We study a class of wrapping operators acting on the space of formal languages over a fixed finite alphabet. The underlying space is equipped with a length-based ultrametric, in which two languages are close whenever they coincide on all sufficiently short words. We prove that every wrapping operator generated by a finite family of guards with positive total guard length is a contraction. As a consequence, Banach’s contraction principle yields existence and uniqueness of a fixed point for […]

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Reinforcement Learning (RL) has demonstrated strong potential for industrial process control, yet policies trained in simulation often suffer from a significant sim-to-real gap when deployed on physical hardware. This work systematically analyzes how core Markov Decision Process (MDP) design choices — state composition, target inclusion, reward formulation, termination criteria, and environment dynamics models — affect this transfer. Using a color mixing task, we evaluate different MDP configurations and mixing dynamics across simulation and real-world experiments. We validate our […]

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arXiv:2601.09849v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly deployed to support human decision-making. This use of LLMs has concerning implications, especially when their prescriptions affect the welfare of others. To gauge how LLMs make social decisions, we explore whether five leading models produce sensible strategies in the repeated prisoner’s dilemma, which is the main metaphor of reciprocal cooperation. First, we measure the propensity of LLMs to cooperate in a neutral setting, without using language reminiscent […]

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arXiv:2505.19134v2 Announce Type: replace-cross Abstract: Human-annotated data plays a vital role in training large language models (LLMs), such as supervised fine-tuning and human preference alignment. However, it is not guaranteed that paid human annotators produce high-quality data. In this paper, we study how to incentivize human annotators to do so. We start from a principal-agent model to model the dynamics between the company (the principal) and the annotator (the agent), where the principal can only monitor the annotation […]

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Table of Links Abstract and 1. Introduction Related Work Preliminaries and Notations Differentiable Structural Information 4.1. A New Formulation 4.2. Properties 4.3. Differentiability & Deep Graph Clustering LSEnet 5.1. Embedding Leaf Nodes 5.2. Learning Parent Nodes 5.3. Hyperbolic Partitioning Tree Experiments 6.1. Graph Clustering 6.2. Discussion on Structural Entropy Conclusion, Broader Impact, and References Appendix A. Proofs B. Hyperbolic Space C. Technical Details D. Additional Results D. Additional Results The hyperbolic partitioning trees of Cora is visualized in […]

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arXiv:2304.04724v3 Announce Type: replace-cross Abstract: We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies isoperimetry. We bound the gradient complexity to reach $epsilon$ error in total variation distance from a warm start by $tilde O(d^{1/4}text{polylog}(1/epsilon))$ and demonstrate the benefit of choosing the number of leapfrog steps to be larger than 1. To surpass […]

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It is sometimes said that neural networks are “just” logistic regression. (Remember neural networks? LLMs are neural networks, but nobody talks about neural networks anymore.) In some sense a neural network is logistic regression with more parameters, a lot more parameters, but more is different. New phenomena emerge at scale that could not have been anticipated at a smaller scale. Logistic regression can work surprisingly well on small data sets. One of my clients filed a patent on a simple […]

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arXiv:2604.06300v1 Announce Type: new Abstract: Large language model-based agents are increasingly being integrated into core battlefield functions, including intelligence analysis, data fusion, and battlefield management. This paper argues that the very features that make such agents operationally attractive, namely their capacity for initiative, interpretation, their goal-directedness, and dynamic memory, are the same features that render context-appropriate human judgment and control substantively ineffectual in those parts of the kill chain where agents operate. Drawing on specific use cases, the […]

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arXiv:2509.10853v2 Announce Type: replace Abstract: Although conceptually related, variable selection and relative importance (RI) analysis have been treated quite differently in the literature. While RI is typically used for post-hoc model explanation, this paper explores its potential for variable or feature ranking and filter-based selection before model creation. Specifically, we anticipate strong performance from the RI measures because they incorporate both direct and combined effects of predictors, addressing a key limitation of marginal correlation, which ignores dependencies among […]

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