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greydanus.github.io | ||
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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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thenumb.at
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| | | | | [AI summary] This text provides a comprehensive overview of differentiable programming, focusing on its application in machine learning and image processing. It explains the fundamentals of automatic differentiation, including forward and backward passes, and demonstrates how to implement these concepts in a custom framework. The text also discusses higher-order differentiation and its implementation in frameworks like JAX and PyTorch. A practical example is given using differentiable programming to de-blur an image, showcasing how optimization techniques like gradient descent can be applied to solve real-world problems. The text emphasizes the importance of differentiable programming in enabling efficient and flexible computation for various domains, includ... | |
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jxmo.io
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| | | | | A primer on variational autoencoders (VAEs) culminating in a PyTorch implementation of a VAE with discrete latents. | |
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thomvolker.github.io
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| | | Many different ways of calculating OLS regression coefficients exist, but some ways are more efficient than others. In this post we discuss some of the most common ways of calculating OLS regression coefficients, and how they relate to each other. Throughout, I assume some knowledge of linear algebra (i.e., the ability to multiply matrices), but other than that, I tried to simplify everything as much as possible. | ||
