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walkingrandomly.com | ||
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opguides.info
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| | | | | 6 - Matrix Theory / Linear Algebra # Below is a 15 video series that totals a bit under 3 hours. Interactive Linear Algebra, text book that actually uses the web Linear Algebra Done Wrong - Sergei Treil @ Brown University Matrices, Diagrammatically Linear Algebra - Jim Hefferson Linear Algebra and Applications: An Inquiry-Based Approach | |
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nhigham.com
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| | | | | Backward error is a measure of error associated with an approximate solution to a problem. Whereas the forward error is the distance between the approximate and true solutions, the backward error is how much the data must be perturbed to produce the approximate solution. For a function $latex f$ from $latex \mathbb{R}^n$ to $latex \mathbb{R}^n$ | |
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nla-group.org
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| | | | | by Sven Hammarling and Nick Higham It is often thought that Jim Wilkinson developed backward error analysis because of his early involvement in solving systems of linear equations. In his 1970 Turing lecture [5] he described an experience, during world war II at the Armament Research Department, of solving a system of twelve linear equations | |
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iclr-blogposts.github.io
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| | | The product between the Hessian of a function and a vector, the Hessian-vector product (HVP), is a fundamental quantity to study the variation of a function. It is ubiquitous in traditional optimization and machine learning. However, the computation of HVPs is often considered prohibitive in the context of deep learning, driving practitioners to use proxy quantities to evaluate the loss geometry. Standard automatic differentiation theory predicts that the computational complexity of an HVP is of the same order of magnitude as the complexity of computing a gradient. The goal of this blog post is to provide a practical counterpart to this theoretical result, showing that modern automatic differentiation frameworks, JAX and PyTorch, allow for efficient computat... | ||
