Deep Manifold Part 1: Anatomy of Neural Network Manifold
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909327069020160 |
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| author | Ma, Max Y. Shi, Gen-Hua |
| author_facet | Ma, Max Y. Shi, Gen-Hua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deep Manifold Part 1: Anatomy of Neural Network Manifold Ma, Max Y. Shi, Gen-Hua Machine Learning Artificial Intelligence 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. |
| title | Deep Manifold Part 1: Anatomy of Neural Network Manifold |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2409.17592 |