Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can dramatically affect performance. Yet, theoretical understanding of optimal learning strategies remains sparse, especially due to the intricate interplay between evolving meta-parameters and nonlinear learning dynamics. The search for optimal protocols is further hindered by the high dimensionality of the learning space, often resulting in predominantly heuristic, difficult to interpret, and computationally demanding solutions. Here, we combine statistical physics with control theory in a unified theoretical framework to identify optimal protocols in prototypical neural network models. In the high-dimensional limit, we derive closed-form ordinary differential equations that track online stochastic gradient descent through low-dimensional order parameters. We formulate the design of learning protocols as an optimal control problem directly on the dynamics of the order parameters with the goal of minimizing the generalization error at the end of training. This framework encompasses a variety of learning scenarios, optimization constraints, and control budgets. We apply it to representative cases, including optimal curricula, adaptive dropout regularization and noise schedules in denoising autoencoders. We find nontrivial yet interpretable strategies highlighting how optimal protocols mediate crucial learning tradeoffs, such as maximizing alignment with informative input directions while minimizing noise fitting. Finally, we show how to apply our framework to real datasets. Our results establish a principled foundation for understanding and designing optimal learning protocols and suggest a path toward a theory of meta-learning grounded in statistical physics.

Unknown dynamic load carrying is one important practical application for quadruped robots. Such a problem is non-trivial, posing three major challenges in quadruped locomotion control. First, how to model or represent the dynamics of the load in a generic manner. Second, how to make the robot capture the dynamics without any external sensing. Third, how to enable the robot to interact with load handling the mutual effect and stabilizing the load. In this work, we propose a general load modeling approach called load characteristics modeling to capture the dynamics of the load. We integrate this proposed modeling technique and leverage recent advances in Reinforcement Learning (RL) based locomotion control to enable the robot to infer the dynamics of load movement and interact with the load indirectly to stabilize it and realize the sim-to-real deployment to verify its effectiveness in real scenarios. We conduct extensive comparative simulation experiments to validate the effectiveness and superiority of our proposed method. Results show that our method outperforms other methods in sudden load resistance, load stabilizing and locomotion with heavy load on rough terrain. \href{https://leixinjonaschang.github.io/leggedloadadapt.github.io/}{Project Page}.

We introduce Skywork-R1V3, an advanced, open-source vision-language model (VLM) that pioneers a new approach to visual reasoning. Its key innovation lies in effectively transferring reasoning skills from text-only Large Language Models (LLMs) to visual tasks. The strong performance of Skywork-R1V3 primarily stems from our elaborate post-training RL framework, which effectively activates and enhances the model's reasoning ability, without the need for additional continue pre-training. Through this framework, we further uncover the fundamental role of the connector module in achieving robust cross-modal alignment for multimodal reasoning models. In addition, we introduce a unique indicator of reasoning capability, the entropy of critical reasoning tokens, which has proven highly effective for checkpoint selection during RL training. Skywork-R1V3 achieves state-of-the-art results on MMMU, significantly improving from 64.3% to 76.0%. This performance matches entry-level human capabilities. Remarkably, our RL-powered post-training approach enables even the 38B parameter model to rival top closed-source VLMs. The implementation successfully transfers mathematical reasoning to other subject-related reasoning tasks. We also include an analysis of curriculum learning and reinforcement finetuning strategies, along with a broader discussion on multimodal reasoning. Skywork-R1V3 represents a significant leap in multimodal reasoning, showcasing RL as a powerful engine for advancing open-source VLM capabilities.

Logical rule learning, a prominent category of knowledge graph (KG) reasoning methods, constitutes a critical research area aimed at learning explicit rules from observed facts to infer missing knowledge. However, like all KG reasoning methods, rule learning suffers from a critical weakness-its dependence on the I.I.D. assumption. This assumption can easily be violated due to selection bias during training or agnostic distribution shifts during testing (e.g., as in query shift scenarios), ultimately undermining model performance and reliability. To enable robust KG reasoning in wild environments, this study investigates logical rule learning in the presence of agnostic test-time distribution shifts. We formally define this challenge as out-of-distribution (OOD) KG reasoning-a previously underexplored problem, and propose the Stable Rule Learning (StableRule) framework as a solution. StableRule is an end-to-end framework that combines feature decorrelation with rule learning network, to enhance OOD generalization in KG reasoning. By leveraging feature decorrelation, StableRule mitigates the adverse effects of covariate shifts arising in OOD scenarios, improving the robustness of the rule learning network. Extensive experiments on seven benchmark KGs demonstrate the framework's superior effectiveness and stability across diverse heterogeneous environments, highlighting its practical significance for real-world applications.

Large language models (LLMs) demand considerable computational, energy, and financial resources during both training and deployment. While scaling laws for training have guided much of the field's recent progress, inference costs now represent a significant and growing component of the overall resource burden, particularly for reasoning-focused models. Existing characterizations of compute-optimality that consider model size, dataset size, and inference tokens in isolation or in fixed combinations risk overlooking more efficient operating points. We introduce directed stochastic skill search (DS3), a general framework that represents inference as stochastic traversal over a learned skill graph. From a simplified yet expressive instantiation, we derive closed-form expressions for task success and compute cost across a wide range of inference strategies -- including chain-of-thought (CoT) and tree-of-thought (ToT) -- enabling comparative analysis as a function of task difficulty and model capability. To that end, we extend a prior first-principles tripartite graph framework of LLM training to incorporate inference, and separately bridge DS3 with empirical methods that characterize LLM scaling behavior. We theoretically recover empirically observed patterns, including: linear accuracy scaling with logarithmic compute; variation in preferred inference strategies as a function of task difficulty and model capability; emergent behavior elicited by reasoning even when performance plateaus under parameter scaling; and both best-of-N (BoN) and majority voting behavior captured within a unified analytical framework. By explicitly characterizing training-inference interdependencies, our framework deepens theoretical understanding and supports principled algorithmic design and resource allocation.

This paper studies the problem of learning computable functions in the limit by extending Gold's inductive inference framework to incorporate \textit{computational observations} and \textit{restricted input sources}. Complimentary to the traditional Input-Output Observations, we introduce Time-Bound Observations, and Policy-Trajectory Observations to study the learnability of general recursive functions under more realistic constraints. While input-output observations do not suffice for learning the class of general recursive functions in the limit, we overcome this learning barrier by imposing computational complexity constraints or supplementing with approximate time-bound observations. Further, we build a formal framework around observations of \textit{computational agents} and show that learning computable functions from policy trajectories reduces to learning rational functions from input and output, thereby revealing interesting connections to finite-state transducer inference. On the negative side, we show that computable or polynomial-mass characteristic sets cannot exist for the class of linear-time computable functions even for policy-trajectory observations.

Two-class classification problems are often characterized by an imbalance between the number of majority and minority datapoints resulting in poor classification of the minority class in particular. Traditional approaches, such as reweighting the loss function or naïve resampling, risk overfitting and subsequently fail to improve classification because they do not consider the diversity between majority and minority datasets. Such consideration is infeasible because there is no metric that can measure the impact of imbalance on the model. To obviate these challenges, we make two key contributions. First, we introduce MOODS~(Multi-Objective Optimization for Data Sampling), a novel multi-objective bilevel optimization framework that guides both synthetic oversampling and majority undersampling. Second, we introduce a validation metric -- `$ε/ δ$ non-overlapping diversification metric' -- that quantifies the goodness of a sampling method towards model performance. With this metric we experimentally demonstrate state-of-the-art performance with improvement in diversity driving a $1-15 \%$ increase in $F1$ scores.

This paper establishes the first comprehensive review of Large Language Models (LLMs) applied within the legal domain. It pioneers an innovative dual lens taxonomy that integrates legal reasoning frameworks and professional ontologies to systematically unify historical research and contemporary breakthroughs. Transformer-based LLMs, which exhibit emergent capabilities such as contextual reasoning and generative argumentation, surmount traditional limitations by dynamically capturing legal semantics and unifying evidence reasoning. Significant progress is documented in task generalization, reasoning formalization, workflow integration, and addressing core challenges in text processing, knowledge integration, and evaluation rigor via technical innovations like sparse attention mechanisms and mixture-of-experts architectures. However, widespread adoption of LLM introduces critical challenges: hallucination, explainability deficits, jurisdictional adaptation difficulties, and ethical asymmetry. This review proposes a novel taxonomy that maps legal roles to NLP subtasks and computationally implements the Toulmin argumentation framework, thus systematizing advances in reasoning, retrieval, prediction, and dispute resolution. It identifies key frontiers including low-resource systems, multimodal evidence integration, and dynamic rebuttal handling. Ultimately, this work provides both a technical roadmap for researchers and a conceptual framework for practitioners navigating the algorithmic future, laying a robust foundation for the next era of legal artificial intelligence. We have created a GitHub repository to index the relevant papers: https://github.com/Kilimajaro/LLMs_Meet_Law.

--The integration of high-level assistance algorithms in surgical robotics training curricula may be beneficial in establishing a more comprehensive and robust skillset for aspiring surgeons, improving their clinical performance as a consequence. This work presents the development and validation of a haptic-enhanced Virtual Reality simulator for surgical robotics training, featuring 8 surgical tasks that the trainee can interact with thanks to the embedded physics engine. This virtual simulated environment is augmented by the introduction of high-level haptic interfaces for robotic assistance that aim at re-directing the motion of the trainee's hands and wrists toward targets or away from obstacles, and providing a quantitative performance score after the execution of each training exercise. An experimental study shows that the introduction of enhanced robotic assistance into a surgical robotics training curriculum improves performance during the training process and, crucially, promotes the transfer of the acquired skills to an unassisted surgical scenario, like the clinical one. The increase of surgical robotics procedures in the last decade demands a high number of trained surgeons [1] [2], capable of teleoperating such advanced and complex systems and at the same time able to take advantage of the benefits of Robot-Assisted Minimally Invasive Surgery (RAMIS) safely and effectively.

This paper proposes NOrmed Index of Retention (NOIR), a quantitative objective metric for evaluating summarization quality of arbitrary texts that relies on both the retention of semantic meaning and the summary length compression. This gives a measure of how well the recall-compression tradeoff is managed, the most important skill in summarization. Experiments demonstrate that NOIR effectively captures the token-length / semantic retention tradeoff of a summarizer and correlates to human perception of sumarization quality. Using a language model-embedding to measure semantic similarity, it provides an automated alternative for assessing summarization quality without relying on time-consuming human-generated reference summaries. The proposed metric can be applied to various summarization tasks, offering an automated tool for evaluating and improving summarization algorithms, summarization prompts, and synthetically-generated summaries.