ICML 2025 Papers

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive embedding lengths, but it requires full model retraining and suffers from noticeable performance degradations at short lengths. In this paper, we show that *sparse coding* offers a compelling alternative for achieving adaptive representation with minimal overhead and higher fidelity. We propose **Contrastive Sparse Representation** (**CSR**), a method that specifies pre-trained embeddings into a high-dimensional but *selectively activated* feature space. By leveraging lightweight autoencoding and task-aware contrastive objectives, CSR preserves semantic quality while allowing flexible, cost-effective inference at different sparsity levels. Extensive experiments on image, text, and multimodal benchmarks demonstrate that CSR consistently outperforms MRL in terms of both accuracy and retrieval speed—often by large margins—while also cutting training time to a fraction of that required by MRL. Our results establish sparse coding as a powerful paradigm for adaptive representation learning in real-world applications where efficiency and fidelity are both paramount. Code is available at [this URL.](https://github.com/neilwen987/CSR_Adaptive_Rep)

We address the challenge of achieving angular super-resolution in multi-antenna radar systems that are widely used for localization, navigation, and automotive perception. A multi-antenna radar achieves very high resolution by computationally creating a large virtual sensing system using very few physical antennas. However, practical constraints imposed by hardware, noise, and a limited number of antennas can impede its performance. Conventional supervised learning models that rely on extensive pre-training with large datasets, often exhibit poor generalization in unseen environments. To overcome these limitations, we propose NEAR, an untrained implicit neural representation (INR) framework that predicts radar responses at unseen locations from sparse measurements, by leveraging latent harmonic structures inherent in radar wave propagation. We establish new theoretical results linking antenna array response to expressive power of INR architectures, and develop a novel physics-informed and latent geometry-aware regularizer. Our approach integrates classical signal representation with modern implicit neural learning, enabling high-resolution radar sensing that is both interpretable and generalizable. Extensive simulations and real-world experiments using radar platforms demonstrate NEAR's effectiveness and its ability to adapt to unseen environments.

We study the problem of multiclass classification when the number of labels can be unbounded within the PAC learning framework. Our main contribution is a theory that demonstrates a *simple* and *elegant* agnostic to realizable reduction for this framework. This resolves an open problem raised by the recent work of (Hopkins et al., 2022). Notably, our result is the first *representation preserving* multiclass agnostic to realizable reduction, in contrast with the compression based approach of the work of (David et al., 2017). Furthermore, our main theorem is stated in an abstract framework, called ``Unified PAC Learning'', which encompasses a range of frameworks, including multiclass PAC learning, list PAC learning, and multilabel PAC learning. In addition, we explore representation preserving reductions to the realizable setting for two noise models, namely Massart noise and Tsybakov noise, in the multiclass PAC learning framework. We believe our technique may find other applications in ensuing studies of theoretical machine learning.

Volume parameterizations abound in recent literature, encompassing methods from classic voxel grids to implicit neural representations. While implicit representations offer impressive capacity and improved memory efficiency compared to voxel grids, they traditionally require training through nonconvex optimization, which can be slow and sensitive to initialization and hyperparameters. We introduce GA-Planes, a novel family of implicit neural volume representations inspired by Geometric Algebra that can be trained using convex optimization, addressing the limitations of nonconvex methods. GA-Planes models generalize many existing representations including any combination of features stored in tensor basis elements followed by a neural feature decoder, and can be adapted to convex or nonconvex training as needed for various inverse problems. In the 2D setting, we prove GA-Planes models are equivalent to a low-rank plus low-resolution matrix factorization that outperforms the classic low-rank plus sparse decomposition for fitting a natural image. In 3D, GA-Planes models exhibit competitive expressiveness, model size, and optimizability across tasks such as radiance field reconstruction, 3D segmentation, and video segmentation.

Effective visual representation learning is crucial for reinforcement learning (RL) agents to extract task-relevant information from raw sensory inputs and generalize across diverse environments. However, existing RL benchmarks lack the ability to systematically evaluate representation learning capabilities in isolation from other learning challenges. To address this gap, we introduce the Sliding Puzzles Gym (SPGym), a novel benchmark that transforms the classic 8-tile puzzle into a visual RL task with images drawn from arbitrarily large datasets. SPGym's key innovation lies in its ability to precisely control representation learning complexity through adjustable grid sizes and image pools, while maintaining fixed environment dynamics, observation, and action spaces. This design enables researchers to isolate and scale the visual representation challenge independently of other learning components. Through extensive experiments with model-free and model-based RL algorithms, we uncover fundamental limitations in current methods' ability to handle visual diversity. As we increase the pool of possible images, all algorithms exhibit in- and out-of-distribution performance degradation, with sophisticated representation learning techniques often underperforming simpler approaches like data augmentation. These findings highlight critical gaps in visual representation learning for RL and establish SPGym as a valuable tool for driving progress in robust, generalizable decision-making systems.

Reliable estimation of treatment effects from observational data is important in many disciplines such as medicine. However, estimation is challenging when unconfoundedness as a standard assumption in the causal inference literature is violated. In this work, we leverage arbitrary (potentially high-dimensional) instruments to estimate bounds on the conditional average treatment effect (CATE). Our contributions are three-fold: (1) We propose a novel approach for partial identification through a mapping of instruments to a discrete representation space so that we yield valid bounds on the CATE. This is crucial for reliable decision-making in real-world applications. (2) We derive a two-step procedure that learns tight bounds using a tailored neural partitioning of the latent instrument space. As a result, we avoid instability issues due to numerical approximations or adversarial training. Furthermore, our procedure aims to reduce the estimation variance in finite-sample settings to yield more reliable estimates. (3) We show theoretically that our procedure obtains valid bounds while reducing estimation variance. We further perform extensive experiments to demonstrate the effectiveness across various settings. Overall, our procedure offers a novel path for practitioners to make use of potentially high-dimensional instruments (e.g., as in Mendelian randomization).

Humans develop _world models_ that capture the underlying generation process of data. Whether neural networks can learn similar world models remains an open problem. In this work, we present the first theoretical results for this problem, showing that in a _multi-task_ setting, models with a _low-degree bias_ provably recover latent data-generating variables under mild assumptions--even if proxy tasks involve complex, non-linear functions of the latents. However, such recovery is sensitive to model architecture. Our analysis leverages Boolean models of task solutions via the Fourier-Walsh transform and introduces new techniques for analyzing invertible Boolean transforms, which may be of independent interest. We illustrate the algorithmic implications of our results and connect them to related research areas, including self-supervised learning, out-of-distribution generalization, and the linear representation hypothesis in large language models.

Group fairness based on adversarial training has gained significant attention on graph data, which was implemented by masking sensitive attributes to generate fair feature views. However, existing models suffer from training instability due to uncertainty of the generated masks and the trade-off between fairness and utility. In this work, we propose a stable fair Graph Neural Network (SFG) to maintain training stability while preserving accuracy and fairness performance. Specifically, we first theoretically derive a tight upper Lipschitz bound to control the stability of existing adversarial-based models and employ a stochastic projected subgradient algorithm to constrain the bound, which operates in a block-coordinate manner. Additionally, we construct the uncertainty set to train the model, which can prevent unstable training by dropping some overfitting nodes caused by chasing fairness. Extensive experiments conducted on three real-world datasets demonstrate that SFG is stable and outperforms other state-of-the-art adversarial-based methods in terms of both fairness and utility performance. Codes are available at https://github.com/sh-qiangchen/SFG.

Contrastive Representation Learning (CRL) has achieved impressive success in various domains in recent years. Nevertheless, the theoretical understanding of the generalization behavior of CRL has remained limited. Moreover, to the best of our knowledge, the current literature only analyzes generalization bounds under the assumption that the data tuples used for contrastive learning are independently and identically distributed. However, in practice, we are often limited to a fixed pool of reusable labeled data points, making it inevitable to recycle data across tuples to create sufficiently large datasets. Therefore, the tuple-wise independence condition imposed by previous works is invalidated. In this paper, we provide a generalization analysis for the CRL framework under non-$i.i.d.$ settings that adheres to practice more realistically. Drawing inspiration from the literature on U-statistics, we derive generalization bounds which indicate that the required number of samples in each class scales as the logarithm of the covering number of the class of learnable feature representations associated to that class. Next, we apply our main results to derive excess risk bounds for common function classes such as linear maps and neural networks.

We define the *local complexity* of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn low-dimensional feature representations have a lower local complexity. This allows us to connect recent empirical observations on feature learning at the level of the weight matrices with concrete properties of the learned functions. In particular, we show that the local complexity serves as an upper bound on the total variation of the function over the input data distribution and thus that feature learning can be related to adversarial robustness. Lastly, we consider how optimization drives ReLU networks towards solutions with lower local complexity. Overall, this work contributes a theoretical framework towards relating geometric properties of ReLU networks to different aspects of learning such as feature learning and representation cost.

We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits of RFNNs. In the case of MSE loss, we obtain closed-form solutions to greedy layer-wise boosting with random features. For general loss functions, we show that fitting random feature residual blocks reduces to solving a quadratically constrained least squares problem. Through extensive numerical experiments on tabular datasets for both regression and classification, we show that RFRBoost significantly outperforms RFNNs and end-to-end trained MLP ResNets in the small- to medium-scale regime where RFNNs are typically applied. Moreover, RFRBoost offers substantial computational benefits, and theoretical guarantees stemming from boosting theory.

Estimating causal effects of joint interventions on multiple variables is crucial in many domains, but obtaining data from such simultaneous interventions can be challenging. Our study explores how to learn joint interventional effects using only observational data and single-variable interventions. We present an identifiability result for this problem, showing that for a class of nonlinear additive outcome mechanisms, joint effects can be inferred without access to joint interventional data. We propose a practical estimator that decomposes the causal effect into confounded and unconfounded contributions for each intervention variable. Experiments on synthetic data demonstrate that our method achieves performance comparable to models trained directly on joint interventional data, outperforming a purely observational estimator.

Data imbalance remains a fundamental challenge in real-world machine learning. However, most existing work has focused on classification, leaving imbalanced regression underexplored despite its importance in many applications. To address this gap, we propose PRIME, a framework that leverages learnable proxies to construct a balanced and well-ordered feature space for imbalanced regression. At its core, PRIME arranges proxies to be uniformly distributed in the feature space while preserving the ordinal structure of regression targets, and then aligns each sample feature to its corresponding proxy. By using proxies as reference points, PRIME induces the desired structure of learned representations, promoting better generalization, especially in underrepresented target regions. Moreover, since proxy-based alignment resembles classification, PRIME enables the seamless application of class imbalance techniques to regression, facilitating more balanced feature learning. Extensive experiments demonstrate the effectiveness and broad applicability of PRIME, achieving state-of-the-art performance on four real-world regression benchmark datasets across diverse target domains.

Safe offline reinforcement learning (RL), which aims to learn the safety-guaranteed policy without risky online interaction with environments, has attracted growing recent attention for safety-critical scenarios. However, existing approaches encounter out-of-distribution problems during the testing phase, which can result in potentially unsafe outcomes. This issue arises due to the infinite possible combinations of reward-related and cost-related states. In this work, we propose State Decoupling with Q-supervised Contrastive representation (SDQC), a novel framework that decouples the global observations into reward- and cost-related representations for decision-making, thereby improving the generalization capability for unfamiliar global observations. Compared with the classical representation learning methods, which typically require model-based estimation (e.g., bisimulation), we theoretically prove that our Q-supervised method generates a coarser representation while preserving the optimal policy, resulting in improved generalization performance. Experiments on DSRL benchmark problems provide compelling evidence that SDQC surpasses other baseline algorithms, especially for its exceptional ability to achieve almost zero violations in more than half of the tasks, while the state-of-the-art algorithm can only achieve the same level of success in a quarter of the tasks. Further, we demonstrate that SDQC possesses superior generalization ability when confronted with unseen environments.

A common belief in the representational comparison literature is that if two representations can be functionally aligned, they must capture similar information. In this paper we focus on model stitching and show that models can be functionally aligned, but represent very different information. Firstly, we show that discriminative models with very different biases can be stitched together. We then show that models trained to solve entirely different tasks on different data modalities, and even clustered random noise, can be successfully stitched into MNIST or ImageNet-trained models. We end with a discussion of the wider impact of our results on the community's current beliefs. Overall, our paper draws attention to the need to correctly interpret the results of such functional similarity measures and highlights the need for approaches that capture informational similarity.

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation or infer local geometry by constructing a graph on the input data. More recently, topological data analysis popularized the use of simplicial complexes to represent data topology with two main methodologies: topological inference with geometric complexes and large-scale topology representation with Mapper graphs -- central to these is the nerve construction from topology, which builds a simplicial complex given any cover of a space by subsets. While successful, these have limitations: geometric complexes scale poorly with data size, and Mapper graphs can be hard to tune and only contain low dimensional information. In this paper, we propose to study the problem of learning covers in its own right, and from the perspective of optimization. We describe a method to learn topologically-faithful covers of geometric datasets, and show that the simplicial complexes thus obtained can outperform standard topological inference approaches in terms of size, and Mapper-type algorithms in terms of representation of large-scale topology.

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a connection between manifold learning and computational algebra by demonstrating how vanishing ideals can characterize the latent manifolds of deep networks. To that end, we propose a new neural architecture that (i) truncates a pretrained network at an intermediate layer, (ii) approximates each class manifold via polynomial generators of the vanishing ideal, and (iii) transforms the resulting latent space into linearly separable features through a single polynomial layer. The resulting models have significantly fewer layers than their pretrained baselines, while maintaining comparable accuracy, achieving higher throughput, and utilizing fewer parameters. Furthermore, drawing on spectral complexity analysis, we derive sharper theoretical guarantees for generalization, showing that our approach can in principle offer tighter bounds than standard deep networks. Numerical experiments confirm the effectiveness and efficiency of the proposed approach.

We aim to develop a fundamental understanding of modality collapse, a recently observed empirical phenomenon wherein models trained for multimodal fusion tend to rely only on a subset of the modalities, ignoring the rest. We show that modality collapse happens when noisy features from one modality are entangled, via a shared set of neurons in the fusion head, with predictive features from another, effectively masking out positive contributions from the predictive features of the former modality and leading to its collapse. We further prove that cross-modal knowledge distillation implicitly disentangles such representations by freeing up rank bottlenecks in the student encoder, denoising the fusion-head outputs without negatively impacting the predictive features from either modality. Based on the above findings, we propose an algorithm that prevents modality collapse through explicit basis reallocation, with applications in dealing with missing modalities. Extensive experiments on multiple multimodal benchmarks validate our theoretical claims. Project page: https://abhrac.github.io/mmcollapse/.

This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph invariants that are isomorphism-invariant and capable of embedding richer graph structures - including attributed graphs, multilayer graphs, and hypergraphs - which the Skew Spectrum could not handle. Our generalization further defines a family of functions that enables a trade-off between computational complexity and expressivity. By applying generalization-preserving heuristics to this family, we improve the Skew Spectrum's expressivity at the same computational cost. We formally prove the invariance of our generalization, demonstrate its improved expressiveness through experiments, and discuss its efficient computation.