ICML 2025 Papers

Test-Time Adaptation (TTA) enables deep neural networks to adapt to arbitrary distributions during inference. Existing TTA algorithms generally tend to select benign samples that help achieve robust online prediction and stable self-training. Although malicious samples that would undermine the model's optimization should be filtered out, it also leads to a waste of test data. To alleviate this issue, we focus on how to make full use of the malicious test samples for TTA by transforming them into benign ones, and propose a plug-and-play method, PTTA. The core of our solution lies in the purification strategy, which retrieves benign samples having opposite effects on the objective function to perform Mixup with malicious samples, based on a saliency indicator for encoding benign and malicious data. This strategy results in effective utilization of the information in malicious samples and an improvement of the models' online test accuracy. In this way, we can directly apply the purification loss to existing TTA algorithms without the need to carefully adjust the sample selection threshold. Extensive experiments on four types of TTA tasks as well as classification, segmentation, and adversarial defense demonstrate the effectiveness of our method. Code is available at https://github.com/HAIV-Lab/PTTA.

Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect actual discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorization, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods on LLM-SRBench, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy. These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.

Autoregressive attention-based time series forecasting (TSF) has drawn increasing interest, with mechanisms like linear attention often outperforming vanilla attention. However, deeper Transformer architectures frequently misalign with autoregressive objectives, obscuring the underlying VAR structure embedded within linear attention and hindering their ability to capture the data generative processes in TSF. In this work, we first show that a single linear attention layer can be interpreted as a dynamic vector autoregressive (VAR) structure. We then explain that existing multi-layer Transformers have structural mismatches with the autoregressive forecasting objective, which impair interpretability and generalization ability. To address this, we show that by rearranging the MLP, attention, and input-output flow, multi-layer linear attention can also be aligned as a VAR model. Then, we propose Structural Aligned Mixture of VAR (SAMoVAR), a linear Transformer variant that integrates interpretable dynamic VAR weights for multivariate TSF. By aligning the Transformer architecture with autoregressive objectives, SAMoVAR delivers improved performance, interpretability, and computational efficiency, comparing to SOTA TSF models.

Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures. This approach enhances the ability to capture the topological structures of integration domains in Sliced Optimal Transport while maintaining low computational costs. Building on this foundation, we propose a novel nonlinear projectional framework for the Tree-Sliced Wasserstein (TSW) distance, substituting the linear projections in earlier versions with general projections, while ensuring the injectivity of the associated Radon Transform and preserving the well-definedness of the resulting metric. By designing appropriate projections, we construct efficient metrics for measures on both Euclidean spaces and spheres. Finally, we validate our proposed metric through extensive numerical experiments for Euclidean and spherical datasets. Applications include gradient flows, self-supervised learning, and generative models, where our methods demonstrate significant improvements over recent SW and TSW variants.

Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.

Autoregressive next-token prediction with the Transformer decoder has become a de facto standard in large language models (LLMs), achieving remarkable success in Natural Language Processing (NLP) at scale. Extending this paradigm to audio poses unique challenges due to its inherently continuous nature. We research audio generation with a causal language model (LM) without discrete tokens. We leverage token-wise diffusion to model the continuous distribution of the next continuous-valued token. Our approach delivers significant improvements over previous discrete solution, AudioGen, achieving 20% and 40% relative gains on AudioCaps in Frechet Audio Distance (FAD) and Kullback-Leibler (KL) divergence, respectively. Additionally, we propose a novel masked next-token prediction task that incorporates masked prediction into the causal LM framework. On AudioCaps, the innovation yields 41% and 33% relative FAD improvements over AudioGen Base (285M) and AudioGen Large (1B) models, respectively, and is on par with the state-of-the-art (SOTA) diffusion models. Furthermore, we achieve these results with significantly fewer parameters—193M for our Base and 462M for our Large models.

Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its spectral components often face theoretical limitations and depend on predefined dictionaries. Residual Dynamic Mode Decomposition (ResDMD) advanced the field by introducing the \emph{spectral residual} to assess Koopman operator approximation accuracy; however, its approach of only filtering precomputed spectra prevents the discovery of the operator's complete spectral information, a limitation known as the `spectral inclusion' problem. We introduce ResKoopNet (Residual-based Koopman-learning Network), a novel method that directly addresses this by explicitly minimizing the \emph{spectral residual} to compute Koopman eigenpairs. This enables the identification of a more precise and complete Koopman operator spectrum. Using neural networks, our approach provides theoretical guarantees while maintaining computational adaptability. Experiments on a variety of physical and biological systems show that ResKoopNet achieves more accurate spectral approximations than existing methods, particularly for high-dimensional systems and those with continuous spectra, which demonstrates its effectiveness as a tool for analyzing complex dynamical systems.

Autoregressive Transformers rely on Key-Value (KV) caching to accelerate inference. However, the linear growth of the KV cache with context length leads to excessive memory consumption and bandwidth constraints. Existing methods drop distant tokens or compress states in a lossy manner, sacrificing accuracy by discarding vital context or introducing bias. We propose ${MorphKV}$, an inference-time technique that maintains a constant-sized KV cache while preserving accuracy. MorphKV balances long-range dependencies and local coherence during text generation. It eliminates early-token bias while retaining high-fidelity context by adaptively ranking tokens through correlation-aware selection. Unlike heuristic retention or lossy compression, MorphKV iteratively refines the KV cache via lightweight updates guided by attention patterns of recent tokens. This approach captures inter-token correlation with greater accuracy, which is crucial for tasks like content creation and code generation. Our studies on long-response tasks show 52.9\% memory savings and 18.2\% higher accuracy on average compared to state-of-the-art prior works, enabling efficient deployment.

Many variants of Optimal Transport (OT) have been developed to address its heavy computation. Among them, notably, Sliced Wasserstein (SW) is widely used for application domains by projecting the OT problem onto one-dimensional lines, and leveraging the closed-form expression of the univariate OT to reduce the computational burden. However, projecting measures onto low-dimensional spaces can lead to a loss of topological information. To mitigate this issue, in this work, we propose to replace one-dimensional lines with a more intricate structure, called \emph{tree systems}. This structure is metrizable by a tree metric, which yields a closed-form expression for OT problems on tree systems. We provide an extensive theoretical analysis to formally define tree systems with their topological properties, introduce the concept of splitting maps, which operate as the projection mechanism onto these structures, then finally propose a novel variant of Radon transform for tree systems and verify its injectivity. This framework leads to an efficient metric between measures, termed Tree-Sliced Wasserstein distance on Systems of Lines (TSW-SL). By conducting a variety of experiments on gradient flows, image style transfer, and generative models, we illustrate that our proposed approach performs favorably compared to SW and its variants.

In large language model (LLM) pretraining, data quality is believed to determine model quality. In this paper, we re-examine the notion of "quality" from the perspective of pre- and post-training co-design. Specifically, we explore the possibility that pre-training on more toxic data can lead to better control in post-training, ultimately decreasing a model's output toxicity. First, we use a toy experiment to study how data composition affects the geometry of features in the representation space. Next, through controlled experiments with Olmo-1B models trained on varying ratios of clean and toxic data, we find that the concept of toxicity enjoys a less entangled linear representation as the proportion of toxic data increases. Furthermore, we show that although toxic data increases the generational toxicity of the base model, it also makes the toxicity easier to remove. Evaluations on Toxigen and Real Toxicity Prompts demonstrate that models trained on toxic data achieve a better trade-off between reducing generational toxicity and preserving general capabilities when detoxifying techniques such as inference-time intervention (ITI) are applied. Our findings suggest that, with post-training taken into account, bad data may lead to good models.

As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult. Learning-based methods, such as Constrained Reinforcement Learning (CRL), achieve strong performance but lack formal safety guarantees due to safety being enforced as soft constraints, limiting their use in safety-critical settings. Conversely, formal methods such as Hamilton-Jacobi (HJ) Reachability Analysis and Control Barrier Functions (CBFs) provide rigorous safety assurances but often neglect performance, resulting in overly conservative controllers. To bridge this gap, we formulate the co-optimization of safety and performance as a state-constrained optimal control problem, where performance objectives are encoded via a cost function and safety requirements are imposed as state constraints. We demonstrate that the resultant value function satisfies a Hamilton-Jacobi-Bellman (HJB) equation, which we approximate efficiently using a novel physics-informed machine learning framework. In addition, we introduce a conformal prediction-based verification strategy to quantify the learning errors, recovering a high-confidence safety value function, along with a probabilistic error bound on performance degradation. Through several case studies, we demonstrate the efficacy of the proposed framework in enabling scalable learning of safe and performant controllers for complex, high-dimensional autonomous systems.

Achieving effective unified pretraining on large time series corpora remains an open challenge in developing time series foundation models. Existing methods, such as Moirai, introduce multiple projection layers for time series of different frequencies to account for high data heterogeneity. We identify major drawbacks to this human-imposed frequency-level model specialization. First, frequency is not a reliable indicator for grouping pretraining data. Second, time series can display varied distributions even within a short window. Frequency-level specialization overlooks the diversity at this granularity. To address these issues, this paper introduces Moirai-MoE, excluding human-defined data groupings while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With this design, Moirai-MoE eliminates reliance on heuristics and enables automatic token-level specialization. Extensive evaluations on 39 datasets demonstrate the superiority of Moirai-MoE over state-of-the-art foundation models. This study also conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models.

The success of sequential decision-making approaches, such as *reinforcement learning* (RL), is closely tied to the availability of a reward feedback. However, designing a reward function that encodes the desired objective is a challenging task. In this work, we address a more realistic scenario: sequential decision making with preference feedback provided, for instance, by a human expert. We aim to build a theoretical basis linking *preferences*, (non-Markovian) *utilities*, and (Markovian) *rewards*, and we study the connections between them. First, we model preference feedback using a partial (pre)order over trajectories, enabling the presence of incomparabilities that are common when preferences are provided by humans but are surprisingly overlooked in existing works. Second, to provide a theoretical justification for a common practice, we investigate how a preference relation can be approximated by a multi-objective utility. We introduce a notion of preference-utility compatibility and analyze the computational complexity of this transformation, showing that constructing the minimum-dimensional utility is NP-hard. Third, we propose a novel concept of preference-based policy dominance that does not rely on utilities or rewards and discuss the computational complexity of assessing it. Fourth, we develop a computationally efficient algorithm to approximate a utility using (Markovian) rewards and quantify the error in terms of the suboptimality of the optimal policy induced by the approximating reward. This work aims to lay the foundation for a principled approach to sequential decision making from preference feedback, with promising potential applications in RL from human feedback.

Learning to control an unknown dynamical system with respect to high-level temporal specifications is an important problem in control theory. We present the first regret-free online algorithm for learning a controller for linear temporal logic (LTL) specifications for systems with unknown dynamics. We assume that the underlying (unknown) dynamics is modeled by a finite-state and action Markov decision process (MDPs). Our core technical result is a regret-free learning algorithm for infinite-horizon reach-avoid problems on MDPs. For general LTL specifications, we show that the synthesis problem can be reduced to a reach-avoid problem once the graph structure is known. Additionally, we provide an algorithm for learning the graph structure, assuming knowledge of a minimum transition probability, which operates independently of the main regret-free algorithm. Our LTL controller synthesis algorithm provides sharp bounds on how close we are to achieving optimal behavior after a finite number of learning episodes. In contrast, previous algorithms for LTL synthesis only provide asymptotic guarantees, which give no insight into the transient performance during the learning phase.

We introduce the *Local Intersectional Visual Spaces* (LIVS) dataset, a benchmark for multi-criteria alignment, developed through a two-year participatory process with 30 community organizations to support the pluralistic alignment of text-to-image (T2I) models in inclusive urban planning. The dataset encodes 37,710 pairwise comparisons across 13,462 images, structured along six criteria—Accessibility, Safety, Comfort, Invitingness, Inclusivity, and Diversity—derived from 634 community-defined concepts. Using Direct Preference Optimization (DPO), we fine-tune Stable Diffusion XL to reflect multi-criteria spatial preferences and evaluate the LIVS dataset and the fine-tuned model through four case studies: (1) DPO increases alignment with annotated preferences, particularly when annotation volume is high; (2) preference patterns vary across participant identities, underscoring the need for intersectional data; (3) human-authored prompts generate more distinctive visual outputs than LLM-generated ones, influencing annotation decisiveness; and (4) intersectional groups assign systematically different ratings across criteria, revealing the limitations of single-objective alignment. While DPO improves alignment under specific conditions, the prevalence of neutral ratings indicates that community values are heterogeneous and often ambiguous. LIVS provides a benchmark for developing T2I models that incorporate local, stakeholder-driven preferences, offering a foundation for context-aware alignment in spatial design.

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes **S**imultaneous **M**RMP **D**iffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments. The code and implementation are available at https://github.com/RAISELab-atUVA/Diffusion-MRMP.

Off-Policy Evaluation (OPE) aims to estimate the value of a target policy using offline data collected from potentially different policies. In real-world applications, however, logged data often suffers from missingness. While OPE has been extensively studied in the literature, a theoretical understanding of how missing data affects OPE results remains unclear. In this paper, we investigate OPE in the presence of monotone missingness and theoretically demonstrate that the value estimates remain unbiased under ignorable missingness but can be biased under nonignorable (informative) missingness. To retain the consistency of value estimation, we propose an inverse probability weighting value estimator and conduct statistical inference to quantify the uncertainty of the estimates. Through a series of numerical experiments, we empirically demonstrate that our proposed estimator yields a more reliable value inference under missing data.

We introduce PokéChamp, a minimax agent powered by Large Language Models (LLMs) for Pokémon battles. Built on a general framework for two-player competitive games, PokéChamp leverages the generalist capabilities of LLMs to enhance minimax tree search. Specifically, LLMs replace three key modules: (1) player action sampling, (2) opponent modeling, and (3) value function estimation, enabling the agent to effectively utilize gameplay history and human knowledge to reduce the search space and address partial observability. Notably, our framework requires no additional LLM training. We evaluate PokéChamp in the popular Gen 9 OU format. When powered by GPT-4o, it achieves a win rate of 76\% against the best existing LLM-based bot and 84\% against the strongest rule-based bot, demonstrating its superior performance. Even with an open-source 8-billion-parameter Llama 3.1 model, PokéChamp consistently outperforms the previous best LLM-based bot, Pokéllmon powered by GPT-4o, with a 64\% win rate. PokéChamp attains a projected Elo of 1300-1500 on the Pokémon Showdown online ladder, placing it among the top 30\%-10\% of human players. In addition, this work compiles the largest real-player Pokémon battle dataset, featuring over 3 million games, including more than 500k high-Elo matches. Based on this dataset, we establish a series of battle benchmarks and puzzles to evaluate specific battling skills. We further provide key updates to the local game engine. This work establishes Pokémon as a benchmark to integrate LLM technologies with game-theoretic algorithms addressing general multi-agent problems. Videos, code, and dataset are available online.

In reinforcement learning, specifying reward functions that capture the intended task can be very challenging. Reward learning aims to address this issue by *learning* the reward function. However, a learned reward model may have a low error on the data distribution, and yet subsequently produce a policy with large regret. We say that such a reward model has an *error-regret mismatch*. The main source of an error-regret mismatch is the distributional shift that commonly occurs during policy optimization. In this paper, we mathematically show that a sufficiently low expected test error of the reward model guarantees low worst-case regret, but that for any *fixed* expected test error, there exist realistic data distributions that allow for error-regret mismatch to occur. We then show that similar problems persist even when using policy regularization techniques, commonly employed in methods such as RLHF. We hope our results stimulate the theoretical and empirical study of improved methods to learn reward models, and better ways to measure their quality reliably.