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greydanus.github.io | ||
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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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bayesianneuron.com
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| | | | | [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. | |
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mcyoung.xyz
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| | | | | [AI summary] This text provides an in-depth explanation of linear algebra concepts, including vector spaces, linear transformations, matrix multiplication, and field extensions. It emphasizes the importance of understanding these concepts through the lens of linear maps and their composition, which naturally leads to the matrix multiplication formula. The text also touches on the distinction between vector spaces and abelian groups, and discusses the concept of field extensions, such as [R:Q] and [C:R]. The author mentions their art blog and acknowledges their own drawing of the content. | |
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alanrendall.wordpress.com
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| | | In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I... | ||
