ICLR 2026 Papers

Real-world out-of-distribution (OOD) data exhibit broad, continually evolving distributions, rendering reliance solely on in-distribution (ID) data insufficient for robust detection. Consequently, methods leveraging auxiliary Outlier Exposure (OE) data have emerged, substantially enhancing generalization by jointly fine-tuning models on ID and large-scale OE data. However, many existing approaches primarily enforce orthogonality between ID and OE features while pushing OE predictions toward near-uniform, low-confidence scores, thus overlooking the controllability of representation geometry. We propose Vast Predefined Classifiers (VPC), which constructs a pre-specified Orthogonal Equiangular Feature Space (OEFS) to explicitly separate ID and OOD representations while capturing the rich variability of OOD features. We employ evidential priors to align ID features with their class-specific Equiangular Basic Vectors (EBVs), thereby preserving ID performance. In parallel, a new VEBV loss encourages OE features to explore the subspace spanned by Vast EBVs (VEBVs), enabling a rich characterization of diverse OOD patterns. This dual optimization, coupled with the prescribed geometric representation space, promotes optimal orthogonality between ID and OOD representations. Furthermore, we introduce the VPC Score, a discriminative metric based on the L2 activation intensity of features over the predefined classifiers. Extensive experiments across diverse OOD settings and training paradigms on benchmarks including CIFAR-10/100 and the ImageNet-1k, demonstrate strong and robust performance, validating VPC's effectiveness.

Tasks ranging from sleep staging to clinical diagnosis traditionally rely on standard polysomnography (PSG) devices, bedside monitors and wearable devices, which capture diverse nocturnal biosignals (e.g., EEG, EOG, ECG, SpO$_2$). However, heterogeneity across devices and frequent sensor dropout pose significant challenges for unified modelling of these multimodal signals. We present sleep2vec, a foundation model for diverse and incomplete nocturnal biosignals that learns a shared representation via cross-modal alignment. sleep2vec is contrastively pre-trained on 42,249 overnight recordings spanning nine modalities using a Demography, Age, Site & History-aware InfoNCE objective that incorporates physiological and acquisition metadata (e.g., age, gender, recording site) to dynamically weight negatives and mitigate cohort-specific shortcuts. On downstream sleep staging and clinical outcome assessment, sleep2vec consistently outperforms strong baselines and remains robust to any subset of available modalities and sensor dropout. We further characterize, to our knowledge for the first time, scaling laws for nocturnal biosignals with respect to modality diversity and model capacity. Together, these results show that unified cross-modal alignment, coupled with principled scaling, enables label-efficient, general-purpose modelling of real-world nocturnal biosignals.

In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional (e.g., 4096), incurring substantial costs in storage, memory, and inference latency. To address these, Contrastive Sparse Representation (CSR) is recently proposed as a promising direction, mapping dense embeddings into high-dimensional but $k$-sparse vectors, in contrast to compact dense embeddings such as Matryoshka Representation Learning (MRL). Despite its promise, CSR suffers severe degradation in the ultra-sparse regime (e.g., $k \leq 4$), where over 80\% of neurons remain inactive, leaving much of its efficiency potential unrealized. In this paper, we introduce CSRv2, a principled training approach designed to make ultra-sparse embeddings viable. CSRv2 stabilizes sparsity learning through progressive $k$-annealing, enhances representational quality via supervised contrastive objectives, and ensures end-to-end adaptability with full backbone finetuning. CSRv2 reduces dead neurons from 80\% to 20\% and delivers a 14\% accuracy gain at $k=2$, bringing ultra-sparse embeddings on par with CSR at $k=8$ and MRL at 32 dimensions, all with only two active features. While maintaining comparable performance, CSRv2 delivers a 7$\times$ speedup over MRL, and yields up to 300$\times$ improvements in compute and memory efficiency relative to dense embeddings in e5-mistral-7b-instruct-based text representation. Extensive experiments across text (MTEB, multiple state-of-the-art LLM embeddings (Qwen and e5-Mistral-7B), SPLADEv3, GraphRAG) and vision (ImageNet-1k) demonstrate that CSRv2 makes ultra-sparse embeddings practical without compromising performance, where CSRv2 achieves 7\%/4\% improvement over CSR when $k=4$ and further increases this gap to 14\%/6\% when $k=2$ in text/vision representation. By making extreme sparsity viable, CSRv2 broadens the design space for large-scale, real-time, and edge-deployable AI systems where both embedding quality and efficiency are critical. Code is available at https://github.com/Y-Research-SBU/CSRv2.

Multi-view clustering achieves outstanding performance but relies on the assumption of complete multi-view samples. However, certain views may be partially unavailable due to failures during acquisition or storage, resulting in distribution shifts across views. Although some incomplete multi-view clustering (IMVC) methods have been proposed, they still confront the following limitations: 1) Missing-view data imputation methods increase the unnecessary computational complexity; 2) Consensus representation imputation methods always ignore the inter-view distribution bias due to missing views. To tackle these issues, we propose a novel IMVC based on projection debiasing and denoising (PDD). Specifically, it utilizes the unbiased projection learned from complete views to refine the biased projection learned from data with missing views. Additionally, we introduce a robust contrastive learning for consensus projection to mitigate cluster collapse risk induced by misalignment noise. Comprehensive experiments demonstrate that PDD achieves superior performance compared with state-of-the-art methods.

Contrastive learning has been at the bedrock of unsupervised learning in recent years, allowing training with massive unlabeled data for both task-specific and general (foundation) models. A prototypical loss in contrastive training is InfoNCE and its variants. In this paper we show that the embedding of the features which emerge from InfoNCE training can be well approximated by a multivariate Gaussian distribution. We justify this claim by taking two approaches. First, we show that under certain alignment and concentration assumptions, finite projections of a high dimensional representation approach multivariate Gaussian distribution, as the representation dimensions approach infinity. Next, under less strict assumptions, we show that adding a small regularization term (which vanishes asymptotically) that promotes low feature norm and high feature entropy, we reach similar asymptotic results. We demonstrate experimentally, in a synthetic setting, CIFAR-10 and on pretrained foundation models, that the features indeed follow almost precise Gaussian distribution. One can use the Gaussian model to easily derive analytic expressions in the representation space and to obtain very useful measures, such as likelihood, data entropy and mutual information. Hence, we expect such theoretical grounding to be very useful in various applications involving contrastive learning.

We propose an accelerated exact $k$-means algorithm, Angle $k$-means. As its name suggests, the algorithm mainly leverages angular relationships between data points and cluster centers to reduce computational overhead. Although grounded in straightforward geometric principles, it delivers substantial performance improvements in empirical evaluations. In contrast to existing acceleration techniques, our model introduces no new hyperparameters, preserving full compatibility with standard $k$-means. Theoretical analysis shows that Angle $k$-means maintains linear time complexity with respect to both sample size and dimensionality, while empirical evaluations on diverse real-world datasets demonstrate significant speedup over state-of-the-art algorithms such as ball $k$-means and Exp-ns.

Model merging, which combines multiple domain-specialized experts into a single model, offers a practical path to endow Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) with broad capabilities without the cost of joint training or serving many models. However, training-free methods rely on hand-tuned coefficients, whereas training-based methods primarily align parameters rather than downstream task behavior and typically treat all layers uniformly, ignoring inter-layer heterogeneity. We introduce Expert Merging, a training-light method that learns a small set of layer-wise coefficients using only unlabeled calibration data. The coefficients are optimized to explicitly align the merged model’s hidden states and logits with those of the corresponding experts, with a coefficient regularizer for stability and task-weighted losses for controllable trade-offs. To capture inter-layer variation, Expert Merging++ augments this design with importance-guided chunking: a normalized layer-importance metric, derived from learned coefficients, task-vector magnitudes, and parameter counts, allocates more chunk-wise coefficients to high-importance layers while keeping low-importance layers lightweight. The result is a label-free, parameter-efficient, and scalable approach to multi-expert model merging across LLMs and MLLMs. Across MLLM backbones (InternVL and Qwen2-VL) and the LLM backbone (Mistral), our method surpasses strong training-free and training-based merging baselines, with Expert Merging++ delivering further gains and, in some cases, even exceeding supervised Mixture Training. Our code is available at https://anonymous.4open.science/r/ExpertMeging and in the supplementary materials.

We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve, particularly conservation laws whose physically relevant solutions contain shocks and discontinuities. FV methods are widely used for their mathematical properties: convergence to entropy solutions, flow conservation, or total variation diminishing, but often lack accuracy and flexibility in complex settings. Neural Finite Volume addresses these limitations by learning update rules over extended spatial and temporal stencils while preserving conservation structure. It supports both supervised training on solution data (NFV) and unsupervised training via weak-form residual loss (UNFV). Applied to first-order conservation laws, (U)NFV achieves up to 10x lower error than Godunov's method, outperforms ENO/WENO, and rivals discontinuous Galerkin solvers with lower implementation burden. On traffic modeling problems, both from PDEs and from experimental highway data, (U)NFV captures nonlinear wave dynamics with significantly higher fidelity and scalability than traditional FV approaches.

Computed Tomography (CT) plays a vital role in inspecting the internal structures of industrial objects. Furthermore, achieving high-quality CT reconstruction from sparse views is essential for reducing production costs. While classic implicit neural networks have shown promising results for sparse reconstruction, they are unable to leverage shape priors of objects. Motivated by the observation that numerous industrial objects exhibit rectangular structures, we propose a novel \textbf{N}eural \textbf{A}daptive \textbf{B}inning (\textbf{NAB}) method that effectively integrates rectangular priors into the reconstruction process. Specifically, our approach first maps coordinate space into a binned vector space. This mapping relies on an innovative binning mechanism based on differences between shifted hyperbolic tangent functions, with our extension enabling rotations around the input-plane normal vector. The resulting representations are then processed by a neural network to predict CT attenuation coefficients. This design enables end-to-end optimization of the encoding parameters---including position, size, steepness, and rotation---via gradient flow from the projection data, thus enhancing reconstruction accuracy. By adjusting the smoothness of the binning function, NAB can generalize to objects with more complex geometries. This research provides a new perspective on integrating shape priors into neural network-based reconstruction. Extensive experiments demonstrate that NAB achieves superior performance on two datasets.

Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (\textit{RoPE}) encode positions through \textit{fixed-angle} rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce \textit{Selective RoPE}, an \textit{input-dependent} rotary embedding mechanism, that generalizes \textit{RoPE}, and enables rotation in \textit{arbitrary angles} for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with \textit{Selective RoPE}, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.

Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by (Steck, 2020), use quadratic loss during training. However, the original EDLAE only provides closed-form solutions for the hyperparameter choice $b = 0$, which limits its capacity. In this work, we generalize EDLAE objective function into a Decoupled Expected Quadratic Loss (DEQL). We show that DEQL simplifies the process of deriving EDLAE solutions and reveals solutions in a broader hyperparameter range $b > 0$, which were not derived in Steck’s original paper. Additionally, we propose an efficient algorithm based on Miller’s matrix inverse theorem to ensure the computational tractability for the $b > 0$ case. Empirical results on benchmark datasets show that the $b > 0$ solutions provided by DEQL outperform the $b = 0$ EDLAE baseline, demonstrating that DEQL expands the solution space and enables the discovery of models with better testing performance.

Vision Foundation Models (VFMs) have achieved remarkable success when applied to various downstream 2D tasks. Despite their effectiveness, they often exhibit a critical lack of 3D awareness. To this end, we introduce Splat and Distill, a framework that instills robust 3D awareness into 2D VFMs by augmenting the teacher model with a fast, feed-forward 3D reconstruction pipeline. Given 2D features produced by a teacher model, our method first lifts these features into an explicit 3D Gaussian representation, in a feedforward manner. These 3D features are then "splatted" onto novel viewpoints, producing a set of novel 2D feature maps used to supervise the student model, "distilling" geometrically grounded knowledge. By replacing slow per-scene optimization of prior work with our feed-forward lifting approach, our framework avoids feature-averaging artifacts, creating a dynamic learning process where the teacher’s consistency improves alongside that of the student. We conduct a comprehensive evaluation on a suite of downstream tasks, including monocular depth estimation, surface normal estimation, multi-view correspondence, and semantic segmentation. Our method significantly outperforms prior works, not only achieving substantial gains in 3D awareness but also enhancing the underlying semantic richness of 2D features. Our project page and code are available [here](https://davidshavin4.github.io/Splat-and-Distill/)

Model collapse occurs when generative models degrade after repeatedly training on their own synthetic outputs. We study this effect in overparameterized linear regression in a setting where each iteration mixes fresh real labels with synthetic labels drawn from the model fitted in the previous iteration. We derive precise generalization error formulae for minimum-$\ell_2$-norm interpolation and ridge regression under this iterative scheme. Our analysis reveals intriguing properties of the optimal mixing weight that minimizes long-term prediction error and provably prevents model collapse. For instance, in the case of min-$\ell_2$-norm interpolation, we establish that the optimal real-data proportion converges to the reciprocal of the golden ratio for fairly general classes of covariate distributions. Previously, this property was known only for ordinary least squares, and additionally in low dimensions. For ridge regression, we further analyze two popular model classes -- the random-effects model and the spiked covariance model -- demonstrating how spectral geometry governs optimal weighting. In both cases, as well as for isotropic features, we uncover that the optimal mixing ratio should be at least one-half, reflecting the necessity of favoring real-data over synthetic. We study three additional settings: (i) where real data is fixed and fresh labels are not obtained at each iteration, (ii) where covariates vary across iterations but fresh real labels are available each time, and (iii) where covariates vary with time but only a fraction of them receive fresh real labels at each iteration. Across these diverse settings, we characterize when model collapse is inevitable and when synthetic data improves learning. We validate our theoretical results with extensive simulations.

Recent 3D generative models produce high-quality textures for 3D mesh objects. However, they commonly rely on the heavy assumption that input 3D meshes are accompanied by manual mesh parameterization (UV mapping), a manual task that requires both technical precision and artistic judgment. Industry surveys show that this process often accounts for a significant share of asset creation, creating a major bottleneck for 3D content creators. Moreover, existing automatic methods often ignore two perceptually important criteria: (1) semantic awareness (UV charts should align semantically similar 3D parts across shapes) and (2) visibility awareness (cutting seams should lie in regions unlikely to be seen). To overcome these shortcomings and to automate the mesh parameterization process, we present an unsupervised differentiable framework that augments standard geometry-preserving UV learning with semantic- and visibility-aware objectives. For semantic-awareness, our pipeline (i) segments the mesh into semantic 3D parts, (ii) applies an unsupervised learned per-part UV-parameterization backbone, and (iii) aggregates per-part charts into a unified UV atlas. For visibility-awareness, we use ambient occlusion (AO) as an exposure proxy and back-propagate a soft differentiable AO-weighted seam objective to steer cutting seams toward occluded regions. By conducting qualitative and quantitative evaluations against state-of-the-art methods, we show that the proposed method produces UV atlases that better support texture generation and reduce perceptible seam artifacts compared to recent baselines. We will make our implementation code publicly available upon acceptance of the paper.

Evaluating machine unlearning remains challenging, as existing methods typically require retraining reference models or performing membership inference attacks—both rely on prior access to training configuration or supervision label, making them impractical in realistic scenarios. Motivated by the fact that most unlearning algorithms remove a small, random subset of the training data, we propose a subset-level evaluation framework based on statistical independence. Specifically, we design a tailored use of the Hilbert–Schmidt Independence Criterion to assess whether the model outputs on a given subset exhibit statistical dependence, without requiring model retraining or auxiliary classifiers. Our method provides a simple, standalone evaluation procedure that aligns with unlearning workflows. Extensive experiments demonstrate that our approach reliably distinguishes in-training from out-of-training subsets and clearly differentiates unlearning effectiveness, even when existing evaluations fall short.

Graph neural networks (GNNs) are the standard for learning on graphs, yet they have limited expressive power, often expressed in terms of the Weisfeiler-Leman (WL) hierarchy or within the framework of first-order logic. In this context, topological neural networks (TNNs) have recently emerged as a promising alternative for graph representation learning. By incorporating higher-order relational structures into message-passing schemes, TNNs offer higher representational power than traditional GNNs. However, a fundamental question remains open: _what is the logical expressiveness of TNNs?_ Answering this allows us to characterize precisely which binary classifiers TNNs can represent. In this paper, we address this question by analyzing isomorphism tests derived from the underlying mechanisms of general TNNs. We introduce and investigate the power of higher-order variants of WL-based tests for combinatorial complexes, called $k$-CCWL test. In addition, we introduce the topological counting logic $TC_{k}$, an extension of standard counting logic featuring a novel pairwise counting quantifier $\exists^{N}(x_i,x_j) \varphi(x_i,x_j),$ which explicitly quantifies pairs $(x_i, x_j)$ satisfying property $\varphi$. We rigorously prove the exact equivalence: $\text{k-CCWL} \equiv \text{TC}_{k{+}2} \equiv \text{Topological }(k{+}2)\text{-pebble game}.$ These results establish a logical expressiveness theory for TNNs.

General continual learning (GCL) challenges intelligent systems to learn from single-pass, non-stationary data streams without clear task boundaries. While recent advances in continual parameter-efficient tuning (PET) of pretrained models show promise, they typically rely on multiple training epochs and explicit task cues, limiting their effectiveness in GCL scenarios. Moreover, existing methods often lack targeted design and fail to address two fundamental challenges in continual PET: how to allocate expert parameters to evolving data distributions, and how to improve their representational capacity under limited supervision. Inspired by the fruit fly's hierarchical memory system characterized by sparse expansion and modular ensembles, we propose FlyPrompt, a brain-inspired framework that decomposes GCL into two subproblems: expert routing and expert competence improvement. FlyPrompt introduces a randomly expanded analytic router for instance-level expert activation and a temporal ensemble of output heads to dynamically adapt decision boundaries over time. Extensive theoretical and empirical evaluations demonstrate FlyPrompt's superior performance, achieving up to 11.23%, 12.43%, and 7.62% gains over state-of-the-art baselines on CIFAR-100, ImageNet-R, and CUB-200, respectively. Our source code is available at https://github.com/AnAppleCore/FlyGCL.

Recent advances in diffusion transformers have empowered video generation models to generate high-quality video clips from texts or images. However, world models with the ability to predict long-horizon futures from past observations and actions remain underexplored, especially for general-purpose scenarios and various forms of actions. To bridge this gap, we introduce Astra, an interactive general world model that generates real-world futures for diverse scenarios (e.g., autonomous driving, robot grasping) with precise action interactions (e.g., camera motion, robot action). We propose an autoregressive denoising architecture and use temporal causal attention to aggregate past observations and support streaming outputs. We use a noise-augmented history memory to avoid over-reliance on past frames to balance responsiveness with temporal coherence. For precise action control, we introduce an action-aware adapter that directly injects action signals into the denoising process. We further develop a mixture of action experts that dynamically route heterogeneous action modalities, enhancing versatility across diverse real-world tasks such as exploration, manipulation, and camera control. Astra achieves interactive, consistent, and general long-term video prediction and supports various forms of interactions. Experiments across multiple datasets demonstrate the improvements of Astra in fidelity, long-range prediction, and action alignment over existing state-of-the-art world models.

Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing bespoke architectures for each group of symmetries, limiting scalability and preventing knowledge transfer across related symmetries. In the case of the space groups—symmetries critical to modeling crystalline solids in materials science and condensed matter physics—this challenge is particularly salient as there are 230 such groups in three dimensions. In this work we present a new approach to such crystallographic symmetries by developing a single machine learning architecture that is capable of adapting its weights automatically to enforce invariance to any input space group. Our approach is based on constructing symmetry-adapted Fourier bases through an explicit characterization of constraints that group operations impose on Fourier coefficients. Encoding these constraints into a neural network layer enables weight sharing across different space groups, allowing the model to leverage structural similarities between groups and overcome data sparsity when limited measurements are available for specific groups. We demonstrate the effectiveness of this approach in achieving competitive performance on material property prediction tasks and performing zero-shot learning to generalize to unseen groups.