ICML 2025 Papers

We study the computational model where we can access a matrix $\mathbf{A}$ only by computing matrix-vector products $\mathbf{A}\mathrm{x}$ for vectors of the form $\mathrm{x} = \mathrm{x}_1 \otimes \cdots \otimes \mathrm{x}_q$. We prove exponential lower bounds on the number of queries needed to estimate various properties, including the trace and the top eigenvalue of $\mathbf{A}$. Our proofs hold for all adaptive algorithms, modulo a mild conditioning assumption on the algorithm's queries. We further prove that algorithms whose queries come from a small alphabet (e.g., $\mathrm{x}_i \in \\{\pm1\\}^n$) cannot test if $\mathbf{A}$ is identically zero with polynomial complexity, despite the fact that a single query using Gaussian vectors solves the problem with probability 1. In steep contrast to the non-Kronecker case, this shows that sketching $\mathbf{A}$ with different distributions of the same subguassian norm can yield exponentially different query complexities. Our proofs follow from the observation that random vectors with Kronecker structure have exponentially smaller inner products than their non-Kronecker counterparts.

This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate three desirable properties (axioms) of a reliable diversity measure: monotonicity, uniqueness, and continuity. We show that none of the existing measures has all three properties and thus these measures are not suitable for quantifying diversity. Then, we construct two examples of measures that have all the desirable properties, thus proving that the list of axioms is not self-contradictory. Unfortunately, the constructed examples are too computationally expensive (NP-hard) for practical use. Thus, we pose an open problem of constructing a diversity measure that has all the listed properties and can be computed in practice or proving that all such measures are NP-hard to compute.

Neural causal discovery methods have recently improved in terms of scalability and computational efficiency. However, our systematic evaluation highlights significant room for improvement in their accuracy when uncovering causal structures. We identify a fundamental limitation: \textit{unavoidable likelihood score estimation errors disallow distinguishing the true structure}, even for small graphs and relatively large sample sizes. Furthermore, we identify the faithfulness property as a critical bottleneck: (i) it is likely to be violated across any reasonable dataset size range, and (ii) its violation directly undermines the performance of neural penalized-likelihood discovery methods. These findings lead us to conclude that progress within the current paradigm is fundamentally constrained, necessitating a paradigm shift in this domain.

The rapid advancement of large language model (LLM) agents has raised new concerns regarding their safety and security. In this paper, we propose GuardAgent, the first guardrail agent to protect target agents by dynamically checking whether their actions satisfy given safety guard requests. Specifically, GuardAgent first analyzes the safety guard requests to generate a task plan, and then maps this plan into guardrail code for execution. By performing the code execution, GuardAgent can deterministically follow the safety guard request and safeguard target agents. In both steps, an LLM is utilized as the reasoning component, supplemented by in-context demonstrations retrieved from a memory module storing experiences from previous tasks. In addition, we propose two novel benchmarks: EICU-AC benchmark to assess the access control for healthcare agents and Mind2Web-SC benchmark to evaluate the safety policies for web agents. We show that GuardAgent effectively moderates the violation actions for different types of agents on these two benchmarks with over 98% and 83% guardrail accuracies, respectively. Project page: https://guardagent.github.io/

Irregular Multivariate Time Series (IMTS) forecasting is challenging due to the unaligned nature of multi-channel signals and the prevalence of extensive missing data. Existing methods struggle to capture reliable temporal patterns from such data due to significant missing values. While pre-trained foundation models show potential for addressing these challenges, they are typically designed for Regularly Sampled Time Series (RTS). Motivated by the visual Mask AutoEncoder's (MAE) powerful capability for modeling sparse multi-channel information and its success in RTS forecasting, we propose **VIMTS**, a framework adapting **V**isual MAE for **IMTS** forecasting. To mitigate the effect of missing values, VIMTS first processes IMTS along the timeline into feature patches at equal intervals. These patches are then complemented using learned cross-channel dependencies. Then it leverages visual MAE's capability in handling sparse multichannel data for patch reconstruction, followed by a coarse-to-fine technique to generate precise predictions from focused contexts. In addition, we integrate self-supervised learning for improved IMTS modeling by adapting the visual MAE to IMTS data. Extensive experiments demonstrate VIMTS's superior performance and few-shot capability, advancing the application of visual foundation models in more general time series tasks. Our code is available at https://github.com/WHU-HZY/VIMTS.

Weight matrix compression has been demonstrated to effectively reduce overfitting and improve the generalization performance of deep neural networks. Compression is primarily achieved by filtering out noisy eigenvalues of the weight matrix. In this work, a novel **Population Double Bulk (PDB) model** is proposed to characterize the eigenvalue behavior of the weight matrix, which is more general than the existing Population Unit Bulk (PUB) model. Based on PDB model and Random Matrix Theory (RMT), we have discovered a new **PDBLS algorithm** for determining the boundary between noisy eigenvalues and information. A **PDB Noise-Filtering algorithm** is further introduced to reduce the rank of the weight matrix for compression. Experiments show that our PDB model fits the empirical distribution of eigenvalues of the weight matrix better than the PUB model, and our compressed weight matrices have lower rank at the same level of test accuracy. In some cases, our compression method can even improve generalization performance when labels contain noise. The code is avaliable at https://github.com/xlwu571/PDBLS.

Latent diffusion models have emerged as the leading approach for generating high-quality images and videos, utilizing compressed latent representations to reduce the computational burden of the diffusion process. While recent advancements have primarily focused on scaling diffusion backbones and improving autoencoder reconstruction quality, the interaction between these components has received comparatively less attention. In this work, we perform a spectral analysis of modern autoencoders and identify inordinate high-frequency components in their latent spaces, which are especially pronounced in the autoencoders with a large bottleneck channel size. We hypothesize that this high-frequency component interferes with the coarse-to-fine nature of the diffusion synthesis process and hinders the generation quality. To mitigate the issue, we propose scale equivariance: a simple regularization strategy that aligns latent and RGB spaces across frequencies by enforcing scale equivariance in the decoder. It requires minimal code changes and only up to $20$K autoencoder fine-tuning steps, yet significantly improves generation quality, reducing FID by 19% for image generation on ImageNet-1K 256x256 and FVD by at least 44% for video generation on Kinetics-700 17x256x256. The source code is available at https://github.com/snap-research/diffusability.

While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system's underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system's dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system's behavior, such as the trajectory's shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.

Recently, latent action learning, pioneered by Latent Action Policies (LAPO), have shown remarkable pre-training efficiency on observation-only data, offering potential for leveraging vast amounts of video available on the web for embodied AI. However, prior work has focused on distractor-free data, where changes between observations are primarily explained by ground-truth actions. Unfortunately, real-world videos contain action-correlated distractors that may hinder latent action learning. Using Distracting Control Suite (DCS) we empirically investigate the effect of distractors on latent action learning and demonstrate that LAPO struggle in such scenario. We propose LAOM, a simple LAPO modification that improves the quality of latent actions by **8x**, as measured by linear probing. Importantly, we show that providing supervision with ground-truth actions, as few as 2.5% of the full dataset, during latent action learning improves downstream performance by **4.2x** on average. Our findings suggest that integrating supervision during Latent Action Models (LAM) training is critical in the presence of distractors, challenging the conventional pipeline of first learning LAM and only then decoding from latent to ground-truth actions.

Long-range graph tasks --- those dependent on interactions between `distant' nodes --- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize long-range interactions in graph tasks, introduce a **range measure** for operators on graphs, and validate it with synthetic experiments. We then leverage our measure to examine commonly used tasks and architectures, and discuss to what extent they are, in fact, long-range. We believe our work advances efforts to define and address the long-range problem on graphs, and that our range measure will aid evaluation of new datasets and architectures.

Theory-of-mind (ToM) enables humans to infer mental states—such as beliefs, desires, and intentions—forming the foundation of social cognition. Existing computational ToM methods rely on structured workflows with ToM-specific priors or deep model fine-tuning but struggle with scalability in multimodal environments. They remain trapped within the gravitational pull of multi-step planning complexity, failing to generalize as task demands increase. To overcome these limitations, we propose a scalable Bayesian ToM planner. It breaks down ToM complexity into stepwise Bayesian updates. Meanwhile, weak-to-strong control specializes smaller LMs to refine ToM-specific likelihood estimation, transferring their ToM reasoning behavior to larger LMs (7B to 405B) for social and world knowledge integration. This synergistic approach enables scalability, aligning large-model inference with human mental states with Bayesian principles. Extensive experiments demonstrate a 4.6% improvement in accuracy over state-of-the-art methods on multimodal ToM benchmarks, including unseen scenarios, establishing a new standard for modeling human mental states in complex environments.

Diffusion policies have shown promise in learning complex behaviors from demonstrations, particularly for tasks requiring precise control and long-term planning. However, they face challenges in robustness when encountering distribution shifts. This paper explores improving diffusion-based imitation learning models through online interactions with the environment. We propose OTPR (Optimal Transport-guided score-based diffusion Policy for Reinforcement learning fine-tuning), a novel method that integrates diffusion policies with RL using optimal transport theory. OTPR leverages the Q-function as a transport cost and views the policy as an optimal transport map, enabling efficient and stable fine-tuning. Moreover, we introduce masked optimal transport to guide state-action matching using expert keypoints and a compatibility-based resampling strategy to enhance training stability. Experiments on three simulation tasks demonstrate OTPR's superior performance and robustness compared to existing methods, especially in complex and sparse-reward environments. In sum, OTPR provides an effective framework for combining IL and RL, achieving versatile and reliable policy learning.

Protein's backbone flexibility is a crucial property that heavily influences its functionality. Recent work in the field of protein diffusion probabilistic modelling has leveraged Normal Mode Analysis (NMA) and, for the first time, introduced information about large scale protein motion into the generative process. However, obtaining molecules with both the desired dynamics and designable quality has proven challenging. In this work, we present NMA-tune, a new method that introduces the dynamics information to the protein design stage. NMA-tune uses a trainable component to condition the backbone generation on the lowest normal mode of oscillation. We implement NMA-tune as a plug-and-play extension to RFdiffusion, show that the proportion of samples with high quality structure and the desired dynamics is improved as compared to other methods without the trainable component, and we show the presence of the targeted modes in the Molecular Dynamics simulations.

Graph Neural Networks (GNNs) have demonstrated superior performance in a variety of graph mining and learning tasks. However, when node representations involve sensitive personal information or variables related to individuals, learning from graph data can raise significant privacy concerns. Although recent studies have explored local differential privacy (LDP) to address these concerns, they often introduce significant distortions to graph data, severely degrading private learning utility (e.g., node classification accuracy). In this paper, we present UPGNET, an LDP-based privacy-preserving graph learning framework that enhances utility while protecting user data privacy. Specifically, we propose a three-stage pipeline that generalizes the LDP protocols for node features, targeting privacy-sensitive scenarios. Our analysis identifies two key factors that affect the utility of privacy-preserving graph learning: *feature dimension* and *neighborhood size*. Based on the above analysis, UPGNET enhances utility by introducing two core layers: High-Order Aggregator (HOA) layer and the Node Feature Regularization (NFR) layer. Extensive experiments on real-world datasets indicate that UPGNET significantly outperforms existing methods in terms of both privacy protection and learning utility.

This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings—where local control variates mitigate client drift—is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms.

Turning the multi-round vanilla Federated Learning into one-shot FL (OFL) significantly reduces the communication burden and makes a big leap toward practical deployment. However, this work empirically and theoretically unravels that existing OFL falls into a garbage (inconsistent one-shot local models) in and garbage (degraded global model) out pitfall. The inconsistency manifests as divergent feature representations and sample predictions. This work presents a novel OFL framework FAFI that enhances the one-shot training on the client side to essentially overcome inferior local uploading. Specifically, unsupervised feature alignment and category-wise prototype learning are adopted for clients' local training to be consistent in representing local samples. On this basis, FAFI uses informativeness-aware feature fusion and prototype aggregation for global inference. Extensive experiments on three datasets demonstrate the effectiveness of FAFI, which facilitates superior performance compared with 11 OFL baselines (+10.86% accuracy). Code available at https://github.com/zenghui9977/FAFI_ICML25

We introduce the *linear-transformation model*, a distributed model of differentially private data analysis. Clients have access to a trusted platform capable of applying a public matrix to their inputs. Such computations can be securely distributed across multiple servers using simple and efficient secure multiparty computation techniques. The linear-transformation model serves as an intermediate model between the highly expressive *central model* and the minimal *local model*. In the central model, clients have access to a trusted platform capable of applying any function to their inputs. However, this expressiveness comes at a cost, as it is often expensive to distribute such computations, leading to the central model typically being implemented by a single trusted server. In contrast, the local model assumes no trusted platform, which forces clients to add significant noise to their data. The linear-transformation model avoids the single point of failure for privacy present in the central model, while also mitigating the high noise required in the local model. We demonstrate that linear transformations are very useful for differential privacy, allowing for the computation of linear sketches of input data. These sketches largely preserve utility for tasks such as private low-rank approximation and private ridge regression, while introducing only minimal error, critically independent of the number of clients.

Designing effective reward functions in multi-agent reinforcement learning (MARL) is a significant challenge, often leading to suboptimal or misaligned behaviors in complex, coordinated environments. We introduce Multi-agent Reinforcement Learning from Multi-phase Human Feedback of Mixed Quality ($\text{M}^3\text{HF}$), a novel framework that integrates multi-phase human feedback of mixed quality into the MARL training process. By involving humans with diverse expertise levels to provide iterative guidance, $\text{M}^3\text{HF}$ leverages both expert and non-expert feedback to continuously refine agents' policies. During training, we strategically pause agent learning for human evaluation, parse feedback using large language models to assign it appropriately and update reward functions through predefined templates and adaptive weights by using weight decay and performance-based adjustments. Our approach enables the integration of nuanced human insights across various levels of quality, enhancing the interpretability and robustness of multi-agent cooperation. Empirical results in challenging environments demonstrate that $\text{M}^3\text{HF}$ significantly outperforms state-of-the-art methods, effectively addressing the complexities of reward design in MARL and enabling broader human participation in the training process.

We propose a novel method for measuring the discrepancy between a set of samples and a desired posterior distribution for Bayesian inference. Classical methods for assessing sample quality like the effective sample size are not appropriate for scalable Bayesian sampling algorithms, such as stochastic gradient Langevin dynamics, that are asymptotically biased. Instead, the gold standard is to use the kernel Stein Discrepancy (KSD), which is itself not scalable given its quadratic cost in the number of samples. The KSD and its faster extensions also typically suffer from the curse-of-dimensionality and can require extensive tuning. To address these limitations, we develop the polynomial Stein discrepancy (PSD) and an associated goodness-of-fit test. While the new test is not fully convergence-determining, we prove that it detects differences in the first $r$ moments for Gaussian targets. We empirically show that the test has higher power than its competitors in several examples, and at a lower computational cost. Finally, we demonstrate that the PSD can assist practitioners to select hyper-parameters of Bayesian sampling algorithms more efficiently than competitors.