Large language models (LLMs) have achieved unprecedented performance by leveraging vast pretraining corpora, yet their performance remains suboptimal in knowledge-intensive domains such as medicine and scientific research, where high factual precision is required. While synthetic data provides a promising avenue for augmenting domain knowledge, existing methods frequently generate redundant samples that do not align with the model's true knowledge gaps. To overcome this limitation, we propose a novel Structural Entropy-guided Knowledge Navigator (SENATOR) framework that addresses the intrinsic knowledge deficiencies of LLMs. Our approach employs the Structure Entropy (SE) metric to quantify uncertainty along knowledge graph paths and leverages Monte Carlo Tree Search (MCTS) to selectively explore regions where the model lacks domain-specific knowledge. Guided by these insights, the framework generates targeted synthetic data for supervised fine-tuning, enabling continuous self-improvement. Experimental results on LLaMA-3 and Qwen2 across multiple domain-specific benchmarks show that SENATOR effectively detects and repairs knowledge deficiencies, achieving notable performance improvements.

Selective prediction [Dru13, QV19] models the scenario where a forecaster freely decides on the prediction window that their forecast spans. Many data statistics can be predicted to a non-trivial error rate without any distributional assumptions or expert advice, yet these results rely on that the forecaster may predict at any time. We introduce a model of Prediction with Limited Selectivity (PLS) where the forecaster can start the prediction only on a subset of the time horizon. We study the optimal prediction error both on an instance-by-instance basis and via an average-case analysis. We introduce a complexity measure that gives instancedependent bounds on the optimal error. For a randomly-generated PLS instance, these bounds match with high probability.

Recent advances in reinforcement learning (RL) have strengthened the reasoning capabilities of vision-language models (VLMs). However, enhancing policy exploration to better scale test-time compute remains largely underexplored. In addition, VLMs continue to struggle with imperfect visual perception, which in turn affects the subsequent reasoning process. We introduce NoisyRollout, a simple yet effective data augmentation method that addresses these issues by mixing training trajectories from both clean and moderately distorted images. This approach injects perceptual diversity, encouraging better policy exploration and leading to more robust reasoning. A noise annealing schedule gradually reduces distortion strength, aiding exploration early in training while ensuring later stability. Crucially, our method is easy-to-adopt--requiring no additional training cost and no modifications to the RL objective. Extensive experiments on 2distinct training datasets demonstrate that NoisyRollout achieves state-of-the-art performance among opensource RL-tuned models across 5 out-of-domain reasoning and perception benchmarks.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics--InfoBias and InfoGain--to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Long-horizon planning in robotic manipulation requires translating under-specified, symbolic goals into executable control programs that satisfy spatial, temporal, and physical constraints.

Mixture-of-Experts (MoEs) achieve scalability by dynamically activating subsets of their components. Yet, understanding how expertise emerges through joint training of gating mechanisms and experts remains incomplete, especially in scenarios without clear task partitions. Motivated by inference costs and data heterogeneity, we study how joint training of gating functions and experts can dynamically allocate domain-specific expertise across multiple underlying data distributions. As an outcome of our framework, we develop an instance tailored specifically to decentralized training scenarios, introducing Dynamically Decentralized Orchestration of MoEs or DDOME. DDOME leverages heterogeneity emerging from distributional shifts across decentralized data sources to specialize experts dynamically. By integrating a pretrained common expert to inform a gating function, DDOMEachieves personalized expert subset selection on-the-fly, facilitating just-in-time personalization.

Language is the dress of thought.

The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting η (0,1] as the fraction of data with correctly matched modalities among npaired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: (i) the error without filtering is upper and lower bounded by 1/η n, and (ii)the error with teacher-based filtering is upper bounded by 1/ ηn in the large η regime, and by 1/ n in the small ηregime.

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Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question: when can learning be implemented as a computer program? We address this question for universal online learning, a generalist theoretical model of online binary classification, recently characterized by Bousquet et al. (STOC 2021). In this model, there is no hypothesis fixed in advance; instead, Adversary--playing the role of Nature--can change their mind as long as local consistency with the given class of hypotheses is maintained. We require Learner to achieve a finite number of mistakes while using a strategy that can be implemented as a computer program. We show that universal online learning does not imply computable universal online learning, even if the class of hypotheses is relatively easy from a computability-theoretic perspective. We then study the agnostic variant of computable universal online learning and provide an exact characterization of classes that are learnable in this sense. We also consider a variant of proper universal online learning and show exactly when it is possible. Together, our results give a more realistic perspective on the existing theory of online binary classification and the related problem of inductive inference.