ICLR 2026 Papers

Learning generative models directly from corrupted observations is a long-standing challenge across natural and scientific domains. We introduce *Distillation from Corrupted Data (DCD)*, a unified framework for learning high-fidelity, one-step generative models using **only** degraded data of the form $ y = \mathcal{A}(x) + \sigma \varepsilon, \ x\sim p_X,\ \varepsilon\sim \mathcal{N}(0,I_m), $ where the mapping $\mathcal{A}$ may be the identity or a non-invertible corruption operator (e.g., blur, masking, subsampling, Fourier acquisition). DCD first pretrains a *corruption-aware diffusion teacher* on the observed measurements, then *distills* it into an efficient one-step generator whose samples are statistically closer to the clean distribution $p_X$. The framework subsumes identity corruption (denoising task) as a special case of our general formulation. Empirically, DCD consistently reduces Fréchet Inception Distance (FID) relative to corruption-aware diffusion teachers across noisy generation (*CIFAR-10*, *FFHQ*, *CelebA-HQ*, *AFHQ-v2*), image restoration (Gaussian deblurring, random inpainting, super-resolution, and mixtures with additive noise), and multi-coil MRI—*without access to any clean images*. The distilled generator inherits one-step sampling efficiency, yielding up to $30\times$ speedups over multi-step diffusion while surpassing the teachers after substantially fewer training iterations. These results establish score distillation as a practical tool for generative modeling from corrupted data, *not merely for acceleration*. We also provide theoretical support for the use of distillation in enhancing generation quality in the Appendix.

Recent advancements in large language models (LLMs) and agentic systems have shown exceptional decision-making capabilities, revealing significant potential for autonomic finance. Current financial trading agents predominantly simulate anthropomorphic roles that inadvertently introduce emotional biases and rely on peripheral information, while being constrained by the necessity for continuous inference during deployment. In this paper, we pioneer the harmonization of strategic depth in agents with the mechanical rationality essential for quantitative trading. Consequently, we present TiMi (Trade in Minutes), a rationality-driven multi-agent system that architecturally decouples strategy development from minute-level deployment. TiMi leverages specialized LLM capabilities of semantic analysis, code programming, and mathematical reasoning within a comprehensive policy-optimization-deployment chain. Specifically, we propose a two-tier analytical paradigm from macro patterns to micro customization, layered programming design for trading bot implementation, and closed-loop optimization driven by mathematical reflection. Extensive evaluations across 200+ trading pairs in stock and cryptocurrency markets empirically validate the efficacy of TiMi in stable profitability, action efficiency, and risk control under volatile market dynamics.

With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with sufficiently many draws (e.g., $\texttt{pass@1024}$), existing base models already solve nearly all questions on widely used math benchmarks such as MATH-500 and AIME 2024. This suggests that the RL fine-tuning methods prevalent in the LLM reasoning literature largely sharpen existing solution modes rather than discovering entirely new ones. Such sharpening stands in contrast to the broader promise of RL: to foster exploration and to acquire new skills. To move beyond this plateau, we introduce MATH-Beyond (MATH-B), a benchmark deliberately constructed to defeat common open-source models of up to 8B parameters even under large sampling budgets. Improving performance on our benchmark via RL requires methods that learn to reason in ways that go beyond base model capabilities in repeated sampling. Since the problems are drawn from subsets of DAPO-Math-17K and DeepScaleR datasets, they remain topically equivalent to standard high-school math. Validating our premise, RL fine-tuned models such as Nemotron-Research-Reasoning-Qwen-1.5B and DeepScaleR-1.5B-Preview perform poorly on MATH-B at $\texttt{pass@1024}$, showing how existing approaches fall short on tackling harder instances. We hope MATH-B will catalyze exploration-driven RL approaches that elicit deeper reasoning capabilities.

Neural network architectures have made considerable advances in their ability to solve reasoning problems, but many state-of-the-art methods fail at systematic compositional generalization. To address this, we propose a novel architecture which uses a nonparametric latent space, information-theoretic regularization of this space, and test-time gradient-based search to achieve strong performance on OOD compositional meta-learning tasks such as ARC-like program induction, Raven's progressive matrices, and linguistic systematicity tasks. Our proposed architecture, Abduction Transformer, uses nonparametric mixture distributions to represent inferred hidden causes of few-shot meta-learning instances. These representations are refined at test-time via gradient descent to better account for the observed few-shot examples, a form of variational posterior inference which allows Abduction Transformer to solve meta-learning tasks that require novel recombinations of knowledge acquired during training. Our method outperforms standard transformer architectures and previous test-time adaptive approaches, indicating a promising new direction for neural networks capable of systematic generalization.

As AI systems progresses, we rely more on them to make decisions with us and for us. To ensure that such decisions are aligned with human values, it is imperative for us to understand not only what decisions they make but also how they come to those decisions. Reasoning language models, which provide both final responses and (partially transparent) intermediate thinking traces, present a timely opportunity to study AI procedural reasoning. Unlike math and code problems which often have objectively correct answers, moral dilemmas are an excellent testbed for process-focused evaluation because they allow for multiple defensible conclusions. To do so, we present MoReBench: 1,000 moral scenarios, each paired with a set of rubric criteria that experts consider essential to include (or avoid) when reasoning about the scenarios. MoReBench contains over 23 thousand criteria including identifying moral considerations, weighing trade-offs, and giving actionable recommendations to cover cases on AI advising humans moral decisions as well as making moral decisions autonomously. Separately, we curate MoReBench-Theory: 150 examples to test whether AI can reason under five major frameworks in normative ethics. Our results show that scaling laws and existing benchmarks on math, code, and scientific reasoning tasks (fail to) predict models' abilities to perform moral reasoning. Models also show partiality towards specific moral frameworks (e.g., Benthamite Act Utilitarianism and Kantian Deontology), which might be side effects of popular training paradigms. Together, these benchmarks advance process-focused reasoning evaluation towards safer and more transparent AI.

Quantifying uncertainty is crucial in safety-critical learning systems where decisions are made based on uncertainty. Conformal prediction is one promising way to quantify uncertainty that comes with a theoretical guarantee. However, the theoretical guarantee comes with a price of the assumption on data generation process, including exchangeability or full feedback. In this paper, we propose a novel conformal prediction method with less data generation assumption, i.e., a learning method for online conformal prediction with partial feedback from an adaptive adversary. In particular, we leverage matured literatures in sequential prediction and adversarial bandits to design our online conformal prediction algorithm. The great benefit of the reliance on adversarial bandits is that we can exploit theoretical regret bounds for conformal prediction guarantees. Here, we explicitly connect the regret and a desired miscoverage guarantee in conformal prediction such that our algorithm via adversarial bandits can naturally provide a miscoverage guarantee from the regret bounds. Furthermore, we extend an existing adversarial bandit method to leverage the properties of conformal prediction, resulting in a bandit method with a tighter regret bound. We empirically demonstrate the efficacy of our conformal prediction method over various learning setups, including a stochastic setup and covariate shift setup, showing a controllability on a micoverage rate while achieving a reasonable conformal set size.

In recent years, deep learning-based single-channel speech separation has improved considerably, in large part driven by increasingly compute- and parameter-efficient neural network architectures. Most such architectures are, however, designed with a fixed compute and parameter budget, and consequently cannot scale to varying compute demands or resources, which limits their use in embedded and heterogeneous devices such as mobile phones and hearables. To enable such use-cases we design a neural network architecture for speech separation and enhancement capable of early-exit, and we propose an uncertainty-aware probabilistic framework to jointly model the clean speech signal and error variance which we use to derive probabilistic early-exit conditions in terms of desired signal-to-noise ratios. We evaluate our methods on both speech separation and enhancement tasks where we demonstrate that early-exit capabilities can be introduced without compromising reconstruction, and that our early-exit conditions are well-calibrated on training data and can easily be post-calibrated on validation data, leading to large energy savings when used with early-exit over single-exit baselines. Our framework enables fine-grained dynamic compute-scaling of neural networks while achieving state-of-the-art performance and interpretable exit conditions.

Reinforcement Learning with Verifiable Reward (RLVR) effectively solves complex tasks but demands extremely long context lengths during training, leading to substantial computational costs. While multi-stage training can partially mitigate this, starting with overly short contexts often causes irreversible performance degradation, ultimately failing to reduce overall training compute significantly. In this paper, we introduce **T**hinking-**F**ree **P**olicy **I**nitialization (**TFPI**), a simple yet effective adaptation to RLVR that bridges long Chain-of-Thought (CoT) distillation and standard RLVR. TFPI employs a simple *ThinkFree* operation, explicitly discarding the thinking content via a direct *</think>* append, to reduce token usage during inference. Training with *ThinkFree*-adapted inputs improves performance and lowers token consumption, even in the original slow-thinking mode. Extensive experiments across various benchmarks have shown that {\method} accelerates RL convergence, achieves a higher performance ceiling, and yields more token-efficient reasoning models without specialized rewards or complex training designs. With TFPI only, we train a 4B model to reach 89.0% accuracy on AIME24 and 65.5% on LiveCodeBench using less than 4K H20 hours.

Wireless Signal Recognition (WSR) aims to identify the property of received signals using Artificial Intelligence (AI) without any prior knowledge, which has been widely used in civil and military radios. The current AI trend of pre-training and fine-tuning has shown great performance, and the existing pre-trained WSR models also achieve impressive results. However, they either apply the "mask-reconstruction" pre-training strategy, which may disrupt intricate local dependencies of signals, or overlook latent spectral characteristics. Therefore, in this paper, we follow the diffusion models and propose a pre-training framework for WSR, named the Temporal-Spectral Denoising Diffusion AutoEncoder (TS-DDAE), which learns signal representations by corrupting signals with temporal and spectral noise, and then reconstructing the original data with a learned neural network. Moreover, we design a novel neural architecture, named TS-Net, which couples self-attention for temporal encoder with channel attention for spectral encoder. Extensive experiments on several datasets and WSR tasks show that TS-DDAE achieves superior performance compared to state-of-the-art (SOTA) baselines, which demonstrate the potential to be a foundation model for WSR.

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of transformers, with particular emphasis on the role of the number of attention heads. Our analysis begins with the introduction of a generalized $D$-retrieval task, which we prove to be dense in the space of continuous functions, thereby providing the basis for our theoretical framework. We then establish both upper and lower bounds on the parameter complexity required for $\epsilon$-approximation. Specifically, we show that transformers with sufficiently many heads admit efficient approximation, whereas with too few heads, the number of parameters must scale at least as $O(1/\epsilon^{cT})$, for some constant $c$ and sequence length $T$. To the best of our knowledge, this constitutes the first rigorous lower bound of this type in a nonlinear and practically relevant setting. We further examine the single-head case and demonstrate that an embedding dimension of order $O(T)$ allows complete memorization of the input, resulting in the approximation entirely achieved by the feed-forward block. Finally, we validate our theoretical findings with experiments on both synthetic data and real-world tasks, illustrating the practical relevance of our results.

Transport-based methods have emerged as a leading paradigm for building generative models from large, clean datasets. However, in many scientific and engineering domains, clean data are often unavailable: instead, we only observe measurements corrupted through a noisy, ill-conditioned channel. A generative model for the original data thus requires solving an inverse problem at the level of distributions. In this work, we introduce a novel approach to this task based on Stochastic Interpolants: we iteratively update a transport map between corrupted and clean data samples using only access to the corrupted dataset as well as black box access to the corruption channel. Under appropriate conditions, this iterative procedure converges towards a self-consistent transport map that effectively inverts the corruption channel, thus enabling a generative model for the clean data. The resulting method (i) is computationally efficient compared to variational alternatives, (ii) highly flexible, handling arbitrary nonlinear forward models with only black-box access, and (iii) enjoys theoretical guarantees. We demonstrate superior performance on inverse problems in natural image processing and scientific reconstruction, and establish convergence guarantees of the scheme under appropriate assumptions.

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies---such as self-consistency, best-of-$n$, and self-correction---remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $\Theta(1/\Delta^2)$ samples to produce the correct answer, while best-of-$n$ only needs $\Theta(1/\Delta)$, where $\Delta < 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.

While Large Vision-Language Models (LVLMs) have demonstrated remarkable capabilities for reasoning and self-correction at the textual level, these strengths provide minimal benefits for complex tasks centered on visual perception, such as Chart Parsing. Existing models often struggle with visually dense charts, leading to errors like data omission, misalignment, and hallucination. Inspired by the human strategy of using a finger as a ``visual anchor'' to ensure accuracy when reading complex charts, we propose a new paradigm named Visual Self-Refine (VSR). The core idea of VSR is to enable a model to generate pixel-level localization outputs, visualize them, and then feed these visualizations back to itself, allowing it to intuitively inspect and correct its own potential visual perception errors. We instantiate the VSR paradigm in the domain of Chart Parsing by proposing ChartVSR. This model decomposes the parsing process into two stages: a Refine Stage, where it iteratively uses visual feedback to ensure the accuracy of all data points' Pixel-level Localizations, and a Decode Stage, where it uses these verified localizations as precise visual anchors to parse the final structured data. To address the limitations of existing benchmarks, we also construct ChartP-Bench, a new and highly challenging benchmark for chart parsing. Our work also highlights VSR as a general-purpose visual feedback mechanism, offering a promising new direction for enhancing accuracy on a wide range of vision-centric tasks.

In multimodal learning, CLIP has been recognized as the \textit{de facto} method for learning a shared latent space across multiple modalities, placing similar representations close to each other and moving them away from dissimilar ones. Although CLIP-based losses effectively align modalities at the semantic level, the resulting latent spaces often remain only partially shared, revealing a structural mismatch known as the modality gap. While the necessity of addressing this phenomenon remains debated, particularly given its limited impact on instance-wise tasks (e.g., retrieval), we prove that its influence is more pronounced in group-level tasks (e.g., clustering). To support this claim, we introduce a novel method designed to consistently reduce this discrepancy in two-modal settings, with a straightforward extension to the general $n$-modal case. Through our extensive evaluation, we prove our novel insight: while reducing the gap provides only marginal or inconsistent improvements in traditional instance-wise tasks, it significantly enhances group-wise tasks. These findings may reshape our understanding of the modality gap, highlighting its key role in improving performance on tasks requiring semantic grouping.

Large Language Models (LLMs) can perform new tasks from in-context demonstrations, a phenomenon known as in-context learning (ICL). Recent work suggests that these demonstrations are compressed into task vectors (TVs), compact task representations that LLMs exploit for predictions. However, prior studies typically extract TVs from model outputs or hidden states using cumbersome and opaque methods, and they rarely elucidate the mechanisms by which TVs influence computation. In this work, we address both limitations. First, we propose directly training Learned Task Vectors (LTVs), which surpass extracted TVs in accuracy and exhibit superior flexibility—acting effectively at arbitrary layers, positions, and even with ICL prompts. Second, through systematic analysis, we investigate the mechanistic role of TVs, showing that at the low level they steer predictions primarily through attention-head OV circuits, with a small subset of “key heads” most decisive. At a higher level, we find that despite Transformer nonlinearities, TV propagation is largely linear: early TVs are rotated toward task-relevant subspaces to improve logits of relevant labels, while later TVs are predominantly scaled in magnitude. Taken together, LTVs not only provide a practical approach for obtaining effective TVs but also offer a principled lens into the mechanistic foundations of ICL.

Existing feed-forward 3D Gaussian Splatting methods typically rely on pixel-aligned primitives, which makes scaling to higher resolutions (e.g., 4K) prohibitive as the number of Gaussians grows quadratically with image resolution. We introduce LGTM (Less Gaussians, Texture More), a feed-forward and pose-free framework that predicts both compact geometric primitives and associated per-primitive texture maps in a single forward pass without per-scene optimization.

Mixture-of-Experts (MoE) architectures have emerged as a promising approach for scaling deep learning models while maintaining computational efficiency. However, existing MoE adaptations for Contrastive Language-Image Pre-training (CLIP) models suffer from significant computational overhead during sequential training and degradation of zero-shot capabilities. To address these limitations, we propose CLIP-FMoE, a novel approach that integrates MoE architecture into CLIP fine-tuning. Our method uses Isolated Constrained Contrastive Learning, a pipeline that trains specialized experts on cluster-based data partitions to accelerate expert specialization. Additionally, we introduce a Fusion Gate mechanism to mitigate catastrophic forgetting of pre-trained knowledge. Extensive experiments across multiple benchmarks demonstrate that our approach achieves consistent improvements on downstream tasks while preserving zero-shot capabilities. Furthermore, our method demonstrates robust performance across varying context lengths, making it particularly suitable for diverse real-world applications.

Implicit Neural Representations (INRs) have shown great promise in solving inverse problems, but their lack of inherent regularization often leads to a trade-off between expressiveness and smoothness. While Lipschitz continuity presents a principled form of implicit regularization, it is often applied as a rigid, uniform 1-Lipschitz constraint, limiting its potential in inverse problems. In this work, we reframe Lipschitz regularization as a flexible *Lipschitz budget framework*. We propose a method to first derive a principled, task-specific total budget $K$, then proceed to distribute this budget *non-uniformly* across all network components, including linear weights, activations, and embeddings. Across extensive experiments on deformable registration and image inpainting, we show that non-uniform allocation strategies provide a measure to balance regularization and expressiveness within the specified global budget. Our *Lipschitz lens* introduces an alternative, interpretable perspective to Neural Tangent Kernel (NTK) and Fourier analysis frameworks in INRs, offering practitioners actionable principles for improving network architecture and performance.

Recently, many generative models for de novo protein structure design have emerged. Yet, only few tackle the difficult task of directly generating fully atomistic structures jointly with the underlying amino acid sequence. This is challenging, for instance, because the model must reason over side chains that change in length during generation. We introduce La-Proteina for atomistic protein design based on a novel partially latent protein representation: coarse backbone structure is modeled explicitly, while sequence and atomistic details are captured via per-residue latent variables of fixed dimensionality, thereby effectively side-stepping challenges of explicit side-chain representations. Flow matching in this partially latent space then models the joint distribution over sequences and full-atom structures. La-Proteina achieves state-of-the-art performance on multiple generation benchmarks, including all-atom co-designability, diversity, and structural validity, as confirmed through detailed structural analyses and evaluations. Notably, La-Proteina also surpasses previous models in atomistic motif scaffolding performance, unlocking critical atomistic structure-conditioned protein design tasks. Moreover, La-Proteina is able to generate co-designable proteins of up to 800 residues, a regime where most baselines collapse and fail to produce valid samples, demonstrating La-Proteina's scalability and robustness.