2024/09/26 by Max Ma, Ma, Max Y., Gen‐hua Shi +1
Computer Science · #Image Processing and 3D Reconstruction #Neural Networks and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2409.17592
Based on the numerical manifold method principle, we developed a mathematical framework of a neural network manifold: Deep Manifold and discovered that neural networks: 1) is numerical computation combining forward and inverse; 2) have near infinite degrees of freedom; 3) exponential learning capacity with depth; 4) have self-progressing boundary conditions; 5) has training hidden bottleneck. We also define two concepts: neural network learning space and deep manifold space and introduce two concepts: neural network intrinsic pathway and fixed point. We raise three fundamental questions: 1). What is the training completion definition; 2). where is the deep learning convergence point (neural network fixed point); 3). How important is token timestamp in training data given negative time is critical in inverse problem.