ICML 2026 Papers

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Monte Carlo sampling and statistical optimal transport, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have relied on dual reformulation techniques, we contribute a sound and complete gradient flow view based on SDEs or PDEs that can be used to construct new algorithms for general, potentially non-convex, losses. Without loss of generality, we solve a class of Wasserstein and entropy-regularized DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limits and optimization dynamics of DRO. Numerical studies based on stochastic gradient descent on machine learning tasks provide empirical backing for our theoretical findings.

Generative Flow Networks (GFNs) offer a powerful paradigm for diverse sampling, yet they often exhibit instability and poor convergence when applied to stochastic or sparse-reward environments. To mitigate the high variance inherent in these settings, we propose a fundamental re-framing of the GFlowNet training objective within the frequency domain. We present \textbf{Spectral Time-Dependent GFlowNets (ST-GFNs)}, a framework that leverages Fourier analysis to enforce smoothness and stability in learned policies. Our theoretical analysis proves that our proposed spectral loss is mathematically equivalent to regularized value iteration, acting as a principled low-pass filter that separates signal from noise. Furthermore, we tackle the challenge of exploration in sparse landscapes by introducing a novel autocorrelated intrinsic reward derived from the Wiener-Khinchin theorem. Through extensive experiments ranging from adversarial games and noisy sequence generation to high-dimensional single-cell perturbation modelling, we demonstrate that ST-GFNs significantly outperform existing baselines in terms of robustness, sample efficiency, and mode discovery.

Emotional support plays an important role in dialogue systems, and its success depends on adapting to a user’s evolving and implicit needs across multi-turn interactions while leveraging the strong reasoning capacity of large language models. However, since signals about user needs are often weak, indirect, and can only be disambiguated through multi-turn interaction, existing emotional support methods often struggle to acquire and generalize relevant conversational knowledge efficiently. To bridge this gap, we introduce User-Aware Active Knowledge Acquisition (UKA), a gradient-free active dialogue learning framework that explicitly represents uncertainty about user needs and incorporates active learning into both knowledge acquisition and response selection. We propose a Theory-of-Mind uncertainty estimation mechanism that allows the model to prioritize responses, thereby eliciting more informative user feedback. UKA is capable of efficiently exploring user-aligned conversational knowledge during training while maintaining robustness at test time. Experiments across multiple dialogue benchmarks and model architectures demonstrate that our approach consistently outperforms strong baselines in dialogue quality and user alignment.

Conversational query reformulation (CQR) has become indispensable for improving retrieval in dialogue-based applications. However, existing approaches typically rely on reference passages for optimization, which are **impractical** to acquire in real-world scenarios. To address this limitation, we introduce a novel **reference-free** preference optimization framework ***DualReform*** that generates **pseudo reference passages** from **commonly-encountered** conversational datasets containing only queries and responses. DualReform attains this goal through two key innovations: (1) **response-based inference**, where responses serve as proxies to infer pseudo reference passages, and (2) **response refinement via the dual-role of CQR**, where a CQR model refines responses based on the shared objectives between response refinement and CQR. Despite not relying on reference passages, ***DualReform*** achieves 96.9--99.1% of the retrieval accuracy attainable only with reference passages and surpasses the state-of-the-art method by up to 31.6%.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing RLVR methods typically rely on on-policy optimization from scratch, resulting in high sampling costs and inefficient utilization of accumulated experience. As model capabilities and policy behaviors evolve during training, recent attempts to reuse experience via fixed reasoning trajectories further suffer from policy mismatch. Motivated by these limitations, we argue that experience in RLVR should not be reused as fixed reasoning trajectories, but instead expressed in a policy-adaptive manner. In this work, we propose Experience-Augmented Policy Optimization (EAPO), which leverages a prior RL-optimized policy as an action-level experience prior and selectively injects experience at critical decision points during rollout. To ensure stable and unbiased learning from experience-augmented rollouts, EAPO further incorporates an adapted importance sampling scheme. Experiments on using Qwen-2.5-math 7b and Qwen-3-8B on five different benchmarks demonstrate that EAPO consistently improves reasoning performance over state-of-the-art RLVR methods.

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level strong convexity assumption, which significantly restricts their applicability to modern machine learning problems of growing complexity. In this paper, we make the first attempt to extend BLO to the multi-task setting under a relaxed lower-level general convexity (LLGC) assumption. To this end, we reformulate the multi-task bilevel learning (MTBL) problem with LLGC into an equality constrained multi-objective optimization (ECMO) problem. However, ECMO itself is a new problem that has not yet been studied in the literature. To address this gap, we first establish a new Karush–Kuhn–Tucker (KKT)-based Pareto stationarity as the convergence criterion for ECMO algorithm design. Based on this foundation, we propose a weighted Chebyshev (WC)-penalty algorithm that achieves a finite-time convergence rate of $\mathcal{O}(ST^{-\frac{1}{2}})$ to KKT-based Pareto stationarity in both deterministic and stochastic settings, where $S$ denotes the number of objectives, and $T$ is the total iterations. Moreover, by varying the preference vector over the $S$-dimensional simplex, our WC-penalty method systematically explores the Pareto front. Finally, solutions to the ECMO problem translate directly into solutions for the original MTBL problem, thereby closing the loop between these two foundational optimization frameworks.

For denoising Spatially Resolved Transcriptomics (SRT) data, existing methods often construct spot and gene graphs to model inter-spot and inter-gene relationships, respectively. However, these methods often introduce spurious similarity biases among spots when constructing the spot graph and fail to capture nonlinear relationships among genes when constructing the gene graph. Moreover, ineffective graph fusion strategies further bottleneck denoising performance. To address these challenges, we propose SpaEF, which innovatively constructs spot and gene graphs with two Large Models (LMs) to inject prior knowledge for mitigating biases and capture nonlinear relationships, and then fuses them with the proposed element-wise graph autoencoder. As far as we know, SpaEF is the first SRT denoising method that utilizes pre-trained LMs to construct spot and gene graphs. Experiments on four real-world datasets with corresponding downstream tasks demonstrate that SpaEF not only outperforms SOTA denoising methods in accuracy but also exhibits strong robustness across tasks.

Vision-Language Models (VLMs) are costly at inference time because they must process long sequences of visual tokens. Existing token pruning methods often degrade under high compression by blindly discarding information, breaking spatial structure or collapsing diversity. We propose SpecFlow, a training-free framework that shifts the paradigm from destructive pruning to conservative condensation, strictly enforcing spatial coverage and statistical conservation to ensure stability. Treating visual tokens as nodes in a $k$NN graph, SpecFlow (i) computes a stable importance field via spectral heat flow to preserve structural coherence, (ii) allocates budgets via adaptive spatial partitioning to guarantee coverage, and (iii) aggregates discarded information into coreset sinks to maintain statistical conservation. The method is plug-and-play, requires no fine-tuning, and is compatible with FlashAttention. Experiments confirm that our SpecFlow outperforms SOTA methods across tasks, VLM architectures, and pruning ratios. Notably, LLaVA-1.5 with SpecFlow retains 95.6\% of original performance despite pruning 88.9\% of visual tokens, offering an exceptional efficiency-accuracy balance.

Decentralized Federated Learning (DFL) enables collaborative model training across connected clients without a central server, effectively mitigating communication bottlenecks and avoiding the single point of failure in Centralized Federated Learning (CFL). However, existing DFL methods mostly focus on parameter averaging with compromised update directions, which limits their performance potential due to insufficient exploration of the loss landscape, especially for complex models. We observe that layer exchanges among clients enhance exploration while introducing instability due to highly diverse update directions. To address these limitations, we propose Decentralized Layer-wise Fusion (DecFus), the first DFL framework that unifies layer-level exchange and averaging to balance exploration and exploitation. DecFus dynamically transitions the decentralized training process from exploration-dominant to exploitation-dominant phases, guided by the loss variance among connected neighbors. Furthermore, a layer-wise fusion strategy, informed by pairwise cosine similarity, categorizes all layers into two groups: an exchange group for exploration and an averaging group for exploitation. Specifically, we theoretically establish the convergence of DecFus without relying on the common assumption in existing literature that the aggregation matrix must be doubly stochastic. Extensive experiments demonstrate that DecFus achieves superior performance in both IID and non-IID scenarios, substantially outperforming existing CFL and DFL methods.

Zeroth-order (ZO) optimization offers a more memory-efficient alternative to first-order methods for fine-tuning large language models (LLMs). Recent ZO methods, exemplified by LOZO, estimate gradients within low-rank subspaces to align with the low-rank structure of LLM gradients. However, these methods rely on randomly generated subspaces of a fixed rank, which provides no guarantee of alignment with the actual dominant subspaces of the gradients; essentially, they remain ZO gradient descent with stochastic subspace sampling. To more effectively exploit the low-rank nature of LLM gradients, we propose \textbf{LOZO+}, an efficient \textbf{ZO} fine-tuning algorithm for LLMs that incorporates greedy \textbf{Lo}w-Rank subspace selection. Specifically, LOZO+ leverages loss-based feedback to assess alignment between candidate directions and the dominant low-rank gradient subspaces, and employs an adaptive thresholding criterion to retain only directions yielding substantial gradient descent, thereby steering ZO optimization toward more effective convergence. Importantly, we establish a theoretical framework that characterizes the convergence behavior of LOZO+, formally prove its superiority over existing methods. Extensive experiments demonstrate that LOZO+ consistently outperforms existing ZO methods and achieves performance competitive with FO algorithm, while retaining the memory efficiency inherent to ZO optimization.

Heavy-tailed distributions are ubiquitous in real-world data, where rare but extreme events dominate risk and variability. However, standard Variational Autoencoders (VAEs) employ simple decoder distributions (e.g., Gaussian) that fail to capture heavy-tailed behavior, while existing heavy-tail-aware extensions remain restricted to predefined parametric families whose tail behavior is fixed a priori. We propose the Phase-Type Variational Autoencoder (PH-VAE), whose decoder distribution is a latent-conditioned Phase-Type (PH) distribution—defined as the absorption time of a continuous-time Markov chain (CTMC). This formulation composes multiple exponential time scales, yielding a flexible, analytically tractable decoder that adapts its finite-range tail behavior directly from the observed data. Experiments on synthetic and real-world benchmarks demonstrate that PH-VAE accurately approximates diverse heavy-tailed distributions, significantly outperforming Gaussian, Student-t, and extreme-value-based VAE decoders in modeling observed tail behavior and extreme quantiles. In multivariate settings, PH-VAE captures realistic cross-dimensional tail dependence through its shared latent representation. To our knowledge, this is the first work to integrate Phase-Type distributions into deep generative modeling, bridging applied probability and representation learning.

Multimodal Large Language Models (MLLMs) frequently produce hallucinations (i.e., assertions that contradict the image or facts), undermining reliability in high-risk applications. Existing detection approaches typically feed images and texts jointly and estimate hallucination scores by measuring the consistency of model outputs. However, because the visual module often lags behind the language module in understanding and reasoning, MLLMs can repeatedly produce similar yet incorrect answers, yielding overestimated trustworthiness and missed detections. To address this, we propose a simple yet effective model-agnostic method, dubbed Decoupled Object-level Understanding and Bridging via vMF-based Trustworthiness (DOUBT). DOUBT first employs Object-level Understanding and Bridging (OUB), a two-step prompting scheme that decouples object recognition from relational reasoning by prompting the model to identify objects and then reason based on them. It further introduces a von Mises-Fisher (vMF)-based trustworthiness metric, which is more stable than semantic entropy metrics in small-sample settings. Extensive experiments and ablation studies on multiple benchmarks show that DOUBT consistently outperforms state-of-the-art baselines, demonstrating its robustness and generalizability for hallucination detection in MLLMs. The code is available at https://github.com/XLearning-SCU/2026-ICML-DOUBT.

The rapid evolution of Large Language Models (LLMs) has shifted their role from passive information providers to active agents capable of executing complex workflows. However, the realization of a true "AI worker" is currently hindered by benchmarks that fail to capture the intricacy of professional environments, which demand long-horizon planning, complex tool usage, and adherence to strict access protocols. To bridge this gap, we introduce EnterpriseOps-Gym, a benchmark environment designed to evaluate agentic planning in realistic enterprise settings. EnterpriseOps-Gym provides: (i) 1,150 expert-curated tasks across eight interconnected domains (including HR, IT, Customer Service and productivity tools) that require managing persistent state and adhering to strict outcome-based verification logic; and (ii) a high-fidelity, containerized sandbox environment hosting 164 database tables and 512 functional tools. Our evaluation reveals critical limitations in state-of-the-art models: even the top-performing Claude Sonnet~4.5 achieves only 34.1\% success, struggling significantly with planning consistency, error recovery, and policy constraints. Furthermore, we observe that agents frequently fail to refuse infeasible tasks, leading to unintended and potentially harmful side effects on the system. These findings indicate that current agents are not yet ready for enterprise deployment. By releasing EnterpriseOps-Gym, we provide a concrete testbed to advance the reliability of autonomous agents in professional workflows.

Graph class-incremental learning (GCIL) has emerged to address the challenge of learning from dynamically evolving graphs, which continuously learns new classes over a sequence of tasks while retaining performance on previously seen classes. However, existing GCIL methods assume a closed-set test distribution drawn only from seen tasks. This fundamentally contradicts real-world open-ended scenarios where future unknown classes inevitably emerge. Empirically, we observe that existing GCIL methods falter in such open-set settings due to severe representation drift and generalized overconfidence. To bridge this gap, we investigate the Open-Set GCIL problem and propose \textbf{SAFER} (\underline{S}ubspace-\underline{A}ware \underline{FE}ature \underline{R}eshaping), a novel framework that endows GCIL with intrinsic open-set capabilities under a replay-free constraint. Specifically, \textbf{SAFER} performs subspace-aware feature reshaping with drift-free fingerprints, unifying task routing and open-set rejection into a single energy-based metric. Furthermore, we introduce a geometric space-consistency regularization that explicitly improves intra-class compactness and suppresses cross-task representation drift. Extensive experiments on four benchmarks demonstrate that SAFER outperforms state-of-the-art baselines by margins of up to 5.2\% in accuracy and 31.3\% in open-set AUROC, all while maintaining near-zero forgetting under strict no-replay constraints.

Large language models (LLMs) are evolving from conversational systems into strong reasoners for tasks such as Olympiad mathematics and competitive programming. While scaling parameters and test-time computation has driven progress, a key bottleneck is the lack of high-quality training problems: human-curated datasets are costly and limited, while existing synthetic corpora are often too easy or narrow. PromptCoT showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptScale, a scalable framework that replaces hand-crafted heuristics with an expectation-maximization (EM) loop, where rationales are iteratively refined to guide prompt construction. This produces problems that are both harder and more diverse than prior corpora. The synthetic prompts support two post-training regimes: (1) \emph{Self-Play}, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) \emph{Supervised Fine-Tuning (SFT)}, where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptScale to \texttt{Qwen3-30B-A3B-Thinking-2507} sets new state-of-the-art results \emph{at the 30B scale}, with +4.4, +4.8, and +5.3 on AIME 24/25 and HMMT 25, +6.1 and +5.0 on LiveCodeBench v5/v6, and +35 Elo on Codeforces. In SFT, training \texttt{Qwen2.5-7B-Instruct} solely on synthetic prompts boosts accuracy to 73.1 (AIME 24), 65.6 (AIME 25), and 53.4 (LiveCodeBench v5), surpassing models trained on human or hybrid data. Analyses further confirm that PromptScale yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptScale as a scalable foundation for future open-source models. The implementation is available at \url{https://github.com/inclusionAI/PromptCoT}.

Speculative decoding has emerged as a powerful approach to accelerate large language model (LLM) inference by employing lightweight draft models to propose candidate tokens that are subsequently verified by the target model. The effectiveness of this paradigm critically depends on the quality of the draft model. While recent advances such as the EAGLE series achieve state-of-the-art speedup, existing draft models remain limited by error accumulation: they condition only on the current prefix, causing their predictions to drift from the target model over steps. In this work, we propose ConFu (Contemplate the Future), a novel speculative decoding framework that enables draft models to anticipate the future direction of generation. ConFu introduces (i) contemplate tokens and soft prompts that allow the draft model to leverage future-oriented signals from the target model at negligible cost, (ii) a dynamic contemplate token mechanism with MoE to enable context-aware future prediction, and (iii) a training framework with anchor token sampling and future prediction replication that learns robust future prediction. Experiments demonstrate that ConFu improves token acceptance rates and generation speed over EAGLE-3 by 8-11%, across various downstream tasks with Llama-3 3B and 8B models. We believe our work is the first to bridge speculative decoding with continuous reasoning tokens, offering a new direction for accelerating LLM inference.

Many practical samplers rely on time-dependent drifts---often induced by annealing or tempering schedules---to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusion and their discretizations. We provide a convergence analysis that includes non-asymptotic bounds for the continuous-time diffusion and its Euler--Maruyama discretization in the forward-Kullback--Leibler divergence under a single set of abstract conditions on the time-dependent drift. The results apply to many practically-relevant annealing schemes, including geometric tempering and annealed Langevin sampling. In addition, we provide numerical experiments comparing the annealing schemes covered by our theory in low- as well as high-dimensional settings.

Multi-turn human-AI collaboration is fundamental to deploying interactive services such as adaptive tutoring, conversational recommendation, and professional consultation. However, optimizing these interactions via reinforcement learning is hindered by the sparsity of verifiable intermediate rewards and the high stochasticity of user responses. To address these challenges, we introduce Implicit Turn-wise Policy Optimization (ITPO). ITPO leverages an implicit process reward model to derive fine-grained, turn-wise process rewards from sparse outcome signals. Unlike volatile token-level rewards, these turn-level signals exhibit superior robustness and may utilize a normalization mechanism to further enhance training stability. We evaluate ITPO across three representative multi-turn collaborative tasks: math tutoring, document writing, and medical recommendation. Empirical results demonstrate that ITPO, when combined with PPO, GRPO, or RLOO, consistently achieves improved convergence than existing baselines. Elaborate trajectory analysis confirms that ITPO infers turn-wise preferences that are semantically aligned with human judgment.