Beijing Institute of Mathematical Sciences and Applications

Shing Toung Yau

Meng Lu

Wednesday, October 16, 2024 8:00 PM - 9:00 PM

Online

Understanding intelligence has long been a central pursuit in neuroscience, cognitive science, and artificial intelligence. It encompasses complex phenomena such as learning, problem-solving, creativity, and consciousness. While recent advancements in geometric analysis have shed light on the representation and organization of high-dimensional information in neural and artificial systems, a comprehensive framework that unifies the static and dynamic aspects of intelligence remains elusive. In this talk, I will introduce a novel mathematical framework based on Riemannian geometry that models both the structure and dynamics of intelligence and consciousness. In this framework, elements of intelligence are conceptualized as tokens embedded in a high-dimensional space. These token embeddings capture the relationships between various scenarios and tasks, forming manifolds in the intelligence space. Thought flow is represented as the sequential activation of tokens along geodesics within these manifolds. Consciousness, as a self-referential process, perceives and evaluates the thought flow, providing feedback through prediction errors. These errors adjust the geodesic paths, restructuring the manifolds and facilitating learning. This dynamic interaction between intelligence and consciousness guides the evolution of their underlying geometry, offering new insights into both biological and artificial intelligence systems. This unified framework opens avenues for future research and empirical validation. Altogether, this framework can be summarised as “geometry dictates how consciousness navigates, while consciousness guides the evolution of geometry.” Reference: Lu, Meng. A mathematical framework of intelligence and consciousness based on Riemannian Geometry. arXiv preprint arXiv:2407.11024 (2024).

本人于2024年1月在北京大学成立人工智能与动态结构实验室，致力于通过理论与实验相结合的方法探索智能的本质。实验上，我们开发先进的工具，获取高质量的数据并基于此构建理论，通过理论对实验进行指导从而获得更好的数据，推动理论的不断完善。本人希望通过跨学科的协同研究，促进人工智能与神经科学领域的深度融合与发展，逐步深入对智能本质的探索。近五年发表相关论文20篇，其中在Nature Methods、Science Advances等期刊以独立一作发表论文8篇，受邀于瑞士联邦理工（EPFL）、国际理论物理研究中心（ICTP）等知名机构和国际学术会议做报告，任英国阿尔兹海默研究基金会（Alzheimer’s Research UK）基金评委，并于2023年受剑桥大学出版社之邀成为生物成像和分析领域的国际期刊Biological Imaging 的副编辑（Associate Editor）。 Science for AI: 探索构建基于黎曼几何的智能与意识理论框架，研究智能的几何化本质，核心思想可总结为：the geometry of intelligence guides how the consciousness navigate, the consciousness dictates how the geometry of intelligence evolves. AI for Science: 开发先进的人工智能工具，并将其与其他技术结合，研究神经元网络的结构动力学。主要成果包括：1）研发了基于石墨烯微电极阵列的多模态神经元结构与活动检测系统，实现了光学成像与电生理记录的同步，首次实现了神经元动作电位与突触级亚结构形变的同时检测；2）结合超分辨成像技术开发了人工智能视频图像分析工具ERnet，成功解决了内质网结构的精确识别与定量分析难题，精准量化了其在不同疾病模型中的形态变化。