ICML 2025 论文列表

Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty quantification, it is limited to univariate responses and scalar criteria. To address this, we propose Multivariate Conformal Selection (mCS), a generalization of CS designed for multivariate response settings. Our method introduces regional monotonicity and employs multivariate nonconformity scores to construct conformal $p$-values, enabling finite-sample False Discovery Rate (FDR) control. We present two variants: $\texttt{mCS-dist}$, using distance-based scores, and $\texttt{mCS-learn}$, which learns optimal scores via differentiable optimization. Experiments on simulated and real-world datasets demonstrate that mCS significantly improves selection power while maintaining FDR control, establishing it as a robust framework for multivariate selection tasks.

Neural operators have emerged as a promising approach for solving high-dimensional partial differential equations (PDEs). However, existing neural operators often have difficulty in dealing with constrained PDEs, where the solution must satisfy additional equality or inequality constraints beyond the governing equations. To close this gap, we propose a novel neural operator, Hyper Extended Adaptive PDHG (HEAP) for constrained high-dim PDEs, where the learned operator evolves in the parameter space of PDEs. We first show that the evolution operator learning can be formulated as a quadratic programming (QP) problem, then unroll the adaptive primal-dual hybrid gradient (APDHG) algorithm as the QP-solver into the neural operator architecture. This allows us to improve efficiency while retaining theoretical guarantees of the constrained optimization. Empirical results on a variety of high-dim PDEs show that HEAP outperforms the state-of-the-art neural operator model.

Semi-supervised Federated Learning (SSFL) is a promising approach that allows clients to collaboratively train a global model in the absence of their local data labels. The key step of SSFL is the re-labeling where each client adopts two types of available models, namely global and local models, to re-label the local data. While various technologies such as using the global model or the average of two models have been proposed to conduct the re-labeling step, little literature delves deeply into the performance dominance and limitations of the two models. In this paper, we first theoretically and empirically demonstrate that the local model achieves higher re-labeling accuracy over local data while the global model can progressively improve the re-labeling performance by introducing the extra data knowledge of other clients. Based on these findings, we propose BSemiFL which re-labels the local data through the collaboration between the local and global model in a Bayesian approach. Specifically, to re-label any given local sample, BSemiFL first uses Bayesian inference to assess the closeness of the local/global model to the sample. Then, it applies a weighted combination of their pseudo labels, using the closeness as the weights. Theoretical analysis shows that the labeling error of our method is smaller than that of simply using the global model, the local model, or their simple average. Experimental results show that BSemiFL improves the performance by up to $9.8\%$ as compared to state-of-the-art methods.

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates *continual learning* (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of *large pre-trained models* (LPMs), *efficiency* has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs *layer-wise* adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ *bandit* techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both *vision transformers* (ViTs) and *large language models* (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

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.

Supervised fine-tuning (SFT) is the most common way of adapting large language models (LLMs) to a new domain. In this paper, we improve the efficiency of SFT by selecting an informative subset of training examples. Specifically, for a fixed budget of training examples, which determines the computational cost of fine-tuning, we select those that maximize information gain, as measured by the Fisher information matrix of the SFT objective. We approximate it efficiently by linearization at the last layer of the LLM. Our approach is computationally efficient, analyzable, and performs well empirically. We demonstrate this on several problems, with both quantitative results and LLM-as-a-judge evaluations.

The Area Under the ROC Curve (AUC) is a key metric for classification, especially under class imbalance, with growing research focus on optimizing AUC over accuracy in applications like medical image analysis and deepfake detection. This leads to fairness in AUC optimization becoming crucial as biases can impact protected groups. While various fairness mitigation techniques exist, fairness considerations in AUC optimization remain in their early stages, with most research focusing on improving AUC fairness under the assumption of clean protected groups. However, these studies often overlook the impact of noisy protected groups, leading to fairness violations in practice. To address this, we propose the first robust AUC fairness approach under noisy protected groups with fairness theoretical guarantees using distributionally robust optimization. Extensive experiments on tabular and image datasets show that our method outperforms state-of-the-art approaches in preserving AUC fairness. The code is in https://github.com/Purdue-M2/AUC_Fairness_with_Noisy_Groups.

Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional mean functions involved in the population measure. The test statistic is thoughtfully constructed to ensure that even slowly decaying nonparametric estimation errors do not affect the asymptotic accuracy of the test. Our approach demonstrates strong empirical performance in scenarios with high-dimensional covariates and response variable, can handle multivariate responses, and maintains nontrivial power against local alternatives outside an $n^{-1/2}$ neighborhood of the null hypothesis. We also use numerical simulations and real-world imaging data applications to highlight the efficacy and versatility of our testing procedure.

Factored Markov Decision Processes (FMDPs) offer a promising framework for overcoming the curse of dimensionality in reinforcement learning (RL) by decomposing high-dimensional MDPs into smaller and independently evolving components. Despite their potential, existing studies on FMDPs face three key limitations: reliance on perfectly factorizable models, suboptimal sample complexity guarantees for model-based algorithms, and the absence of model-free algorithms. To address these challenges, we introduce approximate factorization, which extends FMDPs to handle imperfectly factored models. Moreover, we develop a model-based algorithm and a model-free algorithm (in the form of variance-reduced Q-learning), both achieving the first near-minimax sample complexity guarantees for FMDPs. A key novelty in the design of these two algorithms is the development of a graph-coloring-based optimal synchronous sampling strategy. Numerical simulations based on the wind farm storage control problem corroborate our theoretical findings.

In this paper, we focus on the out-of-distribution (OOD) generalization of self-supervised learning (SSL). By analyzing the mini-batch construction during the SSL training phase, we first give one plausible explanation for SSL having OOD generalization. Then, from the perspective of data generation and causal inference, we analyze and conclude that SSL learns spurious correlations during the training process, which leads to a reduction in OOD generalization. To address this issue, we propose a post-intervention distribution (PID) grounded in the Structural Causal Model. PID offers a scenario where the spurious variable and label variable is mutually independent. Besides, we demonstrate that if each mini-batch during SSL training satisfies PID, the resulting SSL model can achieve optimal worst-case OOD performance. This motivates us to develop a batch sampling strategy that enforces PID constraints through the learning of a latent variable model. Through theoretical analysis, we demonstrate the identifiability of the latent variable model and validate the effectiveness of the proposed sampling strategy. Experiments conducted on various downstream OOD tasks demonstrate the effectiveness of the proposed sampling strategy.

Node equivalence is common in graphs, such as computing networks, encompassing automorphic equivalence (preserving adjacency under node permutations) and attribute equivalence (nodes with identical attributes). Despite their importance for learning node representations, these equivalences are largely ignored by existing graph models. To bridge this gap, we propose a GrAph self-supervised Learning framework with Equivalence (GALE) and analyze its connections to existing techniques. Specifically, we: 1) unify automorphic and attribute equivalence into a single equivalence class; 2) enforce the equivalence principle to make representations within the same class more similar while separating those across classes; 3) introduce approximate equivalence classes with linear time complexity to address the NP-hardness of exact automorphism detection and handle node-feature variation; 4) analyze existing graph encoders, noting limitations in message passing neural networks and graph transformers regarding equivalence constraints; 5) show that graph contrastive learning are a degenerate form of equivalence constraint; and 6) demonstrate that GALE achieves superior performance over baselines.

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected units that generate and rely on neural representations. Accordingly, researchers employ multivariate pattern analysis to decode and compare the neural codes of artificial and biological networks, aiming to uncover their functions. However, there is limited analytical understanding of how a network’s representation and function relate, despite this being essential to any quantitative notion of underlying function or functional similarity. We address this question using fully analysable two-layer linear networks and numerical simulations in nonlinear networks. We find that function and representation are dissociated, allowing representational similarity without functional similarity and vice versa. Further, we show that neither robustness to input noise nor the level of generalisation error constrain representations to the task. In contrast, networks robust to parameter noise have limited representational flexibility and must employ task-specific representations. Our findings suggest that representational alignment reflects computational advantages beyond functional alignment alone, with significant implications for interpreting and comparing the representations of connectionist systems

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary classification loss. However, optimizing these metrics present significant computational and statistical challenges. Existing approaches often rely on the characterization of the Bayes-optimal classifier, and use threshold-based methods that first estimate class probabilities and then seek an optimal threshold. This leads to algorithms that are not tailored to restricted hypothesis sets and lack finite-sample performance guarantees. In this work, we introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds. Our approach reformulates metric optimization as a generalized cost-sensitive learning problem, enabling the design of novel surrogate loss functions with provable $H$-consistency guarantees. Leveraging this framework, we develop new algorithms, METRO (*Metric Optimization*), with strong theoretical performance guarantees. We report the results of experiments demonstrating the effectiveness of our methods compared to prior baselines.

Graph neural networks (GNNs) have achieved remarkable success, yet most are developed under the in-distribution assumption and fail to generalize to out-of-distribution (OOD) environments. To tackle this problem, some graph invariant learning methods aim to learn invariant subgraph against distribution shifts, which heavily rely on predefined or automatically generated environment labels. However, directly annotating or estimating such environment labels from biased graph data is typically impractical or inaccurate for real-world graphs. Consequently, GNNs may become biased toward variant patterns, resulting in poor OOD generalization. In this paper, we propose to learn disentangled invariant subgraph via self-supervised contrastive variant subgraph estimation for achieving satisfactory OOD generalization. Specifically, we first propose a GNN-based invariant subgraph generator to disentangle the invariant and variant subgraphs. Then, we estimate the degree of the spurious correlations by conducting self-supervised contrastive learning on variant subgraphs. Thanks to the accurate identification and estimation of the variant subgraphs, we can capture invariant subgraphs effectively and further eliminate spurious correlations by inverse propensity score reweighting. We provide theoretical analyses to show that our model can disentangle the ground-truth invariant and variant subgraphs for OOD generalization. Extensive experiments demonstrate the superiority of our model over state-of-the-art baselines.

Contrastive learning has achieved remarkable success in learning effective representations, with supervised contrastive learning often outperforming self-supervised approaches. However, in real-world scenarios, data annotations are often ambiguous or inaccurate, meaning that class labels may not reliably indicate whether two examples belong to the same class. This limitation restricts the applicability of supervised contrastive learning. To address this challenge, we introduce the concept of ``continuous semantic similarity'' to define positive and negative pairs. Instead of directly relying on imprecise class labels, we measure the semantic similarity between example pairs, which quantifies how closely they belong to the same category by iteratively refining weak supervisory signals. Based on this concept, we propose a graph-theoretic framework for weakly-supervised contrastive learning, where semantic similarity serves as the graph weights. Our framework is highly versatile and can be applied to many weakly-supervised learning scenarios. We demonstrate its effectiveness through experiments in two common settings, i.e., noisy label and partial label learning, where existing methods can be easily integrated to significantly improve performance. Theoretically, we establish an error bound for our approach, showing that it can approximate supervised contrastive learning under mild conditions. The implementation code is available at [https://github.com/Speechless-10308/WSC](https://github.com/Speechless-10308/WSC).

Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification --- an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.

Pseudo-labeling is a widely used strategy in semi-supervised learning. Existing methods typically select predicted labels with high confidence scores and high training stationarity, as pseudo-labels to augment training sets. In contrast, this paper explores the pseudo-labeling potential of predicted labels that **do not** exhibit these characteristics. We discover a new type of predicted labels suitable for pseudo-labeling, termed *two-phase labels*, which exhibit a two-phase pattern during training: *they are initially predicted as one category in early training stages and switch to another category in subsequent epochs.* Case studies show the two-phase labels are informative for decision boundaries. To effectively identify the two-phase labels, we design a 2-*phasic* metric that mathematically characterizes their spatial and temporal patterns. Furthermore, we propose a loss function tailored for two-phase pseudo-labeling learning, allowing models not only to learn correct correlations but also to eliminate false ones. Extensive experiments on eight datasets show that **our proposed 2-*phasic* metric acts as a powerful booster** for existing pseudo-labeling methods by additionally incorporating the two-phase labels, achieving an average classification accuracy gain of 1.73% on image datasets and 1.92% on graph datasets.