ICLR 2026 Papers

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their inherent ability to self-correct, making them more preferable than autoregressive or masked diffusion models in these settings. Yet, their sampling efficiency has been limited by reliance on standard posterior samplers, which plateau in quality as steps increase. In this work, we introduce a novel family of Predictor–Corrector (PC) samplers for discrete diffusion models that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers significantly outperform ancestral sampling on both language and vision tasks: achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve generation quality with more sampling steps, narrowing the gap with Masked diffusion. Beyond sampling, we develop a fast and memory-efficient curriculum for Duo$^{++}$'s (our method) Gaussian relaxation phase, which avoids materializing large Gaussian-diffused one-hot vectors. This reduces training time by 25\% compared to Duo while maintaining similar validation perplexity on OpenWebText and LM1B and strong downstream performance.

We introduce Music Flamingo, a novel large audio–language model, designed to advance music (including song) understanding in foundational audio models. While audio–language research has progressed rapidly, music remains challenging due to its dynamic, layered, and information-dense nature. Progress has been further limited by the difficulty of scaling open audio understanding models, primarily because of the scarcity of high-quality music data and annotations. As a result, prior models are restricted to producing short, high-level captions, answering only surface-level questions, and showing limited generalization across diverse musical cultures. To address these challenges, we curate MF-Skills, a large-scale dataset labeled through a multi-stage pipeline that yields rich captions and question–answer pairs covering harmony, structure, timbre, lyrics, and cultural context. We fine-tune an enhanced Audio Flamingo 3 backbone on MF-Skills and further strengthen multiple skills relevant to music understanding. To improve the model's reasoning abilities, we introduce a post-training recipe: we first cold-start with MF-Think, a novel chain-of-thought dataset grounded in music theory, followed by GRPO-based reinforcement learning with custom rewards. Music Flamingo achieves state-of-the-art results across 10+ benchmarks for music understanding and reasoning, establishing itself as a generalist and musically intelligent audio–language model. Beyond strong empirical results, Music Flamingo sets a new standard for advanced music understanding by demonstrating how models can move from surface-level recognition toward layered, human-like perception of songs. We believe this work provides both a benchmark and a foundation for the community to build the next generation of models that engage with music as richly and meaningfully as humans do. Demo: https://musicflamingo.github.io

In this paper, we establish a dimension- and precision-independent impossibility result for a simplified transformer model. Due to their size, a comprehensive understanding of the internal operations of frontier large language models (LLMs) is beyond the reach of current methods, but research into small and interpretable models has proven successful. We study the representational limits of attention, the core of transformer models, through the lens of the Endpoint Selection Problem (ESP), a simple yet expressive learning task defined over arcs of a directed graph. Our main theoretical results are twofold: (i) 1-head, 1-layer, attention-only transformers cannot solve ESP on any graph containing a cycle, even with unbounded dimension and precision; but, all DAGs (Directed Acyclic Graph) are solvable with zero error (ii) in contrast, a 2-head, 1-layer, attention-only transformer can solve ESP on arbitrary directed graphs with constant embedding dimension and logarithmic precision. Prior lower bounds were conditional on bounds on dimension and precision. Through a transformation, we extend our impossibility result from ESP to the much studied 2-hop induction head problem. Further, we uncover a surprising connection to NP-completeness by showing that the optimal error of the 1-head transformer is em exactly related to the size of MAS (Maximum Acyclic Subgraph) and hence inapproximable. Finally, we validate our theory with experiments and observe that gradient-based optimization can reliably find 1-head solutions for DAGs and 2-head solutions for arbitrary graphs with cycles, whereas 1-head models struggle to reach the optimal solution in graphs with cycles. We believe that our techniques are of independent interest and have the potential to establish a new fine-grained hierarchy of transformer architectures, each with greater problem-solving power than the last.

Treating human motion and camera trajectory generation separately overlooks a core principle of cinematography: the tight interplay between actor performance and camera work in the screen space. In this paper, we are the first to cast this task as a text-conditioned joint generation, aiming to maintain consistent on-screen framing while producing two heterogeneous, yet intrinsically linked, modalities: human motion and camera trajectories. We propose a simple, model-agnostic framework that enforces multimodal coherence via an auxiliary modality: the on-screen framing induced by projecting human joints onto the camera. This on-screen framing provides a natural and effective bridge between modalities, promoting consistency and leading to more precise joint distribution. We first design a joint autoencoder that learns a shared latent space, together with a lightweight linear mapping from the human and camera latents to a framing latent. We then introduce Auxiliary Sampling, which exploits this linear map to steer generation toward a coherent framing modality. To support this task, we also introduce the PulpMotion dataset, a camera-motion and human-motion dataset with rich captions, and high-quality human motions. Extensive experiments across DiT- and MAR-based architectures show the generality and effectiveness of our method in generating on-frame coherent camera-human motions, while also achieving gains on textual alignment for both modalities. Our qualitative results yield more cinematographically meaningful framings setting the new state of the art for this task.

Softmax Attention has a quadratic time complexity in sequence length, which becomes prohibitive to run at long contexts, even with highly optimized GPU kernels. For example, FlashAttention-2/3 (exact, GPU-optimized implementations of Softmax Attention) cannot complete a single forward–backward pass of a single attention layer once the context exceeds $\sim 4$ million tokens on an NVIDIA GH200 (96 GB). We introduce **R**epeated **A**rrays-of-**C**ount **E**stimators (RACE) Attention, a kernel-inspired alternative to Softmax Attention that is strictly linear in sequence length and embedding size. RACE Attention replaces the exponential kernel with a sharpened angular similarity, and approximates attention outputs via Gaussian random projections and \emph{soft} Locality-Sensitive Hashing (LSH), avoiding construction of the full attention matrix. Across language modeling, masked language modeling, and text/image classification, RACE Attention matches or outperforms strong baselines up to $64$K seqeuence length while reducing wall-clock time and memory usage. In addition, we conduct a controlled scaling study on a single attention layer and demonstrate processing of up to 12 million tokens on an NVIDIA GH200 GPU and 75 million tokens on an Intel Xeon® Gold 5220R CPU in a single forward–backward pass, which is well beyond the capabilities of current state-of-the-art attention implementations. RACE Attention thus offers a practical and theoretically grounded mechanism for long-context training on today’s hardware.

We present ProbHardE2E, a probabilistic forecasting framework that incorporates hard operational/physical constraints and provides uncertainty quantification. Our methodology uses a novel differentiable probabilistic projection layer (DPPL) that can be combined with a wide range of neural network architectures. DPPL allows the model to learn the system in an end-to-end manner, compared to other approaches where constraints are satisfied either through a post-processing step or at inference. ProbHardE2E optimizes a strictly proper scoring rule, without making any distributional assumptions on the target, which enables it to obtain robust distributional estimates (in contrast to existing approaches that generally optimize likelihood-based objectives, which can be biased by their distributional assumptions and model choices); and it can incorporate a range of non-linear constraints (increasing the power of modeling and flexibility). We apply ProbHardE2E in learning partial differential equations with uncertainty estimates and to probabilistic time-series forecasting, showcasing it as a broadly applicable general framework that connects these seemingly disparate domains.

Let $(X,d)$ be a metric space and let $\mu,\nu$ be discrete distributions supported on finite point sets $A,B \subseteq X$. For any $p \in [1,\infty]$, the $W_p$-distance between $\mu$ and $\nu$, $W_p(\mu, \nu)$, is defined as the $p$-th root of the minimum cost of transporting the mass from $\mu$ to $\nu$, where moving a unit of mass from $a \in A$ to $b \in B$ incurs a cost of $d^p(a,b)$. We give a (Las Vegas) randomized algorithm that always computes a $(4+\epsilon)$-approximate $W_p$ optimal-transport (OT) plan in $O(n^2 + (n^{3/2}\epsilon^{-1}\log^2\Delta)^{1+o(1)})$ expected time, for all $p \in [1,\infty]$, where $\epsilon > 0$ is an arbitrarily small constant and $\Delta$ is the spread of $A \cup B$. The best previous result achieved an $O(\log n)$-approximation in $O(pn^2)$ time, but only for constant $p$. Our algorithm significantly improves the approximation factor and, importantly, is the first quadratic-time method that extends to the $W_\infty$-distance. In contrast, additive approximation methods such as Sinkhorn are efficient only for constant $p$ and fail to handle $p=\infty$. Finally, we show that obtaining a relative approximation factor better than $2$ in $O(n^2)$ time would resolve the long-standing open problem of computing a perfect matching in an arbitrary bipartite graph in quadratic time.

Preference alignment is an essential step in adapting large language models (LLMs) to human values, but existing approaches typically depend on costly human annotations or large-scale API-based models. We explore whether a weak LLM can instead act as an effective annotator. We surprisingly find that selecting only a subset of a weak LLM's highly confident samples leads to substantially better performance than using full human annotations. Building on this insight, we propose **C**onfidence-**W**eighted **P**reference **O**ptimization (CW-PO), a general framework that re-weights training samples by a weak LLM’s confidence and can be applied across different preference optimization objectives. Notably, the model aligned by CW-PO with just 20\% of human annotations outperforms the model trained with 100\% of annotations under standard DPO. These results suggest that weak LLMs, when paired with confidence weighting, can dramatically reduce the cost of preference alignment while even outperforming methods trained on fully human-labeled data.

Text-to-motion generation, a rapidly evolving field in computer vision, aims to produce realistic and text-aligned motion sequences. Current methods primarily focus on spatial-temporal modeling or independent frequency domain analysis, lacking a unified framework for joint optimization across spatial, temporal, and frequency domains. This limitation hinders the model's ability to leverage information from all domains simultaneously, leading to suboptimal generation quality. Additionally, in motion generation frameworks, motion-irrelevant cues caused by noise are often entangled with features that contribute positively to generation, thereby leading to motion distortion. To address these issues, we propose Tri-Domain Causal Text-to-Motion Generation (TriC-Motion), a novel diffusion-based framework integrating spatial-temporal-frequency-domain modeling with causal intervention. TriC-Motion includes three core modeling modules for domain-specific modeling, namely Temporal Motion Encoding, Spatial Topology Modeling, and Hybrid Frequency Analysis. After comprehensive modeling, a Score-guided Tri-domain Fusion module integrates valuable information from the triple domains, simultaneously ensuring temporal consistency, spatial topology, motion trends, and dynamics. Moreover, the Causality-based Counterfactual Motion Disentangler is meticulously designed to expose motion-irrelevant cues to eliminate noise, disentangling the real modeling contributions of each domain for superior generation. Extensive experimental results validate that TriC-Motion achieves superior performance compared to state-of-the-art methods, attaining an outstanding R@1 of 0.612 on the HumanML3D dataset. These results demonstrate its capability to generate high-fidelity, coherent, diverse, and text-aligned motion sequences. Code is available at: \url{https://caoyiyang1105.github.io/TriC-Motion/}.

Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection. Existing methods often rely on padded representations or must explicitly infer the set size, which often poses challenges. We present a novel strategy for addressing this challenge by casting prediction of variable-sized sets as a continuous inference problem. Our approach, CORDS (Continuous Representations of Discrete Structures), provides an invertible mapping that transforms a set of spatial objects into continuous fields: a density field that encodes object locations and count, and a feature field that carries their attributes over the same support. Because the mapping is invertible, models operate entirely in field space while remaining exactly decodable to discrete sets. We evaluate CORDS across molecular generation and regression, object detection, simulation-based inference, and a mathematical task involving recovery of local maxima, demonstrating robust handling of unknown set sizes with competitive accuracy.

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.