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 matthewmcateer.me
The Math Behind ML (the important stuff) - matthewmcateer.me
| | francisbach.com
Sums-of-squares for dummies: a view from the Fourier domain - Machine Learning Research Blog
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| | fa.bianp.net
On the Convergence of the Unadjusted Langevin Algorithm
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| | The Langevin algorithm is a simple and powerful method to sample from a probability distribution. It's a key ingredient of some machine learning methods such as diffusion models and differentially private learning. In this post, I'll derive a simple convergence analysis of this method in the special case when the ...
| | 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...
| | argumatronic.com
argumatronic - The Nesting Instinct
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| Occasional writings about Haskell.