ICLR 2026 Papers

The rapid scaling of large language models (LLMs) has made low-precision training essential for reducing memory, improving efficiency, and enabling larger models and datasets. Existing convergence theories for adaptive optimizers, however, assume all components are exact and neglect hardware-aware quantization, leaving open the question of why low-precision training remains effective. We introduce the first theoretical framework for analyzing the convergence of adaptive optimizers, including Adam and Muon, under floating-point quantization of gradients, weights, and optimizer states (e.g., moment estimates). Within this framework, we derive convergence rates on smooth non-convex objectives under standard stochastic gradient assumptions, explicitly characterizing how quantization errors from different components affect convergence. We show that both algorithms retain rates close to their full-precision counterparts provided mantissa length scales only logarithmically with the number of iterations. Our analysis further reveals that Adam is highly sensitive to weights and second-moment quantization due to its reliance on $\beta_2 \to 1$, while Muon requires weaker error control and is thus potentially more robust. These results narrow the gap between empirical success and theoretical understanding of low-precision training methods. Numerical experiments on synthetic and real-world data corroborate our theory.

Large language models (LLMs) have exhibited strong instruction-following capabilities; however, they often struggle with compositional instructions involving multiple interleaved yet logically independent sub-tasks. These sub-tasks are typically organized in mutually exclusive structures, such as branching, chaining, or paralleling, where only one sub-task should be active at each generation step, while the others remain dormant. Despite their inactivity, dormant sub-tasks can inadvertently attract the model's attention due to structural entanglement within the input context or intermediate representations, leading to interference that compromises output fidelity. To address this challenge, we propose ATA, a structure-aware dynamic attention mechanism grounded in compositional structures, which dynamically identifies the active sub-task during generation while suppressing attention to inactive ones. By precisely steering the model’s focus, ATA mitigates interference and explicitly enhances model adherence to the active sub-task. Importantly, ATA operates within a single forward pass without requiring parameter updates. Extensive experiments show that ATA consistently enhances LLMs' instruction-following ability across various compositional structures, effectively mitigating attention distraction and demonstrating a strong generalization ability.

Preference‑based reward learning is widely used for shaping agent behavior to match a user's preference, yet its sparse binary feedback makes it especially vulnerable to causal confusion. The learned reward often latches onto spurious features that merely co‑occur with preferred trajectories during training, collapsing when those correlations disappear or reverse at test time. We introduce ReCouPLe, a lightweight framework that uses natural language rationales to provide the missing causal signal. Each rationale is treated as a guiding projection axis in embedding space, training the model to score trajectories based on features aligned with that axis while de-emphasizing context that is unrelated to the stated reason. Because identical rationales can arise across multiple tasks (e.g., "_it avoids collisions with a fragile object_"), ReCouPLe naturally reuses the same causal direction whenever tasks share semantics, and transfers preference knowledge to novel tasks without extra data or language‑model fine‑tuning. Our learned reward model can ground preferences on the articulated reason, aligning better with user intent and generalizing beyond spurious features.

The dataset distributions in offline reinforcement learning (RL) often exhibit complex and multi-modal distributions, necessitating expressive policies to capture such distributions beyond widely-used Gaussian policies. To handle such complex and multi-modal datasets, in this paper, we propose Flow Actor-Critic, a new actor-critic method for offline RL, based on recent flow policies. The proposed method not only uses the flow model for actor as in previous flow policies but also exploits the expressive flow model for conservative critic acquisition to prevent Q-value explosion in out-of-data regions. To this end, we propose a new form of critic regularizer based on the flow behavior proxy model obtained as a byproduct of flow-based actor design. Leveraging the flow model in this joint way, we achieve new state-of-the-art performance for test datasets of offline RL including the D4RL and recent OGBench benchmarks.

We examine gradient descent in matrix factorization and show that under large step sizes the parameter space develops a fractal structure. We derive the exact critical step size for convergence in scalar-vector factorization and show that near criticality the selected minimizer depends sensitively on the initialization. Moreover, we show that adding regularization amplifies this sensitivity, generating a fractal boundary between initializations that converge and those that diverge. The analysis extends to general matrix factorization with orthogonal initialization. Our findings reveal that near-critical step sizes induce a chaotic regime of gradient descent where the training outcome is unpredictable and there are no simple implicit biases, such as towards balancedness, minimum norm, or flatness.

Recent advancements in Large Language Models (LLMs) and their multimodal extensions (MLLMs) have substantially enhanced machine reasoning across diverse tasks. However, these models predominantly rely on pure text as the medium for both expressing and structuring reasoning, even when visual information is present. In this work, we argue that language may not always be the most natural or effective modality for reasoning, particularly in tasks involving spatial and geometrical information. Motivated by this, we propose a new paradigm, Visual Planning, which enables planning through purely visual representations for these "vision-first'' tasks, as a supplementary channel to language-based reasoning. In this paradigm, planning is executed via sequences of images that encode step-by-step inference in the visual domain, akin to how humans sketch or visualize future actions. We introduce a novel reinforcement learning framework, Visual Planning via Reinforcement Learning (VPRL), empowered by GRPO for post-training large vision models, leading to substantial improvements in planning in a selection of representative visual navigation tasks, FrozenLake, Maze, and MiniBehavior. Our visual planning paradigm outperforms all other planning variants that conduct reasoning in the text-only space. Our results establish Visual Planning as a viable and promising supplement to language-based reasoning, opening new avenues for tasks that benefit from intuitive, image-based inference.

The Mixture-of-Experts (MoE) architecture is a powerful technique for scaling language models, yet it often suffers from expert homogenization, where experts learn redundant functionalities, thereby limiting MoE's full potential. To address this, we introduce Expert Divergence Learning, a novel pre-training strategy that explicitly encourages functional specialization among experts. Our method incorporates a label-driven auxiliary loss that leverages domain labels inherent in pre-training corpora to maximize the Jensen-Shannon Divergence between the expert routing distributions of different data domains. This optimization objective guides the model to develop diverged routing policies for varied domains and closer routing policies for the same domain, which leads to emergent and organized expert specialization. We validate our approach by pre-training MoE models of up to 15 billion parameters from scratch. Experimental results demonstrate that models trained with Expert Divergence Learning not only achieve a lower language modeling loss but also exhibit significant performance improvements across a diverse range of downstream benchmarks. Further analysis confirms that our method effectively mitigates expert homogenization and brings greater functional specialization, all with negligible computational overhead during training.

Diffusion models have demonstrated remarkable success in high-fidelity image generation, yet aligning them with human preferences remains challenging. Direct Preference Optimization (DPO) offers a promising framework, but its effectiveness is critically hindered by noisy data arising from mislabeled preference pairs and individual preference pairs. We theoretically show that existing DPO objectives are equivalent to minimizing the Forward Kullback–Leibler (KL) divergence, whose mass-covering nature makes it intrinsically sensitive to such noise. To address this limitation, we propose $\alpha$-DPO, which reformulates preference alignment through the lens of $\alpha$-divergence. This formulation promotes mode-seeking behavior and bounds the influence of outliers, thereby enhancing robustness. Furthermore, we introduce a dynamic scheduling mechanism that adaptively adjusts $\alpha$ according to the observed preference distribution, providing data-aware noise tolerance during training. Extensive experiments on synthetic and real-world datasets validate that $\alpha$-DPO consistently outperforms existing baselines, achieving superior robustness and preference alignment.

Video Foundation Models (VFMs) exhibit remarkable visual generation performance, but struggle in compositional scenarios (\eg, motion, numeracy, and spatial relation). In this work, we introduce **Test-Time Optimization and Memorization (TTOM)**, a training-free framework that aligns VFM outputs with spatiotemporal layouts during inference for better text-image alignment. Rather than direct intervention to latents or attention per-sample in existing work, we integrate and optimize new parameters guided by a general layout-attention objective. Furthermore, we formulate video generation within a streaming setting, and maintain historical optimization contexts with a parametric memory mechanism that supports flexible operations, such as insert, read, update, and delete. Notably, we found that TTOM disentangles compositional world knowledge, showing powerful transferability and generalization. Experimental results on the T2V-CompBench and Vbench benchmarks establish TTOM as an effective, practical, scalable, and efficient framework to achieve cross-modal alignment for compositional video generation on the fly.

Large vision-language models (LVLMs) achieve strong performance on multimodal tasks, yet they often default to their language prior (LP)---memorized textual patterns from pre-training while under-utilizing visual evidence. Prior analyses of LP mostly rely on input–output probing, which fails to reveal the internal mechanisms governing when and how vision influences model behavior. To address this gap, we present the first systematic analysis of language prior through the lens of chain-of-embedding, which examines the layer-wise representation dynamics within LVLMs. Our analysis reveals a universal phenomenon: each model exhibits a Visual Integration Point (VIP), a critical layer at which visual information begins to meaningfully reshape hidden representations and influence decoding for multimodal reasoning. Building on this observation, we introduce the Total Visual Integration (TVI) estimator, which aggregates representational discrepancy beyond the VIP to quantify how strongly visual query influences response generation. Across 60 model–dataset combinations spanning 10 contemporary LVLMs and 6 benchmarks, we demonstrate that VIP consistently emerges, and that TVI reliably predicts the strength of language prior. This offers a principled toolkit for diagnosing and understanding language prior in LVLMs.

The minimum-cost bipartite matching between two sets of points $R$ and $S$ in a metric space has a wide range of applications in machine learning, computer vision, and logistics. For instance, it can be used to estimate the $1$-Wasserstein distance between continuous probability distributions and for efficiently matching requests to servers while minimizing cost. However, the computational cost of determining the minimum-cost matching for general metrics spaces, poses a significant challenge, particularly in dynamic settings where points arrive over time and each update requires re-executing the algorithm. In this paper, given a fixed set $S$, we describe a deterministic algorithm that maintains, after $i$ additions to $R$, an $O(1/\delta^{0.631})$-approximate minimum-cost matching of cardinality $i$ between sets $R$ and $S$ in any metric space, with an amortized insertion time of $\widetilde{O}(n^{1+\delta})$ for adding points in $R$. To the best of our knowledge, this is the first algorithm for incremental minimum-cost matching that applies to arbitrary metric spaces. Interestingly, an important subroutine of our algorithm lends itself to efficient parallelization. We provide both a CPU implementation and a GPU implementation that leverages parallelism. Extensive experiments on both synthetic and real world datasets showcase that our algorithm either matches or outperforms all benchmarks in terms of speed while significantly improving upon the accuracy.

Large language models (LLMs), despite being safety-aligned, exhibit brittle refusal behaviors that can be circumvented by simple linguistic changes. As tense jailbreaking demonstrates that models refusing harmful requests often comply when rephrased in past tense, a critical generalization gap is revealed in current alignment methods whose underlying mechanisms are poorly understood. In this work, we introduce Activation-Scaling Guard (ASGuard), an insightful, mechanistically-informed framework that surgically mitigates this specific vulnerability. For the first step, we use circuit analysis to identify the specific attention heads causally linked to the targeted jailbreaking, the tense-changing attack. Second, we train a precise, channel-wise scaling vector to recalibrate the activation of tense vulnerable heads. Lastly, we apply it into a "preventative fine-tuning", forcing the model to learn a more robust refusal mechanism. Across four LLMs, ASGuard effectively reduces the attack success rate of targeted jailbreaking while preserving general capabilities and minimizing over refusal, achieving a Pareto-optimal balance between safety and utility. Our findings underscore how adversarial suffixes suppress the propagation of the refusal-mediating direction, based on mechanistic analysis. Furthermore, our work showcases how a deep understanding of model internals can be leveraged to develop practical, efficient, and targeted methods for adjusting model behavior, charting a course for more reliable and interpretable AI safety.

Generating multiview-consistent $360^\circ$ ground-level scenes from satellite imagery is a challenging task with broad applications in simulation, autonomous navigation, and digital twin cities. Existing approaches primarily focus on synthesizing individual ground-view panoramas, often relying on auxiliary inputs like height maps or handcrafted projections, and struggle to produce multiview consistent sequences. In this paper, we propose SatDreamer360, a framework that generates geometrically consistent multi-view ground-level panoramas from a single satellite image, given a predefined pose trajectory. To address the large viewpoint discrepancy between ground and satellite images, we adopt a triplane representation to encode scene features and design a ray-based pixel attention mechanism that retrieves view-specific features from the triplane. To maintain multi-frame consistency, we introduce a panoramic epipolar-constrained attention module that aligns features across frames based on known relative poses. To support the evaluation, we introduce VIGOR++, a large-scale dataset for generating multi-view ground panoramas from a satellite image, by augmenting the original VIGOR dataset with more ground-view images and their pose annotations. Experiments show that SatDreamer360 outperforms existing methods in both satellite-to-ground alignment and multiview consistency.

Hierarchical reinforcement learning (HRL) enables agents to solve complex, long-horizon tasks by decomposing them into manageable sub-tasks. However, HRL methods face two fundamental challenges: (i) non-stationarity caused by the evolving lower-level policy during training, which destabilizes higher-level learning, and (ii) the generation of infeasible subgoals that lower-level policies cannot achieve. To address these challenges, we introduce DIPPER, a novel HRL framework that formulates goal-conditioned HRL as a bi-level optimization problem and leverages direct preference optimization (DPO) to train the higher-level policy. By learning from preference comparisons over subgoal sequences rather than rewards that depend on the evolving lower-level policy, DIPPER mitigates the impact of non-stationarity on higher-level learning. To address infeasible subgoals, DIPPER incorporates lower-level value function regularization that encourages the higher-level policy to propose achievable subgoals. We introduce two novel metrics to quantitatively verify that DIPPER mitigates non-stationarity and infeasible subgoal generation issues in HRL. Empirical evaluation on challenging robotic navigation and manipulation benchmarks shows that DIPPER achieves upto 40% improvements over state-of-the-art baselines on challenging sparse-reward scenarios, highlighting the potential of preference-based learning for addressing longstanding HRL limitations.

Recent advances in large language models (LLMs) have intensified the need to deliver both rapid responses and high-quality outputs. More powerful models yield better results but incur higher inference latency, whereas smaller models are faster yet less capable. Recent work proposes balancing this latency–quality trade-off using model cascades, which route simpler queries to smaller models and more complex ones to larger models. However, enabling efficient cascade serving remains challenging. Current frameworks lack effective mechanisms for handling (i) the huge and varying resource demands of different LLMs, (ii) the inherent heterogeneity of LLM workloads, and (iii) the co-optimization of system deployment and routing strategy. Motivated by these observations, we introduce Cascadia, a novel cascade serving framework designed explicitly to schedule request routing and deploy model cascades for fast, quality-preserving LLM serving. Cascadia employs a bi-level optimization method: at the deployment level, it uses a mixed-integer linear program to select resource allocations and parallelism strategies based on LLM information and workload characteristics; at the routing level, it applies a Chebyshev-guided method to iteratively co-optimize the routing strategy and the system deployment produced by the deployment level. Our extensive evaluation on diverse workload traces and different model cascades (DeepSeek and the Llama series) demonstrates that Cascadia significantly outperforms both single-model deployments and the state-of-the-art cascade serving baseline, achieving up to 4$\times$ (2.3$\times$ on average) tighter latency SLOs and up to 5$\times$ (2.4$\times$ on average) higher throughput while maintaining target answer quality.

Data curriculums have become central to successful LLM training, yet principles governing optimal data placement remain unclear. We introduce the *training re-evaluation curve (TREC)*, a diagnostic that retrospectively evaluates training batches *using the final model weights*. The TREC characterizes how well a trained model retains training data as a function of *when* the data was encountered during training. Analyzing TRECs for models from 111M to 3.9B parameters, we show that placing high-quality data at low points on the TREC significantly improves performance. Importantly, while a TREC is initially observable only after training, we demonstrate it can be *predicted in advance* from AdamW’s implicit EMA coefficients, enabling proactive curriculum design. By predicting TRECs for published training recipes, we explain prior ablations and reveal suboptimal data placements. We also align high-quality data with TREC minima in order to improve continual pre-training of a 3.9B-parameter LLM trained on 900B tokens.

Large visual language models (VLMs) have shown strong multi-modal medical reasoning ability, but most operate as end-to-end black boxes, diverging from clinicians’ evidence-based, staged workflows and hindering clinical accountability. Complementarily, expert visual grounding models can accurately localize regions of interest (ROIs), providing explicit, reliable evidence that improves both reasoning accuracy and trust. In this paper, we introduce **CARE**, advancing **C**linical **A**ccountability in multi-modal medical **R**easoning with an **E**vidence-grounded agentic framework. Unlike existing approaches that couple grounding and reasoning within a single generalist model, CARE decomposes the task into coordinated sub-modules to reduce shortcut learning and hallucination: a compact VLM proposes relevant medical entities; an expert entity-referring segmentation model produces pixel-level ROI evidence; and a grounded VLM reasons over the full image augmented by ROI hints. The VLMs are optimized with reinforcement learning with verifiable rewards to align answers with supporting evidence. Furthermore, a VLM coordinator plans tool invocation and reviews evidence-answer consistency, providing agentic control and final verification. Evaluated on standard medical VQA benchmarks, our **CARE-Flow** (coordinator-free) improves average accuracy by **10.9%** over the same size (10B) state-of-the-art (SOTA). With dynamic planning and answer review, our **CARE-Coord** yields a further gain, outperforming the heavily pre-trained SOTA by **5.2%**. Our experiments demonstrate that an agentic framework that emulates clinical workflows, incorporating decoupled specialized models and explicit evidence, yields more accurate and accountable medical AI.

Speculative Decoding (SD) is a key technique for accelerating Large Language Model (LLM) inference, but it typically requires training a draft model on a large dataset. We approach this problem from a data-centric perspective, finding that not all training samples contribute equally to the SD acceptance rate. Specifically, our theoretical analysis and empirical validation reveals that tokens inducing flatter predictive distributions from the target model are more valuable than those yielding sharply peaked distributions. Based on this insight, we propose flatness, a new metric to quantify this property, and develop the Sample-level-flatness-based Dataset Distillation (SFDD) approach, which filters the training data to retain only the most valuable samples. Experiments on the EAGLE framework demonstrate that SFDD can achieve over 2$\times$ training speedup using only 50\% of the data, while keeping the final model's inference speedup within 4\% of the full-dataset baseline. This work introduces an effective, data-centric approach that substantially improves the training efficiency for Speculative Decoding. Our code is available at https://github.com/fjm9933/Flatness.

The ability of modern language models to easily extract unstructured sensitive information has made redaction—the selective removal of such information—an essential task for data security. However, existing benchmarks and evaluation methods for redaction are often limited to predefined categories of data like personally identifiable information (PII), or particular techniques like masking. To bridge this gap, we introduce RedacBench, a novel benchmark for a comprehensive evaluation of redaction capabilities, independent of specific domains or redaction strategies. Constructed from 514 human-written texts from individuals, corporations, and governments, along with 187 security policies, RedacBench measures a model's ability to selectively remove policy-violating information while preserving the original text's utility. We robustly quantify this performance using metrics derived from 8,053 inferable propositions, assessing both security—through the redaction of sensitive propositions—and utility—through the preservation of non-sensitive ones. Our experiments on various redaction strategies using state-of-the-art language models reveal that while more advanced models and strategies can increase security, maintaining utility remains a significant challenge. To facilitate future research, we publicly release RedacBench along with a web-based playground for custom dataset creation and evaluation at https://redacbench.vercel.app/.