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www.jeremykun.com | ||
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www.depthfirstlearning.com
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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... | |
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francisbach.com
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| | | | | [AI summary] This article explores the properties of matrix relative entropy and its convexity, linking it to machine learning and information theory. It discusses the use of positive definite matrices in various contexts, including concentration inequalities and kernel methods. The article also includes a lemma on matrix cumulant generating functions and its proof, as well as references to relevant literature. | |
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blog.georgeshakan.com
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| | | | | Principal Component Analysis (PCA) is a popular technique in machine learning for dimension reduction. It can be derived from Singular Value Decomposition (SVD) which we will discuss in this post. We will cover the math, an example in python, and finally some intuition. The Math SVD asserts that any $latex m \times d$ matrix $latex... | |
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www.unofficialgoogledatascience.com
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| | | by STEVEN L. SCOTT Time series data are everywhere, but time series modeling is a fairly specialized area within statistics and data scien... | ||
