ICML 2026 Papers

In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the *Functional Anisotropy Hypothesis*: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augments the CSD objective with an explicit penalty on structural overlap across multiple discovery runs, enabling the discovery of circuits or sheaves with strong task performance but minimal shared structure across a plethora of common CSD benchmarks. We find that this phenomenon becomes increasingly pronounced as the number of discovered sheaves grows and persists robustly across major CSD methods. We further identify an ultra-sparse three-edge sheaf and show that none of its edges is individually indispensable, undermining even weakened notions of canonical or essential components. To explain these findings, we propose a *Distributive Dense Circuit Hypothesis* and provide a theoretical analysis demonstrating that non-unique, low-overlap circuit explanations arise naturally from high-dimensional superposition under mild assumptions. Together, our results suggest that mechanistic explanations in LLMs are inherently non-canonical and call for a rethinking of how CSD results should be interpreted and evaluated.

Current LLM agents are proficient at calling isolated APIs but struggle with the "last mile" of commercial software automation. In real-world scenarios, tools are not independent; they are atomic, interdependent, and prone to environmental noise. We introduce $\textbf{ComplexMCP}$, a benchmark designed to evaluate agents in these rigorous conditions. Built on the Model Context Protocol (MCP), $\textbf{ComplexMCP}$ provides over 300 meticulously tested tools derived from 7 stateful sandboxes, ranging from office suites to financial systems. Unlike existing datasets, our benchmark utilizes a seed-driven architecture to simulate dynamic environment states and unpredictable API failures, ensuring a deterministic yet diverse evaluation. We evaluate various LLMs across full-context and RAG paradigms, revealing a stark performance gap: even top-tier models fail to exceed a 60% success rate, far trailing human performance 90%. Granular trajectory analysis identifies three fundamental bottlenecks: (1) $\textbf{tool retrieval saturation}$ as action spaces scale; (2) $\textbf{over-confidence}$, where agents skip essential environment verifications; and (3) $\textbf{strategic defeatism}$, a tendency to rationalize failure rather than pursuing recovery. These findings underscore the insufficiency of current agents for interdependent workflows, positioning $\textbf{ComplexMCP}$ as a critical testbed for the next generation of resilient autonomous systems. The codebase and benchmark implementation are publicly available at https://github.com/AIDC-AI/complex-mcp.

We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. We examine why existing quality functions are insufficient for this problem and introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models that predict hazard functions, and the *conditional rank statistics (CRS)*, which quantifies individual point deviation from a subgroup's survival time distribution. We study the EPE and CRS theoretically and show they address problems with existing metrics. We then introduce eight algorithms for Cox subgroup discovery. Our main algorithm is based on the DDGroup framework of Izzo et al. (2023) and leverages both the EPE and CRS, allowing theoretical correctness guarantees in well-specified settings. Empirical evaluation on synthetic and real data confirms our theory, showing our methods recover ground-truth subgroups in well-specified cases and achieve better model fit than naively fitting the Cox model to the entire dataset. A case study on NASA jet engine simulation data demonstrates that discovered subgroups uncover known nonlinearities in the data and suggest design choices mirrored in practice.

In this paper, we study a structured class of nonconvex constrained stochastic problems with difference-of-convex (DC) regularization, where the feasible set is possibly nonconvex and the concave part of the DC regularizer is allowed to be nonsmooth. The fundamental challenge lies in maintaining feasibility for nonconvex constraints while achieving favorable oracle complexity. Although single-loop algorithms efficiently solve unconstrained DC optimization problems, their potential for constrained optimization with DC structure remains largely unexplored. To address this gap, we develop **MoSSP**, a **Mo**mentum-based **S**ingle-loop **S**tochastic **P**enalty method for such problems with provable complexity guarantees. The key idea is to apply a single stochastic proximal-gradient step to the Moreau envelope of the penalty plus the convex DC part, with the concave part's proximal mapping computed in parallel. We derive two algorithm variants: a Polyak-momentum version with $\mathcal{O}(\varepsilon^{-4})$ oracle complexity for finding stochastic $\varepsilon$-KKT points, and an improved $\mathcal{O}(\varepsilon^{-3})$ version incorporating recursive momentum. Experimental results demonstrate the effectiveness of the proposed algorithms.

We introduce Genome-Factory, the first integrated Python library for tuning, deploying, and interpreting genomic foundation models. Our core contribution is to simplify and unify the workflow for genomic model development: data collection, model tuning, inference, benchmarking, and interpretability. For data collection, Genome-Factory offers an automated pipeline to download genomic sequences and preprocess them. For model tuning, Genome-Factory supports both full and parameter-efficient fine-tuning across diverse genomic models. For inference, Genome-Factory enables both embedding extraction and DNA sequence generation. For benchmarking, we include two existing benchmarks and provide a flexible interface to incorporate additional benchmarks. For interpretability, Genome-Factory introduces an open-source biological interpreter based on a sparse auto-encoder. We validate the utility of Genome-Factory across three dimensions: (i) Compatibility with diverse models and fine-tuning methods; (ii) Benchmarking downstream performance using two open-source benchmarks; (iii) Biological interpretation of learned representations with DNABERT-2. These results highlight its practical value for real-world genomic analysis. GitHub: https://github.com/WeiminWu2000/Genome_Factory.

Semantic Typography aims to visualize the meaning of an input word through the form of a character, while preserving its legibility. Existing vector-based methods, which primarily rely on text-driven optimization like Score Distillation Sampling (SDS), often produce glyphs that lack rich semantic details. Furthermore, these approaches struggle to maintain the overall structural integrity of the glyphs and frequently suffer from visual artifacts caused by intersections, compromising both readability and aesthetic quality. To address these challenges, we propose VecDesigner, a novel optimization-based method for vector semantic typography. Specifically, we introduce Visual-Guided Score Distillation Sampling (VGSDS), which leverages text-related reference images as visual guidance to infuse the glyphs with richer and more concrete semantic details. To preserve legibility and structural integrity, we design a vector-based Procrustes loss to constrain the overall deformation of the glyph. Concurrently, we effectively mitigate the intersection problem by imposing positional relationship constraints on the control points. Comprehensive experiments demonstrate that VecDesigner outperforms existing methods in both semantic expression and structural preservation, generating high-quality, expressive, and clearly legible semantic glyphs.

Natural language to optimization (NL2Opt) requires translating unstructured text into executable mathematical models. Beyond simple syntax errors, this task suffers from silent modeling failures, where incorrect formulations execute successfully but yield invalid results. We propose \textbf{Draft-and-Audit RL (DA-RL)}, a framework that learns optimization modeling as a two-step iterative workflow. Unlike inference-time scaffolds that rely on intermediate solver feedback to guide repairs, DA-RL optimizes a shared-parameter policy using terminal-only verification: the model is rewarded solely based on the execution of the final audited program. This constraint forces the model to internalize rubric-guided revision as a learned capability and encourages the emergence of cross-turn synergy, where the policy learns to generate drafts that are structurally amenable to self-correction.

Formal verification of system software with complex heap manipulations remains challenging. Standard automated solvers frequently fail to discharge separation logic verification conditions even when correct specifications like loop invariants are provided, forcing verification engineers to manually construct proofs. While large language models (LLMs) have shown promise in proof synthesis, specialized approaches for separation logic remain unexplored. To bridge this gap, we introduce SL-VC (Separation Logic Verification Conditions), a benchmark of 289 verification conditions from textbook implementations of data structures and algorithms together with real-world C code, including the LiteOS kernel's linked list library and the mini-gmp library. Our evaluation reveals that general-purpose LLMs and existing LLM-based Rocq provers struggle to effectively discharge these verification conditions. To address this challenge, we propose SPLIT (Split spatial and pure Proving with LLM-frIendly Tactics), a novel framework that enables predictable proof state transitions through an LLM-friendly tactic library, combined with a two-stage workflow that separates spatial and pure reasoning to align with separation logic semantics. Experimental results on SL-VC demonstrate that SPLIT consistently outperforms existing approaches, showing that LLM-assisted proof synthesis is a promising solution for separation logic verification of real-world system software.

Non-Markovian dynamics are commonly found in real-world environments due to long-range dependencies, partial observability, and memory effects. The Bellman equation that is the central pillar of Reinforcement learning (RL) becomes only approximately valid under Non-Markovian. Existing work often focus on practical algorithm designs and offer limited theoretical treatment to address key questions, such as what dynamics are indeed capturable by the Bellman framework and how to inspire new algorithm classes with optimal approximations. In this paper, we present a novel topological viewpoint on temporal-difference (TD) based RL. We show that TD errors can be viewed as 1-cochain in the topological space of state transitions, while Markov dynamics are then interpreted as topological integrability. This novel view enables us to obtain a Hodge-type decomposition of TD errors into an integrable component and a topological residual, through a Bellman–de Rham projection. We further propose HodgeFlow Policy Search (HFPS) by fitting a {potential network} to minimize the non-integrable projection residual in RL, achieving stability/sensitivity guarantees. In numerical evaluations, HFPS is shown to significantly improve RL performance under non-Markovian.

Trained attention layers exhibit striking and reproducible spectral structure of the weights, including low-rank collapse, bulk deformation, and isolated spectral outliers, yet the origin of these phenomena and their implications for generalization remain poorly understood. We study empirical risk minimization in a single-head tied-attention layer trained on synthetic high-dimensional sequence tasks generated from the attention-indexed model. Using tools from random matrix theory, spin-glass theory, and approximate message passing, we obtain an exact high-dimensional characterization of training and test error, interpolation and recovery thresholds, and the spectrum of the key and query matrices. Our theory predicts the full singular-value distribution of the trained query–key map—including low-rank structure and isolated spectral outliers—in qualitative agreement with observations in more realistic transformers. Finally, for targets with power-law spectra, we show that learning proceeds through sequential spectral recovery, leading to the emergence of power-law scaling laws.

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

Diffusion models have recently set new benchmarks in Speech Enhancement (SE). However, most existing score-based models treat speech spectrograms merely as generic 2D images, applying uniform processing that ignores the intrinsic structural sparsity of audio, which results in inefficient spectral representation and prohibitive computational complexity. To bridge this gap, we propose **DVPD**, an extremely lightweight **D**ual-**V**iew **P**redictive **D**iffusion model, which uniquely exploits the dual nature of spectrograms as both visual textures and physical frequency-domain representations across both training and inference stages. Specifically, during training, we optimize spectral utilization via the Frequency-Adaptive Non-uniform Compression (FANC) encoder, which preserves critical low-frequency harmonics while pruning high-frequency redundancies. Simultaneously, we introduce a Lightweight Image-based Spectro-Awareness (LISA) module to capture features from a visual perspective with minimal overhead. During inference, we propose a Training-free Lossless Boost (TLB) strategy that leverages the same dual-view priors to refine generation quality without any additional fine-tuning. Extensive experiments across various benchmarks demonstrate that DVPD achieves state-of-the-art performance while requiring only **35%** of the parameters and **40%** of the inference MACs compared to SOTA lightweight model, PGUSE. These results highlight DVPD's superior ability to balance high-fidelity speech quality with extreme architectural efficiency. Code and audio samples are available at https://github.com/ke12345213/dvpd_demo

Large Language Model (LLM)-based agents demonstrate strong reasoning and execution capabilities on complex tasks when guided by structured instructions, commonly referred to as workflows. However, existing workflow-assisted agent serving systems typically rely on predefined templates and shallow matching mechanisms, which limit their ability to capture deep semantic relationships and generalize to previously unseen tasks. To address these limitations, we propose a new workflow management paradigm that represents workflows using a unified graph, termed wGraph, where each node corresponds to an atomic operation. wGraph serves as a shared substrate from which task-specific workflows are dynamically instantiated. Building on wGraph primitives, we introduce GraphFlow, a system that efficiently integrates workflows into agent serving through two key designs. First, adaptive workflow generation dynamically constructs workflows from wGraph based on task semantics and constraint requirements. Second, workflow state management exploits wGraph structure to efficiently manage Key-Value (KV) caches, reducing redundant computation during agent serving. Extensive experiments across five benchmark datasets show that GraphFlow consistently outperforms state-of-the-art methods, yielding an average performance improvement of approximately 4.95 percentage points, while achieving an approximately 4× reduction in memory footprint.

Tool-calling is a central component of modern large language model (LLM) agents, equipping them with skills beyond their parametric knowledge. This paper studies tool-calling along two complementary axes: **effectiveness**, i.e., how this capability is *measured*, and **efficiency**, i.e., how it is *learned*. On effectiveness, we systematically analyze tool-calling evaluation pipelines and show that results can be highly sensitive to seemingly minor, often undocumented implementation choices including the *random seed*, *system prompt*, *multi-turn template construction*, and how *prior interaction/reasoning history* is carried forward. These choices can lead to substantial differences in reported performance, especially in multi-turn settings where without rigorous standardization, leaderboard rankings are unreliable. On efficiency, we examine standard reinforcement learning (RL) for tool-calling and identify two sources of computational waste: (i) during rollouts, many prompts produce no learning signal, and (ii) during policy updates, optimization incurs high computational cost. Guided by these findings, we introduce two techniques that accelerate RL-based tool-calling training, achieving substantial wall-clock speedup without degrading performance.

Reasoning in knowledge-intensive domains remains challenging as intermediate steps are often not locally verifiable: unlike math or code, evaluating step correctness may require synthesizing clues across large external knowledge sources. As a result, subtle errors can propagate through reasoning traces, potentially never to be detected. Prior work has proposed process reward models (PRMs), including retrieval-augmented variants, but these methods operate post hoc, scoring completed trajectories, which prevents their integration into dynamic inference procedures. Here, we introduce Process Reward Agents (PRA), an inference-time method for providing domain-grounded, online, step-wise rewards to a frozen policy. In contrast to prior retrieval-augmented PRMs, PRA enables search-based decoding to rank and prune candidate trajectories at every generation step. Experiments on multiple medical reasoning benchmarks demonstrate that PRA consistently outperforms strong baselines, achieving 81.9% accuracy on MedQA with Qwen3-4B, a new state of the art at the 4B scale. Importantly, PRA generalizes to unseen frozen policy models ranging from 0.5B to 8B parameters, improving their accuracy by up to 25.7% without any policy model updates. More broadly, PRA suggests a paradigm in which frozen reasoners are decoupled from domain-specific reward modules, allowing the deployment of new backbones in complex domains without retraining. All code and data are publicly available at https://process-reward-agents.github.io/.

Parametric partial differential equations (PDEs) serve as fundamental models across science and engineering, yet constructing fast and accurate surrogate models from sparse, irregularly sampled observations with reliable uncertainty quantification remains challenging. Existing approaches struggle to simultaneously handle variable observation patterns, preserve physics consistency, and provide well-calibrated predictive uncertainty. We introduce Bias-Spectrum Neural Processes (BSNP), a unified meta-learning framework that systematically integrates weak structural priors (translation equivariance, locality) with strong physical priors (governing equations and boundary conditions). BSNP addresses two critical obstacles: discretization overfitting through stochastic collocation that resamples residual evaluation points, and uncertainty collapse through mean-field enforcement that applies PDE constraints only to predictive means while preserving learned uncertainty. Comprehensive experiments on nonlinear Poisson equations, Burgers dynamics, and Navier-Stokes flows demonstrate that BSNP achieves superior accuracy and well-calibrated uncertainty quantification in sparse-data regimes.

Reinforcement learning has been widely applied to diffusion and flow models for visual tasks such as text-to-image generation. However, these tasks remain challenging because diffusion models have intractable likelihoods, which creates a barrier for directly applying popular policy-gradient type methods. Existing approaches primarily focus on crafting new objectives built on already heavily engineered LLM objectives, using ad hoc estimators for likelihood, without a thorough investigation into how such estimation affects overall algorithmic performance. In this work, we provide a systematic analysis of the RL design space by disentangling three factors: i) policy-gradient objectives, ii) likelihood estimators, and iii) rollout sampling schemes. We show that adopting an evidence lower bound (ELBO) based model likelihood estimator, computed only from the final generated sample, is the dominant factor enabling effective, efficient, and stable RL optimization, outweighing the impact of the specific policy-gradient loss functional. We validate our findings across multiple reward benchmarks using SD 3.5 Medium, and observe consistent trends across all tasks. Our method improves the GenEval score from $0.24$ to $0.95$ in $90$ GPU hours, which is $4.6\times$ more efficient than FlowGRPO and $2\times$ more efficient than the SOTA method DiffusionNFT without reward hacking.

Multimodal Large Language Models (MLLMs) have demonstrated significant achievements in general visual question answering (VQA) tasks. However, they remain brittle on mechanical en- gineering drawings, where high annotation den- sity and weak domain knowledge, compounded by unreliable spatial relation reasoning under strict projection rules and geometric constraints, make decisive cues easy to miss and frequently lead to wrong answers. To bridge this gap, we introduce the first comprehensive mechani- cal drawing understanding dataset, MechVQA, created through a semi-automated construction and quality-control pipeline. MechVQA con- tains 3.3k high-density pictures with 21K ques- tion–answer pairs, spanning 10 different fine- grained tasks across three capability levels: Recognition, Reasoning, and Judging, provid- ing a testbed to evaluate and improve MLLM understanding on real-world mechanical draw- ings. On top of MechVQA, we then develop the MechVL model through a multi-stage training paradigm, building a strong domain-specialized baseline. Extensive experimental results demon- strate that MechVL outperforms the strongest closed-source baseline by 7.57 percentage points on the MechVQA total score, significantly en- hancing mechanical drawing understanding abil- ity and providing a reusable foundation for deploy- ing MLLMs in mechanical design and inspection scenarios.

Large language models have shown strong reasoning abilities and are increasingly explored as high-level coordinators for multi-agent systems. However, directly deploying LLMs for coordination remains challenging, as effective policies often fail to reliably emerge at the low-level control stage, and inference costs limit scalability. We propose SynCoord (Synthetic Coordination Distillation), a self-supervised pipeline that distills task-level decision-making for cooperation from high-capacity reasoning models into lightweight agent policies. Our approach does not rely on explicit supervision or handcrafted coordination rules. Instead, we define a set of task-level tool interfaces that constrain LLM interaction and enable the collection of interaction trajectories, which are then used to train compact coordinated policies. This distillation process transfers coordination behaviors that are difficult to elicit through prompting alone, while substantially reducing inference overhead at execution time. We evaluate our method on cooperative multi-agent benchmarks including Overcooked-AI and Level-Based Foraging (LBF), under varying team sizes and environment scales. Experimental results show that the distilled policies achieve success rates and execution efficiency comparable to reinforcement learning–based methods, while exhibiting fewer erroneous or redundant actions. Moreover, the learned task-level coordination policy generalizes effectively to unseen team compositions and larger layouts without retraining.