ICLR 2025 Papers

The increasing complexity and parameter count of Convolutional Neural Networks (CNNs) and Transformers pose challenges in terms of computational efficiency and resource demands. Pruning has been identified as an effective strategy to address these challenges by removing redundant elements such as neurons, channels, or connections, thereby enhancing computational efficiency without heavily compromising performance. This paper builds on the foundational work of Optimal Brain Damage (OBD) by advancing the methodology of parameter importance estimation using the Hessian matrix. Unlike previous approaches that rely on approximations, we introduce Optimal Brain Apoptosis (OBA), a novel pruning method that calculates the Hessian-vector product value directly for each parameter. By decomposing the Hessian matrix across network layers and identifying conditions under which inter-layer Hessian submatrices are non-zero, we propose a highly efficient technique for computing the second-order Taylor expansion of parameters. This approach allows for a more precise pruning process, particularly in the context of CNNs and Transformers, as validated in our experiments including VGG19, ResNet32, ResNet50, and ViT-B/16 on CIFAR10, CIFAR100 and Imagenet datasets. Our code is available at https://github.com/NEU-REAL/OBA.

Subspace clustering is a classical unsupervised learning task, built on a basic assumption that high-dimensional data can be approximated by a union of subspaces (UoS). Nevertheless, the real-world data are often deviating from the UoS assumption. To address this challenge, state-of-the-art deep subspace clustering algorithms attempt to jointly learn UoS representations and self-expressive coefficients. However, the general framework of the existing algorithms suffers from feature collapse and lacks a theoretical guarantee to learn desired UoS representation. In this paper, we present a Principled fRamewOrk for Deep Subspace Clustering (PRO-DSC), which is designed to learn structured representations and self-expressive coefficients in a unified manner. Specifically, in PRO-DSC, we incorporate an effective regularization on the learned representations into the self-expressive model, prove that the regularized self-expressive model is able to prevent feature space collapse, and demonstrate that the learned optimal representations under certain condition lie on a union of orthogonal subspaces. Moreover, we provide a scalable and efficient approach to implement our PRO-DSC and conduct extensive experiments to verify our theoretical findings and demonstrate the superior performance of our proposed deep subspace clustering approach.

360-degree cameras streamline data collection for radiance field 3D reconstruction by capturing comprehensive scene data. However, traditional radiance field methods do not address the specific challenges inherent to 360-degree images. We present SC-OmniGS, a novel self-calibrating omnidirectional Gaussian splatting system for fast and accurate omnidirectional radiance field reconstruction using 360-degree images. Rather than converting 360-degree images to cube maps and performing perspective image calibration, we treat 360-degree images as a whole sphere and derive a mathematical framework that enables direct omnidirectional camera pose calibration accompanied by 3D Gaussians optimization. Furthermore, we introduce a differentiable omnidirectional camera model in order to rectify the distortion of real-world data for performance enhancement. Overall, the omnidirectional camera intrinsic model, extrinsic poses, and 3D Gaussians are jointly optimized by minimizing weighted spherical photometric loss. Extensive experiments have demonstrated that our proposed SC-OmniGS is able to recover a high-quality radiance field from noisy camera poses or even no pose prior in challenging scenarios characterized by wide baselines and non-object-centric configurations. The noticeable performance gain in the real-world dataset captured by consumer-grade omnidirectional cameras verifies the effectiveness of our general omnidirectional camera model in reducing the distortion of 360-degree images.

When optimizing transportation systems, anticipating traffic flows is a central element. Yet, computing such traffic equilibria remains computationally expensive. Against this background, we introduce a novel combinatorial optimization augmented neural network pipeline that allows for fast and accurate traffic flow predictions. We propose WardropNet, a neural network that combines classical layers with a subsequent equilibrium layer: the first ones inform the latter by predicting the parameterization of the equilibrium problem's latency functions. Using supervised learning we minimize the difference between the actual traffic flow and the predicted output. We show how to leverage a Bregman divergence fitting the geometry of the equilibria, which allows for end-to-end learning. WardropNet outperforms pure learning-based approaches in predicting traffic equilibria for realistic and stylized traffic scenarios. On realistic scenarios, WardropNet improves on average for time-invariant predictions by up to 72\% and for time-variant predictions by up to 23\% over pure learning-based approaches.

We initiate the study of the computational complexity of training graph neural networks (GNNs). We consider the classical node classification setting; there, the intractability of training multidimensonal GNNs immediately follows from known lower bounds for training classical neural networks (and holds even for trivial GNNs). However, one-dimensional GNNs form a crucial case of interest: the computational complexity of training such networks depends on both the graphical structure of the network and the properties of the involved activation and aggregation functions. As our main result, we establish the NP-hardness of training ReLU-activated one-dimensional GNNs via a highly non-trivial reduction. We complement this result with algorithmic upper bounds for the training problem in the ReLU-activated and linearly-activated settings.

Learning effective graph similarities is crucial for tasks like clustering, yet selecting the optimal kernel to evaluate such similarities in unsupervised settings remains a major challenge. Despite the development of various graph kernels, determining the most appropriate one for a specific task is particularly difficult in the absence of labeled data. Existing methods often struggle to handle the complex structure of graph data and rely on heuristic approaches that fail to adequately capture the global relationships between graphs. To overcome these limitations, we propose Unsupervised Multiple Kernel Learning for Graphs (UMKL-G), a model that combines multiple graph kernels without requiring labels or predefined local neighbors. Our approach preserves the topology of the data by maintaining ordinal relationships among graphs through a probability simplex, allowing for a unified and adaptive kernel learning process. We provide theoretical guarantees on the stability, robustness, and generalization of our method. Empirical results demonstrate that UMKL-G outperforms individual kernels and other state-of-the-art methods, offering a robust solution for unsupervised graph analysis.

Identifying time-delayed latent causal process is crucial for understanding temporal dynamics and enabling downstream reasoning. While recent methods have made progress in identifying latent time-delayed causal processes, they cannot address the dynamics in which the influence of some latent factors on both the subsequent latent states and the observed data can become inactive or irrelevant at different time steps. Therefore, we introduce intermittent temporal latent processes, where: (1) any subset of latent factors may be missing during nonlinear data generation at any time step, and (2) the active latent factors at each step are unknown. This framework encompasses both nonstationary and stationary transitions, accommodating changing or consistent active factors over time. Our work shows that under certain assumptions, the latent causal variables are block-wise identifiable. With further conditional independence assumption, each latent variable can even be recovered up to component-wise transformations. Using this identification theory, we propose an unsupervised approach, InterLatent, to reliably uncover the representations of the intermittent temporal latent process. The experimental findings on both synthetic and real-world datasets verify our theoretical claims.

Electrocardiogram (ECG) is essential for the clinical diagnosis of arrhythmias and other heart diseases, but deep learning methods based on ECG often face limitations due to the need for high-quality annotations. Although previous ECG self-supervised learning (eSSL) methods have made significant progress in representation learning from unannotated ECG data, they typically treat ECG signals as ordinary time-series data, segmenting the signals using fixed-size and fixed-step time windows, which often ignore the form and rhythm characteristics and latent semantic relationships in ECG signals. In this work, we introduce a novel perspective on ECG signals, treating heartbeats as words and rhythms as sentences. Based on this perspective, we first designed the QRS-Tokenizer, which generates semantically meaningful ECG sentences from the raw ECG signals. Building on these, we then propose HeartLang, a novel self-supervised learning framework for ECG language processing, learning general representations at form and rhythm levels. Additionally, we construct the largest heartbeat-based ECG vocabulary to date, which will further advance the development of ECG language processing. We evaluated HeartLang across six public ECG datasets, where it demonstrated robust competitiveness against other eSSL methods. Our data and code are publicly available at https://github.com/PKUDigitalHealth/HeartLang.

Predictive coding has been established as a promising neuroscientific theory to describe the mechanism of information processing in the retina or cortex. This theory hypothesises that cortex predicts sensory inputs at various levels of abstraction to minimise prediction errors. Inspired by predictive coding, Chen et al. (2024) proposed another theory, temporal prediction hypothesis, to claim that sequence memory residing in hippocampus has emerged through predicting input signals from the past sensory inputs. Specifically, they supposed that the CA3 predictor in hippocampus creates synaptic delay between input signals, which is compensated by the following CA1 predictor. Though recorded neural activities were replicated based on the temporal prediction hypothesis, its validity has not been fully explored. In this work, we aim to explore the temporal prediction hypothesis from the perspective of self-supervised learning (SSL). Specifically, we focus on non-contrastive learning, which generates two augmented views of an input image and predicts one from another. Non-contrastive learning is intimately related to the temporal prediction hypothesis because the synaptic delay is implicitly created by StopGradient. Building upon a popular non-contrastive learner, SimSiam, we propose PhiNet, an extension of SimSiam to have two predictors explicitly corresponding to the CA3 and CA1, respectively. Through studying the PhiNet model, we discover two findings. First, meaningful data representations emerge in PhiNet more stably than in SimSiam. This is initially supported by our learning dynamics analysis: PhiNet is more robust to the representational collapse. Second, PhiNet adapts more quickly to newly incoming patterns in online and continual learning scenarios. For practitioners, we additionally propose an extension called X-PhiNet integrated with a momentum encoder, excelling in continual learning. All in all, our work reveals that the temporal prediction hypothesis is a reasonable model in terms of the robustness and adaptivity.

In the field of equivariant networks, achieving affine equivariance, particularly for general group representations, has long been a challenge. In this paper, we propose the steerable EquivarLayer, a generalization of InvarLayer (Li et al., 2024), by building on the concept of equivariants beyond invariants. The steerable EquivarLayer supports affine equivariance with arbitrary input and output representations, marking the first model to incorporate steerability into networks for the affine group. To integrate it with canonicalization, a promising approach for making pre-trained models equivariant, we introduce a novel Det-Pooling module, expanding the applicability of EquivarLayer and the range of groups suitable for canonicalization. We conduct experiments on image classification tasks involving group transformations to validate the steerable EquivarLayer in the role of a canonicalization function, demonstrating its effectiveness over data augmentation.

Combining data from different sources can improve data analysis tasks such as clustering. However, most of the current multi-view clustering methods are limited to specific domains or rely on a suboptimal and computationally intensive two-stage process of representation learning and clustering. We propose an end-to-end deep learning-based multi-view clustering framework for general data types (such as images and tables). Our approach involves generating meaningful fused representations using a novel permutation-based canonical correlation objective. We provide a theoretical analysis showing how the learned embeddings approximate those obtained by supervised linear discriminant analysis (LDA). Cluster assignments are learned by identifying consistent pseudo-labels across multiple views. Additionally, we establish a theoretical bound on the error caused by incorrect pseudo-labels in the unsupervised representations compared to LDA. Extensive experiments on ten multi-view clustering benchmark datasets provide empirical evidence for the effectiveness of the proposed model.

Multi-modal models, such as CLIP, have demonstrated strong performance in aligning visual and textual representations, excelling in tasks like image retrieval and zero-shot classification. Despite this success, the mechanisms by which these models utilize training data, particularly the role of memorization, remain unclear. In uni-modal models, both supervised and self-supervised, memorization has been shown to be essential for generalization. However, it is not well understood how these findings would apply to CLIP, which incorporates elements from both supervised learning via captions that provide a supervisory signal similar to labels, and from self-supervised learning via the contrastive objective. To bridge this gap in understanding, we propose a formal definition of memorization in CLIP (CLIPMem) and use it to quantify memorization in CLIP models. Our results indicate that CLIP’s memorization behavior falls between the supervised and self-supervised paradigms, with "mis-captioned" samples exhibiting highest levels of memorization. Additionally, we find that the text encoder contributes more to memorization than the image encoder, suggesting that mitigation strategies should focus on the text domain. Building on these insights, we propose multiple strategies to reduce memorization while at the same time improving utility---something that had not been shown before for traditional learning paradigms where reducing memorization typically results in utility decrease.

We propose a novel formulation for dictionary learning with an overcomplete dictionary, i.e., when the number of atoms is larger than the dimension of the dictionary. The proposed formulation consists of a weighted sum of $\ell_1$ norms of the rows of the sparse coefficient matrix plus the log of the matrix volume of the dictionary matrix. The main contribution of this work is to show that this novel formulation guarantees global identifiability of the overcomplete dictionary, under a mild condition that the sparse coefficient matrix satisfies a strong scattering condition in the hypercube. Furthermore, if every column of the coefficient matrix is sparse and the dictionary guarantees $\ell_1$ recovery, then the coefficient matrix is identifiable as well. This is a major breakthrough for not only dictionary learning but also general matrix factorization models as identifiability is guaranteed even when the latent dimension is higher than the ambient dimension. We also provide a probabilistic analysis and show that if the sparse coefficient matrix is generated from the widely adopted sparse-Gaussian model, then the $m\times k$ overcomplete dictionary is globally identifiable if the sample size is bigger than a constant times $(k^2/m)\log(k^2/m)$ with overwhelming probability. Finally, we propose an algorithm based on alternating minimization to solve the new proposed formulation.

In order to train agents that can quickly adapt to new objectives or reward functions, efficient unsupervised representation learning in sequential decision-making environments can be important. Frameworks such as the Exogenous Block Markov Decision Process (Ex-BMDP) have been proposed to formalize this representation-learning problem (Efroni et al., 2022b). In the Ex-BMDP framework, the agent's high-dimensional observations of the environment have two latent factors: a controllable factor, which evolves deterministically within a small state space according to the agent's actions, and an exogenous factor, which represents time-correlated noise, and can be highly complex. The goal of the representation learning problem is to learn an encoder that maps from observations into the controllable latent space, as well as the dynamics of this space. Efroni et al. (2022b) has shown that this is possible with a sample complexity that depends only on the size of the controllable latent space, and not on the size of the noise factor. However, this prior work has focused on the episodic setting, where the controllable latent state resets to a specific start state after a finite horizon. By contrast, if the agent can only interact with the environment in a single continuous trajectory, prior works have not established sample-complexity bounds. We propose STEEL, the first provably sample-efficient algorithm for learning the controllable dynamics of an Ex-BMDP from a single trajectory, in the function approximation setting. STEEL has a sample complexity that depends only on the sizes of the controllable latent space and the encoder function class, and (at worst linearly) on the mixing time of the exogenous noise factor. We prove that STEEL is correct and sample-efficient, and demonstrate STEEL on two toy problems. Code is available at: https://github.com/midi-lab/steel.

Deep clustering has made remarkable progress in recent years. However, most existing deep clustering methods assume that distributions of different clusters are balanced or roughly balanced, which are not consistent with the common long-tailed distributions in reality. In nature, the datasets often follow long-tailed distributions, leading to biased models being trained with significant performance drop. Despite the widespread proposal of many long-tailed learning approaches with supervision information, research on long-tailed deep clustering remains almost uncharted. Unaware of the data distribution and sample labels, long-tailed deep clustering is highly challenging. To tackle this problem, we propose a novel contrastive mixup method for long-tailed deep clustering, named ConMix. The proposed method makes innovations to mixup representations in contrastive learning to enhance deep clustering in long-tailed scenarios. Neural networks trained with ConMix can learn more discriminative representations, thus achieve better long-tailed deep clustering performance. We theoretically prove that ConMix works through re-balancing loss for classes with different long-tailed degree. We evaluate our method on widely used benchmark datasets with different imbalance ratios, suggesting it outperforms many state-of-the-art deep clustering approaches. The code is available at https://github.com/LZX-001/ConMix.

The Transformer architecture has inarguably revolutionized deep learning, overtaking classical architectures like multi-layer perceptions (MLPs) and convolutional neural networks (CNNs). At its core, the attention block differs in form and functionality from most other architectural components in deep learning—to the extent that, in comparison to MLPs/CNNs, Transformers are more often accompanied by adaptive optimizers, layer normalization, learning rate warmup, etc. The root causes behind these outward manifestations and the precise mechanisms that govern them remain poorly understood. In this work, we bridge this gap by providing a fundamental understanding of what distinguishes the Transformer from the other architectures—grounded in a theoretical comparison of the (loss) Hessian. Concretely, for a single self-attention layer, (a) we first entirely derive the Transformer’s Hessian and express it in matrix derivatives; (b) we then characterize it in terms of data, weight, and attention moment dependencies; and (c) while doing so further highlight the important structural differences to the Hessian of classical networks. Our results suggest that various common architectural and optimization choices in Transformers can be traced back to their highly non-linear dependencies on the data and weight matrices, which vary heterogeneously across parameters. Ultimately, our findings provide a deeper understanding of the Transformer’s unique optimization landscape and the challenges it poses.

Contrastive Language-Image Pre-training (CLIP) excels in global alignment with language but exhibits limited sensitivity to spatial information, leading to strong performance in zero-shot classification tasks but underperformance in tasks requiring precise spatial understanding. Recent approaches have introduced Region-Language Alignment (RLA) to enhance CLIP's performance in dense multimodal tasks by aligning regional visual representations with corresponding text inputs. However, we find that CLIP ViTs fine-tuned with RLA suffer from notable loss in spatial awareness, which is crucial for dense prediction tasks. To address this, we propose the Spatial Correlation Distillation (SCD) framework, which preserves CLIP's inherent spatial structure and mitigates above degradation. To further enhance spatial correlations, we introduce a lightweight Refiner that extracts refined correlations directly from CLIP before feeding them into SCD, based on an intriguring finding that CLIP naturally capture high-quality dense features. Together, these components form a robust distillation framework that enables CLIP ViTs to integrate both visual-language and visual-centric improvements, achieving state-of-the-art results across various open-vocabulary dense prediction benchmarks.

Vector quantization is a fundamental technique for compression and large-scale nearest neighbor search. For high-accuracy operating points, multi-codebook quantization associates data vectors with one element from each of multiple codebooks. An example is residual quantization (RQ), which iteratively quantizes the residual error of previous steps. Dependencies between the different parts of the code are, however, ignored in RQ, which leads to suboptimal rate-distortion performance. Qinco recently addressed this inefficiency by using a neural network to determine the quantization codebook in RQ based on the vector reconstruction from previous steps. In this paper we introduce Qinco2 which extends and improves Qinco with (i) improved vector encoding using codeword pre-selection and beam-search, (ii) a fast approximate decoder leveraging codeword pairs to establish accurate short-lists for search, and (iii) an optimized training procedure and network architecture. We conduct experiments on four datasets to evaluate Qinco2 for vector compression and billion-scale nearest neighbor search. We obtain outstanding results in both settings, improving the state-of-the-art reconstruction MSE by 44% for 16-byte vector compression on BigANN, and search accuracy by 24% with 8-byte encodings on Deep1M.

Vision-and-Language Navigation (VLN) tasks mainly evaluate agents based on one-time execution of individual instructions across multiple environments, aiming to develop agents capable of functioning in any environment in a zero-shot manner. However, real-world navigation robots often operate in persistent environments with relatively consistent physical layouts, visual observations, and language styles from instructors. Such a gap in the task setting presents an opportunity to improve VLN agents by incorporating continuous adaptation to specific environments. To better reflect these real-world conditions, we introduce GSA-VLN (General Scene Adaptation for VLN), a novel task requiring agents to execute navigation instructions within a specific scene and simultaneously adapt to it for improved performance over time. To evaluate the proposed task, one has to address two challenges in existing VLN datasets: the lack of out-of-distribution (OOD) data, and the limited number and style diversity of instructions for each scene. Therefore, we propose a new dataset, GSA-R2R, which significantly expands the diversity and quantity of environments and instructions for the Room-to-Room (R2R) dataset to evaluate agent adaptability in both ID and OOD contexts. Furthermore, we design a three-stage instruction orchestration pipeline that leverages large language models (LLMs) to refine speaker-generated instructions and apply role-playing techniques to rephrase instructions into different speaking styles. This is motivated by the observation that each individual user often has consistent signatures or preferences in their instructions, taking the use case of home robotic assistants as an example. We conducted extensive experiments on GSA-R2R to thoroughly evaluate our dataset and benchmark various methods, revealing key factors enabling agents to adapt to specific environments. Based on our findings, we propose a novel method, Graph-Retained DUET (GR-DUET), which incorporates memory-based navigation graphs with an environment-specific training strategy, achieving state-of-the-art results on all GSA-R2R splits.