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Max Y. Ma

Publications and source records attributed to Max Y. Ma.

2 recordsLinked to original sources
arXiv2025

Deep Manifold Part 2: Neural Network Mathematics

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a learnable numerical computation shaped by manifold complexity, high-order nonlinearity, and boundary conditions. Real-world data impose strong data complexity, near-infinite scope, scale, and minibatch fragmentation, while training dynamics produce learning complexity through shifting node covers, curvature accumulation, and the rise and decay of plasticity. These forces constrain learnability and explain why capability emerges only when fixed-point regions stabilize. Neural networks do not begin with fixed points; they construct them through residual-driven iteration. This perspective clarifies the limits of monolithic models under geometric and data-induced plasticity and motivates architectures and federated systems that distribute manifold complexity across many elastic models, forming a coherent world-modeling framework grounded in geometry, algebra, fixed points, and real-data complexity.

cs.LG↗
arXiv2024

Deep Manifold Part 1: Anatomy of Neural Network Manifold

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.

cs.LG↗