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 vladfeinberg.com
Sketching Algorithms for Matrix Preconditioning in Neural Network Optimization
| | algassert.com
Using Eigendecomposition to Convert Rotations and Interpolate Operations
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| | Craig Gidney's computer science blog
| | francisbach.com
Scaling laws of optimization - Machine Learning Research Blog
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| | www.depthfirstlearning.com
Resurrecting the Sigmoid: Theory and Practice ยท Depth First Learning
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| | [AI summary] The provided text is a detailed exploration of the mathematical and statistical foundations of neural networks, focusing on the Jacobian matrix, its spectral properties, and the implications for dynamical isometry. The key steps and results are as follows: 1. **Jacobian and Spectral Analysis**: The Jacobian matrix $ extbf{J} $ of a neural network is decomposed into $ extbf{J} = extbf{W} extbf{D} $, where $ extbf{W} $ is the weight matrix and $ extbf{D} $ is a diagonal matrix of derivatives. The spectral properties of $ extbf{J} extbf{J}^T $ are analyzed using the $ S $-transform, which captures the behavior of the eigenvalues of the Jacobian matrix. 2. **$ S $-Transform Derivation**: The $ S $-transform of $ extbf{J} extbf{J}^T $ is...
| | learnopengl.com
LearnOpenGL - Cubemaps
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| Learn OpenGL . com provides good and clear modern 3.3+ OpenGL tutorials with clear examples. A great resource to learn modern OpenGL aimed at beginners.