ICML 2025 Papers

Forecasting is a critical task in decision-making across numerous domains. While historical numerical data provide a start, they fail to convey the complete context for reliable and accurate predictions. Human forecasters frequently rely on additional information, such as background knowledge and constraints, which can efficiently be communicated through natural language. However, in spite of recent progress with LLM-based forecasters, their ability to effectively integrate this textual information remains an open question. To address this, we introduce "Context is Key" (CiK), a time-series forecasting benchmark that pairs numerical data with diverse types of carefully crafted textual context, requiring models to integrate both modalities; crucially, every task in CiK requires understanding textual context to be solved successfully. We evaluate a range of approaches, including statistical models, time series foundation models, and LLM-based forecasters, and propose a simple yet effective LLM prompting method that outperforms all other tested methods on our benchmark. Our experiments highlight the importance of incorporating contextual information, demonstrate surprising performance when using LLM-based forecasting models, and also reveal some of their critical shortcomings. This benchmark aims to advance multimodal forecasting by promoting models that are both accurate and accessible to decision-makers with varied technical expertise. The benchmark can be visualized at https://servicenow.github.io/context-is-key-forecasting/v0.

We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific mechanisms. Unlike prior work, we tackle more complex environments where changes extend beyond function coefficients to entirely different function forms. For example, we demonstrate the discovery of ideal pendulum's natural motion $\alpha^2 \sin{\theta_t}$ by observing pendulum dynamics in different environments, such as the damped environment $\alpha^2 \sin(\theta_t) - \rho \omega_t$ and powered environment $\alpha^2 \sin(\theta_t) + \rho \frac{\omega_t}{\left|\omega_t\right|}$. Here, we formulate this problem as an *invariant function learning* task and propose a new method, known as **D**isentanglement of **I**nvariant **F**unctions (DIF), that is grounded in causal analysis. We propose a causal graph and design an encoder-decoder hypernetwork that explicitly disentangles invariant functions from environment-specific dynamics. The discovery of invariant functions is guaranteed by our information-based principle that enforces the independence between extracted invariant functions and environments. Quantitative comparisons with meta-learning and invariant learning baselines on three ODE systems demonstrate the effectiveness and efficiency of our method. Furthermore, symbolic regression explanation results highlight the ability of our framework to uncover intrinsic laws.

Long-term time series forecasting has been widely studied, yet two aspects remain insufficiently explored: the interaction learning between different frequency components and the exploitation of periodic characteristics inherent in timestamps. To address the above issues, we propose **CFPT**, a novel method that empowering time series forecasting through **C**ross-**F**requency Interaction (CFI) and **P**eriodic-Aware **T**imestamp Modeling (PTM). To learn cross-frequency interactions, we design the CFI branch to process signals in frequency domain and captures their interactions through a feature fusion mechanism. Furthermore, to enhance prediction performance by leveraging timestamp periodicity, we develop the PTM branch which transforms timestamp sequences into 2D periodic tensors and utilizes 2D convolution to capture both intra-period dependencies and inter-period correlations of time series based on timestamp patterns. Extensive experiments on multiple real-world benchmarks demonstrate that CFPT achieves state-of-the-art performance in long-term forecasting tasks. The code is publicly available at this repository: https://github.com/BUPT-SN/CFPT.

Recent advances in visual generation have made significant strides in producing content of exceptional quality. However, most methods suffer from a fundamental problem - a bottleneck of inference computational efficiency. Most of these algorithms involve multiple passes over a transformer model to generate tokens or denoise inputs. However, the model size is kept consistent throughout all iterations, which makes it computationally expensive. In this work, we aim to address this issue primarily through two key ideas - (a) not all parts of the generation process need equal compute, and we design a decode time model scaling schedule to utilize compute effectively, and (b) we can cache and reuse some of the intermediate computation. Combining these two ideas leads to using smaller models to process more tokens while large models process fewer tokens. These different-sized models do not increase the parameter size, as they share parameters. We rigorously experiment with ImageNet256$\times$256 , UCF101, and Kinetics600 to showcase the efficacy of the proposed method for image/video generation and frame prediction. Our experiments show that with almost $3\times$ less compute than baseline, our model obtains competitive performance.

Temporal sequences, even after stationarization, often exhibit leptokurtic distributions with fat tails and persistent distribution shifts. These properties destabilize feature dynamics, amplify model variance, and hinder model convergence in time series forecasting. To address this, we propose Morphing-Flow (MoF), a framework that combines a spline-based transform layer (Flow) and a test-time-trained method (Morph), which adaptively normalizes non-stationary, fat-tailed distributions while preserving critical extreme features. MoF ensures that inputs remain within a network’s effective activation space—a structured, normal-like distribution—even under distributional drift. Experiments across eight datasets show that MoF achieves state-of-the-art performance: With a simple linear backbone architecture, it matches the performance of state-of-the-art models on datasets such as Electricity and ETTh2. When paired with a patch-based Mamba architecture, MoF outperforms its closest competitor by 6.3% on average and reduces forecasting errors in fat-tailed datasets such as Exchange by 21.7%. Moreover, MoF acts as a plug-and-play module, boosting performance in existing models without architectural changes.

Time series foundation models (TSFMs) promise to be powerful tools for a wide range of applications. However, their internal representations and learned concepts are still not well understood. In this study, we investigate the structure and redundancy of representations across various TSFMs, examining the self-similarity of model layers within and across different model sizes. This analysis reveals block-like redundancy in the representations, which can be utilized for informed pruning to improve inference speed and efficiency. We also explore the concepts learned by these models, such as periodicity and trends. We demonstrate how conceptual priors can be derived from TSFM representations and leveraged to steer its outputs toward concept-informed predictions. Our work bridges representational analysis from language and vision models to TSFMs, offering new methods for building more computationally efficient and transparent TSFMs.

Foundation models (FMs) have emerged as a promising approach for time series forecasting. While effective, FMs typically remain fixed during deployment due to the high computational costs of learning them online. Consequently, deployed FMs fail to adapt their forecasts to current data characteristics, despite the availability of online feedback from newly arriving data. This raises the question of whether FM performance can be enhanced by the *efficient* usage of this feedback. We propose *ELF* to answer this question. ELF is a lightweight mechanism for the online adaption of FM forecasts in response to online feedback. ELF consists of two parts: **a)** the *ELF-Forecaster* which is used to learn the current data distribution; and **b)** the *ELF-Weighter* which is used to combine the forecasts of the FM and the ELF-Forecaster. We evaluate the performance of ELF in conjunction with several recent FMs across a suite of standard time series datasets. In *all* of our experiments we find that using ELF improves performance. This work demonstrates how efficient usage of online feedback can be used to improve FM forecasts.

Recent advances in lightweight time series forecasting models suggest the inherent simplicity of time series forecasting tasks. In this paper, we present CMoS, a super-lightweight time series forecasting model. Instead of learning the embedding of the shapes, CMoS directly models the spatial correlations between different time series chunks. Additionally, we introduce a Correlation Mixing technique that enables the model to capture diverse spatial correlations with minimal parameters, and an optional Periodicity Injection technique to ensure faster convergence. Despite utilizing as low as 1% of the lightweight model DLinear's parameters count, experimental results demonstrate that CMoS outperforms existing state-of-the-art models across multiple datasets. Furthermore, the learned weights of CMoS exhibit great interpretability, providing practitioners with valuable insights into temporal structures within specific application scenarios.

The Fourier transform is a fundamental tool in computer science and signal processing. In particular, when the signal is sparse in the frequency domain---having only $k$ distinct frequencies---sparse Fourier transform (SFT) algorithms can recover the signal in a sublinear time (proportional to the sparsity $k$). Most prior research focused on SFT for discrete signals, designing both randomized and deterministic algorithms for one-dimensional and high-dimensional discrete signals. However, SFT for continuous signals (i.e., $x^*(t)=\sum_{j=1}^k v_j e^{2\pi \mathbf{i} f_j t}$ for $t\in [0,T]$) is a more challenging task. The discrete SFT algorithms are not directly applicable to continuous signals due to the sparsity blow-up from the discretization. Prior to this work, there is a randomized algorithm that achieves an $\ell_2$ recovery guarantee in $\widetilde{O}(k\cdot \mathrm{polylog}(F/\eta))$ time, where $F$ is the band-limit of the frequencies and $\eta$ is the frequency gap. Nevertheless, whether we can solve this problem without using randomness remains open. In this work, we address this gap and introduce the first sublinear-time deterministic sparse Fourier transform algorithm in the continuous setting. Specifically, our algorithm uses $\widetilde{O}(k^2 \cdot \mathrm{polylog}(F/\eta))$ samples and $\widetilde{O}(k^2 \cdot \mathrm{polylog}(F/\eta))$ time to reconstruct the on-grid signal with arbitrary noise that satisfies a mild condition. This is the optimal recovery guarantee that can be achieved by any deterministic approach.

We present an operator-theoretic framework for temporal and spatio-temporal forecasting based on learning a *continuous time-shift operator*. Our operator learning paradigm offers a continuous relaxation of the discrete lag factor used in traditional autoregressive models, enabling the history of a system up to a given time to be mapped to its future values. We parametrize the time-shift operator using Khatri-Rao neural operators (KRNOs), a novel architecture based on non-stationary integral transforms with nearly linear computational scaling. Our framework naturally handles irregularly sampled observations and enables forecasting at super-resolution in both space and time. Extensive numerical studies across diverse temporal and spatio-temporal benchmarks demonstrate that our approach achieves state-of-the-art or competitive performance with leading methods.

Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of generating sufficient training data from numerical solvers. In this paper, we present a novel framework for active learning (AL) in PDE surrogate modeling that reduces this cost. Unlike the existing AL methods for PDEs that always acquire entire PDE trajectories, our approach strategically generates only the most important time steps with the numerical solver, while employing the surrogate model to approximate the remaining steps. This dramatically reduces the cost incurred by each trajectory and thus allows the active learning algorithm to try out a more diverse set of trajectories given the same budget. To accommodate this novel framework, we develop an acquisition function that estimates the utility of a set of time steps by approximating its resulting variance reduction. We demonstrate the effectiveness of our method on several benchmark PDEs, including the Burgers' equation, Korteweg–De Vries equation, Kuramoto–Sivashinsky equation, the incompressible Navier-Stokes equation, and the compressible Navier-Stokes equation. Experiments show that our approach improves performance by large margins over the best existing method. Our method not only reduces average error but also the 99\%, 95\%, and 50\% quantiles of error, which is rare for an AL algorithm. All in all, our approach offers a data-efficient solution to surrogate modeling for PDEs.

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either fail to provide a polynomial-time solution or are not applicable in the kernel setting. However, with oracle access to the geometric properties of the input space, we propose a polynomial-time algorithm that learns a classifier with \emph{exact} invariances. Moreover, our approach achieves the same excess population risk (or generalization error) as the original kernel regression problem. To the best of our knowledge, this is the first polynomial-time algorithm to achieve exact (as opposed to approximate) invariances in this setting, partially addressing a question posed by Diaz (2025) regarding the avoidance of prohibitively large and computationally intensive group averaging methods in kernel regression with exact invariances. Our proof leverages tools from differential geometry, spectral theory, and optimization. A key result in our development is a new reformulation of the problem of learning under invariances as optimizing an infinite number of linearly constrained convex quadratic programs, which may be of independent interest.

Sufficiently modeling the correlations among variables (aka channels) is crucial for achieving accurate multivariate time series forecasting (MTSF). In this paper, we propose a novel technique called Temporal Query (TQ) to more effectively capture multivariate correlations, thereby improving model performance in MTSF tasks. Technically, the TQ technique employs periodically shifted learnable vectors as queries in the attention mechanism to capture global inter-variable patterns, while the keys and values are derived from the raw input data to encode local, sample-level correlations. Building upon the TQ technique, we develop a simple yet efficient model named Temporal Query Network (TQNet), which employs only a single-layer attention mechanism and a lightweight multi-layer perceptron (MLP). Extensive experiments demonstrate that TQNet learns more robust multivariate correlations, achieving state-of-the-art forecasting accuracy across 12 challenging real-world datasets. Furthermore, TQNet achieves high efficiency comparable to linear-based methods even on high-dimensional datasets, balancing performance and computational cost. The code is available at: https://github.com/ACAT-SCUT/TQNet.

High-dimensional time-series datasets are common in domains such as healthcare and economics. Variational autoencoder (VAE) models, where latent variables are modeled with a Gaussian process (GP) prior, have become a prominent model class to analyze such correlated datasets. However, their applications are challenged by the inherent cubic time complexity that requires specific GP approximation techniques, as well as the general challenge of modeling both shared and individual-specific correlations across time. Though inducing points enhance GP prior VAE scalability, optimizing them remains challenging, especially since discrete covariates resist gradient‑based methods. In this work, we propose a scalable basis function approximation technique for GP prior VAEs that mitigates these challenges and results in linear time complexity, with a global parametrization that eliminates the need for amortized variational inference and the associated amortization gap, making it well-suited for conditional generation tasks where accuracy and efficiency are crucial. Empirical evaluations on synthetic and real-world benchmark datasets demonstrate that our approach not only improves scalability and interpretability but also drastically enhances predictive performance.

We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications naturally exhibit random (potentially trajectory-dependent) stopping times. Since those stopping times typically depend on the policy, their randomness has an effect on policy gradient formulas, which we (mostly for the first time) derive rigorously in this work both for stochastic and deterministic policies. We present two complementary perspectives, trajectory or state-space based, and establish connections to optimal control theory. Our numerical experiments demonstrate that using the proposed formulas can significantly improve optimization convergence compared to traditional approaches.

While foundation models have been exploited for various expert tasks with their fine-tuned parameters, any foundation model will be eventually outdated due to its old knowledge or limited capability, and thus should be replaced by a new foundation model. Subsequently, to benefit from its latest knowledge or improved capability, the new foundation model should be fine-tuned on each task again, which incurs not only the additional training cost but also the maintenance cost of the task-specific data. Existing work address this problem by inference-time tuning, i.e., modifying the output probability from the new foundation model by the outputs from the old foundation model and its fine-tuned model, which involves an additional inference cost by the latter two models. In this paper, we explore a new fine-tuning principle (which we call portable reward tuning; PRT) that reduces the inference cost by its nature, based on the reformulation of fine-tuning as the reward maximization with Kullback-Leibler regularization. Specifically, instead of fine-tuning parameters of the foundation models, PRT trains the reward model explicitly through the same loss as in fine-tuning. During inference, the reward model can be used with any foundation model (with the same set of vocabularies or labels) through the formulation of reward maximization. Experimental results, including both vision and language models, show that the PRT-trained model can achieve comparable accuracy with less inference cost, in comparison to the existing work of inference-time tuning.

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.

Many forms of sensitive data, such as web traffic, mobility data, or hospital occupancy, are inherently sequential. The standard method for training machine learning models while ensuring privacy for units of sensitive information, such as individual hospital visits, is differentially private stochastic gradient descent (DP-SGD). However, we observe in this work that the formal guarantees of DP-SGD are incompatible with time series specific tasks like forecasting, since they rely on the *privacy amplification* attained by training on small, unstructured batches sampled from an unstructured dataset. In contrast, batches for forecasting are generated by (1) sampling sequentially structured time series from a dataset, (2) sampling contiguous subsequences from these series, and (3) partitioning them into context and ground-truth forecast windows. We theoretically analyze the privacy amplification attained by this *structured subsampling* to enable the training of forecasting models with sound and tight event- and user-level privacy guarantees. Towards more private models, we additionally prove how data augmentation amplifies privacy in self-supervised training of sequence models. Our empirical evaluation demonstrates that amplification by structured subsampling enables the training of forecasting models with strong formal privacy guarantees.

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as $P \neq NP$. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.