Explore >> Select a destination
|
You are here 
|
pomax.github.io | ||
| | | | |
bayesianneuron.com
|
|
| | | | | [AI summary] The user has shared a detailed exploration of optimizing the 0/1 Knapsack problem using dynamic programming with Python and NumPy. They discuss various optimization techniques, including reducing memory usage with a 2-row approach, vectorization using NumPy's `np.where` for faster computation, and the performance improvements achieved. The final implementation shows significant speedups, especially for large-scale problems, and the user highlights the importance of vectorization and efficient memory management in computational tasks. | |
| | | | |
peterbloem.nl
|
|
| | | | | [AI summary] The text provides an in-depth explanation of the Fundamental Theorem of Algebra, which states that every non-constant polynomial of degree $ n $ has exactly $ n $ roots in the complex number system, counting multiplicities. It walks through the proof by first establishing that every polynomial has at least one complex root (using the properties of continuous functions and the complex plane), then using polynomial division to factor the polynomial into linear factors, and finally addressing the nature of roots (real vs. complex) and their multiplicities. The text also touches on the conjugate root theorem, which explains why complex roots of polynomials with real coefficients come in conjugate pairs. | |
| | | | |
www.depthfirstlearning.com
|
|
| | | | | [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... | |
| | | | |
dusted.codes
|
|
| | | The beauty of asymmetric encryption - RSA crash course for developers | ||
