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

May 8, 2026cs.CV

SCOPE: Structured Decomposition and Conditional Skill Orchestration for Complex Image Generation

While text-to-image models have made strong progress in visual fidelity, faithfully realizing complex visual intents remains challenging because many requirements must be tracked across grounding, generation, and verification. We refer to these requirements as semantic commitments and formalize their lifecycle discontinuity as the Conceptual Rift, where commitments may be locally resolved or checked but fail to remain identifiable as the same operational units throughout the generation lifecycle. To address this, we propose SCOPE, a specification-guided skill orchestration framework that maintains semantic commitments in an evolving structured specification and conditionally invokes retrieval, reasoning, and repair skills around unresolved or violated commitments. To evaluate commitment-level intent realization, we introduce Gen-Arena, a human-annotated benchmark with entity- and constraint-level specifications, together with Entity-Gated Intent Pass Rate (EGIP), a strict entity-first pass criterion. SCOPE substantially outperforms all evaluated baselines on Gen-Arena, achieving 0.60 EGIP, and further achieves strong results on WISE-V (0.907) and MindBench (0.61), demonstrating the effectiveness of persistent commitment tracking for complex image generation.

Tianfei Ren, Zhipeng Yan, Yiming Zhao +13

MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China · The Hong Kong Polytechnic University · Nanyang Technological University

Image Generation Text-To-Image Human-Annotated Benchmark Decomposition

May 8, 2026cs.LG

Don't Learn the Shape: Forecasting Periodic Time Series by Rank-1 Decomposition

How few parameters do we really need to forecast a periodic time series? An hourly electricity series, reshaped as a 24-row matrix with one column per day, is approximately rank-1: a daily shape modulated by a daily level (median centered rank-1 energy 0.82 on GIFT-Eval). Should we learn the shape? Smoothing, shrinkage, and low-rank fits all seem like obvious upgrades over the simple average of the last K=2 cycles. On all 97 GIFT-Eval configurations, we tested 8 such alternatives (e.g., Fourier, EWMA, James-Stein, rank-r SVD): none significantly beats the frozen baseline under Holm correction; two are significantly worse. The resulting method, FLAIR, is (a) Effective: matches PatchTST on aggregate GIFT-Eval (relMASE 0.838 vs 0.849); (b) Compact: 28 scalars for hourly, 57 for weekly; (c) Fast: 22 minutes on one CPU core of a MacBook Pro; (d) Closed-form & Hands-Off: one SVD per period candidate, GCV-averaged Ridge, no GPU, no pre-training, no per-task tuning. In the high-rank-1, many-cycle regime, extra flexibility is estimation noise.

Takato Honda

Mellon Inc.

Time Series Low-Rank Structure Singular Value Decomposition Decomposition Context-Sensitive Daily Routines

May 8, 2026cs.AI

2.5-D Decomposition for LLM-Based Spatial Construction

Autonomous systems that build structures from natural-language instructions need reliable spatial reasoning, yet large language models (LLMs) make systematic coordinate errors when generating three-dimensional block placements. We present a neuro-symbolic pipeline based on 2.5-D decomposition: the LLM plans in the two-dimensional horizontal plane while a deterministic executor computes all vertical placements from column occupancy, eliminating an entire class of errors. On the Build What I Mean benchmark (160 rounds), GPT-4o-mini with this pipeline achieves 94.6% mean structural accuracy across 12 independent runs, within 3.0 percentage points of the 97.6% ceiling imposed by architect-agent errors that no builder-side improvement can address. This outperforms both GPT-4o at 90.3% and the best competing system at 76.3%. A controlled ablation confirms that 2.5-D decomposition is the dominant contributor, accounting for 28.7 percentage points of accuracy. The pipeline transfers directly to edge hardware: Nemotron-3 120B on an NVIDIA Jetson Thor AGX achieves 96.0% mean structural accuracy with the identical pipeline, slightly exceeding the cloud result. Expanding the system prompt by four targeted examples to exceed the model's 8,320-token prefix cache page size, combined with low-effort reasoning, reduces mean per-request latency by 3X to 19.7 seconds at 95.6% accuracy. The underlying principle, removing deterministic dimensions from the LLM's output space, applies to any autonomous construction or assembly task where gravity or other physical constraints fix one or more degrees of freedom. A transfer experiment on 500 IGLU collaborative building tasks confirms the effect generalizes beyond the primary benchmark.

Paul Whitten, Li-Jen Chen, Sharath Baddam

Rockwell Automation Mayfield Heights, OH, USA

Large Language Model Planning Spatial Reasoning 3D Layout Generation Construction Neuro-Symbolic Framework Decomposition

May 7, 2026cs.AI

XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction

Multiphase powder X-ray diffraction (PXRD) analysis remains a fundamental bottleneck in structure identification, as real-world synthesis often produces complex mixtures whose constituent phases (components) cannot be reliably disentangled. While recent advances in representation-based crystal retrieval and generation suggest the possibility of inferring structures directly from PXRD, existing approaches largely assume single-phase inputs and break down in multiphase settings. Here, we present XDecomposer, a prior-free framework for joint decomposition and identification of multiphase XRD patterns without requiring candidate phase lists, structural templates, or prior knowledge of phase number. We formulate multiphase diffraction analysis as a set prediction problem, where the model infers an unordered set of phase-resolved components, their mixture proportions, and corresponding structural representations within a unified architecture. A phase-query-driven decomposition mechanism, together with diffraction-consistent physical reconstruction, enables accurate source separation while preserving crystallographic fidelity. Extensive experiments on both simulated and experimental datasets show that XDecomposer substantially improves reconstruction accuracy and phase identification across diverse chemical systems, while maintaining strong generalization to unseen mixtures. These results provide a practical route toward data-driven, source-resolved multiphase XRD analysis and reduce long-standing dependence on prior-guided iteratively phase matching. The code is openly available at https://github.com/Licht0812/XDecomposer

Hanyu Gao, Bin Cao, Yunyue Su +2

New Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences (CASIA) · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · Guangzhou Municipal Key Laboratory of Materials Informatics, The Hong Kong University of Science and Technology (Guangzhou) +1

Powder X-Ray Diffraction Decomposition

May 6, 2026cs.LG

Two-Stage Learned Decomposition for Scalable Routing on Multigraphs

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g., distance vs. time). Multigraphs are highly relevant in practice, yet few neural methods are designed for them, and those that do exist face major scalability issues. We address these scalability issues with Node-Edge Policy Factorization (NEPF), which splits the routing policy into a node permutation stage and an edge selection stage. To enable the decomposition, we introduce a pre-encoding edge aggregation scheme and a non-autoregressive architecture for the edge stage, as well as a hierarchical reinforcement learning method to train the stages jointly. Our experiments across six VRP variants demonstrate that NEPF trains and runs up to orders of magnitude faster than prior neural multigraph methods and scales to considerably larger instances, while matching or improving on their solution quality.

Filip Rydin, Morteza Haghir Chehreghani, Balázs Kulcsár

Chalmers University of Technology · University of Gothenburg

Vehicle Routing Problem Factor Graphs Decomposition

May 5, 2026cs.AI

Automated Large-scale CVRP Solver Design via LLM-assisted Flexible MCTS

Solving large-scale CVRP (LSCVRP) with hundreds to thousands of nodes remains difficult for even state-of-the-art solvers. Divide-and-conquer can scale by decomposing the instance into size-reduced subproblems, but designing decomposition logic and configuring sub-solvers is highly expertise- and labor-intensive. Large Language Models (LLMs) have emerged as promising tools for automated algorithm design. However, existing LLM-driven approaches struggle with LSCVRP primarily due to the difficulty in generating sophisticated search strategies within a limited context window. To bridge this gap, we propose the LLM-assisted Flexible Monte Carlo Tree Search (LaF-MCTS), a novel framework that automates the design of high-performance LSCVRP solvers. We develop a three-tier decision hierarchy to enable incremental design of decomposition policies and sub-solvers for LSCVRP. To enable efficient search within the algorithmic hypothesis space, we introduce semantic pruning to eliminate semantically and structurally redundant codes, and branch regrowth to regenerate codes and preserve diversity. Extensive experiments on CVRPLib demonstrate that LaF-MCTS autonomously composes and optimizes decomposition-enhanced solvers that surpasses various state-of-the-art CVRP solvers.

Tong Guo, Caishun Chen, Yew Soon Ong

College of Computing and Data Science, Nanyang Technological University, Singapore

Vehicle Routing Problem Automated Heuristic Design Monte Carlo Tree Search Decomposition

May 3, 2026cs.CR

Decompose to Understand, Fuse to Detect: Frequency-Decoupled Anomaly Detection for Encrypted Network Traffic

Network traffic anomaly detection represents a critical cybersecurity task, yet widespread encryption makes this task increasingly challenging. In response, image-based methods that model traffic as visual patterns have emerged as the dominant approach. However, this work pioneers the identification of a pervasive full-frequency'' characteristic and an associated limitation termed spectral mismatch'' within this paradigm. Specifically, while encrypted traffic exhibits prominent high-frequency components, mainstream reconstruction methods demonstrate an inherent bias toward learning low-frequency information. This fundamental mismatch results in incomplete representations that consequently degrade anomaly detection performance. To address this challenge, we propose FreeUp, a novel frequency-decoupled framework designed explicitly for encrypted traffic analysis. FreeUp decomposes traffic data into distinct low- and high-frequency bands, processing them through separate, dedicated branches along with a customized training strategy that ensures stable and independent frequency-specific learning. Furthermore, recognizing that simple reconstruction error proves inadequate for evaluating dual-branch architectures, we introduce an uncertainty-inspired fusion scoring mechanism. This mechanism quantifies the reconstruction uncertainty of the frequency-specific branches and dynamically integrates their outputs, yielding a more comprehensive and reliable anomaly score. Extensive experiments across multiple benchmarks demonstrate that FreeUp consistently outperforms state-of-the-art baselines. The code is available at https://github.com/ikun0124/FreeUp.

Xinglin Lian, Chengtai Cao, Ting Zhong +3

School of Information and Software Engineering, University of Electronic Science and Technology of China · Department of Computer Science, City University of Hong Kong · Department of Computer Science and Engineering, Hong Kong University of Science and Technology +1

Graph Anomaly Detection Anomaly Score Threat Detection Text2Cypher Traffic Decomposition

May 2, 2026cs.RO

Decompose and Recompose: Reasoning New Skills from Existing Abilities for Cross-Task Robotic Manipulation

Cross-task generalization is a core challenge in open-world robotic manipulation, and the key lies in extracting transferable manipulation knowledge from seen tasks. Recent in-context learning approaches leverage seen task demonstrations to generate actions for unseen tasks without parameter updates. However, existing methods provide only low-level continuous action sequences as context, failing to capture composable skill knowledge and causing models to degenerate into superficial trajectory imitation. We propose Decompose and Recompose, a skill reasoning framework using atomic skill-action pairs as intermediate representations. Our approach decomposes seen demonstrations into interpretable skill--action alignments, enabling the model to recompose these skills for unseen tasks through compositional reasoning. Specifically, we construct a task-adaptive dynamic demonstration library via visual-semantic retrieval combined with skill sequences from a planning agent, complemented by a coverage-aware static library to fill missing skill patterns. Together, these yield skill-comprehensive demonstrations that explicitly elicit compositional reasoning for skill composition and execution ordering. Experiments on the AGNOSTOS benchmark and real-world environments validate our method's zero-shot cross-task generalization capability.

Xitie Zhang, Aming Wu, Yahong Han

School of Artificial Intelligence, College of Intelligence and Computing, Tianjin University, China · School of Computer Science and Information Engineering, Hefei University of Technology, China

Human-To-Robot Transfer Robotic Manipulation Cross-Task Knowledge Transfer Skills Decomposition Recast+1

May 1, 2026cs.CL

A Systematic Exploration of Text Decomposition and Budget Distribution in Differentially Private Text Obfuscation

The goal of differentially private text obfuscation is to obfuscate, or "perturb", input texts with Differential Privacy (DP) guarantees, such that the private output texts are quantifiably indistinguishable from the originals. While perturbation at the word level is intuitive, meaningful text privatization happens on complete documents. Recent research has laid the groundwork for reasoning about privacy budget distribution, namely, how an overall

\varepsilon

budget can be sensibly distributed among the component pieces of a text. We perform a systematic evaluation of multiple text decomposition and budget distribution techniques in the context of DP text obfuscation, testing how different methods for chunking texts can be combined with techniques for allocating

\varepsilon

to these chunks. Our experiments reveal that such design choices are very important, as even with comparable privacy budgets, significantly different results can occur based on which methods are chosen. In this, we provide credible evidence of the feasibility of maximizing empirical trade-offs by optimizing DP obfuscation procedures.

Stephen Meisenbacher, Angelo Kleinert, Florian Matthes

Technical University of Munich School of Computation, Information and Technology Department of Computer Science Garching, Germany

Obfuscation Text Analysis and Detection Decomposition Exploration

Apr 29, 2026cs.LG

ConformaDecompose: Explaining Uncertainty via Calibration Localization

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates irreducible noise with uncertainty induced by heterogeneous training data (aleatoric), model limitations, or calibration mismatch (epistemic), offering little insight into why an interval is wide or whether it could be reduced. We introduce an uncertainty-aware explainability framework that analyses the reducibility of calibration-induced epistemic conformal uncertainty via progressive calibration localisation for regression tasks. The approach is diagnostic rather than causal: it does not estimate true aleatoric or epistemic uncertainty, but explains how conformal intervals contract and stabilise as calibration support is localised around a test instance. Across benchmarks and real-world data, absolute reducible uncertainty aligns with epistemic proxies, while its relative contribution varies by task, revealing regimes hidden by interval width. This instance-level view complements conformal uncertainty, enhancing interpretability without altering the predictor or coverage.

Fatima Rabia Yapicioglu, Meltem Aksoy, Alberto Rigenti +4

Department of Computer Science and Engineering, University of Bologna, Italy · Marketing and Sales, Automobili Lamborghini S.p.A, Sant’Agata Bolognese, Italy · RCT Data Science and Security, Technical University Dortmund, Germany +4

Uncertainty Decomposition

Apr 29, 2026cs.LG

Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition

Motivated by sensing modalities in modern autonomous systems that involve hardware-constrained spatial sampling over large arrays with limited coherence time, we develop a novel framework for rapid super-resolution multi-signal direction-of-arrival (DoA) estimation based on Hankel-structured sensing and data matrix decomposition of arbitrary rank, under both the

L_2

and

L_1

-norm formulation. The resulting

L_2

-norm estimator is shown to be maximum-likelihood optimal in white Gaussian noise. The

L_1

-norm estimator is shown to be maximum-likelihood optimal in independent, identically distributed (i.i.d.) isotropic Laplace noise, offering broad robustness to impulsive interference and corrupted measurements commonly encountered in practice. Extensive simulations demonstrate that the proposed methods exhibit powerful super-resolution capabilities, requiring significantly lower SNR and achieving substantially higher resolution probability than recent competing approaches.

Georgios I. Orfanidis, Dimitris A. Pados, George Sklivanitis +1

Center for Connected Autonomy and AI and the Dept. of Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL 33431 USA · Air Force Research Laboratory, AFRL/RI, Rome, NY 13441 USA

Microphone Array Spectral Norm Gaussian Noise Decomposition

Apr 29, 2026cs.LG

Hankel and Toeplitz Rank-1 Decomposition of Arbitrary Matrices with Applications to Signal Direction-of-Arrival Estimation

We consider the problems of computing the optimal rank-

1

Hankel and Toeplitz-structured approximation of arbitrary matrices under

L_2

and

L_1

-norm error. Such problems arise naturally in engineered systems, including the basic few-shot signal Direction-of-Arrival (DoA) estimation problem that is of importance to modern autonomous systems applications. We develop accurate and computationally efficient structured matrix decomposition algorithms for both formulations and then derive analytically grounded small-sample-support DoA estimators for practical sensing system deployments. The resulting estimators under the

L_2

and

L_1

norms are formally shown to be maximum-likelihood optimal under white Gaussian and Laplace noise, respectively. The estimators are further validated through extensive simulation studies and real-world data experiments in few-shot DoA inference.

Georgios I. Orfanidis

Center for Connected Autonomy and AI and the Dept. of Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL 33431 USA

Microphone Array Matrix Spectral Norm Decomposition

Apr 29, 2026cs.DS

Flashback: A Reversible Bilateral Run-Peeling Decomposition of Strings

We introduce Flashback, a reversible string decomposition that repeatedly peels the maximal leading and trailing character runs from a sentinel-wrapped input, recording each pair as one bilateral token. Decomposition and reconstruction both run in O(n) time and space. Our central result is a run-pairing theorem: Flashback is equivalent to pairing the first run of the string with the last, the second with the second-to-last, and so on. This gives an exact token count of 1+[r/2] for a string with r maximal runs, and matches a lower bound that holds for any admissible bilateral run-peeling scheme. From the run-pairing theorem the main structural properties follow as corollaries: the irreducible peeling kernel uses at most two symbols; palindromes are precisely the strings whose run-length encoding is symmetric with an odd number of runs; the image of the decomposition admits an explicit finite-state characterisation; and changing one run length rewrites exactly one content token.

Thomas Konstantinovsky, Gur Yaari

Faculty of Engineering, Bar-Ilan University, Ramat Gan 5290002, Israel · Bar-Ilan Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan, Israel · Department of Pathology, Yale School of Medicine, New Haven, CT 06510, United States

Byte-Pair Encoding Decomposition Automata

Apr 27, 2026cs.CL

SEARCH-R: Structured Entity-Aware Retrieval with Chain-of-Reasoning Navigator for Multi-hop Question Answering

Multi-hop Question Answering (MHQA) aims to answer questions that require multi-step reasoning. It presents two key challenges: generating correct reasoning paths in response to the complex user queries, and accurately retrieving essential knowledge in the face of potential limitations in large language models (LLMs). Existing approaches primarily rely on prompt-based methods to generate reasoning paths, which are further combined with traditional sparse or dense retrieval to produce the final answer. However, the generation of reasoning paths commonly lacks effective control over the generative process, thus leading the reasoning astray. Meanwhile, the retrieval methods over-rely on knowledge matching or similarity scores rather than evaluating the practical utility of the information, resulting in retrieving homogeneous or non-useful information. Therefore, we propose a Structured Entity-Aware Retrieval with Chain-of-Reasoning Navigator framework named SEARCH-R. Specifically, SEARCH-R trains an end-to-end reasoning path navigator, which is able to provide a powerful sub-question decomposer by fine-tuning the Llama3.1-8B model. Moreover, a novel dependency tree-based retrieval is designed to evaluate the informational contribution of the document quantitatively. Extensive experiments on three challenging multi-hop datasets validate the effectiveness of the proposed framework. The code and dataset are available at: https://github.com/Applied-Machine-Learning-Lab/ACL2026_SEARCH-R.

Yuqing Fu, Yimin Deng, Wanyu Wang +9

City University of Hong Kong · Xi’an Jiaotong University · Michigan State University +2

Multi-Hop Reasoning Reasoning Paths Decomposition Browser Agent

Apr 27, 2026cs.LG

DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.

Naveen Mysore

Kolmogorov-Arnold Networks Decomposition Global Climate Models

Apr 25, 2026cs.RO

BridgeACT: Bridging Human Demonstrations to Robot Actions via Unified Tool-Target Affordances

Learning robot manipulation from human videos is appealing due to the scale and diversity of human demonstrations, but transferring such demonstrations to executable robot behavior remains challenging. Prior work either relies on robot data for downstream adaptation or learns affordance representations that remain at the perception level and do not directly support real-world execution. We present BridgeACT, an affordance-driven framework that learns robotic manipulation directly from human videos without requiring any robot demonstration data. Our key idea is to model affordance as an embodiment-agnostic intermediate representation that bridges human demonstrations and robot actions. BridgeACT decomposes manipulation into two complementary problems: where to grasp and how to move. To this end, BridgeACT first grounds task-relevant affordance regions in the current scene, and then predicts task-conditioned 3D motion affordances from human demonstrations. The resulting affordances are mapped to robot actions through a grasping module and a lightweight closed-loop motion controller, enabling direct deployment on real robots. In addition, we represent complex manipulation tasks as compositions of affordance operations, which allows a unified treatment of diverse tasks and object-to-object interactions. Experiments on real-world manipulation tasks show that BridgeACT outperforms prior baselines and generalizes to unseen objects, scenes, and viewpoints.

Yifan Han, Jianxiang Liu, Haoyu Zhang +3

Institute of Automation, Chinese Academy of Sciences. · School of Artificial Intelligence, Shanghai Jiao Tong University. · 3South China University of Technology.

Real-World Manipulation Tasks Affordances Bridge Decomposition

Apr 21, 2026cs.LG

Decompose, Structure, and Repair: A Neuro-Symbolic Framework for Autoformalization via Operator Trees

Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training paradigms to optimize end-to-end Large Language Models (LLMs), they typically treat formal code as flat sequences, neglecting the hierarchical logic inherent in mathematical statements. In this work, we introduce Decompose, Structure, and Repair (DSR), a neuro-symbolic framework that restructures autoformalization into a modular pipeline. DSR decomposes statements into logical components and maps them to structured operator trees, leveraging this topological blueprint to precisely localize and repair errors via sub-tree refinement. Furthermore, we introduce PRIME, a benchmark of 156 undergraduate and graduate-level theorems selected from canonical textbooks and expertly annotated in Lean 4. Experimental results demonstrate that DSR establishes a new state-of-the-art, consistently outperforming baselines under equivalent computational budgets. The datasets, model, and code are available at https://github.com/XiaoyangLiu-sjtu/DSR.

Xiaoyang Liu, Zineng Dong, Yifan Bai +3

School of Mathematical Sciences, Shanghai Jiao Tong University · Zhiyuan College, Shanghai Jiao Tong University · Institute of Natural Sciences, MOE-LSC, CMA-Shanghai, Shanghai Jiao Tong University

Autoformalization Neuro-Symbolic Framework Logical Connectives Decomposition

Apr 20, 2026cs.CV

Long-Text-to-Image Generation via Compositional Prompt Decomposition

While modern text-to-image (T2I) models excel at generating images from intricate prompts, they struggle to capture the key details when the inputs are descriptive paragraphs. This limitation stems from the prevalence of concise captions that shape their training distributions. Existing methods attempt to bridge this gap by either fine-tuning T2I models on long prompts, which generalizes poorly to longer lengths; or by projecting the oversize inputs into normal-prompt space and compromising fidelity. We propose Prompt Refraction for Intricate Scene Modeling (PRISM), a compositional approach that enables pre-trained T2I models to process long sequence inputs. PRISM uses a lightweight module to extract constituent representations from the long prompts. The T2I model makes independent noise predictions for each component, and their outputs are merged into a single denoising step using energy-based conjunction. We evaluate PRISM across a wide range of model architectures, showing comparable performances to models fine-tuned on the same training data. Furthermore, PRISM demonstrates superior generalization, outperforming baseline models by 7.4% on prompts over 500 tokens in a challenging public benchmark.

Jen-Yuan Huang, Tong Lin, Yilun Du

Peking University · State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology. · Harvard University

Text-To-Image Decomposition

Apr 18, 2026cs.CV

Conditional Evidence Reconstruction and Decomposition for Interpretable Multimodal Diagnosis

Neurobiological and neurodegenerative diseases are inherently multifactorial, arising from coupled influences spanning genetic susceptibility, brain alterations, and environmental and behavioral factors. Multimodal modeling has therefore been increasingly adopted for disease diagnosis by integrating complementary evidence across data sources. However, in both large-scale cohorts and real-world clinical workflows, modality coverage is often incomplete, making many multimodal models brittle when one or more modalities are unavailable. Existing approaches to incomplete multimodal diagnosis typically rely on group-wise or static priors, which may fail to capture subject-specific cross-modal dependencies; moreover, many models provide limited interpretability into which evidence sources drive the final decision. To address these limitations, we propose Conditional Evidence Reconstruction and Decomposition (CERD), a framework for interpretable multimodal diagnosis with incomplete modalities. CERD first reconstructs missing modality representations conditioned on each subject's observed inputs, then decomposes diagnostic evidence into shared cross-modal corroboration and modality-specific cues via logit-level attribution. Experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) demonstrate that CERD outperforms competitive baselines under incomplete-modality settings while producing structured and clinically aligned evidence attributions for trustworthy decision support.

Shaowen Wan, Yanjun Lv, Lu Zhang +5

Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA · Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA · Department of Computer Science, Indiana University Indianapolis, Indianapolis, IN 46202, USA +1

Multimodal Clinical Data Decomposition

Apr 16, 2026cs.RO

One-Shot Cross-Geometry Skill Transfer through Part Decomposition

Given a demonstration, a robot should be able to generalize a skill to any object it encounters-but existing approaches to skill transfer often fail to adapt to objects with unfamiliar shapes. Motivated by examples of improved transfer from compositional modeling, we propose a method for improving transfer by decomposing objects into their constituent semantic parts. We leverage data-efficient generative shape models to accurately transfer interaction points from the parts of a demonstration object to a novel object. We autonomously construct an objective to optimize the alignment of those points on skill-relevant object parts. Our method generalizes to a wider range of object geometries than existing work, and achieves successful one-shot transfer for a range of skills and objects from a single demonstration, in both simulated and real environments.

Skye Thompson, Ondrej Biza, George Konidaris

Brown University · Northeastern University

Human-To-Robot Transfer Statistical Shape Model Skills Decomposition

Apr 16, 2026stat.ML

Unsupervised feature selection using Bayesian Tucker decomposition

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed and successfully applied to a wide range of problems.

Y-h. Taguchi, Yoh-ichi Mototake

Department of Physics, Chuo University, Tokyo, 112-8551, Japan. · Graduate School of Social Data Science, Hitotsubashi University, Tokyo, 186-8601, Japan.

Feature Selection Tensor Decomposition Unsupervised Decomposition

Apr 16, 2026cs.AI

A Parallel Approach to Counting Exact Covers Based on Decomposability Property

The exact cover problem is a classical NP-hard problem with broad applications in the area of AI. Algorithm DXZ is a method to count exact covers representing by zero-suppressed binary decision diagrams (ZBDDs). In this paper, we propose a zero-suppressed variant of decision decomposable negation normal form (in short, decision-ZDNNF), which is strictly more succinct than ZBDDs. We then design a novel parallel algorithm, namely DXD, which constructs a decision-ZDNNF representing the set of all exact covers. Furthermore, we improve DXD by dynamically updating connected components. The experimental results demonstrate that the improved DXD algorithm outperforms all of state-of-the-art methods.

Liangda Fang, Yaohui Luo, Delong Li +2

Jinan University, China · Nanyang Technological University, Singapore

Np-Hard Exact Decomposition Decisions

Apr 8, 2026cs.CL

Decompose, Look, and Reason: Reinforced Latent Reasoning for VLMs

Vision-Language Models often struggle with complex visual reasoning due to the visual information loss in textual CoT. Existing methods either add the cost of tool calls or rely on localized patch-based embeddings that are insufficient to extract semantics in multi-step reasoning. We propose "Decompose, Look, and Reason" (DLR), a reinforced latent reasoning framework that dynamically decomposes queries into textual premises, extracts premise-conditioned continuous visual latents, and deduces answers through grounded rationales. We introduce a three-stage training pipeline and propose a novel Spherical Gaussian Latent Policy, to enable effective exploration in the latent space. Extensive experiments on vision-centric benchmarks show that DLR consistently outperforms strong baselines, including text-only, interleaved multimodal CoT, and latent reasoning methods, while providing superior stepwise interpretability.

Mengdan Zhu, Senhao Cheng, Liang Zhao

Emory University · University of Michigan, Ann Arbor

Recent Vision-Language Models Visual Reasoning Reasoning Skills Decomposition

Apr 2, 2026cs.LG

A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction

Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure. Neighbor embedding methods such as t-SNE and UMAP prioritize local similarity preservation but do not explicitly constrain global organization, whereas standard spectral methods such as Laplacian Eigenmaps capture smooth, coarse-scale graph structure but offer limited flexibility to depict finer local structure. Second, the flexibility of nonlinear DR methods often comes at the cost of analytical transparency. Many methods do not explicitly reveal how high-dimensional structure produces patterns in the embedding. We introduce SDMP (Spectral Decomposition for Multiscale Projection), a nonlinear DR framework built on an explicit spectral decomposition. In this formulation, each embedding dimension is expressed as a weighted combination of Laplacian eigenvectors derived from a neighborhood graph, with the weights learned via a UMAP-style cross-entropy objective. By progressively expanding the spectral subspace to capture increasingly fine graph structure, SDMP produces a sequence of embeddings, making the evolving balance between global organization and local detail explicit, controllable, and inspectable. The explicit decomposition also reveals which spectral scales shape the overall embedding and how individual eigenvectors influence point positions. Quantitative evaluations on synthetic, image, and single-cell data show competitive local and global structure preservation, while case studies illustrate how the decomposition supports interpretation of clusters and developmental trajectories across spectral scales.

Zeyang Huang, Angelos Chatzimparmpas, Thomas Höllt +1

Linköping University, Sweden · Utrecht University, The Netherlands · University of Bergen, Norway +1

Dimensionality Reduction Graph Edge Sparsification Intrinsic Dimensionality Multiscale Spectral Decomposition Single-Cell Rna+1

Jan 30, 2026cs.LG

Uncertainty-aware Causal Decision Making via Effect Bound Decomposition

Causal inference from observational data can provide strong evidence for finding the best action in a decision-making scenario without having to perform expensive randomized trials. The causal effect of an action is often not pointwise identifiable even with infinite data due to unobserved confounding factors. Furthermore, having only finitely many samples adds another layer of uncertainty to causal effect estimation. Several existing methods can be used to obtain upper and lower bounds to the causal effect, ranging from symbolic methods to the more recent neural network-based approaches, which implicitly incorporate both sources of uncertainty. However, these methods do not inform whether collecting more samples may or may not help identify the best action from observational data, leaving experts in the dark about their data collection strategies. We address this problem with a novel framework that can distinguish the range of causal effect values that might be eliminated by collecting more samples from the range of values that, with high probability, cannot be eliminated with more observational samples. We show that this partitioning can be obtained by solving max-min and min-max optimization problems. We leverage neural causal models to approximately recover this decomposition in practice. We demonstrate via experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. Our framework can help practitioners decide when to resort to non-observational studies or seek to measure some of the unmeasured confounders for optimal decision-making.

Md Musfiqur Rahman, Ziwei Jiang, Hilaf Hasson +1

Electrical and Computer Engineering, Purdue University · Computer Science, Johns Hopkins University · Cohesity

Causal Inferences Causal Modeling Latent Confounders Decomposition

Jan 10, 2026math.OC

Resource-constrained Project Scheduling with Time-of-Use Energy Tariffs and Machine States: A Logic-based Benders Decomposition Approach

In this paper, we investigate the Resource-Constrained Project Scheduling Problem (RCPSP) with Time-of-Use (TOU) energy tariffs and machine states, a variant of RCPSP for production scheduling, where energy price is part of the criteria and one highly energy-demanding machine can be in one of the following three states: proc, idle, or off. The problem involves scheduling all tasks, respecting precedence constraints and resource limitations, while minimizing the combination of the overall makespan and the Total Energy Cost (TEC), which varies according to the TOU tariffs, which can take negative values. We propose two novel approaches to solve it: a monolithic Constraint Programming (CP) approach and a Logic-Based Benders Decomposition (LBBD) approach. The latter combines a master problem handling the energy cost solved using Integer Linear Programming (ILP) with a subproblem handling the RCPSP, resolved using CP. Both approaches outperform the monolithic compact ILP counterpart, but the LBBD significantly outperforms the monolithic CP in most cases, especially when the makespan criterion is not included in the objective function, solving to optimality instances with up to 480 tasks. Finally, we propose a way to generalize our LBBD approach to other problems sharing similar characteristics, and applied it to various problems, such as an RCPSP with blocking times & total weighted tardiness criterion, or a flexible job shop.

Corentin Juvigny, Antonín Novák, Jan Mandík +1

Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugosl´avsk´ych partyz´an˚u 1580/3, 160 00, Prague 6, Czech Republic

Job Shop Scheduling Mixed-Integer Programming Solvers Electricity Markets Resource-Constrained Edge Devices Decomposition+1

Dec 29, 2025cs.CV

MVID: Feed-Forward Multi-View Intrinsic Image Decomposition

Intrinsic image decomposition aims to recover material and illumination factors from RGB observations, but real-world images entangle reflectance with illumination, visibility, shadows, and non-diffuse appearance. Recent single-image methods address this entanglement with a residual image formation model, decomposing RGB into albedo, diffuse shading, and a non-diffuse residual. However, applying such decomposition independently to consecutive frames lacks scene-level context, leading to inconsistent factor assignments, albedo drift, and leakage across views. Meanwhile, multi-view inverse-rendering methods recover properties, such as material, lighting, and geometry, but they rely on synthetic data due to the highly uncertain estimation, and do not generalize to supervision by real images. We present MVID, Multi-View Intrinsic image Decomposition, a feed-forward framework built on the residual image formation model. MVID builds a scene-level multi-view representation and decodes a view-consistent albedo together with coherent per-view shading and residual factors through a factor query adapter, while using the same image formation model for self-supervised RGB reconstruction on unlabeled real-world sequences. Experiments on indoor, real-world, and outdoor benchmarks show that MVID improves both per-frame decomposition quality and cross-view consistency over single-view intrinsic, generative intrinsic, and multi-view inverse-rendering baselines. The resulting view-stable factors support practical image-space applications, including multi-view consistent illumination editing and specularity removal.

Kang Du, Duotun Wang, Wanling Li +2

The Hong Kong University of Science and Technology (Guangzhou) · Tencent · The Hong Kong University of Science and Technology

Intrinsic Image Decomposition Multi-View Inverse Rendering Reflectance Decomposition Image Editing

Nov 4, 2025cs.LG

Leveraging Discrete Function Decomposability for Scientific Design

In the era of AI-driven science and engineering, we often want to design discrete objects in silico according to user-specified properties. For example, we may wish to design a protein to bind its target, arrange components within a circuit to minimize latency, or find materials with certain properties. Given a property predictive model, in silico design typically involves training a generative model over the design space (e.g., protein sequence space) to concentrate on designs with the desired properties. Distributional optimization

\unicode{x2013}

which can be formalized as an estimation of distribution algorithm or as reinforcement learning policy optimization

\unicode{x2013}

finds the generative model that maximizes an objective function in expectation. Optimizing a distribution over discrete-valued designs is in general challenging because of the combinatorial nature of the design space. However, many property predictors in scientific applications are decomposable in the sense that they can be factorized over design variables in a way that could in principle enable more effective optimization. For example, amino acids at a catalytic site of a protein may only loosely interact with amino acids of the rest of the protein to achieve maximal catalytic activity. Current distributional optimization algorithms are unable to make use of such decomposability structure. Herein, we propose and demonstrate use of a new distributional optimization algorithm, Decomposition-Aware Distributional Optimization (DADO), that can leverage any decomposability defined by a junction tree on the design variables, to make optimization more efficient. At its core, DADO employs a soft-factorized "search distribution"

\unicode{x2013}

a learned generative model

\unicode{x2013}

for efficient navigation of the search space, invoking graph message-passing to coordinate optimization across linked factors.

James C. Bowden, Sergey Levine, Jennifer Listgarten

Department of Electrical Engineering and Computer Sciences, UC Berkeley. · Center for Computational Biology, UC Berkeley. · UC Berkeley–UCSF Graduate Program in Bioengineering, UC San Francisco.

Optimal Design Decentralized Optimization Decomposition Scientific Discovery Generative Models

Nov 3, 2025cs.LG

The Optimization Landscape of Carathéodory Decomposition of Toeplitz Covariances

Toeplitz covariance estimation is a classical problem in statistical signal processing, yet the geometry of the Gaussian maximum-likelihood objective remains only partially understood. Recent algorithms, including Newton-type, majorization-minimization, and gradient-based methods, indicate that the nonconvex problem can often be globally solved when the number of samples is sufficiently large, but they also reveal a difficult computational landscape. In this work, we study this phenomenon through an overparameterized Caratheodory representation of positive definite Toeplitz covariance matrices. The Caratheodory decomposition parameterizes the covariance using a combination of steering vectors with different frequencies and amplitudes. Our first result shows that fixed-grid amplitude optimization is fundamentally insufficient. Even in the population setting, and even with arbitrarily many fixed frequency grid points, amplitude-only optimization can have a strictly positive error floor under grid mismatch. This motivates optimizing both amplitudes and frequencies. In this case, our main theoretical result proves that the joint optimization has a benign population landscape: every stationary point that produces a positive definite covariance matrix recovers the true Toeplitz covariance. These findings suggest a simple interpretation of the Toeplitz covariance problem: the population landscape is globally benign, but may be highly ill-conditioned. In our numerical experiments, overparameterization improves convergence speed and finite-sample accuracy. In particular, it allows simple gradient descent to approach the Cramer Rao bound while keeping the implementation simple.

Daniel Busbib, Ami Wiesel

School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Covariance Maximum Likelihood Optimization Landscape Decomposition