ICLR 2026 Papers

The high dimensional parameter space of modern deep neural networks — the neuromanifold — is endowed with a unique metric tensor defined by the Fisher information, estimating which is crucial for both theory and practical methods in deep learning. To analyze this tensor for classification networks, we return to a low dimensional space of probability distributions — the core space — and carefully analyze the spectrum of its Riemannian metric. We extend our discoveries there into deterministic bounds of the metric tensor on the neuromanifold. We introduce an unbiased random estimate of the metric tensor and its bounds based on Hutchinson’s trace estimator. It can be evaluated efficiently through a single backward pass, with a standard deviation bounded by the true value up to scaling.

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor’s outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a $9.02\%$ gain on in-domain tasks and a $5.70\%$ gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

Most state-of-the-art probabilistic time series forecasting models rely on sampling to represent future uncertainty. However, this paradigm suffers from inherent limitations, such as lacking explicit probabilities, inadequate coverage, and high computational costs. In this work, we introduce **Probabilistic Scenarios**, an alternative paradigm designed to address the limitations of sampling. It operates by directly producing a finite set of {Scenario, Probability} pairs, thus avoiding Monte Carlo-like approximation. To validate this paradigm, we propose **TimePrism**, a simple model composed of only three parallel linear layers. Surprisingly, TimePrism achieves 9 out of 10 state-of-the-art results across five benchmark datasets on two metrics. The effectiveness of our paradigm comes from a fundamental reframing of the learning objective. Instead of modeling an entire continuous probability space, the model learns to represent a set of plausible scenarios and corresponding probabilities. Our work demonstrates the potential of the Probabilistic Scenarios paradigm, opening a promising research direction in forecasting beyond sampling.

Even when instructed to adhere to source material, language models often generate unsubstantiated content – a phenomenon known as “closed-domain hallucination.” This risk is amplified in processes with multiple generative steps (MGS), compared to processes with a single generative step (SGS). However, due to the greater complexity of MGS processes, we argue that detecting hallucinations in their final outputs is necessary but not sufficient: it is equally important to trace where hallucinated content was likely introduced and how faithful content may have been derived from the source through intermediate outputs. To address this need, we present VeriTrail, the first closed-domain hallucination detection method designed to provide traceability for both MGS and SGS processes. We also introduce the first datasets to include all intermediate outputs as well as human annotations of final outputs’ faithfulness for their respective MGS processes. We demonstrate that VeriTrail outperforms baseline methods on both datasets.

Robot learning increasingly relies on simulation to advance complex ability such as dexterous manipulations and precise interactions, necessitating high-quality digital assets to bridge the sim-to-real gap. However, existing open-source articulated object datasets for simulation are limited by insufficient visual realism and low physical fidelity, which hinder their utility for training models mastering robotic tasks in real world. To address these challenges, we introduce ArtVIP, a comprehensive open-source dataset comprising high-quality digital-twin articulated objects, accompanied by indoor-scene assets.Crafted by professional 3D modelers adhering to unified standards, ArtVIP ensures visual realism through precise geometric meshes and high-resolution textures, and physical fidelity is achieved via fine-tuned dynamic parameters. Meanwhile, the dataset pioneers embedded modular interaction behaviors within assets and pixel-level affordance annotations. Feature-map visualization and optical motion capture are employed to quantitatively demonstrate ArtVIP's visual and physical fidelity, with its applicability validated across imitation learning and reinforcement learning experiments. Provided in USD format with detailed production guidelines, ArtVIP is fully open-source, benefiting the research community and advancing robot learning research.

Deep clustering has recently achieved remarkable progress across various domains. However, existing clustering methods typically treat all samples equally, neglecting the inherent differences in their feature patterns and learning states. Such redundant learning often drives models to overemphasize simple feature patterns in high-density regions, weakening their ability to capture complex yet diverse ones in low-density regions. To address this issue, we propose a novel plug-in designed to mitigate overfitting to simple and redundant feature patterns while encouraging the learning of more complex yet diverse ones. Specifically, we introduce a density-aware clustering head initialization strategy that adaptively adjusts each sample's contribution to cluster prototypes according to its local density in the feature space. This strategy mitigates the bias towards high-density regions and encourages a more comprehensive attention on medium- and low-density ones. Furthermore, we design a dynamic sample selection strategy that evaluates the learning state of samples based on the feature consistency and pseudo-label stability. By removing sufficiently learned samples and prioritizing unstable ones, this strategy adaptively reallocates training resources, enabling the model to consistently focus on samples that remain under-learned throughout training. Our method can be integrated as a plug-in into a wide range of deep clustering architectures. Extensive experiments on multiple benchmark datasets demonstrate that our method improves clustering accuracy by up to $\textbf{6.1}$\% and enhances training efficiency by up to $\textbf{1.3$\times$}$. $\textbf{Code is available in the supplementary material.}$

We propose a concept-based adversarial attack framework that extends beyond single-image perturbations by adopting a probabilistic perspective. Rather than modifying a single image, our method operates on an entire concept - represented by a distribution - to generate diverse adversarial examples. Preserving the concept is essential, as it ensures that the resulting adversarial images remain identifiable as instances of the original underlying category or identity. By sampling from this concept-based adversarial distribution, we generate images that maintain the original concept but vary in pose, viewpoint, or background, thereby misleading the classifier. Mathematically, this framework remains consistent with traditional adversarial attacks in a principled manner. Our theoretical and empirical results demonstrate that concept-based adversarial attacks yield more diverse adversarial examples and effectively preserve the underlying concept, while achieving higher attack efficiency.

Evaluating modern machine learning models has become prohibitively expensive. Benchmarks such as LMMs-Eval and HELM demand thousands of GPU hours per model. Costly evaluation reduces inclusivity, slows the cycle of innovation, and worsens environmental impact. To address the growing cost of standard evaluation, new methods focused on efficient evaluation have started to appear. The typical approach follows two steps. The typical approach follows two steps. First, select an anchor subset of data. Second, train a mapping from the accuracy on this subset to the final test result. The drawback is that anchor selection depends on clustering, which can be complex and sensitive to design choices. We argue that promoting diversity among samples is not essential; what matters is to select samples that *maximise diversity in model responses*. Our method, **Diversifying Sample Condensation** **(DISCO)**, selects the top-k samples with the greatest model disagreements. This uses greedy, sample-wise statistics rather than global clustering. The approach is conceptually simpler. From a theoretical view, inter-model disagreement provides an information-theoretically optimal rule for such greedy selection. **DISCO** shows empirical gains over prior methods, achieving state-of-the-art results in performance prediction across MMLU, Hellaswag, Winogrande, and ARC.

Online-to-non-convex conversion (O2NC) is an online updates learning framework for producing Goldstein $(\delta,\epsilon)$-stationary points of non-smooth non-convex functions with optimal oracle complexity $\mathcal{O}(\delta^{-1} \epsilon^{-3})$. Subject to auxiliary \emph{random interpolation or scaling}, O2NC recapitulates the stochastic gradient descent with momentum (SGDM) algorithm popularly used for training neural networks. Randomization, however, introduces deviations from practical SGDM. So a natural question arises: Can we derandomize O2NC to achieve the same optimal guarantees while resembling SGDM? On the negative side, the general answer is \emph{no} due to the impossibility results of~\citet{jordan23deterministic}, showing that no dimension-free rate can be achieved by deterministic algorithms. On the positive side, as the primary contribution of the present work, we show that O2NC can be naturally derandomized for \emph{weakly convex} functions. Remarkably, our deterministic algorithm converges at an optimal rate as long as the weak convexity parameter is no larger than $\mathcal{O}(\delta^{-1}\epsilon^{-1})$. In other words, the stronger stationarity is expected, the higher non-convexity can be tolerated by our optimizer. Additionally, we develop a periodically restarted variant of our method to allow for more progressive update when the iterates are far from stationary. The resulting algorithm, which corresponds to a momentum-restarted version of SGDM, has been empirically shown to be effective and efficient for training ResNet and ViT networks.

Automatic polyp segmentation from colonoscopy videos is a crucial technique that assists clinicians in improving the accuracy and efficiency of diagnosis, preventing polyps from developing into cancer. However, video polyp segmentation (VPS) is a challenging task due to (1) the significant inter-frame divergence in videos, (2) the high camouflage of polyps in normal colon structures and (3) the clinical requirement of real-time performance. In this paper, we propose a novel segmentation network, WavePolyp, which consists of two innovative components: a hierarchical wavelet-based feature aggregation (HWFA) module and inter-frame divergence perception (IDP) blocks. Specifically, HWFA excavates and amplifies discriminative information from high-frequency and low-frequency features decomposed by wavelet transform, hierarchically aggregating them into refined spatial representations within each frame. This module enhances the representation capability of intra-frame spatial features, effectively addressing the high camouflage of polyps in normal colon structures. Furthermore, IDP perceives and captures inter-frame polyp divergence through a temporal divergence perception mechanism, enabling accurate polyp tracking while mitigating temporal inconsistencies caused by the significant inter-frame variations across frames. Extensive experiments conducted on the SUN-SEG and CVC-612 datasets demonstrate that our method outperforms other state-of-the-art methods. Codes will be released upon publication.

Developing a mobile system capable of generating responses based on stored user data is a crucial challenge. Since user data is stored in the form of Knowledge Graphs, the field of knowledge graph question answering (KGQA) presents a promising avenue towards addressing this problem. However, existing KGQA systems face two critical limitations that preclude their on-device deployment: resource constraints and the inability to handle data accumulation. Therefore, we propose MobileKGQA, the first on-device KGQA system capable of adapting to evolving databases with minimal resource demands. MobileKGQA significantly reduces computational overhead through embedding hashing. Moreover, it successfully adapts to evolving databases under resource constraints through a novel annotation generation method. Its mobile applicability is validated on the NVIDIA Jetson Orin Nano edge-device platform, achieving 20.3% higher performance while using only 30.4% of the energy consumed by the SOTA (state of the art). On standard KGQA benchmarks, using just 7.2% of the computation and 9% of the parameters, MobileKGQA demonstrates performance that is empirically indistinguishable from the SOTA and outperforms baselines under distribution shift scenarios.

Diffusion-based large language models (dLLMs), despite their promising performance, still suffer from inferior inference efficiency. This is because dLLMs rely on bidirectional attention and cannot directly benefit from the standard key-value (KV) cache as autoregressive models (ARMs) do. To tackle this issue, we introduce \textit{Dual aDaptive Cache} (d$^2$Cache), which is a training-free approximate KV cache framework for accelerating dLLM inference. d$^2$Cache features a two-stage fine-grained selection strategy to identify tokens and adaptively update their KV states at each decoding step, while caching the KV states of the remaining tokens for reuse. Furthermore, d$^2$Cache naturally offers a more reliable decoding alternative, which can enable quasi left-to-right generation and mitigate premature overconfidence in tokens at the end of the sequence. Extensive experimental results on two representative dLLMs (\ie, LLaDA and Dream) demonstrate that d$^2$Cache not only achieves substantial inference speedups, but also yields consistent improvements in generation quality. The anonymous evaluation codes are available at \url{https://anonymous.4open.science/r/d2Cache-5538}.

We study distributed reinforcement learning (RL) with policy gradient methods under asynchronous and parallel computations and communications. While non-distributed methods are well understood theoretically and have achieved remarkable empirical success, their distributed counterparts remain less explored, particularly in the presence of heterogeneous asynchronous computations and communication bottlenecks. We introduce two new algorithms, Rennala NIGT and Malenia NIGT, which implement asynchronous policy gradient aggregation and achieve state-of-the-art efficiency. In the homogeneous setting, Rennala NIGT provably improves the total computational and communication complexity while supporting the AllReduce operation. In the heterogeneous setting, Malenia NIGT simultaneously handles asynchronous computations and heterogeneous environments with strictly better theoretical guarantees. Our results are further corroborated by experiments, showing that our methods significantly outperform prior approaches.

Video stylization plays a key role in content creation, but it remains a challenging problem. Naïvely applying image stylization frame-by-frame hurts temporal consistency and reduces style richness. Alternatively, training a dedicated video stylization model typically requires paired video data and is computationally expensive. In this paper, we propose FreeViS, a training-free video stylization framework that generates stylized videos with rich style details and strong temporal coherence. Our method integrates multiple stylized references to a pretrained image-to-video (I2V) model, effectively mitigating the propagation errors observed in prior works, without introducing flickers and stutters. In addition, it leverages high-frequency compensation to constrain the content layout and motion, together with flow-based motion cues to preserve style textures in low-saliency regions. Through extensive evaluations, FreeViS delivers higher stylization fidelity and superior temporal consistency, outperforming recent baselines and achieving strong human preference. Our training-free pipeline offers a practical and economic solution for high-quality, temporally coherent video stylization.

Hallucinations in Large Language Models (LLMs) pose a major barrier to their reliable use in critical decision-making. Although existing hallucination detection methods have improved accuracy, they still struggle with disentangling semantic and reasoning information and maintaining robustness. To address these challenges, we propose HARP (Hallucination detection via reasoning subspace projection), a novel hallucination detection framework. HARP establishes that the hidden state space of LLMs can be decomposed into a direct sum of a semantic subspace and a reasoning subspace, where the former encodes linguistic expression and the latter captures internal reasoning processes. Moreover, we demonstrate that the Unembedding layer can disentangle these subspaces, and by applying Singular Value Decomposition (SVD) to its parameters, the basis vectors spanning the semantic and reasoning subspaces are obtained. Finally, HARP projects hidden states onto the basis vectors of the reasoning subspace, and the resulting projections are then used as input features for hallucination detection in LLMs. By using these projections, HARP reduces the dimension of the feature to approximately 5% of the original, filters out most noise, and achieves enhanced robustness. Experiments across multiple datasets show that HARP achieves state-of-the-art hallucination detection performance; in particular, it achieves an AUROC of 92.8% on TriviaQA, outperforming the previous best method by 7.5%.

The tendency to find and exploit "shortcuts" to complete tasks poses significant risks for reliable assessment and deployment of large language models (LLMs). For example, an LLM agent with access to unit tests may delete failing tests rather than fix the underlying bug. Such behavior undermines both the validity of benchmark results and the reliability of real-world LLM coding assistant deployments. To quantify, study, and mitigate such behavior, we introduce ImpossibleBench, a benchmark framework that systematically measures LLM agents' propensity to exploit test cases. ImpossibleBench creates "impossible" variants of tasks from existing benchmarks like LiveCodeBench and SWE-bench by introducing direct conflicts between the natural-language specification and the unit tests. We measure an agent's "cheating rate" as its pass rate on these impossible tasks, where any pass necessarily implies a specification-violating shortcut. As a practical framework, ImpossibleBench is not just an evaluation but a versatile tool. We demonstrate its utility for: (1) studying model behaviors, revealing more fine-grained details of cheating behaviors from simple test modification to complex operator overloading; (2) context engineering, showing how prompt, test access and feedback loop affect cheating rates; and (3) developing monitoring tools, providing a testbed with verified deceptive solutions. We hope ImpossibleBench serves as a useful framework for building more robust and reliable LLM systems.

Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the optimal encoding of information under efficiency constraints. Successful normative theories have varied dramatically in complexity, from simple linear models (Atick & Redlich, 1990), to complex deep neural networks (Lindsay, 2021). What complex models gain in flexibility, they lose in tractability and often understandability. Here, we split the difference by constructing a set of tractable but flexible normative representational theories. Instead of optimising the neural activities directly, following (Sengupta et al. 2018), we instead optimise the representational similarity, a matrix formed from the dot products of each pair of neural responses. Using this, we show that a large family of interesting optimisation problems are convex. This includes problems corresponding to linear and some non-linear neural networks, and problems from the literature not previously recognised as convex such as modified versions of semi-nonnegative matrix factorisation or nonnegative sparse coding. We put these findings to work in two ways. First, we extend previous results on modularity and mixed selectivity in neural activity; in so doing we provide the first necessary and sufficient identifiability result for a form of semi-nonnegative matrix factorisations. Second, we seek to understand the meaningfulness of single neural tuning curves as compared to neural representations. In particular we derive an identifiability result stating that, for an optimal representational similarity matrix, if neural tunings are `different enough' then they are uniquely linked to the optimal representational similarity, partially justifying the use of single neuron tuning analysis in neuroscience. In sum, we identify an interesting space of convex problems, and use that to derive neural coding results.

Diffusion Large Language Models (dLLMs) offer a promising alternative to autoregressive models, excelling in text generation tasks due to their bidirectional attention mechanisms. However, their computational complexity, scaling as $\mathcal{O}(L^3)$ with sequence length $L$, poses significant challenges for long-sequence and real-time applications, primarily due to the lack of compatibility with key-value caching and the non-autoregressive nature of denoising steps. Existing acceleration methods rely on static caching or parallel decoding strategies, which fail to account for the dynamic behavior of token properties across layers and decoding steps. We propose \textbf{Dynamic-dLLM}, a training-free framework that enhances dLLM inference efficiency through two components: Dynamic Cache Updating (DCU), which adaptively allocates cache-update budgets based on layer-wise token dynamics, and Adaptive Parallel Decoding (APD), which dynamically calibrates decoding thresholds to balance generation quality and efficiency. Extensive experiments on models like LLaDA-8B-Instruct, LLaDA-1.5, and Dream-v0-7B-Instruct across benchmarks such as MMLU, GSM8K, and HumanEval demonstrate that Dynamic-dLLM significantly improves inference speed, attaining an average speedup of exceeding 3$\times$ while maintaining performance. Dynamic-dLLM outperforms state-of-the-art acceleration methods and provides a plug-and-play solution for efficient dLLM deployment without compromising performance. Code and models will be made publicly available.

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 13 LLMs and 10 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5× speedup while retaining > 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.