ICLR 2026 Papers

We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that the scaling limits of SGD-M coincide with those of online SGD after an appropriate time rescaling and a specific choice of step-size. However, if the step-size is kept the same between the two algorithms, SGD-M will amplify high-dimensional effects, potentially degrading performance relative to online SGD. We demonstrate our framework on two popular learning problems: Spiked Tensor PCA and Single Index Models. In both cases, we also examine online SGD with an adaptive step-size based on normalized gradients. In the high-dimensional regime, this algorithm yields multiple benefits: its dynamics admit fixed points closer to the population minimum and widens the range of admissible step-sizes for which the iterates converge to such solutions. These examples provide a rigorous account, aligning with empirical motivation, of how early preconditioners can stabilize and improve dynamics in settings where online SGD fails.

Traditional multimodal learners find unified representations for tasks like visual question answering, but rely heavily on large paired datasets. However, an overlooked yet potentially powerful question is: can one leverage auxiliary $\textit{unpaired}$ multimodal data to directly enhance representation learning in a $\textit{target}$ modality? We introduce $\textbf{UML}$: $\textbf{U}$npaired $\textbf{M}$ultimodal $\textbf{L}$earner, a modality-agnostic training paradigm in which a single model alternately processes inputs from different modalities while sharing parameters across them. This design exploits the assumption that different modalities are projections of a shared underlying reality, allowing the model to benefit from cross-modal structure without requiring explicit pairs. Theoretically, under linear data-generating assumptions, we show that unpaired auxiliary data can yield representations strictly more informative about the world than unimodal training. Empirically, we show that incorporating unpaired data that share underlying semantic information from auxiliary modalities—such as text, audio, or images—consistently improves downstream performance across diverse unimodal targets such as image and audio.

High-quality scientific illustrations are crucial for effectively communicating complex scientific and technical concepts, yet their manual creation remains a well-recognized bottleneck in both academia and industry. We present FigureBench, the first large-scale benchmark for generating scientific illustrations from long-form scientific texts. It contains 3,300 high-quality scientific text–figure pairs, covering diverse text-to-illustration tasks from scientific papers, surveys, blogs, and textbooks. Moreover, we propose AutoFigure, an agentic framework that automatically generates high-quality scientific illustrations based on long-form scientific text. Specifically, before rendering the final result, AutoFigure engages in extensive thinking, recombination, and validation to produce a layout that is both structurally sound and aesthetically refined, outputting a scientific illustration that achieves both structural completeness and aesthetic appeal. Leveraging the high-quality data from FigureBench, we conduct extensive experiments to test the performance of AutoFigure against various baseline methods. The results demonstrate that Autofigure consistently surpasses all baseline methods, producing publication-ready scientific illustrations.

As widely used neuron model in Spiking Neural Networks (SNNs), the Leaky Integrate-and-Fire (LIF) model assumes the linear summation of injected currents. However, recent studies have revealed that a biological neuron can integrate inputs nonlinearly and perform computations such as XOR while an LIF neuron cannot. To bridge this gap, we propose the Dendritic LIF (DLIF) model, which incorporates a bilinear dendritic integration rule derived from neurophysiological experiments. At the single-neuron level, we theoretically demonstrate that a DLIF neuron can capture input correlations, enabling it to perform nonlinear classification tasks. At the network level, we prove that DLIF neurons can preserve and propagate correlation structures from the input layer to the readout layer. These theoretical findings are further confirmed by our numerical experiments. Extensive experiments across diverse architectures—including ResNet, VGG, and Transformer—demonstrate that DLIF achieves state-of-the-art performance on static (CIFAR-10/100, ImageNet) and neuromorphic (DVS-Gesture, DVS-CIFAR10) benchmarks, surpassing LIF and other advanced alternatives while maintaining comparable computational cost. This work provides a biologically plausible and computationally powerful spiking neuron model, paving the way for next-generation brain-inspired computing.

Learning from multi-variate time-series with heterogeneous channel configurations remains a fundamental challenge for deep neural networks, particularly in clinical domains such as intracranial electroencephalography (iEEG), where channel setups vary widely across subjects. In this work, we introduce multi-variate parallel attention (MVPA), a novel self-attention mechanism that disentangles content, temporal, and spatial attention, enabling flexible, generalizable, and efficient modeling of time-series data with varying channel counts and configurations. We use MVPA to build MVPFormer, a generative foundation model for human electrophysiology, trained to predict the evolution of iEEG signals across diverse subjects. To support this and future efforts by the community, we release the Long-term iEEG dataset, the largest publicly available iEEG dataset to date, comprising nearly 10,000 hours of recordings from heterogeneous clinical sources. MVPFormer leverages MVPA to achieve strong generalization across subjects, demonstrating expert-level performance in several iEEG tasks. MVPFormer surpasses state-of-the-art (SOTA) Transformer baselines in seizure detection across the Long-term, the MAYO, and the FNUSA datasets, while also achieving SOTA performance on four Brain TreeBank iEEG decoding tasks (volume, pitch, onset, and speech). We further validate MVPA on standard time-series forecasting and classification tasks, where it matches or exceeds the performance of existing attention-based models. Together, our contributions establish MVPA as a general-purpose attention mechanism for heterogeneous time-series and MVPFormer as the first open-source, open-weights, and open-data iEEG foundation model with SOTA clinical performance.

Multi-Agent Systems (MAS) offer a powerful paradigm for solving complex problems through distributed reasoning and collaboration. However, their effectiveness is often hindered by the challenge of optimizing interactions among agents. To address this, we introduce AgentPO, a novel framework that directly optimizes agent collaboration. AgentPO employs reinforcement learning to train a specialized Collaborator agent, which refines its interaction policy to enhance overall system performance within a fixed multi-agent topology. We evaluated AgentPO on multiple mathematical reasoning tasks, where it consistently outperformed strong baselines. With Llama-3.2-3B-Instruct as the actor model, AgentPO achieves accuracy improvements of +1.8\% and +7.2\% over strong baselines like Role Assignment and EvoAgent, respectively. When using the larger Llama-3.1-8B-Instruct model, these gains increase to +5.6\% and +11.3\%. Crucially, AgentPO achieves these results with remarkable efficiency: it requires only 500 training samples and operates at just 7.8\% of EvoAgent's inference cost, highlighting its superior scalability and practicality.

We uncover the hidden lattice geometry of large language models (LLMs): a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding space. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction.

Continual Category Discovery (CCD) aims to leverage models trained on known categories to automatically discover novel category concepts from continuously arriving streams of unlabeled data, while retaining the ability to recognize previously known classes. Despite recent progress, existing methods often assume that data across all stages are drawn from a single, stationary distribution—a condition rarely satisfied in open-world scenarios. In this paper, we challenge this stationary-distribution assumption by introducing the Open-World Continual Category Discovery (OW-CCD) setting. We address this challenge with PRISM (\underline{P}rogressive \underline{R}obust d\underline{I}scovery under \underline{S}trea\underline{M}ing data), an adaptive continual discovery framework consisting of three key components. First, inspired by spectral properties, we develop a high-frequency-driven category separation technique that exploits high-frequency components—preserving more global information—to distinguish known from unknown categories. Second, for known categories, we design a sparse assignment matching strategy, which performs proximal sparse sample-to-label matching to assign reliable cluster labels to known-class samples. Finally, to better recognize novel categories, we propose an invariant knowledge transfer module that enforces domain-invariant category relation consistency, thereby facilitating robust knowledge transfer from known to unknown classes under domain shifts. Extensive experiments on the SSB-C and DomainNet benchmarks demonstrate that our method significantly outperforms state-of-the-art CCD approaches, highlighting its effectiveness and superiority.

Large Language Models (LLMs) trained with reinforcement learning and verifiable rewards have achieved strong results on complex reasoning tasks. Recent work extends this paradigm to a multi-agent setting, where a meta-thinking agent proposes plans and monitors progress while a reasoning agent executes subtasks through sequential conversational turns. Despite promising performance, we identify a critical limitation: lazy agent behavior, in which one agent dominates while the other contributes little, undermining collaboration and collapsing the setup to an ineffective single agent. In this paper, we first provide a theoretical analysis showing why lazy behavior naturally arises in multi-agent reasoning. We then introduce a stable and efficient method for measuring causal influence, helping mitigate this issue. Finally, as collaboration intensifies, the reasoning agent risks getting lost in multi-turn interactions and trapped by previous noisy responses. To counter this, we propose a verifiable reward mechanism that encourages deliberation by allowing the reasoning agent to discard noisy outputs, consolidate instructions, and restart its reasoning process when necessary. Extensive experiments demonstrate that our framework alleviates lazy agent behavior and unlocks the full potential of multi-agent framework for complex reasoning tasks.

Combining diverse foundation models is promising, but weight-merging is limited by mismatched architectures and closed APIs. **Trinity** addresses this with a lightweight coordinator that orchestrates collaboration among large language models (LLMs). The coordinator, comprising a compact language model ($\approx 0.6$B parameters) and a lightweight head ($\approx 10$K parameters), is optimized with an evolutionary strategy for efficient and adaptive delegation. **Trinity** processes queries over multiple turns, where at each turn the coordinator assigns one of three roles (*Thinker*, *Worker*, or *Verifier*) to a selected LLM, effectively offloading complex skill acquisition from the coordinator itself. Extensive experiments demonstrate that **Trinity** consistently outperforms individual models and existing methods in various tasks, including coding, math, reasoning, and domain knowledge, while robustly generalizing to out-of-distribution tasks. On established benchmarks, **Trinity** achieves state-of-the-art performance, including a new record of $86.2\%$ on LiveCodeBench. Theoretical and empirical analyses highlight two key factors driving this success: (1) the coordinator’s hidden-state representations provide rich contextualization of inputs, and (2) under high dimensionality and strict budget constraints, the separable Covariance Matrix Adaptation Evolution Strategy algorithm provides substantial advantages over RL, imitation learning, and random search, leveraging potential block-$\varepsilon$-separability.

The deployment of large language models (LLMs) for specialized tasks on resource-constrained edge devices like smartphones and sensors presents a significant scalability problem. To run on such hardware, these massive models must be compressed using techniques like \emph{quantization or pruning} to reduce their memory and computational footprint. Concurrently, foundational LLMs are periodically updated by their developers with new data, making their $\textit{internal parameters shift over time}$. While parameter-efficient methods like Low-Rank Adaptation (LoRA) streamline personalization by fine-tuning only a small fraction of parameters, the resulting adapters are $\textbf{brittle}$; a LoRA trained for one specific compression scheme is incompatible with another, and an adapter trained on an older base model performs poorly on an updated one. This forces a costly cycle of retraining for each unique device and every new model release. To address this, we introduce a novel framework that creates a single, universally portable adapter that is both $\textbf{\textit{(i)} compression-aware and \textit{(ii)} temporally robust}$. We achieve this by augmenting the training process with a variety of simulated compression techniques during a single run, utilizing a quantized forward pass to build resilience while maintaining a full-precision backward pass for stable gradient optimization. $\textit{This method yields a unified adapter robust to diverse compression artifacts and the subtle parameter shifts from model evolution}$. Extensive experiments on models such as $\texttt{Llama-2, Llama-3.1, Gemma-2}$, and $\texttt{Mistral}$ across reasoning benchmarks like $\textit{SQA, MATH, and GSM8K}$ demonstrate that our single adapter achieves performance comparable to specialized adapters ($\textit{e.g.}$, QLoRA) that are individually retrained for each compression scheme. Furthermore, we show this single adapter maintains its high performance when applied to future, evolved versions of the base model, eliminating the need for periodic retraining. Our work pioneers an efficient paradigm for edge AI, creating portable model patches that bridge the gap between cloud-based personalization, the diverse hardware ecosystem, and the lifecycle of evolving LLMs.

Large language model (LLM) unlearning is critical in real-world applications where it is necessary to efficiently remove the influence of private, copyrighted, or harmful data from some users. Existing utility-centric unlearning metrics (based on model utility) may fail to accurately evaluate the extent of unlearning in realistic settings such as when the forget and retain sets have semantically similar content and/or retraining the model from scratch on the retain set is impractical. This paper presents the first data-centric unlearning metric for LLMs called WaterDrum that exploits robust text watermarking to overcome these limitations. We introduce new benchmark datasets (with different levels of data similarity) for LLM unlearning that can be used to rigorously evaluate unlearning algorithms via WaterDrum.

Diffusion models have emerged as powerful priors for image editing tasks such as inpainting and local modification, where the objective is to generate realistic content that remains consistent with observed regions. In particular, zero-shot approaches that leverage a pretrained diffusion model, without any retraining, have been shown to achieve highly effective reconstructions. However, state-of-the-art zero-shot methods typically rely on a sequence of surrogate likelihood functions, whose scores are used as proxies for the ideal score. This procedure however requires vector-Jacobian products through the denoiser at every reverse step, introducing significant memory and runtime overhead. To address this issue, we propose a new likelihood surrogate that yields simple and efficient to sample Gaussian posterior transitions, sidestepping the backpropagation through the denoiser network. Our extensive experiments show that our method achieves strong observation consistency compared with fine-tuned baselines and produces coherent, high-quality reconstructions, all while significantly reducing inference cost.

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of _deep research_ --- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration.To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search—separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of the reasoning traces reveals that systems cover only about half of the necessary search queries, with proprietary models issuing broader and and deeper queries than open source models, highlighting gaps in both coverage and reasoning depth.

Long-horizon sparse-reward tasks, such as goal-conditioned or robot manipulation tasks, remain challenging in offline reinforcement learning due to the credit assignment problem. Hierarchical methods have been proposed to tackle this problem by introducing sub-goal planning guided by value functions, which in principle can shorten the effective planning horizon for both high-level and low-level planners, and thereby avoiding the credit assignment problem. However, we demonstrate that the sub-goal selection mechanism is unreliable, as it relies on value functions suffering from generalization noise, which misguides value estimation and thus leads to sub-optimal sub-goals. In this work, to provide more reliable sub-goals, we novelly introduce a reliability-driven decision mechanism, and propose Reliability-Driven HRL (RD-HRL) as the solution. The reliability-driven decision mechanism provide decision-level targets from transition regions, thereby providing noise-immune decision spaces for high-level policy, ensuring the reliability of sub-goals (which are termed as action-level targets in this paper). Comprehensive experimental results demonstrate that our approach RD-HRL outperforms baseline methods across multiple benchmarks, highlighting the competitive advantages of RD-HRL. Our code is anonymously available at \url{https://anonymous.4open.science/r/RD-HRL-243D }.

Deep reinforcement learning (RL) suffers from plasticity loss severely due to the nature of non-stationarity, which impairs the ability to adapt to new data and learn continually. Unfortunately, our understanding of how plasticity loss arises, dissipates, and can be dissolved remains limited to empirical findings, leaving the theoretical end underexplored. To address this gap, we study the plasticity loss problem from the theoretical perspective of network optimization. By formally characterizing the two culprit factors in online RL process: the non-stationarity of data distributions and the non-stationarity of targets induced by bootstrapping, our theory attributes the loss of plasticity to two mechanisms: the rank collapse of the Neural Tangent Kernel (NTK) Gram matrix and the Θ(1/k) decay of gradient magnitude. The first mechanism echoes prior empirical findings from the theoretical perspective and sheds light on the effects of existing methods, e.g., network reset, neuron recycle, and noise injection. Against this backdrop, we focus primarily on the second mechanism and aim to alleviate plasticity loss by addressing the gradient attenuation issue, which is orthogonal to existing methods. We propose Sample Weight Decay (SWD) --- a lightweight method to restore gradient magnitude, as a general remedy to plasticity loss for deep RL methods based on experience replay. In experiments, we evaluate the efficacy of SWD upon TD3, SAC with SimBa architecture in MuJoCo and DeepMind Control Suite tasks. The results demonstrate that SWD effectively alleviates plasticity loss and consistently improves learning performance across various configurations of deep RL algorithms, UTD, network architectures, and environments, achieving SOTA performance on challenging DMC Humanoid tasks.

We introduce Synthetic Bootstrapped Pretraining (SBP), a language model (LM) pretraining procedure that first learns a model of relations between documents from the pretraining dataset and then leverages it to synthesize a vast new corpus for joint training. While the standard pretraining teaches LMs to learn causal correlations among tokens within a single document, it is not designed to efficiently model the rich, learnable inter-document correlations that can potentially lead to better performance. We validate SBP by designing a compute-matched pretraining setup and pretrain a 3B-parameter model on up to 1T tokens from scratch. We find SBP consistently improves upon a strong repetition baseline and delivers a significant fraction of performance improvement attainable by an oracle upper bound with access to 20x more unique data. Qualitative analysis reveals that the synthesized documents go beyond mere paraphrases -- SBP first abstracts a core concept from the seed material and then crafts a new narration on top of it. Besides strong empirical performance, SBP admits a natural Bayesian interpretation: the synthesizer implicitly learns to abstract the latent concepts shared between related documents.

Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance. However, its standard formulation treats signals on structured spaces---such as fMRI data on brain graphs---as points in Euclidean space, overlooking the rich topological features of their domains. To address this, we introduce \emph{topological flow matching}, a topology-aware generalization of flow matching. We interpret flow matching as a framework for solving a degenerate Schrödinger bridge problem and inject topological information by augmenting the reference process with a Laplacian-derived drift. This principled modification captures the structure of the underlying domain while preserving the desirable properties of flow matching: a stable, simulation-free objective and deterministic sample paths. As a result, our framework serves as a plug-and-play replacement for standard flow matching. We demonstrate its effectiveness on diverse structured datasets, including brain fMRIs, ocean currents, seismic events, and traffic flows.

Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing a probability path that interpolates between reference and data distributions. However, these methods typically model the evolution of individual nodes and edges independently and use linear interpolations in the disjoint space of nodes/edges to build the path. This disentangled interpolation breaks the interconnected patterns of graphs, making the constructed probability path irregular and non-smooth, which causes poor training dynamics and faulty sampling convergence. To address the limitation, this paper first presents a theoretically grounded framework for probability path construction in graph generative models. Specifically, we model the joint evolution of the nodes and edges by representing graphs as connected systems parameterized by Markov random fields (MRF). We then leverage the optimal transport displacement between MRF objects to design a smooth probability path that ensures the co-evolution of graph components. Based on this, we introduce BWFlow, a flow-matching framework for graph generation that utilizes the derived optimal probability path to benefit the training and sampling algorithm design. Experimental evaluations in plain graph generation and molecule generation validate the effectiveness of BWFlow with competitive performance, better training convergence, and efficient sampling.