ICML 2025 论文列表

Structured Kernel Interpolation (SKI) scales Gaussian Processes (GPs) by approximating the kernel matrix via inducing point interpolation, achieving linear computational complexity. However, it lacks rigorous theoretical error analysis. This paper bridges this gap by proving error bounds for the SKI Gram matrix and examining their effect on hyperparameter estimation and posterior inference. We further provide a practical guide to selecting the number of inducing points under convolutional cubic interpolation: they should grow as \(n^{d/3}\) for error control. Crucially, we identify two dimensionality regimes for the SKI Gram matrix spectral norm error vs. complexity trade-off. For \(d<3\), \textit{any} error tolerance can achieve linear time for sufficiently large sample size. For \(d\geq 3\), the error must \textit{increase} with sample size for our guarantees to hold. Our analysis provides key insights into SKI's scalability-accuracy trade-offs, establishing precise conditions for achieving linear-time GP inference with controlled error.

Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates. In recent years, these models have preferred nonparametric specifications that avoid directly estimating survival distributions via discretization. Specifically, they estimate the probability of an individual event at fixed times or the time of an event at fixed probabilities (quantiles), using supervised learning. Borrowing ideas from the quantile regression literature, we propose a parametric survival analysis method based on the Asymmetric Laplace Distribution (ALD). This distribution allows for closed-form calculation of popular event summaries such as mean, median, mode, variation, and quantiles. The model is optimized by maximum likelihood to learn, at the individual level, the parameters (location, scale, and asymmetry) of the ALD distribution. Extensive results on synthetic and real-world data demonstrate that the proposed method outperforms parametric and nonparametric approaches in terms of accuracy, discrimination and calibration.

Recent advancements in time series forecasting have explored augmenting models with text or vision modalities to improve accuracy. While text provides contextual understanding, it often lacks fine-grained temporal details. Conversely, vision captures intricate temporal patterns but lacks semantic context, limiting the complementary potential of these modalities. To address this, we propose Time-VLM, a novel multimodal framework that leverages pre-trained Vision-Language Models (VLMs) to bridge temporal, visual, and textual modalities for enhanced forecasting. Our framework comprises three key components: (1) a Retrieval-Augmented Learner, which extracts enriched temporal features through memory bank interactions; (2) a Vision-Augmented Learner, which encodes time series as informative images; and (3) a Text-Augmented Learner, which generates contextual textual descriptions. These components collaborate with frozen pre-trained VLMs to produce multimodal embeddings, which are then fused with temporal features for final prediction. Extensive experiments demonstrate that Time-VLM achieves superior performance, particularly in few-shot and zero-shot scenarios, thereby establishing a new direction for multimodal time series forecasting. Code is available at https://github.com/CityMind-Lab/ICML25-TimeVLM.

This paper studies the complexity and optimality of Follow-the-Perturbed-Leader (FTPL) policy in the $K$-armed bandit problems. FTPL is a promising policy that achieves the Best-of-Both-Worlds (BOBW) guarantee without solving an optimization problem unlike Follow-the-Regularized-Leader (FTRL). However, FTPL needs a procedure called geometric resampling to estimate the loss, which needs $O(K^2)$ per-round average complexity, usually worse than that of FTRL. To address this issue, we propose a novel technique, which we call Conditional Geometric Resampling (CGR), for unbiased loss estimation applicable to general perturbation distributions. CGR reduces the average complexity to $O(K\log K)$ without sacrificing the regret bounds. We also propose a biased version of CGR that can control the worst-case complexity while keeping the BOBW guarantee for a certain perturbation distribution. We confirm through experiments that CGR does not only significantly improve the average and worst-case runtime but also achieve better regret thanks to the stable loss estimation.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs that use piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.

Accurately predicting user watch-time is crucial for enhancing user stickiness and retention in video recommendation systems. Existing watch-time prediction approaches typically involve transformations of watch-time labels for prediction and subsequent reversal, ignoring both the natural distribution properties of label and the \textit{instance representation confusion} that results in inaccurate predictions. In this paper, we propose ProWTP, a two-stage method combining prototype learning and optimal transport for watch-time regression prediction, suitable for any deep recommendation model. Specifically, we observe that the watch-ratio (the ratio of watch-time to video duration) within the same duration bucket exhibits a multimodal distribution. To facilitate incorporation into models, we use a hierarchical vector quantised variational autoencoder (HVQ-VAE) to convert the continuous label distribution into a high-dimensional discrete distribution, serving as credible prototypes for calibrations. Based on this, ProWTP views the alignment between prototypes and instance representations as a Semi-relaxed Unbalanced Optimal Transport (SUOT) problem, where the marginal constraints of prototypes are relaxed. And the corresponding optimization problem is reformulated as a weighted Lasso problem for solution. Moreover, ProWTP introduces the assignment and compactness losses to encourage instances to cluster closely around their respective prototypes, thereby enhancing the prototype-level distinguishability. Finally, we conducted extensive offline experiments on two industrial datasets, demonstrating our consistent superiority in real-world application.

In this work, we investigate the merits of explicitly optimizing for inference time algorithmic performance during model training. We show how optimizing for inference time performance can improve overall model efficacy. We consider generic inference time objectives with $k$ samples, with focus on pass@$k$ and majority voting as two main applications. With language model training on reasoning datasets, we showcase the performance trade-off enabled by training with such objectives. When training on code generation tasks, we show that the approach significantly improves pass@$k$ objectives compared to the baseline method.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pretraining. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverage historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot setting with much better efficiency compared with existing time series foundation models

As the space of causal sequence modeling architectures continues to grow, the need to develop a general framework for their analysis becomes increasingly important. With this aim, we draw insights from classical signal processing and control theory, to develop a quantitative measure of *memory utilization*: the internal mechanisms through which a model stores past information to produce future outputs. This metric, which we call ***effective state-size*** (ESS), is tailored to the fundamental class of systems with *input-invariant* and *input-varying linear operators*, encompassing a variety of computational units such as variants of attention, convolutions, and recurrences. Unlike prior work on memory utilization, which either relies on raw operator visualizations (e.g. attention maps), or simply the total *memory capacity* (i.e. cache size) of a model, our metrics provide highly interpretable and actionable measurements. In particular, we show how ESS can be leveraged to improve initialization strategies, inform novel regularizers and advance the performance-efficiency frontier through model distillation. Furthermore, we demonstrate that the effect of context delimiters (such as end-of-speech tokens) on ESS highlights cross-architectural differences in how large language models utilize their available memory to recall information. Overall, we find that ESS provides valuable insights into the dynamics that dictate memory utilization, enabling the design of more efficient and effective sequence models.

Despite recent advances in subquadratic attention mechanisms or state-space models, processing long token sequences still imposes significant computational requirements. Token merging has emerged as a solution to increase computational efficiency in computer vision architectures. In this work, we perform the first investigations of token merging in time series analysis on both transformers and state-space models. We further introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, achieving two major benefits: a) Local merging can adjust its computational complexity from quadratic to linear based on the neighborhood size to effectively scale to long sequences; b) Local merging is the first causal merging scheme enabling token merging in transformer decoders. Further, we identify spectral properties of the input data that reliably predict the potential benefits of local merging without requiring evaluation on downstream tasks. Our comprehensive empirical evaluation demonstrates that local merging offers substantial efficiency gains with minimal impact on accuracy, achieving up to 5400% acceleration on the recently proposed Chronos foundation model.

Offline reinforcement learning is widely applied in multiple fields due to its advantages in efficiency and risk control. However, a major problem it faces is the distribution shift between offline datasets and online environments. This mismatch leads to out-of-distribution (OOD) state-action pairs that fall outside the scope of the training data. Therefore, existing conservative training policies may not provide reliable decisions when the test environment deviates greatly from the offline dataset. In this paper, we propose Test-time Adapted Reinforcement Learning (TARL) to address this problem. TARL constructs unsupervised test-time optimization objectives for discrete and continuous control tasks, using test data without depending on environmental rewards. In discrete control tasks, it minimizes the entropy of predicted action probabilities to decrease uncertainty and avoid OOD state-action pairs. For continuous control tasks, it represents and minimizes action uncertainty based on the normal distribution of policy network outputs. Moreover, to prevent model bias caused by overfitting and error accumulation during the test-time update process, TARL enforces a KL divergence constraint between the fine-tuned policy and the original policy. For efficiency, TARL only updates the layer normalization layer parameters during testing. Extensive experiments on popular Atari game benchmarks and the D4RL dataset demonstrate the superiority of our method. Our method achieved a significant improvement over CQL, with a 13.6% episode return relative increase on the hopper-expert-v2 task.

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.

Detecting when a neural sequence model does "interesting" computation is an open problem. The next token prediction loss is a poor indicator: Low loss can stem from trivially predictable sequences that are uninteresting, while high loss may reflect unpredictable but also irrelevant information that can be ignored by the model. We propose a better metric: measuring the model's ability to predict its own future hidden states. We show empirically that this metric–in contrast to the next token prediction loss–correlates with the intuitive interestingness of the task. To measure predictability, we introduce the architecture-agnostic "prediction of hidden states" (PHi) layer that serves as an information bottleneck on the main pathway of the network (e.g., the residual stream in Transformers). We propose a novel learned predictive prior that enables us to measure the novel information gained in each computation step, which serves as our metric. We show empirically that our metric predicts the description length of formal languages learned in-context, the complexity of mathematical reasoning problems, and the correctness of self-generated reasoning chains.

The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from complex datasets, but many approaches assume causal relationships are static over time, limiting their applicability to systems with dynamic, state-dependent behavior, such as the brain. While some techniques attempt dynamic causal discovery through factor models, they often restrict relationships to linear patterns or impose other simplifying assumptions. We propose a novel method that models dynamic graphs as a conditionally weighted superposition of static graphs, where each static graph can capture nonlinear relationships. This approach enables the detection of complex, time-varying interactions between variables beyond linear limitations. Our method improves f1-scores of predicted dynamic causal patterns by roughly 22-28% on average over baselines in some of our experiments, with some improvements reaching well over 60%. A case study on real brain data demonstrates our method's ability to uncover relationships linked to specific behavioral states, offering valuable insights into neural dynamics.

Many important phenomena in scientific fields like climate, neuroscience, and epidemiology are naturally represented as spatiotemporal gridded data with complex interactions. Inferring causal relationships from these data is a challenging problem compounded by the high dimensionality of such data and the correlations between spatially proximate points. We present SPACY (SPAtiotemporal Causal discoverY), a novel framework based on variational inference, designed to model latent time series and their causal relationships from spatiotemporal data. SPACY alleviates the high-dimensional challenge by discovering causal structures in the latent space. To aggregate spatially proximate, correlated grid points, we use spatial factors, parametrized by spatial kernel functions, to map observational time series to latent representations. Theoretically, we generalize the problem to a continuous spatial domain and establish identifiability when the observations arise from a nonlinear, invertible function of the product of latent series and spatial factors. Using this approach, we avoid assumptions that are often unverifiable, including those about instantaneous effects or sufficient variability. Empirically, SPACY outperforms state-of-the-art baselines on synthetic data, even in challenging settings where existing methods struggle, while remaining scalable for large grids. SPACY also identifies key known phenomena from real-world climate data. An implementation of SPACY is available at \url{https://github.com/Rose-STL-Lab/SPACY/}

Molecular Dynamics (MD) simulations are essential for understanding the atomic-level behavior of molecular systems, giving insights into their transitions and interactions. However, classical MD techniques are limited by the trade-off between accuracy and efficiency, while recent deep learning-based improvements have mostly focused on single-domain molecules, lacking transferability to unfamiliar molecular systems. Therefore, we propose **Uni**fied **Sim**ulator (UniSim), which leverages cross-domain knowledge to enhance the understanding of atomic interactions. First, we employ a multi-head pretraining approach to learn a unified atomic representation model from a large and diverse set of molecular data. Then, based on the stochastic interpolant framework, we learn the state transition patterns over long timesteps from MD trajectories, and introduce a force guidance module for rapidly adapting to different chemical environments. Our experiments demonstrate that UniSim achieves highly competitive performance across small molecules, peptides, and proteins.

Recent research has shown an increasing interest in utilizing pre-trained large language models (LLMs) for a variety of time series applications. However, there are three main challenges when using LLMs as foundational models for time series forecasting: (1) Cross-domain generalization. (2) Cross-modality alignment. (3) Error accumulation in autoregressive frameworks. To address these challenges, we proposed **LangTime**, a **lan**guage-**g**uided unified model for **time** series forecasting that incorporates cross-domain pre-training with reinforcement learning-based fine-tuning. Specifically, LangTime constructs Temporal Comprehension Prompts (TCPs), which include dataset-wise and channel-wise instructions, to facilitate domain adaptation and condense time series into a single token, enabling LLMs to understand better and align temporal data. To improve autoregressive forecasting, we introduce TimePPO, a reinforcement learning-based fine-tuning algorithm. TimePPO mitigates error accumulation by leveraging a multidimensional rewards function tailored for time series and a repeat-based value estimation strategy. Extensive experiments demonstrate that LangTime achieves state-of-the-art cross-domain forecasting performance, while TimePPO fine-tuning effectively enhances the stability and accuracy of autoregressive forecasting.

This paper introduces $k$-Dynamic Time Warping ($k$-DTW), a novel dissimilarity measure for polygonal curves. $k$-DTW has stronger metric properties than Dynamic Time Warping (DTW) and is more robust to outliers than the Fréchet distance, which are the two gold standards of dissimilarity measures for polygonal curves. We show interesting properties of $k$-DTW and give an exact algorithm as well as a $(1+\varepsilon)$-approximation algorithm for $k$-DTW by a parametric search for the $k$-th largest matched distance. We prove the first dimension-free learning bounds for curves and further learning theoretic results. $k$-DTW not only admits smaller sample size than DTW for the problem of learning the median of curves, where some factors depending on the curves' complexity $m$ are replaced by $k$, but we also show a surprising separation on the associated Rademacher and Gaussian complexities: $k$-DTW admits strictly smaller bounds than DTW, by a factor $\tilde\Omega(\sqrt{m})$ when $k\ll m$. We complement our theoretical findings with an experimental illustration of the benefits of using $k$-DTW for clustering and nearest neighbor classification.