arXiv:2505.18362v3 Announce Type: replace-cross
Abstract: We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control problems posed on infinite-dimensional spaces of probability distributions and control vector fields. We further derive the Hamilton–Jacobi–Bellman equation for the associated value functional defined on the space of probability distributions. Both results are presented in a concise form and supported by rigorous mathematical analysis, enabling efficient numerical treatment of these problems. Building on the proposed MP, we introduce a scalable numerical algorithm that leverages deep neural networks to handle high-dimensional settings. The effectiveness of the approach is demonstrated through several multi-agent control examples involving domain obstacles and inter-agent interactions.
Depression subtype classification from social media posts: few-shot prompting vs. fine-tuning of large language models
BackgroundSocial media provides timely proxy signals of mental health, but reliable tweet-level classification of depression subtypes remains challenging due to short, noisy text, overlapping symptomatology,