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terrytao.wordpress.com | ||
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gilkalai.wordpress.com
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| | | | | What will be our next polymath project? A polymath project (Wikipedia) is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in January 2009 on Timothy Gowers's blog when he posted a problem... | |
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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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ianwrightsite.wordpress.com
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| | | | | Riemann's Zeta function is an infinite sublation of Hegelian integers. | |
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liverpoolcultureblog.co.uk
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| | | There's nothing much to say about the big wheel in Liverpool One's Chavasse Park, so I did a little video during a ride on it. | ||
