ICML 2026 Papers

Driven by the imperative to leverage privacy-sensitive data scattered across decentralized devices, federated fine-tuning has emerged as a vital paradigm for adapting large language models without compromising data privacy. Yet, its practical efficacy is bottlenecked by severe client resource heterogeneity. Existing truncation-based methods typically couple the transmitted rank with the trainable rank, which (i) under-utilizes bandwidth on communication-rich but compute-limited clients and (ii) exacerbates truncation-induced gradient drift. To address this, we propose FedHera, a resource-decoupled framework that explicitly differentiates information reception from gradient optimization. FedHera employs a spectrum-preserving allocation strategy to maximize the transfer of global knowledge (via high-rank singular values) within bandwidth limits, irrespective of training constraints. Furthermore, we introduce a prefix-gating mechanism that utilizes the downloaded high-capacity basis as a frozen reference to guide local updates, thereby minimizing the optimization gap caused by aggressive truncation. Extensive experiments under different heterogeneous settings show that FedHera improves stability and accuracy over state-of-the-art baselines.

Millimeter-wave (mmWave) sensing enables privacy-preserving, always-on edge perception, but its measurements are often sparse, temporally irregular, and corrupted by high-frequency noise. Existing mmWave pipelines predominantly rely on artificial neural networks (ANNs), which achieve robustness through extensive preprocessing or deep architectures, thereby limiting their efficiency on edge devices. In this work, we study spiking neural networks (SNNs) for mmWave sensing from a mechanism–data alignment perspective. By leveraging the low-pass filtering behavior of leaky integrate-and-fire (LIF) dynamics, we analyze how their implicit temporal filtering interacts with the frequency structure of mmWave signals. Our analysis shows that when discriminative information resides in low-to-mid frequencies, LIF dynamics can inherently suppress high-frequency noise, clarifying when and why SNNs outperform ANNs. Based on this insight, we derive a principled criterion for configuring the membrane decay factor by matching the effective bandwidth of LIF dynamics to the data’s discriminative spectral content. Experimental results across four widely used mmWave datasets validate the proposed frequency-matching hypothesis, yielding an average test-accuracy improvement of 6.22% and a 3.64× reduction in theoretical energy consumption relative to ANN baselines, under a unified evaluation protocol.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Geometric properties of Transformer weights, particularly the unembedding matrix, have been widely useful in language model interpretability research. Yet, their utility for estimating downstream performance remains unclear. In this work, we systematically investigate the relationship between model performance and the unembedding matrix geometry, particularly its effective rank. Our experiments, involving a suite of 108 OLMo-style language models trained under controlled variation, reveal several key findings. While the best-performing models often exhibit a high effective rank, this trend is not universal across tasks and training setups. Contrary to prior work, we find that low effective rank does not cause late-stage performance degradation in small models, but instead co-occurs with it; we find adversarial cases where low-rank models do not exhibit saturation. Moreover, we show that effective rank is strongly influenced by pre-training hyperparameters, such as batch size and weight decay, which in-turn affect the model's performance. Lastly, extending our analysis to other geometric metrics and final-layer representation, we find that these metrics are largely aligned, but none can reliably predict downstream performance. Overall, our findings suggest that the model's geometry, as captured by existing metrics, primarily reflects training choices rather than performance.

Step-level caching accelerates diffusion models by exploiting temporal redundancy across denoising steps. Existing methods make per-step cache decisions using threshold-based heuristics, without directly optimizing for final output quality. As a result, their inference latency varies across inputs and is difficult to control at deployment. In this work, we propose BudCache, which inverts this formulation: rather than letting per-step error thresholds dictate the runtime cost, we fix the compute budget in advance and search for the cache policy that best preserves the final output. To tackle the combinatorial complexity of step selection, we combine Simulated Annealing with deterministic Hill Climbing. This offline search identifies high-quality cache policies within minutes and introduces no online search or thresholding overhead during inference. When the compute budget is very tight, we further introduce cache-aware schedule alignment, which adapts the time discretization to the selected cache policy to reduce cache-induced trajectory mismatch. Experiments on FLUX.1-dev and Wan2.1 show that BudCache achieves better generation quality than heuristic caching baselines under the same inference budgets.

Selective State Space Models (SSMs) such as Mamba have emerged as efficient alternatives to Transformers, achieving linear complexity through input-dependent parameterization. However, this selectivity transforms the system from linear time-invariant (LTI) to linear parameter-varying (LPV), where individually stable matrices can produce unbounded trajectories under switching. Existing work focuses on empirical performance, leaving global stability, robustness bounds, and practical certification unresolved. This paper develops a control-theoretic framework providing the first comprehensive stability and robustness analysis for selective SSMs. We prove BIBO stability by viewing selective scans as continuous-time LTI sampling and establish two-term robustness bounds with linear growth in sequence length. For general LPV systems, we provide common quadratic Lyapunov function conditions and develop algorithms to extract certificate constants directly from trained weights. These results bridge control theory and SSM architectures, enabling formal guarantees for safety-critical deployment.

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned embeddings is associated with generalization performance for a fixed trained model. We derive a post-hoc generalization bound that relates the gap between population risk and held-out empirical risk to two factors: (i) the intrinsic dimension of the embedding, which determines the convergence rate of the empirical embedding distribution to its population counterpart in Wasserstein distance, and (ii) the sensitivity of the downstream mapping from embeddings to predictions, characterized by Lipschitz constants. Together, these provide a post-hoc explanation of generalization for trained models. At the final embedding layer, architectural sensitivity disappears and the bound is dominated by embedding dimension, explaining its strong empirical correlation with generalization performance. Experiments across architectures and datasets validate the theory and demonstrate the utility of embedding-based diagnostics.

Autoregressive large language models (LLMs) have achieved remarkable success in many complex tasks, yet they can still fail in very simple logical reasoning such as the "reversal curse" --- when trained on forward knowledge data of the form "$A \rightarrow B$" (e.g., Alice's husband is Bob), the model is unable to deduce the reversal knowledge "$B \leftarrow A$" (e.g., Bob's wife is Alice) during test. Extensive prior research suggests that this failure is an inherent, fundamental limit of autoregressive causal LLMs, indicating that these models tend to memorize factual-level knowledge rather than capture higher-level rules. In this paper, we challenge this view by showing that this seemingly fundamental limit can be mitigated by slightly tweaking the training data with a simple regularization data recipe called the Identity Bridge of the form "$A \to A$" (e.g., The name of Alice is Alice). Theoretically, we prove that under this recipe, even a one-layer transformer can break the reversal curse by analyzing the implicit bias of gradient descent. Empirically, we show that a 1B pretrained language model finetuned with the proposed data recipe achieves a 50\% success rate on reversal tasks, in stark contrast to a near-zero success rate when trained solely on forward-knowledge data. Our work provides a novel theoretical foundation for the reversal curse and offers a principled, low-cost path to encouraging LLMs to learn higher-level rules from data.

Code repair is an important capability for language models (LMs): given a buggy program and unit tests, an LM must produce a fixed program that passes the tests. We aim to scale supervision for code repair by having an LM generate bug--fix tasks with unconstrained edits, using unit tests as the only verifier. We propose generator-fixer self-play, in which a single model is trained with reinforcement learning to alternate between generating bugs and fixing them. As the fixer improves, the generator adapts to produce increasingly difficult bugs, yielding an automatic curriculum. However, because unit tests certify correctness but not realism, we find that the generator can drift from bugs encountered in practice, improving repair on self-generated bugs while degrading on real-world bugs. We propose Anchored Self Play (ASP), which anchors self-play with a small reference set by (i) adding a code-embedding similarity reward to guide generation and (ii) mixing reference bugs into fixer training to prevent drift. To reflect LM-assisted programming, where bugs come from humans, LMs, and human edits of LM code, we introduce BugSourceBench, a code repair benchmark spanning human-authored bugs, human-edited buggy LM code, and errors in LM-generated code. Across bug sources, ASP achieves the best fix rates, improving average fix rate by $+25$% (relative) / $+7.2$ pp (absolute) over standard self-play, with gains on both LM-error bugs ($+100$% relative / $+11$ pp absolute) and human-authored bugs ($+7.1$% relative / $+3.4$ pp absolute).

Though biological foundation models (Bio-FMs) have delivered strong performance across biomedical tasks, their robustness to small-but-real perturbations is underexplored. In this work, we ask: Are Bio-FMs robust for real-world use? What perturbations compromise their reliability? Our pilot study suggests that due to subtle biological data curation issues and common machine-learning (ML) processing choices, Bio-FMs suffer from two complementary perturbation sources: biologically plausible perturbations (capturing experimental corruptions and curation artifacts) and ML-induced transformations (capturing preprocessing, data augmentation, and embedding choices). Guided by this taxonomy, we design perturbation suites that mimic corruptions frequently encountered in biological experiments, and we systematically probe how transformations in the ML pipeline reshape model behavior. By conducting 2,128 experiments over 11 state-of-the-art Bio-FMs on 7 bio-tasks, we show that most Bio-FMs are vulnerable to both biological perturbations and ML transformations, revealing underappreciated robustness gaps that can directly translate into deployment risk. Interestingly, we find that subtle biological perturbations, which are often imperceptible to current measurement tools, can induce severe discrepancies in Bio-FM outputs and lead to critical failures, yet cryo-EM models (e.g., CryoDRGN) exhibit a surprising level of robustness even under worst-case perturbations. Our study for the first time surfaces critical failure modes and provides a principled perspective for evaluating the robustness of Bio-FMs.

Recent leaderboard-based evaluations of large language models aggregate user feedback by fitting a Bradley--Terry model to pairwise comparisons, producing a single global ranking based on a latent quality score. While appealing for its simplicity, this approach is incompatible with heterogeneous preferences: when LLMs are used across diverse tasks and use cases, users who favor fundamentally different model behaviors can be systematically misrepresented when collapsed into a single quality score. To address this issue, we study *pluralistic leaderboards* that aim to remain *stable* with respect to heterogeneous user populations. Drawing on ideas from social choice theory, we adapt the notion of *local stability*, which requires that no model outside the top-$k$ positions is collectively preferred to the top-$k$ set by more than $O(1/k)$ fraction of users. Building on techniques from the social choice literature, we design an alternative leaderboard mechanism that satisfies local stability while eliciting only $\widetilde{O}(k)$ pairwise comparisons per user, where $k$ is the size of the prefix for which stability is guaranteed. Using data from LMArena, we show that standard Bradley--Terry aggregation can violate local stability in practice, whereas our method provides substantially stronger stability guarantees.

The rapid expansion of remote sensing technology has generated massive amounts of unlabeled multi-view data distributed across different institutions. Analyzing this data presents significant challenges, as centralized processing incurs prohibitive communication costs and raises data privacy concerns. To address these issues, this paper proposes a novel deep federated multi-view clustering (MVC) framework tailored for remote sensing data. Unlike existing methods that transmit sensitive data features, our approach shares only privatized prototypes masked with adaptive noise, ensuring both communication efficiency and privacy preservation. First, we employ superpixel segmentation to reduce the spatial dimensionality of remote sensing data, lowering computational burdens. Furthermore, to resolve the inconsistency of cluster assignments across different clients, we design a co-occurrence structural alignment module that synchronizes local models. Finally, we incorporate a wasserstein prototype contrastive learning mechanism, which models clusters as distributions rather than points, to enhance global consistency and robustness against data heterogeneity. Extensive experiments on four public datasets demonstrate that our framework achieves superior clustering performance and efficiency compared to state-of-the-art methods.

Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models. Notably, LoRA is inherently overparameterized: multiple pairs of low-rank factors can yield the same adapted weight matrix. We show—both theoretically and empirically—that these pairs exhibit significantly different condition numbers. As a result, converging to different loss minimizers directly impacts the convergence rate of LoRA. Building on this observation, we introduce Balanced Low-Rank Adaptation (BaLoRA), a variant of LoRA that projects iterates onto a balanced manifold. This manifold improves the conditioning of the loss landscape while preserving the adapted matrix. The projection step is computationally lightweight and integrates seamlessly into existing fine-tuning pipelines. Empirically, BaLoRA converges faster than standard LoRA and achieves superior performance across a range of fine-tuning tasks.

Counterfactual reasoning is one of the fundamental facets of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. It describes the queries what would have happened had some intervention been performed given that something else, corresponding to Layer 3 of the Pearl Causal Hierarchy. In this project, we examine a specific type of counterfactual quantities, called counterfactual direct (Ctf-DE), indirect (Ctf-IE), and spurious (Ctf-SE) effects for quantifying fairness in a sequential decision-making framework. Building on these measures, we formulate an online causally-fair learning problem with multiple long-term constraints and study it in both non-parametric contextual bandits and parametric logistic bandits settings. We achieve sublinear regret and violations bounds for both bandits settings with roundwise counterfactual fairness constraints (that are a priori unknown) without Slater's condition. For logistic bandits, our method achieves $\mathcal{O}(1)$ per-round time complexity using an online mirror descent estimator, yielding an efficient algorithm.

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view latent chain-of-thought as a manipulable causal process in representation space by modeling latent steps as variables in a structural causal model (SCM) and analyzing their effects through step-wise $\mathrm{do}$-interventions. We study two representative paradigms (i.e., Coconut and CODI) on both mathematical and general reasoning tasks to investigate three key questions: (1) which steps are causally necessary for correctness and when answers become decodable early; (2) how influence propagates across steps and how this structure compares to explicit CoT; and (3) whether intermediate trajectories retain competing answer modes and how output-level commitment differs from representational commitment across steps. We find that latent-step budgets behave less like homogeneous extra depth and more like staged functionality with non-local routing, and we identify a persistent gap between early output bias and late representational commitment. These results motivate mode-conditional and stability-aware analyses, together with corresponding training/decoding objectives, as more reliable tools for interpreting and improving latent reasoning systems. Code is available at https://github.com/J1mL1/causal-latent-cot.

Although peptides are well suited for flexible and shallow binding interfaces, their intrinsic flexibility induces a strongly coupled sequence–structure relationship that current fixed-geometry latent models cannot simultaneously model with conformational diversity and physical feasibility, ultimately limiting design quality. To overcome this bottleneck, PepFGLD is proposed as a receptor-conditioned, flexibility-aware framework for full-atom peptide design. The framework is motivated by a systematic analysis of existing limitations: geometry shifts driven by interfacial flexibility are not well captured by standard equivariant encoders; the static combination of sequence information and 3D geometry cannot represent their dynamic interactions; and diffusion models without timely geometric feedback tend to drift away from physically reasonable energy landscapes. In PepFGLD, FlexEGNN is used to improve the sensitivity of geometric representations to local flexibility, a coherent and adaptable latent conformational manifold is formed through bidirectional sequence–structure interaction and nonlinear latent mapping, and a time-dependent energy-guided diffusion mechanism is incorporated to balance exploration and convergence during diffusion so that sampling trajectories are continuously guided toward physically feasible full-atom structures. PepFGLD yields improved binding affinity and design success across multiple peptide design tasks.

Large Language Models (LLMs) have inherent limitations of faithfulness and factuality, commonly referred to as hallucinations. Several benchmarks have been developed that provide a test bed for factuality evaluation within the context of English-centric datasets, while relying on supplementary informative context like web links or text passages but ignoring the available structured factual resources. To this end, Knowledge Graphs (KGs) have been identified as a useful aid for hallucination mitigation, as they provide a structured way to represent the facts about entities and their relations with minimal linguistic overhead. We bridge the lack of KG paths and multilinguality for factual language modeling within the existing hallucination evaluation benchmarks and propose a KG-based multilingual, multihop benchmark called MultiHal framed for generative text evaluation. As part of our data collection pipeline, we mined 140k KG-paths from open-domain KGs, from which we pruned noisy KG-paths, curating a high-quality subset of 25.9k. Our baseline evaluation shows an absolute scale improvement by approximately 0.12 to 0.36 points for the semantic similarity score, 0.16 to 0.36 for NLI entailment and 0.29 to 0.42 for hallucination detection in KG-RAG over vanilla QA across multiple languages and multiple models, demonstrating the potential of KG integration. We anticipate MultiHal will foster future research towards several graph-based hallucination mitigation and fact-checking tasks.

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for evaluating these capabilities. We propose to use data structures as a principled lens: as fundamental building blocks of algorithms, they naturally probe structural reasoning—the ability to understand and manipulate relationships such as order, hierarchy, and connectivity that underpin algorithmic reasoning. We introduce DSR-Bench (Data Structure Reasoning Benchmark), spanning 20 data structures, 35 operations, and 4,140 problem instances. DSR-Bench features hierarchical task organization, fully automated generation and evaluation, and fine-grained diagnostics. Evaluating 13 state-of-the-art LLMs reveals critical limitations: the top-performing model achieves only 0.46/1 on challenging instances. Three auxiliary probes targeting more realistic usages expose further weaknesses: models perform poorly on spatial data and context-rich scenarios, and they struggle to reason over their own code.