ICML 2025 Papers

Link prediction---a task of distinguishing actual hidden edges from random unconnected node pairs---is one of the quintessential tasks in graph machine learning. Despite being widely accepted as a universal benchmark and a downstream task for representation learning, the link prediction benchmark's validity has rarely been questioned. Here, we show that the common edge sampling procedure in the link prediction task has an implicit bias toward high-degree nodes. This produces a highly skewed evaluation that favors methods overly dependent on node degree. In fact a ``null'' link prediction method based solely on node degree can yield nearly optimal performance in this setting. We propose a degree-corrected link prediction benchmark that offers a more reasonable assessment and better aligns with the performance on the recommendation task. Finally, we demonstrate that the degree-corrected benchmark can more effectively train graph machine-learning models by reducing overfitting to node degrees and facilitating the learning of relevant structures in graphs.

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating---a parallelized version of partial Bayesian inference shaped by architectural constraints. We integrate the model-agnostic theory of optimal prediction with mechanistic interpretability to analyze transformers trained on a tractable family of hidden Markov models that generate rich geometric patterns in neural activations. Our primary analysis focuses on single-layer transformers, revealing how the first attention layer implements these constrained updates, with extensions to multi-layer architectures demonstrating how subsequent layers refine these representations. We find that attention carries out an algorithm with a natural interpretation in the probability simplex, and create representations with distinctive geometric structure. We show how both the algorithmic behavior and the underlying geometry of these representations can be theoretically predicted in detail---including the attention pattern, OV-vectors, and embedding vectors---by modifying the equations for optimal future token predictions to account for the architectural constraints of attention. Our approach provides a principled lens on how architectural constraints shape the implementation of optimal prediction, revealing why transformers develop specific intermediate geometric structures.

We study the question of volume optimality in split conformal regression, a topic still poorly understood in comparison to coverage control. Using the fact that the calibration step can be seen as an empirical volume minimization problem, we first derive a finite-sample upper-bound on the excess volume loss of the interval returned by the classical split method. This important quantity measures the difference in length between the interval obtained with the split method and the shortest oracle prediction interval. Then, we introduce *EffOrt*, a methodology that modifies the learning step so that the base prediction function is selected in order to minimize the length of the returned intervals. In particular, our theoretical analysis of the excess volume loss of the prediction sets produced by *EffOrt* reveals the links between the learning and calibration steps, and notably the impact of the choice of the function class of the base predictor. We also introduce *Ad-EffOrt*, an extension of the previous method, which produces intervals whose size adapts to the value of the covariate. Finally, we evaluate the empirical performance and the robustness of our methodologies.

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.

Domain-Incremental Learning (DIL) focuses on continual learning in non-stationary environments, requiring models to adjust to evolving domains while preserving historical knowledge. DIL faces two critical challenges in the context of imbalanced data: intra-domain class imbalance and cross-domain class distribution shifts. These challenges significantly hinder model performance, as intra-domain imbalance leads to underfitting of few-shot classes, while cross-domain shifts require maintaining well-learned many-shot classes and transferring knowledge to improve few-shot class performance in old domains. To overcome these challenges, we introduce the Dual-Balance Collaborative Experts (DCE) framework. DCE employs a frequency-aware expert group, where each expert is guided by specialized loss functions to learn features for specific frequency groups, effectively addressing intra-domain class imbalance. Subsequently, a dynamic expert selector is learned by synthesizing pseudo-features through balanced Gaussian sampling from historical class statistics. This mechanism navigates the trade-off between preserving many-shot knowledge of previous domains and leveraging new data to improve few-shot class performance in earlier tasks. Extensive experimental results on four benchmark datasets demonstrate DCE’s state-of-the-art performance.

Traditional conformal prediction faces significant challenges with the rise of streaming data and increasing concerns over privacy. In this paper, we introduce a novel online differentially private conformal prediction framework, designed to construct dynamic, model-free private prediction sets. Unlike existing approaches that either disregard privacy or require full access to the entire dataset, our proposed method ensures individual privacy with a one-pass algorithm, ideal for real-time, privacy-preserving decision-making. Theoretically, we establish guarantees for long-run coverage at the nominal confidence level. Moreover, we extend our method to conformal quantile regression, which is fully adaptive to heteroscedasticity. We validate the effectiveness and applicability of the proposed method through comprehensive simulations and real-world studies on the ELEC2 and PAMAP2 datasets.

Large language models have been successfully applied to programming assistance tasks, such as code completion, code insertion, and instructional code editing. However, these applications remain insufficiently automated and struggle to effectively integrate various types of information during the programming process, including coding history, code context, and user instructions. In this work, we propose a new framework that comprehensively integrates these information sources, collect data to train our models and evaluate their performance. Firstly, to thoroughly evaluate how well models align with different types of information and the quality of their outputs, we introduce a new benchmark, APEval (Assist Programming Eval), to comprehensively assess the performance of models in programming assistance tasks. Then, for data collection, we develop a data generation pipeline, Programming-Instruct, which synthesizes training data from diverse sources, such as GitHub and online judge platforms. This pipeline can automatically generate various types of messages throughout the programming process. Finally, using this pipeline, we generate 219K samples, fine-tune multiple models, and develop the CursorCore series. We show that CursorCore outperforms other models of comparable size. This framework unifies applications such as inline chat and automated editing, contributes to the advancement of coding assistants.

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.

Peptide sequencing—the process of identifying amino acid sequences from mass spectrometry data—is a fundamental task in proteomics. Non-Autoregressive Transformers (NATs) have proven highly effective for this task, outperforming traditional methods. Unlike autoregressive models, which generate tokens sequentially, NATs predict all positions simultaneously, leveraging bidirectional context through unmasked self-attention. However, existing NAT approaches often rely on Connectionist Temporal Classification (CTC) loss, which presents significant optimization challenges due to CTC's complexity and increases the risk of training failures. To address these issues, we propose an improved non-autoregressive peptide sequencing model that incorporates a structured protein sequence curriculum learning strategy. This approach adjusts protein's learning difficulty based on the model’s estimated protein generational capabilities through a sampling process, progressively learning peptide generation from simple to complex sequences. Additionally, we introduce a self-refining inference-time module that iteratively enhances predictions using learned NAT token embeddings, improving sequence accuracy at a fine-grained level. Our curriculum learning strategy reduces NAT training failures frequency by more than 90% based on sampled training over various data distributions. Evaluations on nine benchmark species demonstrate that our approach outperforms all previous methods across multiple metrics and species. Model and source code are available at https://github.com/BEAM-Labs/denovo.

A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions to inform risk-sensitive downstream actions, as often required in domains such as medicine. We develop a decision-theoretic foundation linking prediction sets to risk-averse decision-making, addressing three questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. These insights leads to *Risk-Averse Calibration (RAC)*, a principled algorithm that is both *practical*—exploiting black-box predictions to enhance downstream utility—and *safe*—adhering to user-defined risk thresholds. We experimentally demonstrate RAC's advantages in medical diagnosis and recommendation systems, showing that it substantially improves the trade-off between safety and utility, delivering higher utility than existing methods while avoiding critical errors.

Predictive posterior densities (PPDs) are essential in approximate inference for quantifying predictive uncertainty and comparing inference methods. Typically, PPDs are estimated by simple Monte Carlo (MC) averages. In this paper, we expose a critical under-recognized issue: the signal-to-noise ratio (SNR) of the simple MC estimator can sometimes be extremely low, leading to unreliable estimates. Our main contribution is a theoretical analysis demonstrating that even with exact inference, SNR can decay rapidly with an increase in (a) the mismatch between training and test data, (b) the dimensionality of the latent space, or (c) the size of test data relative to training data. Through several examples, we empirically verify these claims and show that these factors indeed lead to poor SNR and unreliable PPD estimates (sometimes, estimates are off by hundreds of nats even with a million samples). While not the primary focus, we also explore an adaptive importance sampling approach as an illustrative way to mitigate the problem, where we learn the proposal distribution by maximizing a variational proxy to the SNR. Taken together, our findings highlight an important challenge and provide essential insights for reliable estimation.

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage. The transformation is based on an estimate of the conditional quantile of conformity scores. The resulting method is particularly beneficial for constructing adaptive confidence sets in multi-output problems where standard conformal quantile regression approaches have limited applicability. We develop a theoretical bound that captures the influence of the accuracy of the quantile estimate on the approximate conditional validity, unlike classical bounds for conformal prediction methods that only offer marginal coverage. We experimentally show that our method is highly adaptive to the local data structure and outperforms existing methods in terms of conditional coverage, improving the reliability of statistical inference in various applications.

Post-hoc calibration of pre-trained models is critical for ensuring reliable inference, especially in safety-critical domains such as healthcare. Conformal Prediction (CP) offers a robust post-hoc calibration framework, providing distribution-free statistical coverage guarantees for prediction sets by leveraging held-out datasets. In this work, we address a decentralized setting where each device has limited calibration data and can communicate only with its neighbors over an arbitrary graph topology. We propose two message-passing-based approaches for achieving reliable inference via CP: quantile-based distributed conformal prediction (Q-DCP) and histogram-based distributed conformal prediction (H-DCP). Q-DCP employs distributed quantile regression enhanced with tailored smoothing and regularization terms to accelerate convergence, while H-DCP uses a consensus-based histogram estimation approach. Through extensive experiments, we investigate the trade-offs between hyperparameter tuning requirements, communication overhead, coverage guarantees, and prediction set sizes across different network topologies. The code of our work is released on: https://github.com/HaifengWen/Distributed-Conformal-Prediction.

Machine learning for protein modeling faces significant challenges due to proteins' inherently dynamic nature, yet most graph-based machine learning methods rely solely on static structural information. Recently, the growing availability of molecular dynamics trajectories provides new opportunities for understanding the dynamic behavior of proteins; however, computational methods for utilizing this dynamic information remain limited. We propose a novel graph representation that integrates both static structural information and dynamic correlations from molecular dynamics trajectories, enabling more comprehensive modeling of proteins. By applying relational graph neural networks (RGNNs) to process this heterogeneous representation, we demonstrate significant improvements over structure-based approaches across three distinct tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction. Our results validate that combining static and dynamic information provides complementary signals for understanding protein-ligand interactions, offering new possibilities for drug design and structural biology applications.

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques such as conformal prediction provide guarantees about the loss black-box models will incur even when the details of the models are hidden. However, such methods are based on frequentist probability, which unduly limits their applicability. We revisit the central aspects of conformal prediction from a Bayesian perspective and thereby illuminate the shortcomings of frequentist guarantees. We propose a practical alternative based on Bayesian quadrature that provides interpretable guarantees and offers a richer representation of the likely range of losses to be observed at test time.

Continual learning has attracted increasing research attention in recent years due to its promising experimental results in real-world applications. In this paper, we study the issue of calibration in continual learning which reliably quantifies the uncertainty of model predictions. Conformal prediction (CP) provides a general framework for model calibration, which outputs prediction intervals or sets with a theoretical high coverage guarantee as long as the samples are exchangeable. However, the tasks in continual learning are learned in sequence, which violates the principle that data should be exchangeable. Meanwhile, the model learns the current task with limited or no access to data from previous tasks, which is not conducive to constructing the calibration set. To address these issues, we propose a CP-based method for model uncertainty quantification in continual learning (CPCL), which also reveals the connection between prediction interval length and forgetting. We analyze the oracle prediction interval in continual learning and theoretically prove the asymptotic coverage guarantee of CPCL. Finally, extensive experiments on simulated and real data empirically verify the validity of our proposed method.

As deep learning models are increasingly deployed in high-risk applications, robust defenses against adversarial attacks and reliable performance guarantees become paramount. Moreover, accuracy alone does not provide sufficient assurance or reliable uncertainty estimates for these models. This study advances adversarial training by leveraging principles from Conformal Prediction. Specifically, we develop an adversarial attack method, termed OPSA (OPtimal Size Attack), designed to reduce the efficiency of conformal prediction at any significance level by maximizing model uncertainty without requiring coverage guarantees. Correspondingly, we introduce OPSA-AT (Adversarial Training), a defense strategy that integrates OPSA within a novel conformal training paradigm. Experimental evaluations demonstrate that our OPSA attack method induces greater uncertainty compared to baseline approaches for various defenses. Conversely, our OPSA-AT defensive model significantly enhances robustness not only against OPSA but also other adversarial attacks, and maintains reliable prediction. Our findings highlight the effectiveness of this integrated approach for developing trustworthy and resilient deep learning models for safety-critical domains. Our code is available at https://github.com/bjbbbb/Enhancing-Adversarial-Robustness-with-Conformal-Prediction.

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this domain, their substantial computational cost—driven by high-order tensor product (TP) operations—restricts their scalability to large molecular systems with extensive basis sets. To address this challenge, we introduce **SPH**Net, an efficient and scalable equivariant network, that incorporates adaptive **SP**arsity into **H**amiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations, significantly reducing tensor product computations while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70\%. Extensive evaluations on QH9 and PubchemQH datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact.

As machine learning models grow increasingly competent, their predictions can supplement scarce or expensive data in various important domains. In support of this paradigm, algorithms have emerged to combine a small amount of high-fidelity observed data with a much larger set of imputed model outputs to estimate some quantity of interest. Yet current hybrid-inference tools target only means or single quantiles, limiting their applicability for many critical domains and use cases. We present QuEst, a principled framework to merge observed and imputed data to deliver point estimates and rigorous confidence intervals for a wide family of quantile-based distributional measures. QuEst covers a range of measures, from tail risk (CVaR) to population segments such as quartiles, that are central to fields such as economics, sociology, education, medicine, and more. We extend QuEst to multidimensional metrics, and introduce an additional optimization technique to further reduce variance in this and other hybrid estimators. We demonstrate the utility of our framework through experiments in economic modeling, opinion polling, and language model auto-evaluation.