ICML 2026 Papers

Riemannian neural networks have proven effective in solving a variety of machine learning tasks. The key to their success lies in the development of principled Riemannian analogs of fundamental building blocks in deep neural networks (DNNs). Among those, Riemannian batch normalization (BN) layers have shown to enhance training stability and improve accuracy. In this paper, we propose BN layers for neural networks on complex domains. The proposed layers have close connections with existing Riemannian BN layers. We derive essential components for practical implementations of BN layers on some complex domains which are less studied in previous works, e.g., the Siegel disk domain. We conduct experiments on radar clutter classification, node classification, and action recognition demonstrating the efficacy of our method.

Existing dimensionality reduction methods all perform dimensionality reduction by preserving some invariant in the space before and after dimensionality reduction. This paper proposes a new dimensionality reduction invariant: preserving the invariant of the point-distributions similarity. We also design a linear and efficient method to achieve dimensionality reduction while preserving this invariant. We theoretically prove the feasibility of our method for dimensionality reduction. Furthermore, our results on benchmark datasets and single-cell expression data demonstrate the effectiveness and efficiency of the proposed method.

We study strong universal Bayes-consistency in the realizable setting for learning with general metric losses, extending classical characterizations beyond $0$-$1$ classification (Bousquet et al., 2021; Hanneke et al., 2021) and real-valued regression (Attias et al., 2024). Given an instance space $(X,\rho)$, a label space $(Y,\ell)$ with possibly unbounded loss, and a hypothesis class $H \subseteq Y^{X}$, we resolve the realizable case of an open problem presented in Tsir Cohen and Kontorovich (2022). Specifically, we find the necessary and sufficient conditions on the hypothesis class $H$ under which there exists a distribution-free learning rule whose risk converges almost surely to the best-in-class risk (which is zero) for every realizable data-generating distribution. Our main contribution is this sharp characterization in terms of a combinatorial obstruction: Similarly to Attias et al. (2023), we introduce the notion of an infinite non-decreasing $(\gamma_k)$-Littlestone tree, where $\gamma_k \to \infty$. This extends the Littlestone tree structure used in Bousquet et al. (2021) to the metric loss setting.

Influence functions are a standard tool for data debugging and unlearning, but they become impractical for **high-query** subset workloads such as large-$K$ cross-validation, repeated resampling, or interactive what-if analysis as each subset query typically requires an expensive inverse-curvature solve. We introduce **Clustered Influence Functions (CiF)**, which turns subset influence into an **amortized subset oracle**. We build a compact cache once by clustering training gradients, solve a damped Generalised Gauss-Newton system only for cluster means, and answer new subset queries by a linear recombination using cluster membership counts. This yields per-query cost of $O(Cp)$ linear in the cache size $C$, and the number of model parameters $p$. We further provide a diagnostic error bound that decomposes approximation error into a **clustering scatter** term and a **solver residual** term, making the accuracy-compute tradeoff explicit through the cache budget and solver tolerance. Evaluations across MNIST, CIFAR-10 show that CiF matches per-query influence rankings while significantly reducing the total runtime in high-$Q$ regimes, enabling influence-based workflows that are otherwise computationally prohibitive.

Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious, domain-specific cues ("shortcut learning"), which limits generalization to unseen domains after deployment. In this paper, we address this limitation through *continual learning of domain-invariant representation*. We introduce a broad class of CL methods that sequentially learn representations capturing invariant structures across domains. Our methods are motivated by the observation that such invariant structures often preserve the underlying causal mechanisms, which can reduce the risk of overfitting to domain-specific cues and thus offer better out-of-domain generalization. Our proposed CL methods combine replay-based training with a tailored sequential invariance alignment to learn---and preserve---invariant structures over time. We evaluate our methods under a deployment-oriented protocol that measures performance on unseen target domains. Across six benchmark and real-world datasets spanning vision, medicine, manufacturing, and ecology, our methods consistently outperform existing CL baselines in terms of generalization to unseen target domains. As an ablation, we further show that naïve extensions of sequential training with existing domain-invariant representation learning (DIRL) methods provide only limited benefits. To the best of our knowledge, this is the first work to develop domain-invariant representation methods for CL.

Appearance-based gaze estimation always suffers from poor generalization due to limited annotated samples and insufficient dataset diversity. Leading approaches adopt weakly supervised learning to generate large-scale pseudo-labeled data from unconstrained real-world scenarios, aiming to mitigate the domain shifts. In this work, we devise a simple yet effective semi-supervised learning architecture that leverages unlabeled data to enhance domain generalization, thereby reducing reliance on labor-intensive manual annotations. Our key insight is to impose Jacobian regularization to disentangle feature representations into discriminative subspaces dedicated to specific gaze components, such as pitch and yaw angles. We further exploit the intrinsic ordinal ranking within each subspace for contrastive learning, enabling the model to learn robust gaze representations from a small set of labeled samples and an abundance of unlabeled ones. This ultimately yields our Disentangled Subspace Contrastive Learning (DSCL) framework. Extensive experiments on multiple benchmarks verify that the proposed DSCL is plug-and-play, achieving competitive performance using only 20\%, 10\%, and even 5\% of the annotated data under both in-domain and cross-domain evaluation settings. The public code is available at \href{https://github.com/da60266/DSCL}{https://github.com/da60266/DSCL}.

Graph neural networks (GNNs) are widely used in graph learning and most architectures propagate information by passing messages between vertices. In this work, we shift our attention to GNNs that perform message passing on *edges* and introduce EB-1WL, an edge-based color-refinement test, and a corresponding architecture, EB-GNN. Our EB-GNN architecture is inspired by the classic triangle-counting algorithm of Chiba and Nishizeki and passes messages along edges and triangles. Our contributions are as follows: 1. Theoretically, we show that EB-1WL is significantly more expressive than 1WL. We provide a complete logical characterization of EB-1WL in first-order logic, along with distinguishability results via homomorphism counting. To the best of our knowledge, EB-GNN has the strongest theoretical expressivity guarantees among edge-based message-passing GNNs in the literature. 2. Unlike many GNN architectures that are more expressive than 1WL, we prove that EB-1WL and EB-GNN admit near-linear time and memory usage on practical graph learning workloads. 3. We show in experiments that EB-GNN is a highly efficient general-purpose architecture: it substantially outperforms simple MPNNs and remains competitive with task-specialized state-of-the-art GNNs at substantially lower computational cost.

Dynamic relational data arise in many machine learning applications, yet their evolving structure poses challenges for learning representations that remain consistent and interpretable over time. A common approach is to learn time varying node embeddings, whose usefulness depends on well defined stability properties across nodes and across time. We introduce Unfolded Laplacian Spectral Embedding (ULSE), a principled extension of unfolded adjacency spectral embedding to normalized Laplacian operators, a setting where stability guarantees have remained out of reach. We prove that ULSE satisfies both cross-sectional and longitudinal stability under a dynamic stochastic block model. Moreover, the Laplacian formulation yields a dynamic Cheeger-type inequality linking the spectrum of the unfolded normalized Laplacian to worst case conductance over time, providing structural insight into the embeddings. Empirical results on synthetic and real-world dynamic networks validate the theory.

Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but doing so is computationally not efficient due to the intractable log-partition term. Existing methods typically resolve this obstacle in one of two ways: by significantly restricting the transport family to obtain closed-form normalization (via Gaussian-mixture parameterizations), or by using general neural parameterizations that require simulation-based training procedures. We propose Variational Entropic Optimal Transport (VarEOT), based on an exact variational reformulation of the log-partition $\log \mathbb{E}[\exp(\cdot)]$ as a tractable minimization over an auxiliary positive normalizer. This yields a differentiable learning objective optimized with stochastic gradients and avoids the necessity of MCMC simulations during the training. We provide theoretical guarantees, including finite-sample generalization bounds and approximation results under universal function approximation. Experiments on synthetic data and unpaired image-to-image translation demonstrate competitive or improved translation quality, while comparisons within the solvers that use the same weak dual EOT objective support the benefit of the proposed optimization principle.

Large language model (LLM) activations are notoriously difficult to understand, with most existing techniques using complex, specialized methods for interpreting them. Recent work has proposed a simpler approach known as LatentQA: training LLMs to directly accept LLM activations as inputs and answer arbitrary questions about them in natural language. However, prior work has focused on narrow task settings for both training and evaluation. In this paper, we instead take a generalist perspective. We evaluate LatentQA-trained models, which we call Activation Oracles (AOs), in far out-of-distribution settings and examine how performance scales with training data diversity. We find that AOs can recover information fine-tuned into a model (e.g., biographical knowledge or malign propensities) that does not appear in the input text, despite never being trained with activations from a fine-tuned model. Our main evaluations are four downstream tasks where we can compare to prior white- and black-box techniques. We find that even narrowly-trained LatentQA models can generalize well, and that adding additional training datasets (such as classification tasks and a self-supervised context prediction task) yields consistent further improvements. Our best AOs match or exceed white-box baselines on all four tasks and the best overall baseline on 3 of 4. These results suggest that diversified training to answer natural-language queries imparts a general capability to verbalize information about LLM activations.

Incremental object detection (IOD) aims to extend detectors to new categories while retaining previously acquired knowledge. Existing methods often adopt a class incremental learning perspective, separating feature spaces to sharpen decision boundaries. However, this separation-oriented paradigm may overlook object symbiosis in detection, where co-occurrence and occlusion introduce spatial and semantic dependencies that benefit from shared representations. Ignoring these dependencies distorts the shared representations, exacerbates confusion between old and new classes, and accelerates catastrophic forgetting. To address this, we propose Symbiosis-Inspired Knowledge Distillation (SIKD), which explicitly leverages object symbiosis at two complementary levels. Spatial Symbiosis Distillation (SpSD) focuses on symbiotic regions where the old model responds with high overlap to objects in the new task. It preserves generalizable old class cues, suppresses class-specific bias and redundancy, and distills the refined evidence to the new model at matched spatial locations with slot-aligned supervision. Semantic Symbiosis Distillation (SeSD) maintains class level structure by forming confidence weighted prototypes for old classes and aligning their inter class soft ranks over the old class logits, which stabilizes the semantic topology during adaptation. Extensive experiments demonstrate the effectiveness and superiority of the proposed method.

The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC). For $K$-armed bandits with a unique best arm, the optimal sample complexities for both settings have been settled down and they match up to logarithmic factors. This prompts an interesting research question about the generic, potentially structured BAI problems: is FB harder than FC or the other way around? In this paper, we show that FB is no harder than FC up to logarithmic factors. We do this constructively: we propose a novel algorithm called FC2FB (fixed confidence to fixed budget), which is a meta algorithm that takes in an FC algorithm $\mathcal{A}$ and turn it into an FB algorithm. We prove that FC2FB enjoys a sample complexity that matches, up to logarithmic factors, that of the sample complexity of $\mathcal{A}$. This means that the optimal FC sample complexity is an upper bound of the optimal FB sample complexity up to logarithmic factors. Our result not only reveals a fundamental relationship between FB and FC, but also has a significant implication: FC2FB combined with existing state-of-the-art FC algorithms, leads to improved sample complexity for a number of FB problems.

This paper presents UniFast-HGR, a scalable surrogate for Hirschfeld--Gebelein--R\'enyi (HGR) maximal correlation in high-dimensional multimodal learning. The method replaces explicit covariance whitening with centered and $\ell_2$-normalized cosine alignment, rewrites the covariance interaction in local-batch Gram space, and removes invariant diagonal self-correlation through Trivial Spectrum Suppression (TSS). This reformulation preserves the standardized dependence-maximization target of HGR-style learning while replacing the finite-sample whitening estimator with a differentiable local-batch objective whose dominant structural cost is $O(m^2K)$ for local batch size $m$ and feature dimension $K$. OptFast-HGR further reduces the practical memory burden by estimating the off-diagonal structural term through stochastic projection. Experiments across retrieval, image classification, remote sensing segmentation, and multimodal emotion recognition show consistent gains over covariance-based HGR/CCA variants and contrastive or neural MI-estimator objectives on strong multimodal backbones, while microbenchmarks confirm stable behavior at extreme feature dimensions.

Contrastive learning has become a leading paradigm for self-supervised representation learning, yet the conditions under which it recovers meaningful latent geometry remain incompletely understood. We develop a measure-theoretic framework formalizing the diversity condition, a support requirement on positive-pair sampling that is necessary for isometric latent recovery. We show that in the standard full-support von Mises-Fisher setting implies the satisfaction of the diversity condition and global minimizers recover latent geometry up to orthogonal transformation, while restricted conditionals can make non-orthogonal maps attain strictly lower asymptotic contrastive loss. We introduce a support-corrected Information Noise Contrastive Estimation (InfoNCE) variant as a theoretical fix: this correction makes orthogonal latent space recovery achievable but does not uniquely select it. Experiments on synthetic benchmarks validate the identifiability predictions, and CIFAR-10 experiments are consistent with the qualitative prediction that architectural inductive bias becomes more important when sampling diversity is limited. Together, our results clarify how sampling mechanisms and encoder inductive bias interact in contrastive representation learning.

Imbalanced Domain Generalization (IDG) focuses on mitigating both *domain and label shifts*, both of which fundamentally shape the model's decision boundaries, particularly under heterogeneous long-tailed distributions across domains. Despite its practical significance, it remains underexplored, primarily due to the *technical* complexity of handling their entanglement and the paucity of *theoretical* foundations. In this paper, we begin by *theoretically* establishing the generalization bound for IDG, highlighting the role of posterior discrepancy and decision margin. This bound motivates us to focus on directly steering decision boundaries, marking a clear departure from existing methods. Then, we *technically* propose a novel Negative-Dominant Contrastive Learning (NDCL) for IDG to enhance discriminability while enforce posterior consistency across domains. Specifically, inter-class decision-boundary separation is enhanced by placing greater emphasis on negatives as the primary signal in our contrastive learning, naturally amplifying gradient signals for minority classes to avoid the decision boundary being biased toward majority classes. Intra-class compactness is encouraged through a re-weighted cross-entropy strategy, and posterior consistency across domains is enforced through a prediction-central alignment strategy. Finally, rigorous yet challenging experiments on benchmarks validate the effectiveness of our NDCL. The code is available at https://github.com/Alrash/NDCL.

Knowledge Distillation (KD) promises to bridge the gap between the high computational costs of Transformer-based models and the expressiveness limitations of linear models in long-term time series forecasting. Many existing time series distillation methods inherit the computer vision paradigm, constraining student models by minimizing point-wise prediction matching (output-level distillation) errors. However, blindly mimicking teacher predictions, which can be uncertain, may induce negative transfer. To address this, we propose Dynamic Structural Distillation (DSD), a robust framework that goes beyond the prediction-matching paradigm. First, we design LMP-Net, leveraging manifold expansion to project features into a high-dimensional latent space, alleviating the expressiveness bottleneck while preserving lightweight inference. Second, to address token–point architectural mismatch, we propose Dual Manifold Alignment, employing Similarity-Preserving Knowledge Distillation (SPKD) and Optimal Transport (OT) to align features at the topological and geometric levels, respectively. Finally, we introduce Regime-Aware Adaptive Distillation (RAAD) to reduce the risk of teacher misguidance via a dataset-level regime prior and a confidence-based adaptive gating mechanism. Extensive experiments on five benchmarks show that DSD is compatible with diverse teacher architectures, improves lightweight students across data regimes, and achieves a favorable accuracy–efficiency trade-off. Code is available at https://github.com/jyh0526/DSD.

Vision-Language Models (VLMs) perform well on commonsense reasoning tasks but struggle with visual spatial reasoning. Most existing solutions introduce extra 3D prior inputs or external spatial encoders, which increase complexity and degrade the underlying VLMs' general-purpose capabilities after spatial fine-tuning. To this end, we propose a parameter-efficient \textit{\textbf{Spatio}-vision \textbf{L}anguage \textbf{M}odels (SpatioLM)}, that enhances spatial intelligence without extra 3D prior inputs or third-party spatial encoders. Concretely, we design a plug-and-play and non-invasive spatio-vision module that elicits the spatial knowledge inherent in VLMs. Furthermore, we innovatively leverage pseudo depth and camera information as supervision to guide the model in learning physically coherent representations. Extensive experiments show that SpatioLM achieves significant improvements in diverse tasks, including spatial perception and understanding while effectively limiting the degradation of general capabilities. Notably, the model achieves an impressive score of 71.6 on the VSI-Bench (the first model to surpass 70). In addition, it attains competitive performance when transferred to embodied manipulation tasks.

Features of the same sample generated by different pretrained models often exhibit inherently distinct feature distributions. Learning invariant representations from large-scale unlabeled visual data in a fully unsupervised transfer manner remains a significant challenge. In this paper, we propose a multiview self-representation learning (MSRL) method in which invariant representations are learned by exploiting the self-representation property of features across heterogeneous views. The features are derived from large-scale unlabeled visual data through transfer learning with various pretrained models and are referred to as heterogeneous multiview data. We introduce an information-passing mechanism that relies on self-representation learning to support feature aggregation over the outputs of the linear model. Moreover, an assignment probability distribution consistency scheme is presented to guide multiview self-representation learning by exploiting complementary information across different views. Consequently, representation invariance across different linear models is enforced through this scheme. Additionally, we provide a theoretical analysis of the assignment probability distribution consistency and the incremental views. Extensive experiments demonstrate that the proposed MSRL method consistently outperforms several state-of-the-art approaches.

As large language models are increasingly deployed in high-stakes settings, there is a growing need for tools that audit not only model outputs but also the internal computations that produce them. Circuit analysis is a central approach in mechanistic interpretability, but it is typically target-conditioned, explaining a single prompt paired with a chosen completion. This target-conditioned setup can obscure heterogeneity across a model's continuation distribution. We introduce distribution-level unsupervised feature discovery, which clusters sampled continuations using both semantic content and sequence-level mechanistic attributions, without manually specifying target outputs. Our method represents each continuation with a semantic embedding and a prefix-to-continuation attribution signature, then optimizes a rate-distortion objective that trades off semantic coherence, mechanistic consistency, and cluster granularity. Across clustering and steering analyses, the discovered clusters expose continuation modes that single-view baselines miss and provide interventional evidence that cluster signatures correspond to actionable mechanistic factors. Overall, our approach complements circuit analysis and behavioral evaluation by providing a scalable audit of the mechanisms underlying a model’s continuation distribution.