ICML 2025 Papers

Classic ensembles generalize better than any single component model. In contrast, recent empirical studies find that modern ensembles of (overparameterized) neural networks may not provide any inherent generalization advantage over single but larger neural networks. This paper clarifies how modern overparameterized ensembles differ from their classic underparameterized counterparts, using ensembles of random feature (RF) regressors as a basis for developing theory. In contrast to the underparameterized regime, where ensembling typically induces regularization and increases generalization, we prove with minimal assumptions that infinite ensembles of overparameterized RF regressors become pointwise equivalent to (single) infinite-width RF regressors, and finite width ensembles rapidly converge to single models with the same parameter budget. These results, which are exact for ridgeless models and approximate for small ridge penalties, imply that overparameterized ensembles and single large models exhibit nearly identical generalization. We further characterize the predictive variance amongst ensemble members, demonstrating that it quantifies the expected effects of increasing capacity rather than capturing any conventional notion of uncertainty. Our results challenge common assumptions about the advantages of ensembles in overparameterized settings, prompting a reconsideration of how well intuitions from underparameterized ensembles transfer to deep ensembles and the overparameterized regime.

This paper introduces two novel criteria: one for feature selection and another for feature elimination in the context of best subset selection, which is a benchmark problem in statistics and machine learning. From the perspective of optimization, we revisit the classical selection and elimination criteria in traditional best subset selection algorithms, revealing that these classical criteria capture only partial variations of the objective function after the entry or exit of features. By formulating and solving optimization subproblems for feature entry and exit exactly, new selection and elimination criteria are proposed, proved as the optimal decisions for the current entry-and-exit process compared to classical criteria. Replacing the classical selection and elimination criteria with the proposed ones generates a series of enhanced best subset selection algorithms. These generated algorithms not only preserve the theoretical properties of the original algorithms but also achieve significant meta-gains without increasing computational cost across various scenarios and evaluation metrics on multiple tasks such as compressed sensing and sparse regression.

Topology optimization plays a crucial role in designing efficient and manufacturable structures. Traditional methods often yield free-form voids that, although providing design flexibility, introduce significant manufacturing challenges and require extensive post-processing. Conversely, feature-mapping topology optimization reduces post-processing efforts by constructing topologies using predefined geometric features. Nevertheless, existing approaches are significantly constrained by the limited set of geometric features available, the variety of parameters that each type of geometric feature can possess, and the necessity of employing differentiable signed distance functions. In this paper, we present a novel method that combines Neural Heaviside Signed Distance Functions (Heaviside SDFs) with structured latent shape representations to generate manufacturable voids directly within the optimization framework. Our architecture incorporates encoder and decoder networks to effectively approximate the Heaviside function and facilitate optimization within a unified latent space, thus addressing the feature diversity limitations of current feature-mapping techniques. Experimental results validate the effectiveness of our approach in balancing structural compliance, offering a new pathway to CAD-integrated design with minimal human intervention.

We study the problem of clustering a set of items based on bandit feedback. Each of the $n$ items is characterized by a feature vector, with a possibly large dimension $d$. The items are partitioned into two unknown groups, such that items within the same group share the same feature vector. We consider a sequential and adaptive setting in which, at each round, the learner selects one item and one feature, then observes a noisy evaluation of the item's feature. The learner's objective is to recover the correct partition of the items, while keeping the number of observations as small as possible. We provide an algorithm which relies on finding a relevant feature for the clustering task, leveraging the Sequential Halving algorithm. With probability at least $1-\delta$, we obtain an accurate recovery of the partition and derive an upper bound on the required budget . Furthermore, we derive an instance-dependent lower bound, which is tight in some relevant cases.

Confounders are extraneous variables that affect both the input and the target, resulting in spurious correlations and biased predictions. There are recent advances in dealing with or removing confounders in traditional models, such as metadata normalization (MDN), where the distribution of the learned features is adjusted based on the study confounders. However, in the context of continual learning, where a model learns continuously from new data over time without forgetting, learning feature representations that are invariant to confounders remains a significant challenge. To remove their influence from intermediate feature representations, we introduce the Recursive MDN (R-MDN) layer, which can be integrated into any deep learning architecture, including vision transformers, and at any model stage. R-MDN performs statistical regression via the recursive least squares algorithm to maintain and continually update an internal model state with respect to changing distributions of data and confounding variables. Our experiments demonstrate that R-MDN promotes equitable predictions across population groups, both within static learning and across different stages of continual learning, by reducing catastrophic forgetting caused by confounder effects changing over time.

Endowing large language models (LLMs) with continual learning (CL) capacities is practically important, which enables them to dynamically acquire new knowledge over time. Although many effective methods have been proposed for CL of LLMs, they did not consider online scenarios, thereby sharing a common problem: information leakage (IL), where the task-related information of learned tasks is accessed or reused again. IL not only imposes potential risks on data privacy protection but also significantly hinders the deployment of LLMs in real-world scenarios. To avoid IL while maintaining outstanding CL performance, we propose a novel CL method for LLMs, which first characterizes a parameter-efficient fine-tuning (PEFT) block by a presentative feature distribution, and then dynamically selects the appropriate PEFT blocks for each instance based on its similarity with the presentative feature distributions. Extensive experiments validate the effectiveness of our method on the CL of LLM, showcasing its potential to enhance both privacy and adaptability in practical applications.

Embedding and visualization techniques are essential for analyzing high-dimensional data, but they often struggle with complex data governed by multiple latent variables, potentially distorting key structural characteristics. This paper considers scenarios where the observed features can be partitioned into mutually exclusive subsets, each capturing a different smooth substructure. In such cases, visualizing the data based on each feature partition can better characterize the underlying processes and structures in the data, leading to improved interpretability. To partition the features, we propose solving an optimization problem that promotes graph Laplacian-based smoothness in each partition, thereby prioritizing partitions with simpler geometric structures. Our approach generalizes traditional embedding and visualization techniques, allowing them to learn multiple embeddings simultaneously. We establish that if several independent or partially dependent manifolds are embedded in distinct feature subsets in high-dimensional space, then our framework can reliably identify the correct subsets with theoretical guarantees. Finally, we demonstrate the effectiveness of our approach in extracting multiple low-dimensional structures and partially independent processes from both simulated and real data.

A data analysis pipeline is a structured sequence of steps that transforms raw data into meaningful insights by integrating various analysis algorithms. In this paper, we propose a novel statistical test to assess the significance of data analysis pipelines. Our approach enables the systematic development of valid statistical tests applicable to any feature selection pipeline composed of predefined components. We develop this framework based on selective inference, a statistical technique that has recently gained attention for data-driven hypotheses. As a proof of concept, we focus on feature selection pipelines for linear models, composed of three missing value imputation algorithms, three outlier detection algorithms, and three feature selection algorithms. We theoretically prove that our statistical test can control the probability of false positive feature selection at any desired level, and demonstrate its validity and effectiveness through experiments on synthetic and real data. Additionally, we present an implementation framework that facilitates testing across any configuration of these feature selection pipelines without extra implementation costs.

Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply through a phase transition. In this work, we show that the phenomenon of grokking is not specific to neural networks nor to gradient descent-based optimization. Specifically, we show that this phenomenon occurs when learning modular arithmetic with Recursive Feature Machines (RFM), an iterative algorithm that uses the Average Gradient Outer Product (AGOP) to enable task-specific feature learning with general machine learning models. When used in conjunction with kernel machines, iterating RFM results in a fast transition from random, near zero, test accuracy to perfect test accuracy. This transition cannot be predicted from the training loss, which is identically zero, nor from the test loss, which remains constant in initial iterations. Instead, as we show, the transition is completely determined by feature learning: RFM gradually learns block-circulant features to solve modular arithmetic. Paralleling the results for RFM, we show that neural networks that solve modular arithmetic also learn block-circulant features. Furthermore, we present theoretical evidence that RFM uses such block-circulant features to implement the Fourier Multiplication Algorithm, which prior work posited as the generalizing solution neural networks learn on these tasks. Our results demonstrate that emergence can result purely from learning task-relevant features and is not specific to neural architectures nor gradient descent-based optimization methods. Furthermore, our work provides more evidence for AGOP as a key mechanism for feature learning in neural networks.

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical understanding of this architecture is falling behind due to its inherent complexity. In this paper, we theoretically study the sample and runtime complexity of MoE following the stochastic gradient descent when learning a regression task with an underlying cluster structure of single index models. On the one hand, we show that a vanilla neural network fails in detecting such a latent organization as it can only process the problem as a whole. This is intrinsically related to the concept of *information exponent* which is low for each cluster, but increases when we consider the entire task. On the other hand, with a MoE, we show that it succeeds in dividing the problem into easier subproblems by leveraging the ability of each expert to weakly recover the simpler function corresponding to an individual cluster. To the best of our knowledge, this work is among the first to explore the benefits of the MoE framework by examining its SGD dynamics in the context of nonlinear regression.