ICLR 2026 Papers

Loss curves are smooth during most of model training, so visible discontinuities stand out as possible conceptual breakthroughs. Studying these breakthroughs enables a deeper understanding of learning dynamics, but only when they are properly identified. This paper argues that similar breakthroughs occur frequently throughout training but they are obscured by a loss metric that collapses all variation into a single scalar. To find these hidden transitions, we introduce POLCA, a method for decomposing changes in loss along arbitrary bases of the low-rank training subspace. We use our method to identify clusters of samples that share similar changes in loss during training, disaggregating the overall loss into that of smaller groups of conceptually similar data. We validate our method on synthetic arithmetic and natural language tasks, showing that POLCA recovers clusters that represent interpretable breakthroughs in the model's capabilities. We demonstrate the promise of these hidden phase transitions as a tool for unsupervised interpretability.

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs, cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

Dense retrievers play a vital role in accessing external and specialized knowledge to augment language models (LMs). Training dense retrievers typically requires annotated query-document pairs, which are costly to create and scarce in specialized domains (e.g., code) or in complex settings (e.g., requiring reasoning). These practical challenges have sparked growing interest in self-supervised retriever learning. Since LMs are trained to capture token-level dependencies through a self-supervised learning objective (i.e., next token prediction), we can analogously cast retrieval as learning dependencies among chunks of tokens. This analogy naturally leads to the question: How can we adapt self‑supervised learning objectives in the spirit of language modeling to train retrievers? To answer this question, we introduce Revela, a unified and scalable training framework for self-supervised retriever learning via language modeling. Revela models semantic dependencies among documents by conditioning next token prediction on local and cross-document context through an in-batch attention mechanism. This attention is weighted by retriever-computed similarity scores, enabling the retriever to be optimized as part of language modeling. We evaluate Revela on domain-specific (CoIR), reasoning-intensive (BRIGHT), and general-domain (BEIR) benchmarks across various retriever backbones. Without annotated or synthetic query-document pairs, Revela surpasses larger supervised models and proprietary APIs on both CoIR and BRIGHT. It achieves BEIR's unsupervised SoTA with ~1000x less training data and 10x less compute. Performance increases with batch size and model size, highlighting Revela's scalability and its promise for self‑supervised retriever learning.

Linear modeling methods like Mamba have been merged as the effective backbone for the 3D object detection task. However, previous Mamba-based methods utilize the bidirectional encoding for the whole non-empty voxel sequence, which contains abundant useless background information in the scenes. Though directly encoding foreground voxels appears to be a plausible solution, it tends to degrade detection performance. We attribute this to the response attenuation and restricted context representation in the linear modeling for fore-only sequences. To address this problem, we propose a novel backbone, termed Fore-Mamba3D, to focus on the foreground enhancement by modifying Mamba-based encoder. The foreground voxels are first sampled according to the predicted scores. Considering the response attenuation existing in the interaction of foreground voxels across different instances, we design a regional-to-global slide window (RGSW) to propagate the information from regional split to the entire sequence. Furthermore, a semantic-assisted and state spatial fusion module (SASFMamba) is proposed to enrich contextual representation by enhancing semantic and geometric awareness within the Mamba model. Our method emphasizes foreground-only encoding and alleviates the distance-based and causal dependencies in the linear autoregression model. The superior performance across various benchmarks demonstrates the effectiveness of Fore-Mamba3D in the 3D object detection task.

Lightweight neural networks, essential for on-device applications, often suffer from a low-frequency bias due to their constrained capacity and depth. This limits their ability to capture the fine-grained, high-frequency details (e.g., textures, edges) that are crucial for complex computer vision tasks. To address this fundamental limitation, we perform the first systematic analysis of gating mechanisms from a frequency perspective. Inspired by the convolution theorem, we show how the interplay between element-wise multiplication and non-linear activation functions within Gated Linear Units (GLUs) provides a powerful mechanism to selectively amplify high-frequency signals, thereby enriching the model's feature representations. Based on these findings, we introduce the Gating Mechanism Network (GmNet), a simple yet highly effective architecture that incorporates our frequency-aware gating principles into a standard lightweight backbone. The efficacy of our approach is remarkable: without relying on complex training strategies or architectural search, GmNet achieves a new state-of-the-art for efficient models.

With the advent of the neural network era, traditional machine learning methods have increasingly been overshadowed. Nevertheless, continuing to research about the role of geometry for learning in data science is crucial to envision and understand new principles behind the design of efficient machine learning. Linear classifiers are favored in certain tasks due to their reduced susceptibility to overfitting and their ability to provide interpretable decision boundaries. However, achieving both scalability and high predictive performance in linear classification remains a persistent challenge. Here, we propose a theoretical framework named geometric discriminant analysis (GDA). GDA includes the family of linear classifiers that can be expressed as function of a centroid discriminant basis (CDB0) - the connection line between two centroids - adjusted by geometric corrections under different constraints. We demonstrate that linear discriminant analysis (LDA) is a subcase of the GDA theoretical framework, and we show its convergence to CDB0 under certain conditions. Then, based on the GDA framework, we propose an efficient linear classifier named centroid discriminant analysis (CDA) which is defined as a special case of GDA under a 2D plane geometric constraint. CDA training is initialized starting from CDB0 and involves the iterative calculation of new adjusted centroid discriminant lines whose optimal rotations on the associated 2D planes are searched via Bayesian optimization. CDA has good scalability (quadratic time complexity) which is lower than LDA and support vectors machine (SVM) (cubic complexity). Results on 27 real datasets across classification tasks of standard images, medical images and chemical properties, offer empirical evidence that CDA outperforms other linear methods such as LDA, SVM and logistic regression (LR) in terms of scalability, performance and stability. Furthermore, we show that linear CDA can be generalized to nonlinear CDA via kernel method, demonstrating improvements on both linear CDA and kernel SVM with tests on three challenging datasets of images and chemical data. GDA general validity as a new theoretical framework may inspire the design of new classifiers under the definition of different geometric constraints, paving the way towards more deeper understanding of the role of geometry in learning from data.

Unsupervised object-centric learning models, particularly slot-based architectures, have shown great promise in decomposing complex scenes. However, their reliance on reconstruction-based training creates a fundamental conflict between the sharp, high-frequency attention maps of the encoder and the spatially consistent but blurry reconstruction maps of the decoder. We identify that this discrepancy gives rise to a vicious cycle; the noisy feature map from the encoder forces the decoder to average over possibilities and produce even blurrier outputs, while the gradient computed from blurry reconstruction maps lacks high-frequency details necessary to supervise encoder features. To break this cycle, we introduce Synergistic Representation Learning (SRL) that establishes a virtuous cycle where the encoder and decoder mutually refine one another. SRL leverages the encoder's sharpness to deblur the semantic boundary within the decoder output, while exploiting the decoder's spatial consistency to denoise the encoder's features. This mutual refinement process is stabilized by a warm-up phase with a slot regularization objective that initially allocates distinct entities per slot. By bridging the representational gap between the encoder and decoder, our approach achieves state-of-the-art results on challenging video object-centric learning benchmarks. Codes will be released.

The self-attention mechanism, at the heart of the transformer model, is able to effectively model pairwise interactions between tokens. However, numerous recent works have shown that it is unable to perform basic tasks involving detecting triples of correlated tokens, or compositional tasks where multiple input tokens need to be referenced to generate a result. Some higher-dimensional alternatives to self-attention have been proposed to address this, including higher-order attention (Sanford et al., 2023) and Strassen attention (Kozachinskiy et al., 2025), which can perform some of these polyadic tasks in exchange for slower, superquadratic running times. In this work, we define a vast class of generalizations of self-attention, which we call poly-attention mechanisms. Our mechanisms can incorporate arbitrary higher-order (tensor) computations as well as arbitrary relationship structures between the input tokens, and they include the aforementioned alternatives as special cases. We then systematically study their computational complexity and representational strength, including giving new algorithms and matching complexity-theoretic lower bounds on the time complexity of computing the attention matrix exactly as well as approximately, and tightly determining which polyadic tasks they can each perform. Our results give interesting tradeoffs between different desiderata for these mechanisms, including a tight relationship between how expressive a mechanism is, and how large the coefficients in the model may be so that the mechanism can be approximated in almost-linear time. Notably, we give a new attention mechanism which can be computed exactly in quadratic time, and which can perform function composition for any fixed number of functions. Prior mechanisms, even for just composing two functions, could only be computed in superquadratic time, and our new lower bounds show that faster algorithms for them are not possible.

Since the advent of AI, games have served as progress benchmarks. Meanwhile, imperfect-information variants of chess have existed for over a century, present extreme challenges, and have been the focus of decades of AI research. Beyond calculation needed in regular chess, they require reasoning about information gathering, the opponent’s knowledge, signaling, _etc_. The most popular variant, _Fog of War (FoW) chess_ (a.k.a. _dark chess_), has been a major challenge problem in imperfect-information game solving since superhuman performance was reached in no-limit Texas hold’em poker. We present _Obscuro_, the first superhuman AI for FoW chess. It introduces advances to search in imperfect-information games, enabling strong, scalable reasoning. Experiments against the prior state-of-the-art AI and human players---including the world's best---show that _Obscuro_ is significantly stronger. FoW chess is the largest (by amount of imperfect information) turn-based zero-sum game in which superhuman performance has been achieved and the largest game in which imperfect-information search has been successfully applied.

Reinforcement learning (RL) is crucial for aligning Vision-Language Models (VLMs), but its practical application is hampered by significant system-level bottlenecks. The typical RL pipeline, encompassing data loading, inference-based rollouts, and model updates, suffers from severe inefficiencies when applied to VLMs due to the extreme heterogeneity of multimodal data. Centralized data loading creates I/O bottlenecks with large media files, while variations in sequence length across text, image, and video inputs lead to critical load imbalance during computation, leaving expensive GPU resources underutilized. Existing systems either focus on text-only RL or employ general load-balancing techniques that are incompatible with the small-batch, iterative nature of RL training. To address these challenges, we present FlexRL, a holistic system designed to optimize the end-to-end VLM RL pipeline. FlexRL introduces two core contributions: (1) a \textbf{Decentralized Data Pipeline} that parallelizes data fetching and preprocessing across worker nodes, facilitates metadata-only scheduling on the single controller, eliminating the central bottleneck and accelerating data-intensive stages; and (2) a novel \textbf{Hybrid Sequence Sharding} mechanism that partitions sequences into fine-grained chunks. This enables sub-sequence level load balancing for both inference and training, effectively mitigating workload skew. Our evaluation on a 128-GPU cluster shows that FlexRL significantly improves training efficiency by 4.2~7.7x end-to-end speedups compared to production baselines, enabling more efficient and scalable RL for large multimodal models.

Multi-view data usually suffer from partially missing views in open scenarios, which inevitably degrades clustering performance. The incomplete multi-view clustering (IMVC) has attracted increasing attention and achieved significant success. Although existing imputation-based IMVC methods perform well, they still face one crucial limitation, i.e., view recovery and subspace representation lack explicit alignment and collaborative interaction in exploring complementarity and consistency across multiple views. To this end, this study proposes a novel IMVC method to Align collaborative view Recovery and tensorial Subspace Learning via latent representation (ARSL-IMVC). Specifically, the ARSL-IMVC infers the complete view from view-shared latent representation and view-specific estimator with Hilbert-Schmidt Independence Criterion regularizer, reshaping the consistent and diverse information intrinsically embedded in original multi-view data. Then, the ARSL-IMVC learns the view-shared and view-specific subspace representations from latent feature and recovered views, and models high-order correlations at the global and local levels in the unified low-rank tensor space. Thus, leveraging the latent representation as a bridge in a unified framework, the ARSL-IMVC seamlessly aligns the complementarity and consistency exploration across view recovery and subspace representation learning, negotiating with each other to promote clustering. Extensive experimental results on seven datasets demonstrate the powerful capacity of ARSL-IMVC in complex incomplete multi-view clustering tasks under various view missing scenarios.

\begin{abstract} Low-rank and sparse composite approximation is a natural idea to compress Large Language Models (LLMs). However, such an idea faces two primary challenges that adversely affect the performance of existing methods. The first challenge relates to the interaction and cooperation between low-rank and sparse matrices, while the second involves determining weight allocation across different layers, as redundancy varies considerably among them. To address these challenges, we propose a novel two-stage LLM compression method with the capability of global resource allocation for rank and sparsity. It is noteworthy that the overall optimization space is vast, making comprehensive optimization computationally prohibitive. Therefore, to reduce the optimization space, our first stage utilizes robust principal component analysis to decompose the weight matrices of LLMs into low-rank and sparse components, which span the low dimensional and sparse spaces containing the resultant low-rank and sparse matrices, respectively. In the second stage, we propose a probabilistic global allocation strategy to jointly identify the low-rank and sparse structures within the above two spaces. The appealing feature of our approach is its ability to automatically detect the redundancy across different layers and to manage the interaction between the sparse and low-rank components. Extensive experimental results indicate that our method significantly surpasses state-of-the-art techniques for sparsification and composite approximation.

General SVG modeling remains challenging due to fragmented datasets, limited transferability of methods across tasks, and the difficulty of handling structural complexity. In response, we leverage the strong transfer and generalization capabilities of multimodal large language models (MLLMs) to achieve unified modeling for SVG understanding, editing, and generation. We present the InternSVG family, an integrated data–benchmark–model suite. At its core is SAgoge, the largest and most comprehensive multimodal dataset for SVG tasks, encompassing both static graphics and dynamic animations. It covers icons, long-sequence illustrations, scientific diagrams, and dynamic animations, supporting tasks of varied difficulty levels and providing deeper hierarchies with richer attributes compared to previous datasets. Based on this resource, we introduce SArena, a companion benchmark with comprehensive task definitions and standardized evaluation that aligns with the domains and difficulty spectrum covered by SAgoge. Building on these foundations, we propose InternSVG, a unified MLLM for SVG understanding, editing, and generation with SVG-specific special tokens, subword-based embedding initialization, and a two-stage training strategy that progresses from short static SVGs to long-sequence illustrations and complex animations. This unified formulation induces positive transfer and improves overall performance. Experiments on \benchset and prior benchmark confirm that InternSVG achieves substantial gains and consistently outperforms leading open and proprietary counterparts.

We introduce AnyUp, a method for feature upsampling that can be applied to any vision feature at any resolution, without encoder-specific training. Existing learning-based upsamplers for features like DINO or CLIP need to be re-trained for every feature extractor and thus do not generalize to different feature types at inference time. In this work, we propose an *inference-time* feature-agnostic upsampling architecture to alleviate this limitation and improve upsampling quality. In our experiments, AnyUp sets a new state of the art for upsampled features, generalizes to different feature types, and preserves feature semantics while being efficient and easy to apply to a wide range of downstream tasks.

Machine unlearning as an emerging research topic for data regulations, aims to adjust a trained model to approximate a retrained one that excludes a portion of training data. Previous studies showed that class-wise unlearning is effective in forgetting the knowledge of a training class, either through gradient ascent on the forgetting data or fine-tuning with the remaining data. However, while these methods are useful, they are insufficient as the class label and the target concept are often considered to coincide. In this work, we expand the scope by considering the label domain mismatch and investigate three problems beyond the conventional all matched forgetting, e.g., target mismatch, model mismatch, and data mismatch forgetting. We systematically analyze the new challenges in restrictively forgetting the target concept and also reveal crucial forgetting dynamics in the representation level to realize these tasks. Based on that, we propose a general framework, namely, TARget-aware Forgetting (TARF). It enables the additional tasks to actively forget the target concept while maintaining the rest part, by simultaneously conducting annealed gradient ascent on the forgetting data and selected gradient descent on the hard-to-affect remaining data. Various experiments under our new settings are conducted to demonstrate the effectiveness of our TARF.

Steering a large language model's attention towards user-specified highlighted text is a critical capability. Existing prompt highlighting methods are incompatible with modern efficient attention mechanisms like Flash Attention due to their reliance on post-hoc matrix editing. We introduce Spectral Editing Key Amplification (SEKA), a training-free steering method that tackles this by directly editing key embeddings before attention computation. SEKA learns universal relevance subspaces offline via spectral decomposition. We extend this to Adaptive SEKA (AdaSEKA), a query-adaptive variant that uses a training-free routing mechanism to dynamically combine multiple expert subspaces based on the prompt's semantic intent. Our experiments show both methods significantly outperform strong baselines on standard steering benchmarks while adding much lower latency and memory overhead, ensuring full compatibility with optimised attention.

High-dimensional linear mappings, or linear layers, dominate both the parameter count and the computational cost of most modern deep-learning models. We introduce lookup multivariate Kolmogorov-Arnold Networks (lmKANs), which deliver a substantially better trade-off between capacity and inference cost. Our construction expresses a general high-dimensional mapping through trainable low-dimensional multivariate functions. These functions can carry dozens or hundreds of trainable parameters each, and yet it takes only a few multiplications to compute them because they are implemented as spline lookup tables. Empirically, lmKANs reduce inference FLOPs by up to 6.0× while matching the flexibility of MLPs in general high-dimensional function approximation. In another feedforward fully connected benchmark, on the tabular-like dataset of randomly displaced methane configurations, lmKANs enable more than 10× higher H100 throughput at equal accuracy. Within the framework of Convolutional Neural Networks, lmKAN-based CNNs cut inference FLOPs at matched accuracy by 1.6–2.1× and by 1.7× on the CIFAR-10 and ImageNet-1k datasets, respectively.

Contrastive learning has achieved remarkable success in self-supervised representation learning, often guided by information-theoretic objectives such as mutual information maximization. Motivated by the limitations of static augmentations and rigid invariance constraints, we propose IE-CL (Incremental-Entropy Contrastive Learning), a framework that explicitly optimizes the entropy gain between augmented views while preserving semantic consistency. Our theoretical framework reframes the challenge by identifying the encoder as an information bottleneck and proposes a joint optimization of two components: a learnable transformation for entropy generation and an encoder regularizer for its preservation. Experiments on CIFAR-10/100, STL-10, and ImageNet demonstrate that IE-CL consistently improves performance under small-batch settings. Moreover, our core modules can be seamlessly integrated into existing frameworks. This work bridges theoretical principles and practice, offering a new perspective in contrastive learning.

Despite the sustained popularity of Q-learning as a practical tool for policy determination, a majority of relevant theoretical literature deals with either constant ($\eta_t\equiv \eta$) or polynomially decaying ($\eta_t = \eta t^{-\alpha}$) learning schedules. However, it is well known the these choices suffer from either persistent bias or prohibitively slow convergence. In contrast, the recently proposed linear decay to zero (\texttt{LD2Z}: $\eta_t=\eta(1-t/n)$) schedule has shown appreciable empirical performance, but its theoretical and statistical properties remain largely unexplored, especially in the Q-learning setting. We address this gap in the literature by first considering a general class of power-law decay to zero (\texttt{PD2Z}-$\nu$: $\eta_t=\eta(1-t/n)^{\nu}$). Proceeding step-by-step, we present a sharp non-asymptotic error bound for Q-learning with \texttt{PD2Z}-$\nu$ schedule, which then is used to derive a central limit theory for a new \textit{tail} Polyak-Ruppert averaging estimator. Finally, we also provide a novel time-uniform Gaussian approximation (also known as \textit{strong invariance principle}) for the partial sum process of Q-learning iterates, which facilitates bootstrap-based inference. All our theoretical results are complemented by extensive numerical experiments. Beyond being new theoretical and statistical contributions to the Q-learning literature, our results definitively establish that \texttt{LD2Z} and in general \texttt{PD2Z}-$\nu$ achieve a best-of-both-worlds property: they inherit the rapid decay from initialization (characteristic of constant step-sizes) while retaining the asymptotic convergence guarantees (characteristic of polynomially decaying schedules). This dual advantage explains the empirical success of \texttt{LD2Z} while providing practical guidelines for inference through our results.