ICLR 2026 Papers

Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to improve running time and reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work typically projects gradients of linear layers using approaches based on Singular Value Decomposition (SVD) or QR-decomposition. Applying these techniques individually to each layer in large models is computationally expensive and incurs additional memory costs due to storing the projection matrices. In this work, we propose a computationally efficient and conceptually simple, two-step procedure to approximate SVD/QR-based gradient projections into lower-dimensional spaces by using a predefined orthogonal matrix of the Discrete Cosine Transform (DCT). We dynamically select columns from the DCT matrix based on their alignment with the gradient of each layer. The effective projection matrices are obtained via a simple matmul with the DCT matrix in $O(n^3)$ time, followed by a lightweight sorting step to identify the most relevant basis vectors. For large layers, DCT can be computed via Makhoul's $N$-point algorithm based on Fast Fourier Transform (FFT) in $O(n^2 \log(n))$ time. Due to the predefined nature of the orthogonal bases, they are computed once at the start of training. Our numerical experiments on both pre-training and fine-tuning tasks demonstrate the effectiveness of our dual strategy in approximating optimal low-rank projections, obtaining an approach with rank-independent running time that matches the performance of costly SVD/QR-based methods while achieving faster runtime and reduced memory usage by up to $25\\%$ across different model sizes.

Current AI-Generated Image (AIGI) detection approaches predominantly rely on binary classification to distinguish real from synthetic images, often lacking interpretable or convincing evidence to substantiate their decisions. This limitation stems from existing AIGI detection benchmarks, which, despite featuring a broad collection of synthetic images, remain restricted in their coverage of artifact diversity and lack detailed, localized annotations. To bridge this gap, we introduce a fine-grained benchmark towards eXplainable AI-Generated image Detection, named X-AIGD, which provides pixel-level, categorized annotations of perceptual artifacts, spanning low-level distortions, high-level semantics, and cognitive-level counterfactuals. These comprehensive annotations facilitate fine-grained interpretability evaluation and deeper insight into model decision-making processes. Our extensive investigation using X-AIGD provides several key insights: (1) Existing AIGI detectors demonstrate negligible reliance on perceptual artifacts, even at the most basic distortion level. (2) While AIGI detectors can be trained to identify specific artifacts, they still substantially base their judgment on uninterpretable features. (3) Explicitly aligning model attention with artifact regions can increase the interpretability and generalization of detectors.

*Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they typically depend on heuristics or approximations and do not offer provable guarantees over continuous input domains for the resulting circuits. In this work, we leverage recent advances in neural network verification to propose a suite of automated algorithms that yield circuits with *provable guarantees*. We focus on three types of guarantees: (1) *input domain robustness*, ensuring the circuit agrees with the model across a continuous input region; (2) *robust patching*, certifying circuit alignment under continuous patching perturbations; and (3) *minimality*, formalizing and capturing a wide array of various notions of succinctness. Interestingly, we uncover a diverse set of novel theoretical connections among these three families of guarantees, with critical implications for the convergence of our algorithms. Finally, we conduct experiments with state-of-the-art verifiers on various vision models, showing that our algorithms yield circuits with substantially stronger robustness guarantees than standard circuit discovery methods, establishing a principled foundation for provable circuit discovery.

We propose a hierarchical entity-centric framework for offline Goal-Conditioned Reinforcement Learning (GCRL) that combines subgoal decomposition with factored structure to solve long-horizon tasks in domains with multiple entities. Achieving long-horizon goals in complex environments remains a core challenge in Reinforcement Learning (RL). Domains with multiple entities are particularly difficult due to their combinatorial complexity. GCRL facilitates generalization across goals and the use of subgoal structure, but struggles with high-dimensional observations and combinatorial state-spaces, especially under sparse reward. We employ a two-level hierarchy composed of a value-based GCRL agent and a factored subgoal-generating conditional diffusion model. The RL agent and subgoal generator are trained independently and composed post hoc through selective subgoal generation based on the value function, making the approach modular and compatible with existing GCRL algorithms. We introduce new variations to benchmark tasks that highlight the challenges of multi-entity domains, and show that our method consistently boosts performance of the underlying RL agent on image-based long-horizon tasks with sparse rewards, achieving over $150$% higher success rates on the hardest task in our suite and generalizing to increasing horizons and numbers of entities. Rollout videos are provided at: https://sites.google.com/view/hecrl.

Dataset Distillation (DD) seeks to create a compact dataset from a large, real-world dataset. While recent methods often rely on heuristic approaches to balance efficiency and quality, the fundamental relationship between original and synthetic data remains underexplored. This paper revisits knowledge distillation-based dataset distillation within a solid theoretical framework. We introduce the concepts of Informativeness and Utility, capturing crucial information within a sample and essential samples in the training set, respectively. Building on these principles, we define \textit{optimal dataset distillation} mathematically. We then present InfoUtil, a framework that balances informativeness and utility in synthesizing the distilled dataset. InfoUtil incorporates two key components: (1) game-theoretic informativeness maximization using Shapley Value attribution to extract key information from samples, and (2) principled utility maximization by selecting globally influential samples based on Gradient Norm. These components ensure that the distilled dataset is both informative and utility-optimized. Experiments demonstrate that our method achieves a 6.1\% performance improvement over the previous state-of-the-art approach on ImageNet-1K dataset using ResNet-18.

Real-time voice conversion and speaker anonymization require causal, low-latency synthesis without sacrificing intelligibility or naturalness. Current systems have a core representational mismatch: content is time-varying, while speaker identity is injected as a static global embedding. We introduce a streamable speech synthesizer that aligns the temporal granularity of identity and content via a content-synchronous, time-varying timbre (TVT) representation. A Global Timbre Memory expands a global timbre instance into multiple compact facets; frame-level content attends to this memory, a gate regulates variation, and spherical interpolation preserves identity geometry while enabling smooth local changes. In addition, a factorized vector-quantized bottleneck regularizes content to reduce residual speaker leakage. The resulting system is streamable end-to-end, with <80 ms GPU latency. Experiments show improvements in naturalness, speaker transfer, and anonymization compared to SOTA streaming baselines, establishing TVT as a scalable approach for privacy-preserving and expressive speech synthesis under strict latency budgets.

Human–object–scene interactions (HOSI) generation has broad applications in embodied AI, simulation, and animation. Unlike human–object interaction (HOI) and human–scene interaction (HSI), HOSI generation requires reasoning over dynamic object–scene changes, yet suffers from limited annotated data. To address these issues, we propose a coarse‑to‑fine instruction‑conditioned interaction generation framework that is explicitly aligned with the iterative denoising process of a consistency model. In particular, we adopt a dynamic perception strategy that leverages trajectories from the preceding refinement to update scene context and condition subsequent refinement at each denoising step of consistency model, yielding consistent interactions. To further reduce physical artifacts, we introduce a bump‑aware guidance that mitigates collisions and penetrations during sampling without requiring fine‑grained scene geometry, enabling real‑time generation. To overcome data scarcity, we design a hybrid training startegy that synthesizes pseudo‑HOSI samples by injecting voxelized scene occupancy into HOI datasets and jointly trains with high‑fidelity HSI data, allowing interaction learning while preserving realistic scene awareness. Extensive experiments demonstrate that our method achieves state‑of‑the‑art performance in both HOSI and HOI generation, and strong generalization to unseen scenes. Code and datasets will be released upon acceptance.

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its dynamical properties have not yet been discussed. In this paper, we analyze the dynamics using an exact approach based on generating functional analysis. We show results on convergence properties of memory retrieval, such as the convergence time and the size of the attraction basins. Our analysis enables a quantitative evaluation of the convergence time and the storage capacity of dense associative memory, which is useful for model design. Unlike the traditional Hopfield model, the retrieval of a pattern does not act as additional noise to itself, suggesting that the structure of modern networks makes recall more robust. Furthermore, the methodology addressed here can be applied to other energy-based models, and thus has the potential to contribute to the design of future architectures.

We present a novel theoretical framework for deep reinforcement learning (RL) in continuous environments by modeling the problem as a continuous-time stochastic process, drawing on insights from stochastic control. Building on previous work, we introduce a viable model of actor–critic algorithm that incorporates both exploration and stochastic transitions. For single-hidden-layer neural networks, we show that the state of the environment can be formulated as a two time scale process: the environment time and the gradient time. Within this formulation, we characterize how the time-dependent random variables that represent the environment's state and estimate of the cumulative discounted return evolve over gradient steps in the infinite width limit of two-layer networks. Using the theory of stochastic differential equations, we derive, for the first time in continuous RL, an equation describing the infinitesimal change in the state distribution at each gradient step, under a vanishingly small learning rate. Overall, our work provides a novel nonparametric formulation for studying overparametrized neural actor-critic algorithms. We empirically corroborate our theoretical result using a toy continuous control task.

Value decomposition is a core approach for cooperative multi-agent reinforcement learning (MARL). However, existing methods still rely on a single optimal action and struggle to adapt when the underlying value function shifts during training, often converging to suboptimal policies. To address this limitation, we propose Successive Sub-value Q-learning (S2Q), which learns multiple sub-value functions to retain alternative high-value actions. Incorporating these sub-value functions into a Softmax-based behavior policy, S2Q encourages persistent exploration and enables $Q^{\text{tot}}$ to adjust quickly to the changing optima. Experiments on challenging MARL benchmarks confirm that S2Q consistently outperforms various MARL algorithms, demonstrating improved adaptability and overall performance. Our code is available at https://github.com/hyeon1996/S2Q.

Large language models (LLMs) struggle with inaccurate and outdated information, driving the emergence of knowledge editing as a lightweight alternative. Despite their effectiveness in modifying structured knowledge, existing editing methods often fail to generalize to unstructured cases, particularly those involving inherently hard-to-edit knowledge, where the original facts tend to be more resistant to change. To address this, we propose a metric, TangleScore, that quantifies the intrinsic difficulty of editing a given knowledge instance. This difficulty, in turn, strongly correlates with the model’s ability to generalize the edit to paraphrased and related prompts. Building on this insight, we introduce a TangleScore-driven method termed Purge-Imprint Patch Editing (PIPE), an editing framework that adaptively modulates the purge and imprint of knowledge based on TangleScore of the target knowledge to be edited, thus adjusting the editing strength to match the instance's difficulty, thereby enabling more precise and effective model updates. Experiments applying PIPE to four LLMs of varying sizes on two unstructured knowledge editing datasets show that PIPE significantly outperforms previous editing methods by 6.49% in terms of generalization performance. Extensive evaluation show that PIPE also exhibits effectiveness in structured knowledge editing and strong robustness under batch and sequential editing.

Random Utility Models (RUMs) are a classical framework for modeling user preferences and play a key role in reward modeling for Reinforcement Learning from Human Feedback (RLHF). However, a crucial shortcoming of many of these techniques is the Independence of Irrelevant Alternatives (IIA) assumption, which collapses \emph{all} human preferences to a universal underlying utility function, yielding a coarse approximation of the range of human preferences. On the other hand, statistical and computational guarantees for models avoiding this assumption are scarce. In this paper, we investigate the statistical and computational challenges of learning a \emph{correlated} probit model, a fundamental RUM that avoids the IIA assumption. First, we establish that the classical data collection paradigm of pairwise preference data is \emph{fundamentally insufficient} to learn correlational information, explaining the lack of statistical and computational guarantees in this setting. Next, we demonstrate that \emph{best-of-three} preference data provably overcomes these shortcomings, and devise a statistically and computationally efficient estimator with near-optimal performance. These results highlight the benefits of higher-order preference data in learning correlated utilities, allowing for more fine-grained modeling of human preferences. Finally, we validate these theoretical guarantees on several real-world datasets, demonstrating improved personalization of human preferences.

Test-Time Training (TTT) models context dependencies by adapting part of the model's weights (often referred to as fast weights) at inference time. This adapted fast weight, similar to recurrent states in RNNs, stores temporary memories of past tokens in the current sequence. Existing TTT methods have struggled to demonstrate effectiveness in handling long-sequence data, due to their computational inefficiency on modern GPUs. The TTT layers in many of these approaches operate with extremely low FLOPs utilization (often below 5%) because they deliberately apply small online mini-batch sizes (e.g., updating fast weights every 16 or 64 tokens). Moreover, a small mini-batch implies fine-grained block-wise causal dependencies in the data, making them unsuitable for data beyond 1D ordered sequences, like sets or N-dimensional grids such as images or videos. In contrast, we pursue the opposite direction by proposing an extremely large chunk update, ranging from 2K to 1M tokens across tasks of varying modalities, which we refer to as Large Chunk Test-Time Training (LaCT). This approach improves hardware utilization by orders of magnitude, and more importantly, facilitates scaling of nonlinear state size (up to 40% of model parameter size), hence substantially improving state capacity, all without requiring cumbersome and error-prone custom kernel implementations. It also allows easy integration of sophisticated optimizers like Muon for online memory updates. We validate our approach across diverse data modalities and tasks, including novel view synthesis from image sets, language models, and auto-regressive video diffusion models. Our approach can scale up to 14-billion-parameter auto-regressive video diffusion models handling sequences of up to 56K tokens. In our longest sequence experiment, we perform novel view synthesis with more than one million context length. Our results highlight the computational and performance benefits of large-chunk test-time training, paving the way for more efficient and scalable long-context sequence modeling. We hope that this work will inspire and accelerate new research in the field of long-context modeling and test-time training.

Large language model (LLM)-based agents increasingly rely on tool use to complete real-world tasks. While existing works evaluate the LLMs' tool use capability, they largely focus on the final answers yet overlook the detailed tool usage trajectory, i.e., whether tools are selected, parameterized, and ordered correctly. We introduce TRAJECT-Bench, a trajectory-aware benchmark to comprehensively evaluate LLMs' tool use capability through diverse tasks with fine-grained evaluation metrics. TRAJECT-Bench pairs high-fidelity, executable tools across practical domains with tasks grounded in production-style APIs, and synthesizes trajectories that vary in breadth (parallel calls) and depth (interdependent chains). Besides final accuracy, TRAJECT-Bench also reports trajectory-level diagnostics, including tool selection and argument correctness, and dependency/order satisfaction. Analyses reveal failure modes such as similar tool confusion and parameter-blind selection, and scaling behavior with tool diversity and trajectory length where the bottleneck of transiting from short to mid-length trajectories is revealed, offering actionable guidance for LLMs' tool use.

Weak-to-Strong generalization (W2SG) is a new trend to elicit the full capabilities of a strong model with supervision from a weak model. While existing W2SG studies focus on simple tasks like binary classification, we extend this paradigm to complex interactive decision-making environments. Specifically, we fine-tune a strong model with trajectories of intermediate actions generated by a weak model. Motivated by the human learning process, we propose to generalize not only successful knowledge but also failed experiences so that the strong model can learn from the failed trajectories accumulated by weak models. To effectively and efficiently elicit the potential of strong agents, we further construct ``trajectory trees," a hierarchical representation that organizes weak model-generated action trajectories, coupled with Monte Carlo Tree Search (MCTS) to optimize the strong model. Through theoretical analysis, we provide formal guarantees for the effectiveness of our method in improving W2SG performance. Our empirical evaluations demonstrate substantial improvements in reasoning and decision-making capabilities across diverse task domains, validating the scalability and robustness of our proposed framework. Our code is available at: https://github.com/yeruimeng/TraTree.git.

Large-scale reinforcement learning with verifiable rewards (RLVR) has proven effective in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs often rely on external tools to assist in task-solving processes. However, current RL algorithms typically employ trajectory-level rollout sampling, consistently neglecting the fine-grained exploration of multi-turn tool-call steps. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Our preliminary experiments reveal that LLMs frequently exhibit increased uncertainty after tool-call steps, as evidenced by higher entropy in the distribution of generated tokens. Motivated by this, ARPO incorporates an entropy-based adaptive rollout mechanism, encouraging the policy model to adaptively branch sampling during high-entropy tool-call rounds, thereby promoting step-level exploration of latent tool-use behaviors. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Experiments across 13 challenging benchmarks demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our codes are released at https://github.com/RUC-NLPIR/ARPO.

We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned input is a forest that must be given additional edges to form a full spanning tree. Veldt et al. (2025) showed that optimally completing the forest takes $\Omega(n^2)$ time, but designed a 2.62-approximation for MFC with subquadratic complexity. The same method is a $(2\gamma + 1)$-approximation for the original MST problem, where $\gamma \geq 1$ is a quality parameter for the initial forest. We introduce a generalized method that interpolates between this prior algorithm and an optimal $\Omega(n^2)$-time MFC algorithm. Our approach considers only edges incident to a growing number of strategically chosen "representative" points. One corollary of our analysis is to improve the approximation factor of the previous algorithm from 2.62 for MFC and $(2\gamma+1)$ for metric MST to 2 and $2\gamma$ respectively. We prove this is tight for worst-case instances, but we still obtain better instance-specific approximations using our generalized method. We complement our theoretical results with a thorough experimental evaluation.

We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to capture realistic view-dependent effects. Our approach leverages the fact that RGB-depth images provide samples of a surface light field. By encoding random subsamples of this surface light field into a compact set of latent vectors, our model learns to represent both geometry and appearance within a unified 3D latent space. This representation can reproduce view-dependent effects such as lighting reflections and Fresnel reflections under complex lighting. We further train a latent flow matching model on this representation to learn its distribution conditioned on a single input image, enabling the generation of 3D objects with appearances consistent with the lighting and materials in the input. Experiments show that our approach achieves higher reconstruction quality and better separation of geometry and appearance than existing methods.

Large language models (LLMs) have demonstrated remarkable and steadily improving performance across a wide range of tasks. However, LLM performance may be highly sensitive to prompt variations especially in scenarios with limited openness or strict output formatting requirements, indicating insufficient robustness. In real-world applications, user prompts provided to LLMs often contain imperfections, which may undermine the quality of the model's responses. To address this issue, previous work has primarily focused on preprocessing prompts, employing external tools or even LLMs to refine prompt formulations in advance. However, these approaches overlook the intrinsic robustness of LLMs, and their reliance on external components introduces additional computational overhead and uncertainty. In this work, we propose a Contrastive Learning-based Inverse Direct Preference Optimization (CoIPO) method that minimizes the discrepancy between the label-aligned logits produced by the model under a clean prompt and its noisy counterpart, and conduct a detailed analysis using mutual information theory. We augment the FLAN dataset by constructing paired prompts, each consisting of a clean prompt and its corresponding noisy version for training. Additionally, to evaluate the effectiveness, we develop NoisyPromptBench, a benchmark enhanced and derived from the existing PromptBench. Experimental results conducted on NoisyPromptBench demonstrate that our proposed method achieves a significant improvement in average accuracy over the current state-of-the-art approaches. The source code of CoIPO, pair-wise FLAN datasets, and NoisyPromptBench have already been released on https://github.com/vegetable-yx/CoIPO.