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matthewmcateer.me | ||
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iamirmasoud.com
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| | | | | Amir Masoud Sefidian | |
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francisbach.com
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| | | | | [AI summary] The blog post discusses the spectral properties of kernel matrices, focusing on the analysis of eigenvalues and their estimation using tools like the matrix Bernstein inequality. It also covers the estimation of the number of integer vectors with a given L1 norm and the relationship between these counts and combinatorial structures. The post includes a detailed derivation of bounds for the difference between true and estimated eigenvalues, highlighting the role of the degrees of freedom and the impact of regularization in kernel methods. Additionally, it touches on the importance of spectral analysis in machine learning and its applications in various domains. | |
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peterbloem.nl
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| | | | | [AI summary] The pseudo-inverse is a powerful tool for solving matrix equations, especially when the inverse does not exist. It provides exact solutions when they exist and least squares solutions otherwise. If multiple solutions exist, it selects the one with the smallest norm. The pseudo-inverse can be computed using the singular value decomposition (SVD), which is numerically stable and handles cases where the matrix does not have full column rank. The SVD approach involves computing the SVD of the matrix, inverting the non-zero singular values, and then reconstructing the pseudo-inverse using the modified SVD components. This method is preferred due to its stability and ability to handle noisy data effectively. | |
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siddhartha-gadgil.github.io
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| | | [AI summary] The text discusses a formalization in Lean 4 of a mathematical result related to the group P and the unit conjecture. It outlines the construction of the group P as a metabelian group with a specific action and cocycle, the proof of its torsion freeness, and the use of decidable equality and enumeration to verify properties. The formalization also includes the construction of the group ring and the verification of Gardam's disproof of the unit conjecture by demonstrating the existence of a non-trivial unit in the group ring over the field F₂. | ||
