descriptive model of human motor behaviour. However, existing methods scale poorly, and no principled method exists to determine whether a decomposition is informative. We propose a spatiotemporal kernel correlation between primitive pairs as an identifiability criterion. Submovement-Identifiable Decomposition (Sub-ID) embeds this criterion in its adaptive-ridge regularisation, biasing the optimiser toward low-correlation solutions. Identifiability is lost when primitives become collinear and recovered when they diverge spatially. On synthetic data, Sub-ID recovers ground-truth parameter distributions where existing methods fail; furthermore, when primitives overlap too heavily to be distinguished, the method explicitly detects this ambiguity rather than outputting misleading results. Sub-ID extracts submovements from real three-dimensional, long-horizon movements, a regime no prior method addresses. This method has the potential to identify physiologically grounded primitives for motor control research and imitation learning.

Adrian Prados, James Hermus, Ramon Barber +1

Universidad Carlos III de Madrid, Leganes, Spain · Idiap Research Institute, Martigny, Switzerland · Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland

Imitation Learning Decomposition Spatio-Temporal Correlations

Sep 30, 2026cs.CV

D-Scope: Decomposing and Steering Diffusion Transformers with Sparse Autoencoders

Sparse autoencoders (SAEs) reveal visual structure in diffusion transformers (DiTs), but interpreting a feature does not establish whether it can be used to control generation. We introduce D-Scope (Diffusion Scope), a framework that connects feature interpretation to generation control through shared visual evidence. D-Scope aggregates SigLIP2 embeddings of highly activating image patches into visual centroids. Matching target text descriptions against these visual centroids in the shared image-text embedding space then enables retrieval of individual features without per-feature text annotations. The underlying patches provide evidence for inspecting each selection, while spatially masked interventions test the corresponding decoder direction at varying strengths under fixed generation conditions. We characterize 150 SAEs across two model families and five layers, and introduce a benchmark of 100 target concepts with ten contexts each spanning under-specified and explicit-conflict conditions. Our empirical results show that high reconstruction fidelity can coexist with low dictionary utilization and limited visual-evidence coverage. Under per-case best-of-sweep strength selection, contrastive retrieval yields larger mean regional SigLIP2 gains than direct retrieval across the tested steering configurations, without consistently improving outside-region preservation. D-Scope provides an inspectable framework for evaluating sparse DiT features through their visual evidence and the effects of their decoder directions on generation. The demo is available at https://jiahaozhang-public.github.io/d-scope/.

Xinyue Xu, Jiahao Zhang, Lijie Hu +2

Pivotal Research · Mohamed bin Zayed University of Artificial Intelligence · Schmidt Sciences +2

Diffusion Transformers Diffusion Models Decomposition

Sep 30, 2026cs.CV

Structural Limits of the Information-Theoretic Uncertainty Decomposition

Uncertainty estimation in machine learning typically decomposes uncertainty into aleatoric uncertainty (AU) and epistemic uncertainty (EU) using the standard information-theoretic framework. However, in practice, two critical issues arise: entanglement (AU and EU are highly correlated) and epistemic collapse (EU magnitude shrinks with increasing model capacity). We analyze this framework on a functional level and discover that significant portions of the assumed AU, EU range are infeasible in finite settings, and cannot be attained with any class probabilities. We characterize how this infeasible region scales with the number of classes and Monte Carlo samples

N

(e.g., from ensembles with

N

members), revealing it is bounded by

\text{AU} \leq \log(2)/N

. Crucially, the infeasible region's boundary helps explain epistemic collapse: when model confidence is high,

\text{AU} > \text{EU}

is guaranteed by this fundamental structural limitation. Our findings show that increasing ensemble size mitigates epistemic collapse by reducing the infeasible area. Lastly, we caution against interpreting AU and EU as independent quantities in low AU regimes, since we show they are coupled when

\text{AU} \leq \log(2)/N

.

Jakob Lønborg Christensen, Christian F. Baumgartner, Morten Rieger Hannemose +2

DTU Compute Technical University of Denmark · Faculty of Health Sciences and Medicine University of Lucerne

Dynamic Epistemic Logic Uncertainty Fundamental Limits Entanglement Decomposition

Sep 30, 2026stat.ML

Towards Optimal Inventory Control under Censored Demand: A Biased Sample-Average Approximation Approach

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.

Yuxuan Han, Xiaoyu Fan, Jiawei Zhang +1

Stern School of Business, New York University

Inventory Control Decomposition

Sep 30, 2026cs.CV

DecoMoE: Decoupling Visual Propagation and Expert Computation for Efficient Multimodal MoE Inference

Multimodal mixture-of-experts (MoE) models combine sparse expert activation with visual-language capabilities, yet their inference remains costly because long visual-token sequences repeatedly incur attention, routing, dispatch, and expert-MLP computation. Existing methods typically compress either the token or expert dimension, leaving redundancy along the other. Our analysis reveals two complementary regularities: the depth required for visual propagation varies across inputs, while text-token routing exhibits concentrated and recurrent expert-importance patterns. Based on these observations, we propose DecoMoE, a two-dimensional structured compression framework that decouples visual propagation from expert computation. The Sample-Adaptive Visual Boundary (SAVB) predicts an input-dependent visual-exit layer at which the visual-token block is removed. The Routing-Calibrated Expert Prefix (RCEP) reorders experts offline using text-token routed mass and, from this predicted exit layer onward, retains at each MoE layer the shortest contiguous prefix covering a target routed-mass fraction. We evaluate DecoMoE on Qwen3-VL-MoE and InternVL3.5-30B-A3B across six benchmarks. On Qwen3-VL-MoE, DecoMoE retains 97.91% of dense-baseline performance while reducing computation from 27.06 to 16.73 TFLOPs and latency from 0.44 to 0.26 seconds, yielding a 1.69x speedup. Code will be available at https://github.com/ShawnTan86/DecoMoE.

Xudong Tan, Peng Ye, Ming Xie +4

Fudan University · The Chinese University of Hong Kong

Mixture-Of-Expert Inference Mixture-Of-Experts Dense Baseline Decomposition Propagation

Sep 29, 2026cs.CV

Multi-Granularity Language-Guided Imitation Learning via Instruction Decomposition

Using language instructions as conditions to guide robot policy learning has recently become an important research domain. However, existing language-guided policy learning methods typically use an overall task description to guide the entire demonstration trajectory. For manipulation tasks involving multiple execution stages, these methods assign the same language description to different subtasks, making it difficult to distinguish the behaviors required at different stages. In this work, we propose a multi-granularity language guidance method based on instruction decomposition. The proposed method decomposes an overall task description into more fine-grained, concrete subtask-level language instructions, thereby enhancing learning efficiency and improving performance. We evaluate the proposed method in the setting of multi-task imitation learning and validate its effectiveness.

Yi-Pei Chiu, Wei-Ta Chu

National Cheng Kung University, Taiwan

Imitation Learning Decomposition

Sep 28, 2026cs.AI

AdaST: Adaptive Coupling for Spatial-Temporal Forecasting

Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

Zhenyu Lei, Chenghao Liu, Yushun Dong +2

University of Virginia Charlottesville, VA, USA · Datadog Paris, France · Florida State University Tallahassee, FL, USA +1

Spatio-Temporal Forecasting Temporal Dynamics Decomposition

Sep 27, 2026cs.AI

How code helps different tasks? A decompositional lens on LLM post-training

Evaluating code data as a single corpus can obscure which types of code data benefit which models and downstream tasks. Effective data selection requires understanding both the benefits of individual categories and whether these benefits persist when categories are combined. We introduce a decompositional lens for studying these effects in LLM post-training. We first decompose an execution-verified code corpus into interpretable categories based on the computational patterns of its solutions. Through controlled fine-tuning experiments, we compare individual categories with a balanced mixture across instruction-tuned models on question answering, mathematics, and code generation. The resulting response maps reveal recurring gains in average question-answering performance, while the same category can improve one model or task and degrade another. The best-performing category also varies with the starting model and target task. We then compose compact mixtures guided by these results and examine whether benefits observed in individual categories persist under joint training. On selected model--task pairs, mixtures whose constituents each improve the target task outperform both their best constituent and full-corpus training while using roughly 10--15% of the full corpus. These exploratory findings illustrate a \emph{less is more} pattern and highlight how the value of code data in post training depends on which categories are combined for which model and task.

Zheng Yu, Yiwei Li, Yishen Chen +4

Sun Yat-sen University · Shenzhen Loop Area Institute · The Chinese University of Hong Kong, Shenzhen +1

Instruction-Tuned Models Post-Training Decomposition

Sep 27, 2026cs.AI

DrafTS: Time-Aware Decomposition with Residual Correction for Time Series Modeling

Real-world time series contain evolving underlying dynamics with irregular variations that lack stable temporal patterns and are often referred to as noise. Existing methods address this mixture by filtering frequencies or suppressing noisy observations. They either miss temporal evolution or risk suppressing useful dynamics. We propose DrafTS, a model-agnostic framework that aims to reduce noise while preserving evolving dynamics through time-aware Decomposition with ResiduAl correction For Time Series. DrafTS uses features derived from instantaneous amplitude and frequency to guide decomposition into a primary component intended to capture underlying dynamics. A task-specific backbone models the primary component, while a lightweight correction module uses residual information to correct the backbone output. Across four time series modeling tasks, DrafTS improves six diverse backbones, demonstrating its effectiveness. Code is at https://github.com/Autumn61q/DrafTS

Yiqiu Liu, Siru Zhong, Zhiguang Wang +2

The Hong Kong University of Science and Technology (Guangzhou), China · Abel AI Lab, USA · Squirrel Ai Learning, USA

Time Series Temporal Dynamics Time-Frequency Decomposition Drafts

Sep 24, 2026math.DS

Functional dynamic mode decomposition: Learning infinite-dimensional systems from data

Dynamic mode decomposition (DMD) is a data-driven method that computes the best linear approximation of the underlying dynamical system and decomposes the dynamics into a superposition of characteristic spatiotemporal patterns. Originally introduced by the fluid dynamics community, DMD and its extensions have found widespread use in many other research areas such as molecular dynamics, climate science, engineering, finance, and neuroscience. Applications include dimensionality reduction, forecasting, system identification, control, and spectral clustering. In order to apply DMD to partial differential equations, the spatial domain is typically first discretized using finite difference or finite element techniques, thus implicitly rendering the problem finite-dimensional. We extend projected and exact DMD to infinite-dimensional systems. Rather than estimating matrices from vector-valued observations, our DMD variants learn finite-rank operators from functional data such as observables, densities, or wavefunctions. We show that conventional DMD algorithms can be regarded as special cases of their functional DMD counterparts. All results will be illustrated with the aid of guiding examples. We focus in particular on Koopman, Perron-Frobenius, and Koopman-von Neumann operators associated with graphons, ordinary differential equations, and stochastic differential equations.

Stefan Klus, Eirini Ioannou

School of Mathematical & Computer Sciences, Heriot–Watt University, Edinburgh, UK · Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University, Edinburgh, UK

Dynamic Mode Decomposition Dynamical Systems Stochastic Differential Equations Decomposition

Sep 22, 2026cs.RO

CODA: Depth-Aligned Scene Completion and Object Decomposition from a Single RGB-D Image

Robots operating safely in cluttered everyday environments often need to infer scene geometry from partial observations. Methods that detect objects in 2D and reconstruct them independently struggle in such scenes: a missed object is never reconstructed, a merged detection can fuse two objects, and separately reconstructed meshes may overlap or fail to touch their supporting surfaces. We introduce CODA (Complete Once, Decompose Afterward), a generative model that instead reconstructs the complete scene geometry from a single unsegmented RGB-D image, then separates the surface into the surrounding environment and movable objects. Still, generated scene geometry can drift from the observed partial point cloud. To reduce this drift, CODA uses two explicit 3D grounding mechanisms to keep reconstructed geometry consistent with observed surfaces while completing unseen regions. Experiments on HomebrewedDB and our custom cluttered-scene dataset show more accurate reconstructions and a higher fraction of objects remaining in place under simulated gravity than both object-first and scene-first baselines.

Dongwon Son, Junhyek Han, Yoontae Cho +5

KAIST · Samsung Heavy Industries Co., Ltd.

Rgb-Depth Cameras Completion Robot Systems Decomposition

Sep 20, 2026cs.LG

Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition

Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment. Existing approaches to out-of-distribution (OOD) generalization in operator learning are largely empirical and black-box: they report aggregate error metrics without explaining why errors arise or when they will grow. We propose a structure-preserving framework that makes OOD generalization predictable and auditable. Our key idea is to parameterize the learned solution operator as a spectral filter

h_θ(λ)

acting on the eigenvalues of the underlying elliptic operator, implemented via Chebyshev polynomial expansions and trained with a weak-form objective. This parameterization admits an exact decomposition of the energy-norm error into two observable components: a model-dependent spectral approximation term and a distribution-dependent spectral weighting term induced by the input. From this decomposition we derive three diagnostics: a conservative in-band supremum

\vareps_{\mathrm{sup}}

, a global RMS proxy

\vareps_{\mathrm{rms}}

, and a sample-dependent effective metric

\vareps_{\mathrm{eff}}(f)

. These diagnostics can be computed without access to ground-truth solutions. Through four controlled experiments, we show that

\vareps_{\mathrm{eff}}(f)\|f\|

consistently predicts energy error under in-distribution, in-band spectral shift, out-of-band tail, and compound shifts, whereas global metrics can be systematically misleading. Our framework shifts OOD assessment of neural operators from black-box benchmarking to operator-structure diagnostics, providing a practical route to auditable scientific machine learning.

Hang-Cheng Dong, Pengcheng Cheng

School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China · School of Mathematics, Jilin University, Changchun 130012, China

Neural Operators Out-Of-Distribution Spectral Representation Method Decomposition

Sep 17, 2026cs.AI

Refuse, Decompose, Refresh: A Claim-Safe Protocol for Closed-Loop AI Evaluation

An AI evaluation can be perfectly reproducible and still support the wrong claim. This risk is acute in closed-loop systems: policy determines visited states, observable components, and which failures leave a measurable trace. We propose a claim-safe protocol with three actions. Refuse: abstain when a clean reference stream or matched runtime comparison lacks support. Decompose: report protocol execution, operational false admission, and structural hypotheses separately rather than as one PASS/FAIL label. Refresh: treat distribution-shift alarms as requests to invalidate and recompute a reference map, not as fault evidence. We instantiate the protocol in an aggregate-only simulator with 24 policy components, three demand regimes, two fault-mask families, and independent development and heldout seeds. The preregistered heldout contains 1,440 cases and 21,600 partition rows. Only 55/72 regime-component units were reference-admitted and 54/55 remained runtime-admitted, making abstention part of the result. Stable false admission was 0/20 represented components, with a one-sided exact 95% upper bound of 0.1391 under a frozen 0.20 rule. Within admitted units, affected clean traffic outpredicted nominal fault-cell fraction: across 540 unit-arm rows nested in 20 component clusters, the cell-minus-traffic negative-log-likelihood difference was 0.1264 nats per row, with a 95% component-cluster interval of [0.0593, 0.1918]. A drift log shows why "null" must be reference-relative: clean fault-null streams triggered 15/15, 0/15, and 14/15 alarms across three regimes, while only the middle regime matched the frozen detector reference. Rather than a universal threshold, we contribute an executable contract linking observable support, statistical calibration, and justified claims.

Peiying Zhu, Sidi Chang

Blossom AI San Francisco, CA, USA

Artificial Intelligence Evaluation Admissibility Decomposition

Sep 17, 2026cs.AI

Perception, Layout, and Validation: Calibrated Confidence for Reliable Straight-Through Processing of Financial Documents

Straight-through processing (STP) on extracted key-value fields from financial documents without human review requires a calibrated probability together with a bounded guarantee on the residual error of the auto-approved tier. The emergence of modern Vision Language Models (VLMs) provides an out-of-the-box capability for extracting the key-values, but their verbalized confidence signals are unreliable and weakly track field correctness. This paper introduces a decomposed confidence layer along three interpretable channels, including perception, layout, and validation. Together with a final conformal risk control, the score can be used for reliable STP of financial documents. The method is validated on three public datasets covering real invoices, synthetic invoices, and ad-buy forms, using two different VLM families (Qwen3.6-27B and Gemini-3.1-Flash-Lite). Our decomposed score consistently improves the separation of correct from incorrect extractions, substantially raising the AUROC from 0.54-0.74 for VLM verbalized signals to 0.90-0.99 with contributions from all three designed channels. Crucially for industrial deployment, this enables usable STP. The native VLM confidence signals could clear only 0.1%-7.0% of fields under risk control at a target error of <10%. In contrast, the proposed method auto-approves 49-72% of fields while holding the empirical error of the accepted tier at or below the target.

Yichao Jin, Yushuo Wang, Yuxuan Han +7

OCBC, Singapore

Validation Large Language Model Reliability Decomposition Layouts

Sep 15, 2026cs.LG

NObSP: Functional Decomposition of Neural Networks via Oblique Subspace Projections

Understanding how deep neural networks make decisions remains a fundamental challenge. We present NObSP (Nonlinear Oblique Subspace Projections), a framework that decomposes predictions into explicit per feature contribution functions and an interaction residual. NObSP exploits the linear final layer of a trained network and uses oblique projections in sample space to reduce double counting when learned feature subspaces overlap, thereby supporting both local explanations and global functional analysis. We establish connections to functional ANOVA and the Kolmogorov-Arnold representation theorem and derive an efficient partial regression algorithm for out of sample evaluation. For convolutional networks, NObSP-CAM produces class activation maps without backward passes after a one time calibration. Experiments on tabular and vision benchmarks show faithfulness comparable to established attribution methods. On a synthetic benchmark with known component functions, NObSP obtains a Function Reproduction Score of 0.989, compared with 0.966 for KernelSHAP and 0.922 for Integrated Gradients. On TinyImageNet, contribution vector embeddings improve mean nearest neighbor class purity from 0.654 for raw activations to 0.713 and reduce mean neighbor distance by more than half. These results indicate that NObSP complements scalar attribution methods by recovering functional contribution profiles with separable positive and negative evidence.

Alexander Caicedo, Víctor De La Hoz, Santiago Alférez

Department of Electronic Engineering, Pontificia Universidad Javeriana, Bogot´a, Colombia · Pontificia Universidad Javeriana, Bogot´a, Colombia · Department of Mathematics, Universitat Polit`ecnica de Catalunya, Barcelona, Spain

Neural Network Subspace Convolutional Neural Networks Decomposition Camera

Sep 15, 2026cs.AI

A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning

Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it. We reconcile these observations with a mechanistic account. We show that the model's internal computation decomposes into a four-stage sequential pipeline, Schema Abstraction, Operation Planning, Operand Binding, and Computation, each stage producing a distinct intermediate representation in an identifiable band of layers. Using the same scaffold to diagnose distractor-induced failure, we localize the corruption to a single stage, Operation Planning, implemented by a set of attention heads whose causal role we validate bidirectionally. In short, we provide a mechanistic interpretation of math word problem reasoning in LLMs, and their failure when distracted.

Zhongdi Qu, Carla P. Gomes

Cornell University

Math Problems LLM Reasoning Strategies Distractor Decomposition Fragility

Sep 15, 2026cs.MA

Decomposition Buys Integrity, Not Yield

Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism. We ask what the split does to how much of what the leaves discover reaches the root. Model a decomposition as a tree in which an agent handed

b

items keeps any one with probability

r(b)

. If

r(b)=1/b

, every tree delivers exactly one finding, for every task size and every shape; we verify this to

2.4 \times 10^{-15}

on 20,000 random irregular trees. If

r(b)=Cb^{-δ}

, a depth-

k

tree over

N

findings yields

C^k N^{1-δ}

: task size and architecture separate, and architecture contributes only

C \le 1

per level, so flat is optimal for yield and no arrangement of agents escapes the exponent

δ

. On 600 production deep-research traces

δ= 0.34

[0.30, 0.38], by three identifications that do not share a failure mode. At a hop where item boundaries come from the tool rather than a text heuristic, and where

b=1

occurs 550 times,

C = 0.571

[0.527, 0.615] is observed rather than extrapolated, over 16,082 hops. A tier also costs alignment: on 1,012 annotated multi-agent traces one brief in sixteen goes off-target, giving

μ= 0.939

and a per-tier penalty

Cμ= 0.536

. Depth is bought on two other axes. The root context is the only state that persists and the only one that cannot cheaply forget, and depth cuts its exposure from

N

items to

N^{1/k}

. Depth is also cheaper: production flat agents bill as

N^{1.39}

, not the

N^2

an append-only context predicts, and at equal spend two tiers overtake flat at 403 findings. Across every parameter we measured the model says 0.7% to 11.3% of production sessions are worth delegating, against 7.8% that do. A hazard model on 743,819 production tool calls finds that delegation does not respond to a filling context and is instead an opening move.

Rong He

Delegation Decomposition Task-Level Deep Research

Sep 14, 2026cs.LG

MoARa: Module-Aware Rank Allocation and Structure-Preserving Decomposition for Low-Rank LLM Pre-training

Low-rank gradient projection reduces the optimizer-state memory cost of large language model (LLM) pretraining, but the steps and wall-clock time needed to reach a target quality remain a meaningful axis for improvement. We attribute this to two design choices in existing methods: the projection-rank budget is allocated uniformly across Transformer modules with heterogeneous projection sensitivity, and projecting a raw gradient attenuates its magnitude and direction jointly. We propose MoARa, which combines a static profiling-based module-aware projection-rank allocation with a block-wise magnitude-direction decomposition; the default block size is set in the neighborhood of the attention head dimension. Across five Transformer architectures spanning Llama, Qwen, and DeepSeek at 300M to 7B scales, GaLore with MoARa reaches standard GaLore's final perplexity in 37% fewer steps and 34% less wall-clock time on Llama 2 7B, with only 0.2% peak reserved memory overhead under standard graph compilation. Across the six low-rank pretraining methods we evaluate, module-aware rank allocation alone delivers directionally consistent step reductions on all six. On compatible hosts, the two-component design reaches up to 41.7% step reduction and 37.1% wall-clock reduction.

Keunyoung Kim, Nojun Kwak

Seoul National University

Large Language Model Pretraining Transformer Architectures Decomposition

Sep 10, 2026stat.ML

Identifiability of Nonnegative Tensor Decompositions via Positive Scattering

Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families. For nonnegative decompositions, however, positivity provides additional information that is not captured by dimension and independence alone: nonnegative terms cannot cancel, and their supports constrain competing decompositions. We introduce a positive scattering term that quantifies this additional source of identifiability and combine it with the dimension budget underlying the Lovitz--Petrov generalization of Kruskal's theorem. For every subset of components, we obtain two sufficient conditions: a threshold of

2|S|-2

guarantees minimality and nonnegative rank, while the stronger threshold

2|S|-1

guarantees uniqueness among nonnegative decompositions of the same length. The key result is a positive splitting inequality for irreducible exchanges of nonnegative rank-one tensors, which combines the dimension constraint with support-induced geometric rigidity. Although the scattering term is defined through an optimization over intermediate factor spaces, we show that its mode costs are exactly

0

,

1

, or

+\infty

, yielding an exact activation characterization in terms of graph connectivity. The resulting criterion can strictly certify sparse nonnegative tensor decompositions beyond the reach of Kruskal and Lovitz--Petrov conditions, including examples for which those conditions fail even after reshaping. In the matrix case, the two criteria reduce respectively to full-rank factorization and two-sided separability.

Haoming Wang, Ming Yuan

Columbia University

Tensor Decomposition Identifiability Decomposition Separability

Sep 10, 2026stat.ML

A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs

Feature-based explanations quantify features' influence on model predictions, but are primarily designed for scalar outputs. In many applications, however, outputs are functional or multivariate, such as time-dependent trajectories in demand forecasting. Consequently, existing approaches typically explain each output location independently, ignoring dependencies across the output components. We address this limitation by developing a unified framework for feature-based explanations of time-dependent outputs. Specifically, we generalize functional decomposition to Hilbert-valued prediction functions and extend an existing feature-based explanation framework to this setting. Our framework introduces kernel-based output representations that enable time-dependency-aware explanations at multiple levels of temporal granularity, including time-specific, time-resolved, and time-aggregated, while providing a unified view in which existing methods arise as special cases. We validate our framework on synthetic and real-world data, including intraday financial market volatility prediction and energy demand forecasting.

Sophie Hanna Langbein, Niklas Koenen, Marvin N. Wright +1

Leibniz Institute for Prevention Research and Epidemiology – BIPS, Bremen, Germany · Faculty of Mathematics and Computer Science, University of Bremen, Germany

Decomposition Electricity Price Forecasting

Sep 10, 2026eess.AS

Diarization Error Decomposition Under Pause Annotation Ambiguity

Speaker diarization evaluation is sensitive to ambiguity in pause annotation, which can inflate diarization error rate (DER) or obscure genuine model errors. We show that morphological closing, which has been used for pause-tolerant diarization evaluation, discards segment-level distinctions. Instead, we propose an exact, overlap-aware decomposition of standard DER into a pause-attributable component, consisting of errors compatible with pause filling, and a residual core component that can serve as a proxy for intrinsic diarization errors. The decomposition leaves DER unchanged, while the pause-attributable and core components vary monotonically with the pause threshold and eventually saturate. Experiments spanning synthetic transformations, annotation mismatch, cross-domain evaluation, and tight-boundary diarization show that the decomposition reveals error sources not apparent from standard DER.

Shota Horiguchi, Marc Delcroix, Naohiro Tawara +1

NTT, Inc., Japan

Speaker Diarization Ambiguity Decomposition Mismatch Closure

Sep 8, 2026cs.CL

ToolLoop: Closed-Loop Tool-Use Data Synthesis via Decomposed Generation and Dynamic Self-Feedback

High-quality tool-use data is critical for training language models to interact effectively with external tools. However, existing synthetic approaches typically follow a generate-then-filter paradigm with static post-hoc verification, often yielding inefficient data with imbalanced feature distributions. We propose ToolLoop, a closed-loop framework that decomposes synthesis into three progressive stages: (1) sampling function name combinations as ground truth; (2) backward derivation of user queries; and (3) forward derivation of tool calls. At each stage, dynamic self-feedback iteratively guides the model toward high-quality generation, realizing a transition from generate-then-filter to generate-verify-refine. On the Berkeley Function Calling Leaderboard (BFCL), a 4B parameter model trained with our 11K synthetic examples achieves 86.40% accuracy in non-reasoning mode, while an Isolate variant that removes BFCL-overlapping candidate functions still reaches 86.07%. Cross-benchmark evaluation on ACEBench further demonstrates strong generalization, with 72.1% overall accuracy using only 18.3% of baseline training data.

Min Zeng, Yuzhou Liu, Zhenyu Cao +5

vivo AI Lab

Loop Decomposition

Sep 7, 2026cs.AI

Aplaud: Adaptive Personalized Low-Rank Decomposition for User-Specific LLM

In this paper, we study the problem of personalized survey response prediction using fine-tuned large language models (LLMs). This task poses unique challenges: limited per-user training data, scalability of model storage, and the need to exploit shared structure across survey questions. To address these issues, we propose Aplaud (Adaptive Personalized Low-rank and User-specific Nested Decomposition), a lightweight and scalable framework for LLM personalization. Aplaud extends the LoRA paradigm by separating adaptation into a frozen, shared low-rank basis and a compact user-specific correction, augmented with a rank-one residual for finer personalization. To further reduce per-user parameter cost and mitigate overfitting, the correction matrix can be factorized into an even lower-rank form. Empirical results demonstrate that Aplaud achieves efficient, scalable personalization across users while outperforming state-of-the-art LoRA-based personalized LLM approaches in both generalization and inference efficiency.

Xinyu Li, Ruoming Jin, Jianfeng Zhu +2

Department of Computer Science, Kent State University · iLambda Inc.

Large Language Model Personalization Personalization Low-Rank Adaptation Framework Large Language Model Fine-Tuning Survey Decomposition

Sep 4, 2026cs.AI

Planning and Scheduling Business Processes under Control-Flow Uncertainty: Extended Version

Scheduling activities in business processes can improve efficiency (e.g., reduce makespan), but is challenging because the exact sequence of activities required to complete a case is often uncertain due to decisions based on data that emerges during execution. Nevertheless, probabilistic information regarding such decisions can often be estimated or derived from historical execution logs, and can help anticipate which execution paths are likely to lead to successful completion. Planning with particular execution paths affects feasibility, i.e., the probability of successful completion, and the expected number of superfluous activities that are planned but never executed. We frame the problem as a chance-constrained optimization problem and present two formulations: A decomposed approach with two stages, a planning stage that minimizes the expected number of superfluous activities subject to a feasibility constraint, and a scheduling stage that minimizes the makespan over the planned activities; and an integrated approach that combines planning and scheduling into a single formulation. Evaluation on two real-world and one synthetic dataset shows that the integrated approach yields superior makespans but is intractable at scale, while the decomposed approach scales to large settings.

Michel Kunkler, Stefanie Rinderle-Ma

Technical University of Munich, Germany TUM School of Computation, Information, and Technology

Job Shop Scheduling Schedule Planning Sequential Decision Making Extended Version Decomposition

Sep 3, 2026cs.CL

Investigating the Ability of Large Language Models to Analyze Recipes for Diabetes

Several studies have evaluated the ability of Large Language Models (LLMs) for meal planning, yielding positive outcomes. These models can process natural language inputs and leverage learned knowledge from their pretraining to generate meal plans. In this work, we investigate the ability of LLMs to analyze the suitability of given recipes for diabetes. The primary challenge for LLMs is to retrieve relevant dietary guidelines for diabetes, decompose recipes into ingredients and cooking methods, and apply these guidelines to determine the recipe's suitability. To study these challenges, we employ three kinds of prompts namely, (i) Direct Query Prompt (ii) Context-Guided Prompt, and (iii) Exemplary Context Prompt that incorporate different levels of diabetes dietary guidelines from medical sources. We introduce a benchmark dataset curated for this investigation consisting of 7607 recipes that include 3807 recipes suitable for diabetes and 3800 recipes not suitable for diabetes. Our results demonstrate that most LLMs are cautious in predicting recipes as suitable to prevent detrimental outcomes. Further, the models that can reason using the dietary guidelines performed better in predicting the suitability of recipes for diabetes. Overall, Mistral-7B and Llama 70B showed superior performance to their counterparts.

Revathy Venkataramanan, Aditya Luthra, Venkatesan Nadimuthu +1

AI Institute, University of South Carolina 1112 Greene Street, Columbia, SC 29201 USA

Diet Diabetes Recipe Decomposition

Aug 31, 2026cs.CV

ObjectSplat: Improving Mesh Fidelity and Interactivity for 3D Scenes via Object-Level Mesh Splatting

Splatting-based algorithms reconstruct photorealistic, real-time-renderable, and mesh-exportable 3D scenes from regular images, but they represent a scene as a single monolithic field. Therefore, the reconstruction has no object-level structure, leaving it infeasible for downstream editing or interaction. Moreover, regions that are never directly observed in the input scans are contaminated by the surrounding texture and left uncorrected, capping both mesh fidelity and novel-view synthesis. We propose a decompose-before-reconstruct approach: we segment the instances out of every frame, consider the remaining as background and inpaint it, reconstruct each instance and the background independently with mesh splatting, and compose them into a single scene. Our method significantly improves mesh fidelity (over a 5% gain in F-score) and novel-view synthesis, while supporting object-wise modifiability and interactivity. The code will be made publicly available.

Minhas Kamal, Hiranya Garbha Kumar, Mahedi Kamal +1

State University of New York at Albany, USA

Scene Reconstruction Novel View Synthesis Decomposition Interactivity Field Evaluation

Aug 29, 2026cs.CV

A Globally Convergent Algorithm for Total Scaled-Gradient Variation via Cone-Constrained Bilinear Decomposition

The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edges and corners in image restoration. However, its highly nonconvex and nonlinear nature poses severe computational challenges, as existing methods often suffer from parameter sensitivity or lack convergence guarantees. To overcome this, we propose a tailored bilinear decomposition that decouples the nonlinear weighted gradient in the TSGV regularizer. This approach yields an equivalent optimization problem governed by cone or sphere constraints, depending on the chosen scaling function. In particular, the cone constraint plays a central role in characterizing edge- and corner-preserving behavior. We solve this reformulation using the alternating minimization method (AMM) equipped with a majorization--minimization strategy, ensuring a monotonic decrease in energy without step-size tuning. Furthermore, we provide a geometric interpretation of the edge-preserving properties of these constraints by analyzing their asymptotic behavior near image singularities. We establish the global convergence of the proposed method to a critical point within the Kurdyka--Łojasiewicz framework. Extensive numerical experiments on Gaussian denoising and non-line-of-sight (NLOS) imaging show that the proposed method achieves PSNR and SSIM competitive with or superior to representative variational methods, especially at high noise levels, and improves the structural reconstruction under dense and sparse scanning.

Haibin Su, Chunlin Wu, Huibin Chang +1

Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China · School of Mathematical Sciences, Nankai University, Tianjin, 300071, China · School of Mathematical Sciences and Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University, Tianjin, 300387, China

Image Restoration Convergence Decomposition Structural Constraints

Aug 13, 2026cs.CV

SCULPT: Subtractive Composition for 3D Part Generation

Part-aware 3D generation aims to create digital assets that are coherent as complete objects while exposing structural parts for editing, material assignment, animation, and reuse. Existing methods impose this structure outside the native generation loop: segmentation-based methods partition an already generated shape, while additive methods synthesize parts from predefined layouts, boxes, or tokens and then reconcile them into a whole. The former preserves the generated geometry but fixes the object before part boundaries are determined; the latter exposes part cardinality but often leaves shared boundaries vulnerable to gaps, interpenetrations, and material discontinuities. In this paper, we propose SCULPT, a framework that addresses these challenges through subtractive composition. Given a complete object represented in a structured 3D latent space, SCULPT iteratively applies a joint split predictor to generate one extracted part together with the remaining object. The predictor performs a coupled denoising process conditioned on both the image and the current 3D state, so the extracted part and updated remainder are generated together rather than reconciled after generation. The joint split predictor processes both outputs on the union of their native sparse 3D supports, allowing neighboring supports to overlap rather than imposing a disjoint voxel partition. The rollout ends when the remainder support becomes empty or reaches a fixed safety cap, allowing the number of generated parts to adapt to each object within that bound. Extensive experiments demonstrate state-of-the-art geometry on PartObjaverse while preserving strong complete-object reconstruction after part assembly. Results on four dataset images, one text-to-image-generated input, and one real-world photograph further show fine-grained textured part decomposition beyond the benchmark.

Sikuang Li, Chen Yang, Jiemin Fang +5

Shanghai Jiao Tong University · This work was done during an internship at Huawei. · Huawei

3D Models Art Decomposition Text-To-Image

Aug 13, 2026cs.CL

Better Decomposition, Free Aggregation: A Synthesizer-Folding Framework for Multilingual Multi-Hop Question Answering

Multilingual retrieval-augmented generation (mRAG) equips large language models with access to globally distributed external knowledge for complex multilingual question answering. Recent approaches either translate retrieved documents into English or the query language to bridge the cross-lingual semantic gap, or decompose a complex query into sub-questions and aggregate the intermediate reasoning process. However, both lines of work suffer from two limitations. First, one-size-fits-all translation alignment, blanket translation discards culturally and linguistically native information unique to the target language, introduces translation noise, and inflates system cost. Second, greedy decomposition and aggregation, uncontrolled decomposition produces redundant sub-questions that compound errors during step-wise reasoning, and the final aggregation over reasoning paths further amplifies these errors. We address both with our method Syfer, a synthesizer-folding framework for multilingual multi-hop question answering that defers translation rather than applying it by default. Syfer first invokes a format-constrained decomposer to produce a sub-question graph in the original language, followed by a decomposition-quality check; when the check passes, sub-questions are answered sequentially under a retrieve-then-answer policy in the target language, and the English translation pathway with bilingual sub-question graph alignment is activated only when the check fails. Experiments across multiple languages show that Syfer attains competitive accuracy while striking a favourable balance between performance and computational cost.

Yilin Wang, Yuchun Fan, Weidong Bao +5

School of Computer Science and Engineering, Northeastern University, Shenyang, China · Yunnan Key Laboratory of Artificial Intelligence, Kunming University of Science and Technology, Kunming, China

Cross-Lingual Consistency Translation Quality Decomposition Free

Aug 13, 2026cs.AI

DMDIntel: Interpreting Large Language Models via Dynamic Mode Decomposition

In this work, we introduce DMDIntel which uses dynamic mode decomposition (DMD) to make the predictions made by LLMs in a classification task interpretable. It develops an input attribution pipeline, that first decomposes the hidden states of an LLM into prominent patterns, also known as modes, and then associates ranks to the input tokens based on the projection values on those modes. Rigorous experiments across three datasets and three model families consistently show that the ranked attribution of input tokens obtained using DMDIntel by far outperforms state-of-the-art techniques such as principal component analysis, integrated gradients and SHAP.

Amogh Joshi, Animesh Mukherjee, Sergey Utyuzhnikov

IIT Kharagpur, India · University of Manchester, UK

Decomposition Dynamic Mode Decomposition Nvidia Principal Component Analysis

Aug 13, 2026cs.AI

Decomposition of Evidence, Contradiction, and Fragility in Perturbation Responses

Perturbation methods explain model decisions by measuring prediction changes under altered inputs, but response magnitude tells us only how much a model reacts, not what that reaction means. The same magnitude can support the final factual-counterfactual difference, oppose it, or arise strongly along the perturbation path yet vanish at the endpoint. We therefore track how the contrast develops as paired inputs are progressively revealed, using the final contrast to interpret the trajectory. We introduce DECAF (Decomposition of Evidence, Contradiction, And Fragility), which routes aligned, opposed, and endpoint-null responses into evidence E, contradiction C, and fragility F. The decomposition preserves ordinary magnitude exactly, Abs = E + C + F, and is unique under endpoint-relative axioms. Across controlled vision and tabular settings, the three components track independently measured behavior. In a 72-model ImageNet-9 audit, we compare cases with nearly identical response magnitude but different independently measured behaviors. The largest DECAF component agrees with an observed behavior in 96.4% of cases, compared with 35.0% for magnitude alone. Changing only the reveal path increases total response by nearly 80%, yet evidence barely changes while fragility grows by more than 4x. On FunnyBirds and ImageNet-1k, short forward-only DECAF trajectories outperform the tested general-purpose attribution baselines. On a 1B-scale DINOv2 model, a short trajectory matches a strong gradient-based baseline with 4.75x lower wall time and 2.36x lower peak memory.

Lei You

Technical University of Denmark

Fragility Contradiction Decomposition Responses

Aug 11, 2026cs.CV

When Visual Signals Mislead: A Mechanistic Study of Attribute Hallucination in Vision-Language Models

Attribute hallucination---where vision-language models (VLMs) correctly identify an object but mischaracterize its properties---is prevalent yet mechanistically poorly understood. The dominant explanation, language-prior dominance, has motivated prior-suppression methods, but this explanation has not been directly tested at the attribute level. We present VISOR (Visual-Operational Remediation), a unified framework that couples null-image-based diagnosis with routed remediation. Its VSNR diagnostic decomposes each prediction into a visual logit signal and a language-prior signal. Across 10,791 negative-ground-truth samples from three VLM families and three attribute types, the visual signal strongly predicts false positives, whereas the language-prior signal is near chance. VISOR uses this diagnosis to separate two failure modes: low-margin but directionally correct visual signals in color/state attributes, and low-SNR or misaligned visual signals in material attributes. The same diagnosis routes each query to the appropriate operator: calibration for threshold-placement errors, abstention for training-free low-SNR handling, or targeted visual adaptation for material failures that prior suppression cannot correct. Across Qwen, InternVL, and LLaVA, VISOR reduces attribute false positives without relying on the prior-dominance assumption.

Yufei Zhang, Chenlu Zhan, Hongwei Wang

Zhejiang University

Object Hallucination Remediation Decomposition

Aug 11, 2026cs.CL

Decomposition-Induced Context-Memory Conflict: When Fact-Checking Pipelines Contradict Their Own Source Text

Decompose-then-verify pipelines, including FActScore-style fact-checkers and long-form factuality evaluators, first split a passage into atomic claims before checking each one. Decomposition itself is treated as a neutral preprocessing step. We show it is not: a decomposer can be induced to substitute its own parametric belief for what the source passage says, producing a claim that contradicts the text it was supposed to summarize faithfully. We call this Decomposition-Induced Context-Memory Conflict (DI-CC) and show it is mechanistically the same phenomenon as classical context-memory conflict, occurring inside a different pipeline stage than prior work has examined. A linear probe trained only on classical context-memory conflict data (NQ-Swap), never exposed to any decomposition output, significantly separates decomposition positions that produce DI-CC from faithful decompositions (AUC = 0.86-0.88, permutation p < 0.0005). An existing reference-free baseline, SelfCheckGPT-style self-consistency sampling, fails to detect DI-CC at all (AUC 0.51, chance-level), because DI-CC content is stably recoverable and recurs across resamples, unlike the variability self-consistency methods rely on. Context-aware decoding, a training-free mitigation from the classical setting, transfers to decomposition and suppresses DI-CC, but at a severe cost: many decompositions under coreference-heavy conditions fail to parse, often because the decomposer fabricates a different identity. We do not consider this mitigation deployment-ready. We further characterize the mechanism's boundaries: its natural occurrence rate is too sparss not manifest on naturally-occurring hallucinatedtext, and it requires a minimum model scale to detecablish DI-CC as a real, mechanistically grounded, andpartially treatable failure mode, with a scope we chhan overstate.

Yu-Feng Yen

Independent Researcher

Fact-Checking Decomposition Text Analysis and Detection

Aug 10, 2026cs.LG

Intrinsic Structure: Spectral Identifiability for Mechanistic Interpretability

Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it. Sparse autoencoders illustrate the problem: different seeds and widths recover materially different features from the same activations, and no theory says whether that variability is incidental or structural. We put dictionary learning for interpretability on an identifiability footing. Treating the forward pass as a controlled dynamical system with depth as time and lifting it with the Koopman operator yields a finite linear realisation whose \emph{spectrum} is a coordinate-free property of the model. We prove the spectrum is recoverable from

M

calibration samples at rate

M^{-1/2}

up to permutation - to our knowledge the first identifiability theorem for a mechanistic-interpretability primitive, with a matching minimax lower bound, a median-of-means variant for heavy-tailed activations, and a dissociation theorem: whenever the realisation is non-normal, the directions carrying activation variance and the directions carrying information across depth cannot coincide. The identifiable object and the legible object are not the same object. On GPT-2 small, Gemma-2-2B and Qwen3-8B-Base the spectrum converges everywhere and attains the predicted exponent on Qwen3-8B-Base (

0.506 \pm 0.031

); shortfalls collapse onto one curve against each cell's sample threshold. Koopman modes beat random directions but lose to principal components on indirect-object identification, with the gap decaying

4.1\times

in depth-distance, as the theorem predicts. The Koopman spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.

Ashim Dhor, Pin-Yu Chen

1IISER Bhopal · 2IBM Research

Mechanistic Interpretability Interpretability Identifiability Koopman Operator Decomposition

Aug 10, 2026cs.RO

Navigating the Proximity-Safety Balance: Constraint Decomposition for Human Following in Pedestrian Crowds

Following a target human in crowded environments involves an inherent conflict between staying close to the target and navigating safely among surrounding pedestrians and obstacles. This conflict becomes more severe in dense scenarios, where aggressive following risks collisions and conservative margins lead to target loss, especially when pedestrian behaviors are unfamiliar or unpredictable. Existing reinforcement learning (RL) methods typically encode these competing objectives into a single dense reward, but the resulting proximity-safety balance is implicit and difficult to adjust across conditions. To address this, we decompose the human-following task into a sparse task reward and independent cost constraints within a multi-constraint RL formulation, where each constraint is managed through cost thresholds with direct behavioral meaning rather than implicit reward weight ratios, allowing explicit and tunable control over the trade-off. We further quantify the prediction uncertainty of human motions and integrate these estimates into the RL costs to enhance safety under unpredictable conditions. Extensive experiments across both in-distribution and out-of-distribution settings demonstrate that our method achieves an effective proximity-safety balance compared to baselines. Real-robot deployment further validates the feasibility of our method in real-world scenarios. More details are available on our project page: https://nav-ps-balance.github.io/.

Shiting Gong, Jianpeng Yao, Jinfeng Wang +2

University of Pennsylvania, PA, USA · University of California, Riverside, CA, USA · 3Stanford University, CA, USA +2

Safety Constraints Pedestrian Human-Robot Collaboration Proximity Operations Multi-Objective Reinforcement Learning Decomposition

Aug 10, 2026cs.RO

Efficient Real-World Online Reinforcement Learning for Robot Manipulation via Centralized Training and Critic Decomposition

Real-world online reinforcement learning (RL) provides a promising approach for training robotic manipulation policies directly in the physical world, avoiding the sim-to-real gap and enabling continuous policy refinement through human-in-the-loop interaction. Recent methods have demonstrated sample-efficient learning through human intervention but remain limited to small randomization ranges and encounter challenges with the non-stationarity induced by concurrently training multiple agents. To address these limitations, we introduce a unified framework that combines centralized training with decentralized execution (CTDE) and a Hybrid Reward Architecture (HRA). This enables multiple actors to share a centralized multi-head critic. The critic is decomposed into task and grasp heads, corresponding to the sparse task reward and a potential-based grasping reward, respectively. We accordingly reformulate the critic and actor objectives to exploit the decomposed Q-values while explicitly accounting for the categorical action distribution of the discrete gripper policy. Experimental results demonstrate that the proposed framework substantially improves both sample efficiency and policy performance. We validate our approach on two robotic arms and a simulated humanoid robot across tennis ball and banana pick-and-place, pot reset, and simulated block relocation tasks under dimension-wise domain randomization, approximately 5-25x larger than those considered in prior work. Compared with a state-of-the-art baseline, our method improves the success rate from 60% to 80% on tennis ball pick-and-place, from 60% to 90% on banana pick-and-place, and from 25% to 95% on simulated block relocation, while also successfully accomplishing a task where the baseline consistently fails. Videos and more details are available at our project website: https://hil-harc.github.io/.

Changhao Li, Yifang Zhang, Heng Zhang +6

HHCM, Istituto Italiano di Tecnologia, Genoa, Italy · DIBRIS, University of Genova, Genova, Italy · Human-Robot Interfaces and Interaction Lab, Istituto Italiano di Tecnologia, Genova, Italy +1

Robotic Manipulation Policies Robotic Manipulation Critic-Free Reinforcement Learning Table Tennis Robot Decomposition

Aug 8, 2026cs.CL

A Grounded and Decomposed Framework for Relation-Level Hallucination Evaluation in Abstractive Summarization

Abstractive text summarization systems frequently generate fluent yet unfaithful summaries by fabricating or distorting relationships between entities and events. Such relation-level hallucinations undermine the reliability of generated summaries, particularly in high-stakes domains. In this work, we present a refined and grounded framework for evaluating relation hallucination in abstractive summarization. We present the empirical Relation Hallucination Index (RHI) by introducing a dependency-aware relation extraction algorithm that incorporates lemmatization-based normalization, named entity grounded subject resolution, passive agent recovery, negation-aware verb modeling, reporting verb filtering, nominal relation fallback, clausal propagation, and systematic deduplication. These enhancements improve the structural fidelity of extracted relation triples and reduce spurious matches during evaluation. In addition, we introduce a normalized formulation of RHI to ensure scale-invariant comparison between datasets and models. The revised metric decomposes hallucination into interpretable components, aggregates relation hallucination metric into a normalized relation faithfulness score. Extensive evaluation across multiple state-of-the-art summarization models demonstrates that the grounded extraction process yields more stable and discriminative hallucination measurements. The proposed framework advances automated relation-level faithfulness evaluation and supports coherence-aware, hallucination-sensitive model analysis.

Praveen Kumar Katwe, Rakesh Chandra Balabantaray, Kali Prasad Vittala +1

Dept. of CSE IIIT Bhubaneswar Bhubaneswar, Odisha, India · Informatica Bengaluru, Karnataka, India · TEKsystems Global Services Bengaluru, Karnataka, India

Citation Hallucination Detection Summarization Relation Extraction Entailment Extraction Decomposition

Aug 7, 2026cs.LG

Omni-modal decomposition autoencoders learn full-stack wearable disentangled representations

Learning disentangled representations is a key requirement for developing versatile, general-purpose, and sustainable models in multi-modal wearable computing. However, existing approaches do not operate as full-stack wearable processors, i.e., they do not simultaneously address task-specific classification performance, disentangled and interpretable representation learning, fusion, and generative modeling of highly heterogeneous multi-modal time series. To address this gap, we introduce Omni-modal Variational Decomposition Autoencoders (OmniDecVAEs), a framework that efficiently learns multi-purpose representations in a unified and scalable manner from arbitrarily many modalities. OmniDecVAEs extend DecVAEs by learning modality-conditioned time-frequency latent subspaces through a multi-view self-supervised decomposition loss and a shared asymmetric autoencoder (AE) architecture. Results on a challenging omni-modal human activity recognition (HAR) setting with up to thirty modalities, demonstrate the ability of OmniDecVAEs to learn full-stack wearable representations. When compared to transformer-based and VAE-based methods, OmniDecVAEs full-stack disentangled representation properties lead to accuracy improvements of 1.01% and 6.75% in activity and identity recognition, respectively. Furthermore, OmniDecVAEs synthesize realistic omni-modal time-frequency data that manifest with enhanced reconstructions (mean absolute error improves by 76.84%) and distributional similarity between real and synthetic data (maximum mean discrepancy improves by 13.85%). Our results highlight OmniDecVAEs potential as a lightweight model suitable for intelligent edge wearables and clinical healthcare, unifying processing requirements and abilities in a single model, through its enhanced representational capacity, modality-invariant spatial complexity (4.1M parameters), and real-time latency.

Ioannis Ziogas, Ensieh Khazaei, Bilal Taha +4

Department of Biomedical Engineering and Biotechnology, Khalifa University, 127788 Abu Dhabi, UAE · Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 1A1, Canada · MIT Media Lab +2

Multimodal Deep Learning Human Activity Recognition Conditional Variational Autoencoder Autoencoder Architectures Omnichem Time-Frequency+1

Aug 5, 2026cs.AI

OrchestraBench: Evaluating Multi-Agent Orchestration Failure Modes, Recovery, and Decomposition Quality

Multi-agent orchestration frameworks are moving from demos to production, yet benchmarks typically report task accuracy without diagnosing why a pipeline failed, where a cascade began, or which routing decision caused the breakdown. OrchestraBench evaluates failure, recovery, and decomposition through a controlled, seed-reproducible failure-injection harness over templated enterprise workflows. It introduces cascade radius and per-failure-mode recovery as primary metrics and compares routing policies with bootstrap confidence intervals and paired tests. On a 26-case gold-labelled diagnostic, a keyword/flag router scored 0% on adversarial cases with misleading or missing surface flags, whereas an intent-reasoning model router scored 100%, matching the oracle. Controlled mechanism probes with a real Claude agent over a verifiable arithmetic dependency chain revealed three failure-handling tiers across five MAST modes: tool faults recovered fully (1.0), ambiguous delegation recovered partially (0.30), and three latent or semantic modes never recovered (0.0). This ordering persisted when the computation was reframed as a loan-approval workflow and across Sonnet, Opus, and Haiku, although absolute rates shifted with context. Blind retry reproduced latent faults and increased time to detection, indicating that detection and attribution are necessary for containment. Cascade radius increased with pipeline depth (mean 0.9 to 4.7 across depths 3-7). A trusted-state repair ablation showed that apparent containment gains primarily came from the trusted-state signal rather than autonomous detection. These results are controlled-chain mechanism probes, not domain-workload claims.

Yidian Chen, Yingzi Gu, Natan Vidra +2

Anote

Multi-Agent Orchestration Orchestration Real-World Cloud Fault Injection Dataset Workload Decomposition

Aug 5, 2026cs.CL

D $^2$ F-ReAG: Dynamic Decomposition and Filtering for Multi-Hop Reasoning-Augmented Generation

Large language models (LLMs) often generate inaccurate answers due to their reliance on static internal knowledge. Retrieval-augmented generation (RAG) addresses this limitation by integrating external knowledge and excelling at single-hop queries. However, it struggles with multi-hop questions that require cross-document reasoning. Existing methods, such as graph structured RAG or question decomposition, often lack dynamic decomposition and effective filtering, which leads to lower efficiency and accuracy. To overcome these limitations, we propose Dynamic Decomposition and Filtering for Multi-Hop Reasoning-Augmented Generation (D2F-ReAG), a novel paradigm that adaptively controls reasoning depth by judging the reliability of the root-level reasoning. If the root reasoning is reliable, the model directly generates the answer. Otherwise, the question is logically decomposed into sub-questions, and the verified reasoning derived from these sub-questions is used to refine the root reasoning. Experiments on three multi-hop benchmarks demonstrate the effectiveness of our method in handling complex multi-hop questions.

Jiaoyang Li, Junhao Ruan, Shengwei Tang +4

Northeastern University, Shenyang, China · Kunming University of Science and Technology, Kunming, China · NiuTrans Research, Shenyang, China

Multi-Hop Reasoning Search-Augmented Reasoning Decomposition

Aug 4, 2026cs.RO

GORDON: Graph-based Object-centric Rewards for Decomposition of Long-Horizon Manipulation

Learning long-horizon manipulation skills with reinforcement learning remains challenging due to the complexity of reward design, the limited guidance of sparse rewards, and the high cost of manual subtask annotation. Visual demonstrations can provide supervision for reward learning, but rewards learned from raw pixels can be brittle and sensitive to visual variation, background appearance, and robot motion. In this work, we propose GORDON, a graph-based object-centric reward learning framework that learns dense rewards from action-free video demonstrations. Each visual scene is represented as a graph of detected objects and spatial relations, and a graph neural network is trained in a self-supervised manner to embed these graphs into a task-aligned latent space. To align the representation with semantic task progress, we introduce an activity-aware weighted pooling mechanism that emphasizes task-relevant objects while masking robot-dominated motion. The dense reward is then computed as distances in the learned latent space of the current state to demonstrated goal configurations, providing a measure of task progress. In long-horizon tasks, the temporal profile of this reward reveals stage-wise object-state transitions, enabling automatic subtask discovery without manual segmentation. The discovered segments are then used to train subtask-specific rewards and specialized policies that are composed sequentially. Experiments on seven manipulation tasks on MAGICAL and ManiSkill3 benchmarks show that our object-centric reward improves reinforcement learning in short-horizon settings and enables successful policy learning in complex long-horizon tasks through automatic decomposition, achieving an average success rate of 74.4% across the long-horizon tasks (on average approximately +35 p.p. vs. best learned baseline and approximately +25 p.p. vs. oracle).

Andrea Protopapa, Davide Buoso, Francesca Pistilli +2

Politecnico di Torino, Turin, Italy. · Interactive Robot Perception & Learning (PEARL) Lab, Computer Science Dept., TU Darmstadt, Germany. · Hessian.AI, Darmstadt, Germany. +1

Robotic Manipulation Policies Long-Horizon Manipulation Decomposition

Aug 4, 2026cs.AI

Solver-Aware Decompositions for Programming-by-Example: When Dividing Requires Knowing how to Conquer

Decomposition-based Programming-by-example (PBE) scales performance by splitting tasks into subtasks that a learned synthesizer solves: a decomposer predicts intermediate subgoals, and a synthesizer generates programs conditioned on them. Current approaches train the decomposer to imitate ground-truth ( GT) subgoals, implicitly treating decomposition quality as intrinsic to the task. We challenge this assumption: for bounded solvers with fixed inductive biases, GT decompositions reflect the annotator's factorization choices - not the solver's search dynamics. A decomposer trained to match GT decompositions may therefore propose subgoals that are logically valid yet intractable for the solver. We propose Solver-Aware Decomposition (SAD), a training framework that retains supervised training on GT subgoals as a structural scaffold, while additionally optimizing the decomposer via direct feedback from a frozen synthesizer. Subgoals are rewarded based on the synthesizer's loss on the target program - a signal of subtask difficulty that encourages decompositions the solver can act on. Our experiments reveal an accuracy paradox: higher agreement with GT decompositions does not improve synthesis success - even though the synthesizer was trained on the very same GT data the decomposer is optimized to mimic. SAD instead learns decompositions that trade GT alignment for solver tractability, yielding consistent gains in synthesis and end-to-end task accuracy across two PBE domains. Moreover, SAD solves tasks that a GT decomposition oracle fails - empirical evidence that GT decompositions are not universally optimal for bounded solvers, and that decomposition quality is solver-relative, not intrinsic.

Janis Zenkner, Tobias Sesterhenn, Tim Grams +1

Clausthal University of Technology Clausthal-Zellerfeld, Germany

Functional Code Solvers Decomposition Synthesis

Aug 2, 2026cs.AI

PROGRESS: Coverage-guided RL to Train Search-augmented LLM Agent

Existing search-augmented LLM agents are trained using Reinforcement Learning to boost its reasoning capabilities. However, these approaches primarily rely on outcome-level rewards, which provide little supervision over search behavior and overlook agent's ability to decompose complex queries properly. To mitigate this issue, we propose PROGRESS which utilizes teacher-guided coverage reward to explicitly shape decomposed query generation of the policy model. During training, frozen teacher models are used to decompose complex queries into essential search queries. These essential search queries are utilized to guide the search behavior of the policy model. Integrated into an R1-style training framework, our approach provides lightweight guidance over query decomposition decisions without dense process-level supervision. Experiments show that coverage-guided RL improves overall task performance, highlighting the importance of explicitly supervising search strategies in agentic LLMs.

Sudipta Paul, Vijay Srinivasan, Vivek Kulkarni +4

AI Center-Mountain View, Samsung Electronics

Search-Augmented Reasoning Decomposition

Jul 28, 2026cs.CV

Explicit Layer Modeling for Video Object Insertion and Video Layer Decomposition

Most video editing systems still lack explicit layered video representations, limiting realistic compositing, object reuse, and consistent manipulation. This limitation is particularly evident in video object insertion and video layer decomposition, where existing methods lack direct supervision for foreground layers that capture both objects and their associated visual effects. We introduce TriLayer, a triplet video dataset containing aligned composite--background--foreground videos, where the foreground layers include both object appearance and associated visual effects. With aligned triplet supervision, TriLayer enables explicit supervised learning of layered video representations for the first time. Building on this dataset, we propose DBL-Diffusion, a dual-branch diffusion framework that jointly models scene-level RGB content and RGBA foreground layers through cross-branch interaction during denoising. We instantiate the framework in two tasks: DBL-Insert for layered object insertion, which generates explicit RGBA layers for realistic compositing and flexible post-editing, and DBL-Decompose for video layer decomposition, which recovers foreground and background layers using triplet supervision. Experiments demonstrate that explicit layer modeling substantially improves both insertion fidelity and decomposition quality.

Kyujin Han, Seungjoo Shin, Sunghyun Cho

POSTECH, Republic of Korea

Layer-Wise Decomposition Process-Level Supervision

Jul 16, 2026stat.ML

Subjective Risk Decomposition: A New View for Uncertainty Quantification

We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.

Raghad Alamri, Michele Caprio, Gavin Brown

Department of Computer Science, The University of Manchester · Department of Computer Science, University of Warwick

Uncertainty Quantification Uncertainty Target Risk Cross-Entropy Losses Decomposition

Jul 16, 2026cs.CL

Dialogue Summarization with Emotion Dynamics Using Topic- and Participant-Centric Decomposition

Existing text summarization research has focused much on monologic information (e.g., newspaper articles, reports) without accounting for the interaction between speakers or authors. In contrast, dialogues are a rich communication channel where multiple participants conduct back and forth exchanges to construct meaning. We propose a dialogue summarization framework that explicitly models both semantic and emotion dynamics using multimodal dialogue inputs, built on an adapted hierarchical Chain-of-Agents approach. We decompose dialogues from two perspectives: (1) topic segments based on the utterances of all participants, and (2) participant-specific utterance segments. These are used to generate corresponding summaries while incorporating automatically inferred emotions. Topic- and participant-level summaries are aggregated into a dialogue summary capturing semantic content and emotion trajectories. To evaluate beyond content accuracy, we introduce emotion trajectory metrics measuring how well summaries preserve emotional flow. Experiments with small language models on multimodal dialogue datasets show that our framework produces summaries with both semantic and emotion content. Further experiments on explicit emotion label availability highlight the efficacy of our proposed methodology and the opportunities in dialogue analysis using language models.

Linyun Xiang, Mark Neerincx, Stephanie Tan

Department of Intelligent Systems, Delft University of Technology

Summarization Conversational Datasets Emotion Recognition Emotional Regulation Emotion Decomposition

Jul 16, 2026cs.AI

Analytic Abduction: Causal Decomposition and Governed Commitment for Human--AI Coordination

Abductive reasoning operates in two directions. The synthetic mode builds explanations from available hypotheses; the analytic mode, conversely, identifies the latent factors whose interaction accounts for a complex observed state. This paper develops the analytic mode as a non-greedy, risk-sensitive discipline of commitment, in which candidate factors coexist and interact, resolving into committed conclusions only when explicit governance conditions are met. The formal core is the

κ

-

τ

apparatus:

κ

encodes the epistemic interaction among hypotheses, and

τ

sets a commitment threshold calibrated to the decision's stakes. The central contribution is the causal cluster, a structured object recording which latent factors participate in a decomposition, with what weights and interaction structure, together with a two-level architecture (intra-cluster

κ^*

, inter-cluster

κ^{**}

) that guards against causal misattribution. Demonstrated in epidemiological crisis decomposition and adversarial cyber threat analysis, the framework's contribution to human-AI reasoning is the legibility of suspended decomposition as a shared coordination object, providing structural resistance to premature convergence. In practice, the decision-maker is handed not a single imposed answer but the competing explanatory scenarios, weighted by plausibility and paired with the evidence that would resolve between them, so that sound action is possible even before the ambiguity is resolved.

Remo Pareschi

Stake Lab, University of Molise, Italy

Abductive Reasoning Causal Commitment Decomposition Coordination Epidemiological Models

Jul 14, 2026cs.IR

Where Does the Noise Come From? A Variance-Components Decomposition of Non-Determinism in LLM Brand Answers

Teams measuring whether large language models (LLMs) recommend a brand face a reproducibility problem: ask the same question twice and the answer moves. Practice resamples each prompt a few times (commonly five) and averages, treating within-prompt resampling as the source of the noise. But a measured brand score moves for at least four separable reasons: within-prompt resampling, prompt paraphrase, model identity, and query language. We specify a crossed random-effects (generalizability-theory) decomposition that partitions the total variance of a response-level brand outcome into these four sources, and embed the components in a decision-study allocation that returns how many repeats, paraphrases, models, and languages to buy for a target reliability. We apply it to a fully crossed corpus of 12,933 LLM responses on 20 Central and Eastern European brands, 8 languages, and 3 models (GPT-5.2 and Gemini 3 Flash in parametric mode, Perplexity in grounded retrieval), with a stability subset of 1,435 cells resampled about five times. The outcome is per-response multilingual sentiment polarity. Query language is the largest systematic facet (26.5% of the variance of one response) against 1.5% for brand identity (ICC 0.0146), so a single AI answer carries almost no brand-discriminating signal. Once a cell term isolates pure resampling, resampling is 34.8% of variance and the brand-in-context interaction 29.6%; brand-by-language is 8.6% (a bilingual penalty) while brand-by-model and brand-by-prompt are near zero. Per unit of query budget, adding languages and models reduces relative-error variance far more than adding repeats: a repeat past the fifth reduces it by only 0.0003. Brand-ranking reliability stays low, near 0.01 for a single answer and about 0.36 at the full crossed design, so reliability is bought by spreading across languages and models, not by repeating one prompt.

Dmitrij Żatuchin

Department of Information Technologies, Estonian Entrepreneurship University of Applied Sciences (EUAS), Tallinn, Estonia. · Rankfor.AI, Wroclaw, Poland; Tallinn, Estonia.

Large Language Model Reliability Brand-As-Memory Bias-Variance Decomposition Sentiment Generalized Linear Model Resampling+1

Jul 14, 2026cs.CV

Open-KNEAD: Knowledge-grounded Nutrition Estimation via Agentic Decomposition

Multimodal Large Language Models (MLLMs) are increasingly used for dietary assessment from meal images, where retrieval-augmented grounding was shown to sharpen nutrition estimates. However, we find this premise no longer holds for current MLLMs. A modern MLLM's direct estimate now matches or surpasses the full retrieval pipeline. This raises a question: if retrieval no longer improves the overall estimate, can it still deliver the two things clinicians value, accurate portions and a traceable, item-by-item record? We pursue this while preserving what matters for clinical adoption: minimal user burden (a single, unannotated meal image), explainability (an auditable record), and privacy (locally hosted inference). We introduce Open-KNEAD, a knowledge-grounded agentic framework for meal nutrition estimation that is training-free and locally deployable. Each decomposed food item is grounded to a Food and Nutrient Database for Dietary Studies (FNDDS) code via selective, nutrient-aware retrieval, composing an auditable per-item record. Across two open MLLM families and three cuisines, Open-KNEAD improves portion estimates over both prior grounding methods and direct estimation in most backbone-dataset settings. An agent-internal recipe-prior step further recovers the invisible cooking-added energy that biases estimates on non-US cuisine. The advantage is largest on the dietitian-verified ACETADA dataset, where the local open agent surpasses the direct portion estimates of two frontier closed models by roughly

30\%

and

53\%

, all while keeping every meal image on local hardware. We release the Open-KNEAD framework and its agent-ready FNDDS knowledge base.

Bruce Coburn, Jingbo Yue, Jinge Ma +3

Purdue University, USA

Diet Multimodal Large Language Models Decomposition

Jul 13, 2026cs.DC

Decomposing Runtime, Kernel, and Quantization Speedups via a Matched FP16 Intermediate: A Hardware-Conditioned Case Study on Four NVIDIA RTX A5000 GPUs

Reported serving speedups from quantized kernels typically bundle the weight format, the kernel, and the inference runtime into one number. We present an attribution study on four NVIDIA RTX A5000 GPUs, 24 GiB each, on a single host with NVLink-bridged pairs. A matched intermediate stack that keeps the faster runtime without the quantized kernel splits the full speedup into a runtime part and a kernel and quantization part. Under matched greedy decoding the full stack reaches

2.58\times

end to end, with the runtime change accounting for about two thirds of that gain on a logarithmic scale; across three similar model families the kernel and quantization part moves by at most 1.5%. Sharding one instance across all four cards falls well below doubling: a profiler trace attributes about 80% of the per token shortfall to coordination, and an NVLink versus PCIe control on the same hardware shows similar realized bandwidth on both links, pointing away from link bandwidth as the cause. Whether to run one sharded instance or several independent ones depends on the workload and the model, with the ranking reversing on the larger model: the smaller model splits between sharding and multiple instances by workload, while the larger model favors two paired instances on every workload. Quantization extends sustainable concurrent users roughly four times past a reproducible half precision memory cliff. Differences in sampling mode and prompt pool between the two stacks are documented as threats to validity.

Weijia Han, Lisha Qu

University of Washington

Matched Fp16 Intermediate Quantized Decomposition Case Study

Jul 12, 2026cs.LG

modelDNA: Calibrated Lineage Verification and Merge Decomposition from Sampled Weight Fingerprints

The lineage graph of open-weight language models is self-reported: Hugging Face's base_model metadata field is optional and unverified, and over 60% of Hub models document no parentage at all. Methods for detecting lineage from weights exist in the research literature, but each ships as paper code tied to one signal and one experiment; when a provenance dispute breaks, the analysis is redone by hand. This report describes modelDNA, a tool that fingerprints a model from roughly 100-300 MB of ranged HTTP reads (instead of a full 15 GB download for a 7B model), compares the fingerprint against a reference database of foundation models across four published signal families, and returns one of eight verdict classes with a calibrated probability, preferring honest abstention to confident error. On a benchmark of 15 real Hub models with org-documented parentage, judged against 8 candidate bases (13 positives, 107 hard negatives), the system achieves AUROC 1.0, zero false positives at its reporting threshold, and 13/13 correct top-1 parent attribution. The report's second contribution is merge decomposition. Every mainstream weight-merging method is (near-)linear per tensor, and fingerprint sample positions are deterministic functions of tensor identity, so a merged model's fingerprint is the same linear combination of its parents' fingerprints. Mixture weights can therefore be recovered from fingerprints alone by sum-to-one constrained least squares. Against merges with published mergekit configurations as ground truth, the method recovers a slerp merge's layer-interpolation curves at r = 0.999 and a dare_ties merge's mixture weights to within 0.011 of the published values, without downloading any weights beyond the fingerprints. All fingerprints, benchmarks, and the inferred lineage graph of 55 models are public and reproducible offline.

Muhammad Awais Bin Adil, Saad Aamir

Independent

Lineages Fingerprint Model Weights Decomposition Humanml3D

Jul 6, 2026stat.ML

Decomposition for Bayesian Networks: Local and Parallel Inference

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

Pei Heng, Xinyi Hu, Yi Sun

Institute of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi, China

Bayesian Networks Probabilistic Inference Network Science Decomposition Convex Sets

Jul 4, 2026math.DS

A Policy Decomposition Framework for Dynamic Order Fulfillment Operations

Modern supply chains span diverse operational environments, ranging from e-commerce distribution networks to customized production-to-order manufacturing lines. Across these settings, operational efficiency depends on coordinating two highly interdependent stages: order preparation and downstream delivery. Although these stages are traditionally managed in isolation, real-world fulfillment systems must satisfy stringent delivery expectations under dynamic stochastic order arrivals. To bridge this gap, we introduce the Dynamic Order Fulfillment Problem (DOFP), a new problem class unifying logistical challenges previously studied separately. We model DOFP as a Markov decision process whose state and decision spaces are partitioned into preparation and delivery sub-spaces, linked by synchronization constraints. While recent approaches attempt to optimize both fulfillment stages simultaneously over myopic rolling horizons, our framework isolates and optimizes the downstream delivery policy, treating preparation strictly as a state-level constraint filter. To solve this, we develop the Decomposition-Driven Framework with Value Function Approximation (DDF-VFA), which utilizes a novel policy-level decomposition. This design partitions the search into a delivery-stage master problem and a preparation-stage compatibility subproblem, iteratively refined via feedback loops. DDF-VFA executes this strategy by combining a large-neighborhood search over partial delivery decisions with a neural-network value function approximation for the cost-to-go. Numerical illustrations on two example variants using real-world datasets show that DDF-VFA consistently outperforms benchmarks that optimize the two stages independently or jointly without decomposition. Finally, the framework naturally scales to accommodate additional real-world complexities such as batched or multi-stage preparation.

Gal Neria, Michal Tzur, Marlin W. Ulmer

Massachusetts Institute of Technology, Cambridge, 02139, MA, USA · School of Industrial and Intelligent Systems Engineering, Tel Aviv University, Tel Aviv, 6997801, Israel · Otto-von-Guericke Universitat Magdeburg, Magdeburg, Germany

Logistics Supply Chain Optimization Manufacturing Decomposition

Jul 1, 2026cs.LG

Local Motion Matters: A Deconstruct-Recompose Paradigm for Reinforcement Learning Pre-training from Videos

Pre-training on large-scale videos to improve reinforcement learning efficiency is promising yet remains challenging. Existing methods typically treat the agent as an indivisible entity, modeling motion patterns globally. Such global modeling is tightly coupled with the morphology, hindering transfer across domains. In contrast, despite the vast disparity in global motions, the local components exhibit similar motion patterns across different agents. Building on this insight, we propose a novel Deconstruct-Recompose Paradigm (DRP) for learning transferable local motion representations. Specifically, in the Deconstruct phase, we identify multiple local points and track their frame-wise motions, defining each as an Atomic Action. We introduce a Dual-Attention Encoder (DAE) to learn local motion representations from these Atomic Actions, capturing their spatiotemporal relationships. In the Recompose phase, we compose local motion representations with a learnable Motion Aggregation Token [MAT] via latent dynamics model learning. Additionally, an adapter bridges local motion and downstream action-specific dynamics to accelerate policy learning. Extensive experiments demonstrate that our method effectively transfers to diverse robotic control and manipulation tasks, significantly improving sample efficiency and performance.

Jinwen Wang, Youfang Lin, Xiaobo Hu +2

Beijing Jiaotong University, China · Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, China

Latent Motion Latent Dynamics Motion Decomposition

Jul 1, 2026cs.LG

Measuring Dead Directions: Decomposing and Classifying Singular Structure off Canonical Alignment

We give a descent-free, alignment-free measurement of singular structure on trained networks. At a single frozen checkpoint the read recovers the order

k

of each dead direction from the directional-Fisher rate, the master invariant from which the per-direction learning coefficient

1/(2k)

follows exactly, in whatever basis the optimizer left. The same read classifies each direction, separating a genuine singularity, whose order the architecture fixes, from a flat gauge symmetry; the directional-Fisher magnitude settles the cases the order cannot. A pluggable detector supplies the directions for transformer, convolutional, and normalisation layers. The read recovers the architecture-predicted order across constructed cells and trained networks, including a fine-tuned vision transformer whose dead structure is the LayerNorm-kernel gauge and a from-scratch one whose compressed MLP forms a node-death at its activation order. Where the singular structure enumerates, the per-direction orders assemble, through the typed intersection of the loci, into the global coefficient

(λ, m)

matching the closed form. The method removes the canonical-alignment and descent preconditions of the underlying rate result, turning order-recovery into a deterministic, architecture-general reading. We then map its reach into the Watanabe triple: the order determines the universal singular fluctuation

ν(k)

, though a trained network's realized

ν

falls below it as the live structure absorbs the dead direction's data fluctuation, and the multiplicity recovers from the dominant structure under a single-locus assumption.

Tejas Pradeep Shirodkar

IIIT, Hyderabad

Decomposition Order

Jun 30, 2026cs.CV

Decompose, Compare, and Decide: Multimodal LLMs are Implicit Few-Shot Learners

Multimodal Large Language Models (MLLMs) have demonstrated remarkable abilities when analyzing images, yet translating these capabilities to few-shot image classification remains challenging. To bridge this gap, we present DeCoDe, a simple yet effective technique that enables off-the-shelf MLLMs to act as strong few-shot classifiers without any additional training. Our approach builds on the idea of few-shot classification as a set of pairwise image comparisons, decomposing the task into a set of binary decisions. Given a query image and a support image from a candidate class, the MLLM is prompted to decide whether the two images depict the same class. The logit corresponding to an affirmative response is then used as a similarity score to assign the query image to the most likely class. While this already yields good results, we show that providing additional high-level information, such as the data domain, to the model further improves performance. Our evaluation provides an extensive analysis of various inference variants on a suite of twelve datasets, six established and six newly curated few-shot benchmarks spanning across diverse domains. The results show that the proposed simple decomposition technique can turn off-the-shelf MLLMs into powerful few-shot learners, significantly outperforming current state-of-the-art few-shot methods on both standard and novel domains. Code is available at https://github.com/yunhanwang1105/DeCoDe.

Yunhan Wang, Eshika Khandelwal, Edson Araujo +3

Tuebingen AI Center, University of Tuebingen, Germany

Few-Shot Learning Image Classification Multimodal Large Language Models Query Image Decomposition Decisions