ICML 2026 Papers

In this paper, we provide a comprehensive convergence analysis for the Lion optimizer. First, we establish that the original Lion achieves a convergence rate of $\mathcal{O}(d^{1/2}T^{-1/4})$, where $d$ denotes the problem dimension and $T$ is the iteration number. To improve this rate, we propose a variance reduction variant of Lion, which attains an enhanced rate of $\mathcal{O}(d^{1/2}T^{-1/3})$ with the average smoothness assumption. Then, we extend our analysis to distributed settings. We demonstrate that the distributed Lion optimizer and its variance reduction counterpart achieve linear speedup with respect to the number of nodes $n$, yielding convergence rates of $\mathcal{O}(d^{1/2}(nT)^{-1/4})$ and $\mathcal{O}(d^{1/2}(nT)^{-1/3})$, respectively. Additionally, we investigate a communication-efficient distributed Lion variant that utilizes sign compression for bidirectional communication. By employing unbiased sign operations, this variant achieves a convergence rate of $\mathcal{O} \left( \max \{ \frac{d^{1/4}}{T^{1/4}}, \frac{d^{1/10}}{n^{1/5}T^{1/5}} \} \right)$, and its variance-reduced counterpart can further improve the rate to $\mathcal{O}\left( \frac{d^{1/4}}{T^{1/4}} \right)$. Finally, we conduct numerical experiments to validate the effectiveness of the proposed methods.

Asynchronous pipeline parallelism maximizes hardware utilization by eliminating the pipeline bubbles inherent in synchronous execution, offering a path toward efficient large-scale distributed training. However, this efficiency gain can be compromised by gradient staleness, where the immediate model updates with delayed gradients introduce noise into the optimization process. Crucially, we identify a critical, yet often overlooked, pathology: this delay scales linearly with pipeline depth, fundamentally undermining the very scalability that the method originally intends to provide. We trace this pathology to a specific property of the optimization landscape: the misalignment between the Hessian eigenbasis and the standard coordinate basis, which triggers oscillations in the update trajectories of coordinate-wise adaptive optimizers. We identify that these oscillations cause delayed updates to diverge from their true counterparts, invalidating their use for current iterations. This insight is formalized through theoretical analysis, including a convergence bound showing that basis misalignment amplifies the delay penalty, and substantiated with empirical evaluation. To address this, we propose basis rotation, a framework that rotates the optimizer's coordinate system to align with the Hessian eigenbasis, keeping delayed updates useful. We theoretically demonstrate that basis rotation minimizes basis misalignment, thereby counteracting the conditions that amplify delay penalties. Empirically, in training up to a 3B-parameter LLM, basis rotation reduces the required iterations by 81.7% compared to the best-performing asynchronous baseline.

We introduce ECSEL, an explainable classification method that learns formal expressions in the form of signomial equations, motivated by the observation that many symbolic regression benchmarks admit compact signomial structure. ECSEL directly constructs a structural, closed-form expression that serves as both a classifier and an explanation. On standard symbolic regression benchmarks, our method recovers a larger fraction of target equations than competing state-of-the-art approaches while requiring substantially less computation. Leveraging this efficiency, ECSEL achieves classification accuracy competitive with established machine learning models without sacrificing interpretability. Further, we show that ECSEL satisfies some desirable properties regarding global feature behaviour, decision-boundary analysis, and local feature attributions. Experiments on benchmark datasets and two real-world case studies i.e., e-commerce and fraud detection, demonstrate that the learned equations expose dataset biases, support counterfactual reasoning, and yield actionable insights.

Surface reconstruction with differentiable rendering has achieved impressive performance in recent years, yet the pervasive photometric ambiguities have strictly bottlenecked existing approaches. This paper presents AmbiSuR, a framework that explores an intrinsic solution upon Gaussian Splatting for the photometric ambiguity-robust surface reconstruction with high performance. Started by revisiting the foundation, our investigation uncovers two built-in primitive-wise ambiguities in representation, while revealing an intrinsic potential for ambiguity self-indication in Gaussian Splatting. Stemming from these, a photometric disambiguation is first introduced, constraining ill-posed geometry solution for definite surface formation. Then, we propose an ambiguity indication module that unleashes the self-indication potential to identify and further guide correcting underconstrained reconstructions. Extensive experiments demonstrate our superior performance in surface reconstruction compared to existing methods across various challenging scenarios, while excelling in broad compatibility. Our code will be made open-source upon acceptance.

Visuomotor policies aim to learn complex manipulation tasks from expert demonstrations. However, generating smooth and coherent trajectories remains challenging, as it requires balancing proximal precision with distal foresight. Existing approaches typically focus on optimizing intra-chunk action distributions, often neglecting the inter-chunk coherence. Consequently, inter-chunk discontinuities significantly impede the learning of coherent long-horizon actions. To overcome this limitation and achieve a synergetic balance between precision and foresight, we propose FocalPolicy, a foresight-aware visuomotor policy that combines Frequency-Optimized Chunking with Locally Anchored flow matching. We introduce a foresight composite objective that supervises time-domain alignment within the proximal actions while regularizing frequency-domain structure over multiple future action chunks to improve cross-chunk coherence. To efficiently learn complex action distributions, we design locally anchored sampling to enhance target signal propagation efficiency during consistency flow matching training. Extensive experiments demonstrate that FocalPolicy outperforms existing approaches and confirm the generalizability of our modules to other baselines. Project website: https://focalpolicy.github.io/

Multi-Agent Systems (MAS) powered by Large Language Models (LLMs) have become a promising paradigm for solving workflow-structured tasks through expert collaboration. However, the data required for such collaboration are often distributed across organizations and cannot be centrally pooled due to privacy, intellectual property, and compliance constraints. Federated Learning preserves data locality, but existing federated paradigms typically treat clients as independent and fail to model workflow dependencies that are crucial for coherent multi-stage collaboration. We introduce **FedWave**, a federated and workflow-aware framework that enables LLM-based experts to solve sequential tasks under data-locality constraints. FedWave combines a *Value Chain Layer* to model inter-stage dependencies, federated LoRA adaptation to preserve role-specific expertise, a shared *Mixture-of-Experts (MoE)* router for input-conditioned expert fusion, and a *Direct Preference Optimization (DPO)* stage based on router-induced preferences. Experiments across workflow datasets and LLM backbones show that FedWave outperforms federated baselines and remains competitive with centralized multi-agent systems while preserving data locality.

Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners. However, the connection between these two abilities remains less explored. In this work, drawing inspiration from self-supervised learning (SSL), we introduce a framework for jointly evaluating the representation and generation capabilities of diffusion models. Specifically, we decompose features into invariant and residual components and derive the Invariant Contamination Ratio (ICR), a Fisher-based metric that quantifies how residual variation contaminates invariant signal in feature space. We use this framework to analyze both discriminative and generative behavior of diffusion models. On the representation side, we find that invariance peaks at intermediate noise levels, which also yield the best downstream classification performance. On the generative side, we study how training transitions from genuine generalization to memorization in data-limited regimes, and show that ICR serves as a sensitive training-time indicator of early learning: increasing residual energy along Fisher directions marks the onset of memorization, detectable from training features alone without external evaluators or held-out test sets. Overall, our results show that diffusion models can be monitored from a self-supervised perspective through the geometry of their learned representations.

Full-Reference image quality assessment (FR IQA) is important for image compression, restoration and generative modeling, yet current neural metrics remain slow and vulnerable to adversarial perturbations. We present BiRQA, a compact FR IQA metric model that processes four fast complementary features within a bidirectional multiscale pyramid. A bottom-up attention module injects fine-scale cues into coarse levels through an uncertainty-aware gate, while a top-down cross-gating block routes semantic context back to high resolution. To enhance robustness, we introduce Anchored Adversarial Training, a theoretically grounded strategy that uses clean "anchor" samples and a ranking loss to bound pointwise prediction error under attacks. On five public FR IQA benchmarks BiRQA outperforms or matches the previous state of the art (SOTA) while running $\sim 3 \times$ faster than previous SOTA models. Under unseen white-box attacks it lifts SROCC from 0.30-0.57 to 0.60-0.84 on KADID-10k, demonstrating substantial robustness gains. To our knowledge, BiRQA is the only FR IQA model combining competitive accuracy with real-time throughput and strong adversarial resilience.

We study the problems of approximate sampling from and distribution testing of \emph{mixture models}, where the modes satisfy a functional inequality called \emph{approximate tensorization of entropy} (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a \emph{data-based initialization}, with \emph{optimal} sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.

Fine-grained traffic prediction is critically important for mitigating traffic congestion in key urban areas and for providing lane-change guidance in autonomous vehicles and navigation systems. However, task-specific models are not efficient enough, city-scale pre-trained models often overlook fine-grained requirements, and the demand for extensive computational resources hinders practical deployment. To address this issue, we developed a lightweight pre-training framework, MiniTraffic. This framework leverages abundant road-level data to address lane-level data scarcity through a frequency domain stability augmentation module and captures road-lane correlations via contrastive clustering to construct small-scale graph structures, significantly reducing model parameters. Fine-tuning with minimal target data provides a unified and efficient solution for fine-grained traffic prediction. In multi-granularity traffic prediction tasks across six fine-grained datasets, MiniTraffic demonstrated superior performance compared to existing baselines.

Neural acoustic fields often model time-domain impulse responses, which struggle to capture the frequency-selective wave behaviors that dominate confined, resonant environments. To address this, we propose INFER (Implicit Neural Frequency Response fields), a framework that directly learns continuous, complex-valued frequency response fields. Unlike prior time-domain methods, our frequency-first approach enables three key innovations: (1) end-to-end learning of frequency-specific attenuation and phase delay in 3D space; (2) a physics-based Kramers–Kronig consistency constraint that causally regularizes attenuation and phase delay; and (3) perceptual and hardware-aware spectral supervision that prioritizes critical auditory bands. We evaluate INFER across diverse settings, ranging from standard room-scale benchmarks (MeshRIR, RAF) to challenging, highly reverberant environments like real car cabins. Our approach significantly outperforms time- and hybrid-domain baselines, reducing average magnitude and phase reconstruction errors by over 39\% and 51\%, respectively, demonstrating state-of-the-art accuracy in modeling complex acoustic spaces.

Off-policy reinforcement learning is vulnerable to overestimation bias, which is rooted in the total value uncertainty. However, existing methods typically misaddress this by targeting the epistemic component, neglecting the aleatoric component. We identify for the first time that this oversight fails to contain a massive bias surge, termed **Aleatoric Impulse**. Although transient, this impulse fundamentally derails the learning trajectory, permanently locking the agent into suboptimal policies. To counteract this, we propose **A**leatoric **I**mpulse **D**amping **(AID)**, the first mechanism that models total value uncertainty by disentangling the return variance into epistemic and aleatoric components, followed by their adaptive weighted recombination. Leveraging this derived uncertainty, the critic constructs a pessimistic lower confidence bound to surgically suppress the impulse. Complementing this, the actor utilizes a symmetrical upper confidence bound to drive optimistic exploration, ensuring that the necessary pessimism does not compromise exploration efficiency. We integrate this mechanism into the Distributional Soft Actor-Critic algorithm to establish **DSAC-AID**. Extensive experiments on the high-dimensional Gym-MuJoCo and DeepMind Control Suite benchmarks demonstrate that it achieves state-of-the-art results in final performance.

Large-scale models are pretrained on massive web-crawled datasets containing documents of mixed quality, making data filtering essential. A popular method is Classifier-based Quality Filtering (CQF), which trains a binary classifier to distinguish between pretraining data and a small, high-quality set. It assigns each pretraining document a quality score defined as the classifier's score and retains only the top-scoring ones. We provide an in-depth analysis of CQF. We show that while CQF improves downstream task performance, it does not necessarily enhance language modeling on the high-quality set. Importantly, we find that training on CQF-selected data can outperform training directly on the high-quality set, even when the latter is sufficiently large. This finding alone is particularly striking, given the substantial effort and cost recently devoted to augmenting high-quality data. We explain this paradox by the fact that CQF implicitly filters the high-quality dataset as well as the low-quality one. Finally, we introduce an optimization-driven notion of data quality and demonstrate that it can be reliably estimated using small-scale proxy experiments. Altogether, our results both elucidate the mechanisms behind CQF and deepen our understanding of data selection methods widely used in practice.

Constitutional AI has focused on single-model alignment using fixed principles. However, multi-agent systems create novel alignment challenges through emergent social dynamics. We present Constitutional Evolution, a framework for automatically discovering behavioral norms in multi-agent LLM systems. Using a grid-world simulation with survival pressure, we study the tension between individual and collective welfare, quantified via a Societal Stability Score $\mathcal{S} \in [0,1]$ that combines productivity, survival, and conflict metrics. Adversarial constitutions lead to societal collapse ($\mathcal{S}=0$), while vague prosocial principles (''be helpful, harmless, honest'') produce inconsistent coordination ($\mathcal{S}=0.249$). Even constitutions designed by Claude 4.5 Opus with explicit knowledge of the objective achieve only moderate performance ($\mathcal{S}=0.332$). Using LLM-driven genetic programming with multi-island evolution, we evolve constitutions maximizing social welfare without explicit guidance toward cooperation. The evolved constitution $\mathcal{C}^*$ achieves $\mathcal{S}=0.556\pm0.008$ (123\% higher than human-designed baselines, $N=10$), eliminates conflict, and discovers that minimizing communication (0.9\% vs 62.2\% social actions) outperforms verbose coordination. Our interpretable rules demonstrate that cooperative norms can be discovered rather than prescribed.

Understanding how and why large language models (LLMs) fail is becoming a central challenge as models rapidly evolve and static evaluations fall behind. While automated probing has been enabled by dynamic test generation, existing approaches often discover isolated failure cases, lack principled control over exploration, and provide limited insight into the underlying structure of model weaknesses. We propose ProbeLLM, a benchmark-agnostic automated probing framework that elevates weakness discovery from individual failures to structured failure modes. ProbeLLM formulates probing as a hierarchical Monte Carlo Tree Search, explicitly allocating limited probing budgets between global exploration of new failure regions and local refinement of recurring error patterns. By restricting probing to verifiable test cases and leveraging tool-augmented generation and verification, ProbeLLM grounds failure discovery in reliable evidence. Discovered failures are further consolidated into interpretable failure modes via failure-aware embeddings and boundary-aware induction. Across diverse benchmarks and LLMs, ProbeLLM reveals substantially broader, cleaner, and more fine-grained failure landscapes than static benchmarks and prior automated methods, supporting a shift from case-centric evaluation toward principled weakness discovery

Diffusion-based Q-learning has emerged as a powerful paradigm for offline reinforcement learning, but its reliance on multi-step denoising makes both training and inference computationally expensive and brittle. Recent efforts to accelerate diffusion Q-learning toward single-step action generation typically introduce auxiliary networks, policy distillation, or multi-phase training, which frequently compromise simplicity, stability, or performance. To address these limitations, we introduce Bootstrapped Flow Q-Learning (BFQ), a novel framework that enables accurate single-step action generation during both training and inference—without auxiliary networks or distillation procedures. BFQ adopts a divide-and-conquer view of the displacement vector along the flow path: it begins by learning short-range displacements that can be accurately estimated from the Flow Matching marginal velocity, and bootstraps these components to directly learn a noise-to-action mapping in a single step. This formulation eliminates multi-step denoising, resulting in a learning procedure that is substantially faster, simpler, and more robust. Extensive D4RL evaluations show that BFQ improves performance while significantly reducing computational cost compared to multi-step diffusion baselines, demonstrating that single-step action generation suffices for high-performance offline Reinforcement Learning.

Computational pathology has made progress in diagnosis and prognosis prediction from whole slide images (WSIs), yet pipelines still rely on patch-level feature extraction and aggregation, departing from the cell-centric reasoning used by pathologists. This gap limits sensitivity to micro-lesions and subtle changes, and current methods rarely provide a unified solution that supports both local and global tasks with trustworthy evidence. We propose Cello, a universal cell-wise feature aggregation framework for reliable pathology image analysis. Cello integrates cell-level representations into WSI modeling via protein-signal–supervised cell-wise learning, preserving fine-grained cellular cues under gigapixel constraints. For local tasks, Cello introduces a flexible prototype-based contrastive module for scalable, task-adaptive representation learning. For global tasks, Cello adopts a weakly supervised gated aggregation that can widely leverage WSI labels. Finally, a cell–local–global decision-route consistency objective dynamically aggregates cellular evidence and aligns local predictions with global outcomes, improving reliability and faithfulness. Trained with only hundreds to thousands of samples, Cello achieves performance gains of 3.0%~7.6% and outperforms SOTA pathology foundation models pretrained on tens of thousands of samples. Code is available at https://github.com/HengruiLou/Cello.

Minimum Bayes Risk (MBR) decoding yields more robust and higher-quality text generation than maximum a posteriori (MAP) decoding by selecting hypotheses that maximize expected utility over sampled pseudo-references. However, there exists a discrepancy in the design: hypothesis selection calculates expected utility scores conditioned on given pseudo-references, while commonly used evaluation metrics, e.g., BLEU and COMET, are asymmetric. Therefore, it is important to consider both hypothesis-to-reference and reference-to-hypothesis directional effects. In this study, we introduce a noisy channel decomposition of MBR decoding that naturally incorporates bidirectional effects to account for these asymmetries. We decompose MBR decoding into four interacting components: hypothesis-to-reference likelihood, reference-to-hypothesis likelihood, hypothesis prior, and reference prior. This decomposition provides a unified interpretation of existing MBR variants and enables metric- and task-specific interpretability by isolating the contribution of each channel. Our comprehensive analysis reveals that channel-wise contributions exhibit distinct characteristics across metrics while remaining consistent across tasks, and suggests that appropriate channel weighting may lead to improvements over original MBR decoding.

The paradigm of visual generation is rapidly shifting from single-image conditioning toward multi-image conditioning, making the ability to synthesize and edit images based on multiple visual references a critical capability. Despite this trend, existing benchmarks remain largely limited to single-reference scenarios or narrowly defined tasks, leaving model behavior under complex multi-concept composition insufficiently explored. To bridge this gap, we introduce **MICE-Bench**, a comprehensive benchmark for **M**ulti-reference **I**mage **C**reation and **E**diting. The benchmark is designed around three core principles: 1) heterogeneous concept composition across seven visual dimensions; 2) varying levels of constraint density, ranging from dual-concept to seven-concept configurations; 3) concept-centric data construction and benchmark evaluation, enabling fine-grained analysis of interactions among multiple concepts. MICE-Bench consists of 3,119 high-quality test cases within a unified concept space. Using an 8-dimensional evaluation metric, we systematically evaluate 13 state-of-the-art models. Our results show that although closed-source models maintain a clear performance advantage, all models experience notable degradation in concept consistency and physical realism as concept complexity increases.This indicates that current models rely on superficial composition rather than genuine multi-concept synthesis, highlighting substantial room for future improvement.