ICLR 2026 Papers

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.

The development of foundation models for functional magnetic resonance imaging (fMRI) time series holds significant promise for predicting phenotypes related to disease and cognition. Current models, however, are often trained using a mask-and-reconstruct objective on small brain regions. This focus on low-level information leads to representations that are sensitive to noise and temporal fluctuations, necessitating extensive fine-tuning for downstream tasks. We introduce Brain-Semantoks, a self-supervised framework designed specifically to learn abstract representations of brain dynamics. Its architecture is built on two core innovations: a semantic tokenizer that aggregates noisy regional signals into robust tokens representing functional networks, and a self-distillation objective that enforces representational stability across time. We show that this objective is stabilized through a novel training curriculum, ensuring the model robustly learns meaningful features from low signal-to-noise time series. We demonstrate that learned representations enable strong performance on a variety of downstream tasks even when only using a linear probe. Furthermore, we provide comprehensive scaling analyses indicating more unlabeled data reliably results in out-of-distribution performance gains without domain adaptation.

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.

Denoising-based generative models have been significantly advanced by representation-alignment (REPA) loss, which leverages pre-trained visual encoders to guide intermediate network features. However, REPA's reliance on external visual encoders introduces two critical challenges: potential \textit{distribution mismatches} between the encoder's training data and the generation target, and the high \textit{computational costs} of pre-training. Inspired by the observation that REPA primarily aids early layers in capturing robust semantics, we propose an unsupervised alternative that avoids external visual encoder and the assumption of consistent data distribution. We introduce \textit{\textbf{DU}al-\textbf{P}ath condition \textbf{A}lignment} (\textbf{DUPA}), a novel self-alignment framework, which independently noises an image multiple times and processes these noisy latents through decoupled diffusion transformer, then aligns the derived conditions\textemdash low-frequency semantic features extracted from each path. Experiments demonstrate that DUPA achieves FID$=$1.46 on ImageNet 256$\times$256 with only 400 training epochs, outperforming all methods that do not rely on external supervision. Critically, DUPA accelerates training of its base model by 5$\times$ and inference by 10$\times$. DUPA is also model-agnostic and can be readily applied to any denoising-based generative model, showcasing its excellent scalability and generalizability.

Cryo-electron microscopy (cryo-EM) has revolutionized structural biology by enabling near-atomic-level visualization of biomolecular assemblies. However, the exponential growth in cryo-EM data throughput and complexity, coupled with diverse downstream analytical tasks, necessitates unified computational frameworks that transcend current task-specific deep learning approaches with limited scalability and generalizability. We present CryoLVM, a foundation model that learns rich structural representations from experimental density maps with resolved structures by leveraging the Joint-Embedding Predictive Architecture (JEPA) integrated with SCUNet-based backbone, which can be rapidly adapted to various downstream tasks. We further introduce a novel histogram-based distribution alignment loss that accelerates convergence and enhances fine-tuning performance. We demonstrate CryoLVM's effectiveness across three critical cryo-EM tasks: density map sharpening, density map super-resolution, and missing wedge restoration. Our method consistently outperforms state-of-the-art baselines across multiple density map quality metrics, confirming its potential as a versatile model for a wide spectrum of cryo-EM applications.

Large-scale instance-level training data is scarce, so models are typically trained on domain-specific datasets. Yet in real-world retrieval, they must handle diverse domains, making generalization to unseen data critical. We introduce ELViS, an image-to-image similarity model that generalizes effectively to unseen domains. Unlike conventional approaches, our model operates in similarity space rather than representation space, promoting cross-domain transfer. It leverages local descriptor correspondences, refines their similarities through an optimal transport step with data-dependent gains that suppress uninformative descriptors, and aggregates strong correspondences via a voting process into an image-level similarity. This design injects strong inductive biases, yielding a simple, efficient, and interpretable model. To assess generalization, we compile a benchmark of eight datasets spanning landmarks, artworks, products, and multi-domain collections, and evaluate ELViS as a re-ranking method. Our experiments show that ELViS outperforms competing methods by a large margin in out-of-domain scenarios and on average, while requiring only a fraction of their computational cost.

Classifier-free Guidance (CFG) is a widely used technique in modern diffusion models for generating high-quality samples. However, through an empirical analysis on both Gaussian mixture models with closed-form solutions and real-world data distributions, we observe a discrepancy between the suboptimal results produced by CFG and the ground truth. The model's excessive reliance on these suboptimal predictions often leads to low fidelity and semantic incoherence. To address this issue, we first empirically demonstrate that the model's suboptimal predictions can be effectively refined using sub-networks of the model itself, without requiring additional training or the integration of external modules. Building on this insight, we propose **$S^2$-Guidance ($S$tochastic $S$elf-Guidance)**, a novel method that leverages stochastic block-dropping during the denoising process to construct sub-networks. This approach effectively guides the model away from potential low-quality predictions, thereby improving sample quality. Extensive qualitative and quantitative experiments across multiple standard benchmarks for text-to-image and text-to-video generation tasks demonstrate that **$S^2$-Guidance** delivers superior performance, consistently surpassing CFG and other advanced guidance strategies. Our code will be released.

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.

Neural Collapse (NC) refers to the emergence of highly symmetric geometric structures in the representations of deep neural networks during the terminal phase of training. Despite its prevalence, the theoretical understanding of NC remains limited. Existing analyses largely ignore the role of the optimizer, thereby suggesting that NC is universal across optimization methods. In this work, we challenge this assumption and demonstrate that the choice of optimizer plays a critical role in the emergence of NC. The phenomenon is typically quantified through NC metrics, which, however, are difficult to track and analyze theoretically. To overcome this limitation, we introduce a novel diagnostic metric, NC0, whose convergence to zero is a necessary condition for NC. Using NC0, we provide theoretical evidence that NC cannot emerge under decoupled weight decay in adaptive optimizers, as implemented in AdamW. Concretely, we prove that SGD, SignGD with coupled weight decay (a special case of Adam), and SignGD with decoupled weight decay (a special case of AdamW) exhibit qualitatively different NC0 dynamics. Also, we show the accelerating effect of momentum on NC (beyond convergence of train loss) when trained with SGD, being the first result concerning momentum in the context of NC. Finally, we conduct extensive empirical experiments consisting of 3,900 training runs across various datasets, architectures, optimizers, and hyperparameters, confirming our theoretical results. This work provides the first theoretical explanation for optimizer-dependent emergence of NC and highlights the overlooked role of weight decay coupling in implicit biases of optimizers.

This paper studies a novel problem of out-of-distribution graph models merging, which aims to construct a generalized model from multiple graph models pre-trained on different domains with distribution discrepancy. This problem is challenging because of the difficulty in learning domain-invariant knowledge implicitly in model parameters and consolidating expertise from potentially heterogeneous GNN backbones. In this work, we propose a graph generation strategy that instantiates the mixture distribution of multiple domains. Then, we merge and fine-tune the pre-trained graph models via a MoE module and a masking mechanism for generalized adaptation. Our framework is architecture-agnostic and can operate without any source/target domain data. Both theoretical analysis and experimental results demonstrate the effectiveness of our approach in addressing the model generalization problem.

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.

Reinforcement learning with human-annotated data has boosted chain-of-thought reasoning in large reasoning models, but these gains come at high costs in labeled data while faltering on harder tasks. A natural next step is experience-driven learning, where models improve without curated labels by adapting to unlabeled data. We introduce REinforcement learning with Self-resTRAINt training (RESTRAIN), a self-penalizing RL framework that converts the absence of gold labels into a useful learning signal. Instead of overcommitting to spurious majority votes, RESTRAIN exploits signals from the model’s entire answer distribution: penalizing overconfident rollouts and low-consistency examples while preserving promising reasoning chains. This self-penalization mechanism integrates seamlessly into policy optimization methods such as GRPO, enabling continual self-improvement without supervision. On challenging reasoning benchmarks, RESTRAIN delivers large gains using only unlabeled data. With Qwen3-4B-Base and OctoThinker Hybrid-8B-Base, it boosts Pass@1 by up to +140.7% on AIME25, +36.2% on MMLU STEM, and +19.6% on GPQA-Diamond, nearly matching gold-label training while using no gold labels. These results demonstrate that RESTRAIN establishes a scalable path toward stronger reasoning without gold labels.

Dynamic feature transformation (the rich regime) does not always align with predictive performance (better representation), yet accuracy is often used as a proxy for richness, limiting analysis of their relationship. We propose a computationally efficient, performance-independent metric of richness grounded in the low-rank bias of rich dynamics, which recovers neural collapse as a special case. The metric is empirically more stable than existing alternatives and captures known lazy-to-rich transitions (e.g., grokking) without relying on accuracy. We further use it to examine how training factors (e.g., learning rate) relate to richness, confirming recognized assumptions and highlighting new observations (e.g., batch normalization promote rich dynamics). An eigendecomposition-based visualization is also introduced to support interpretability, together providing a diagnostic tool for studying the relationship between training factors, dynamics, and representations.

The rising cost of acquiring supervised data has driven significant interest in self-improvement for large language models (LLMs). Straightforward unsupervised signals like majority voting have proven effective in generating pseudo-labels for verifiable tasks, while their applicability to unverifiable tasks (e.g., translation) is limited by the open-ended character of responses. As a result, self-evaluation mechanisms (e.g., self-judging and entropy minimization) are predominantly used to derive pseudo-labels. However, self-evaluation relying on LLMs typically incurs high computational overhead and introduces overconfidence issues due to intrinsic biases. To address these challenges, we propose a novel self-evaluation-free approach for unverifiable tasks, designed for lightweight yet effective self-improvement. Inspired by majority voting commonly employed in verifiable tasks, we propose semantic voting as a novel mechanism that relaxes the principle of hard matching (i.e., exact matching) toward soft matching (i.e., semantic similarity). Soft matching is achieved by leveraging a lightweight sentence embedding model to quantify semantic similarity, thereby mitigating excessive computational burden and intrinsic bias-associated limitations of self-evaluation. Comprehensive experiments demonstrate that our method achieves substantial gains in computational efficiency and overall better performance than self-evaluation methods across diverse model architectures and tasks.

Despite the significant advances in Deep Reinforcement Learning (RL) observed in the last decade, the amount of training experience necessary to learn effective policies remains one of the primary concerns in both simulated and real environments. Looking to solve this issue, previous work has shown that improved efficiency can be achieved by separately modeling the agent and environment, but usually requires a supervisory signal. In contrast to RL, humans can perfect a new skill from a small number of trials and often do so without a supervisory signal, making neuroscientific studies of human development a valuable source of inspiration for RL. In particular, we explore the idea of motor prediction, which states that humans develop an internal model of themselves and of the consequences that their motor commands have on the immediate sensory inputs. Our insight is that the movement of the agent provides a cue that allows the duality between the agent and environment to be learned. To instantiate this idea, we present Ego-Foresight (EF), a self-supervised method for disentangling agent information based on motion and prediction. Our main finding is that, when used as an auxiliary task in feature learning, self-supervised agent-awareness improves the sample-efficiency and performance of the underlying RL algorithm. To test our approach, we study the ability of EF to predict agent movement and disentangle agent information. Then, we integrate EF with both model-free and model-based RL algorithms to solve simulated control tasks, showing improved sample-efficiency and performance.

Generalization beyond training data remains a central challenge in machine learning for biology. A common way to enhance generalization is self-supervised pre-training on large datasets. However, aiming to perform well on all possible proteins can limit a model’s capacity to excel on any specific one, whereas practitioners typically need accurate predictions for individual proteins they study, often not covered in training data. To address this limitation, we propose a method that enables self-supervised customization of protein language models to one target protein at a time, on the fly, and without assuming any additional data. We show that our Protein Test-Time Training (ProteinTTT) method consistently enhances generalization across different models, their sizes, and datasets. ProteinTTT improves structure prediction for challenging targets, achieves new state-of-the-art results on protein fitness prediction, and enhances function prediction on two tasks. We also demonstrate ProteinTTT on two challenging case studies. We show that customization via ProteinTTT enables more accurate antibody–antigen loop modeling and improves 19% of structures in the Big Fantastic Virus Database, delivering improved predictions where general-purpose AlphaFold2 and ESMFold struggle.

Causal representation learning has attracted significant research interest during the past few years, as a means for improving model generalization and robustness. Causal representations of interventional image pairs (also called ``actionable counterfactuals'' in the literature), have the property that only variables corresponding to scene elements affected by the intervention / action are changed between the start state and the end state. While most work in this area has focused on identifying and representing the variables of the scene under a causal model, fewer efforts have focused on representations of the interventions themselves. In this work, we show that an effective strategy for improving out of distribution (OOD) robustness is to focus on the representation of actionable counterfactuals in the latent space. Specifically, we propose that an intervention can be represented by a Causal Delta Embedding that is invariant to the visual scene and sparse in terms of the causal variables it affects. Leveraging this insight, we propose a method for learning causal representations from image pairs, without any additional supervision. Experiments in the Causal Triplet challenge demonstrate that Causal Delta Embeddings are highly effective in OOD settings, significantly exceeding baseline performance in both synthetic and real-world benchmarks.

Existing Graph Neural Networks usually learn long-distance knowledge via stacked layers or global attention, but struggle to balance cost-effectiveness and global receptive field. In this work, we break the dilemma by proposing a novel forest-based graph learning (FGL) paradigm that enables efficient long-range information propagation. Our key insight is to reinterpret message passing on a graph as transportation over spanning trees that naturally facilitates long-range knowledge aggregation, where several trees--a forest--can capture complementary topological pathways. Theoretically, we demonstrate that as edge-homophily estimates improve, the induced distribution biases towards higher-homophily trees, which enables generating a high-quality forest by refining a homophily estimator. Furthermore, we propose a linear-time tree aggregator that realizes quadratic node-pair interactions. Empirically, our framework achieves comparable results against state-of-the-art counterparts on semi-supervised node classification tasks while remaining efficient. Codes are available at \url{https://anonymous.4open.science/r/FGL/}.

Semi-supervised federated learning (SSFL) has emerged as an effective approach to leverage unlabeled data distributed across multiple data owners for improving model generalization. Existing SSFL methods typically assume that labeled and unlabeled data share the same label space. However, in realistic federated scenarios, unlabeled data often contain categories absent from the labeled set, i.e., outliers, which can severely degrade the performance of SSFL algorithms. In this paper, we address this under-explored issue, formally propose the open-set semi-supervised federated learning (OSSFL) problem, and develop the first OSSFL framework, FedOpenMatch. Our method adopts a one-vs-all (OVA) classifier as the outlier detector, equipped with logit adjustment to mitigate inlier-outlier imbalance and a gradient stop mechanism to reduce feature interference between the OVA and inlier classifiers. In addition, we introduce the logit consistency regularization loss, yielding more robust performance. Extensive experiments on standard benchmarks across diverse data settings demonstrate the effectiveness of FedOpenMatch, which significantly outperforms the baselines.