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jhui.github.io | ||
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francisbach.com
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| | | | | [AI summary] The blog post discusses non-convex quadratic optimization problems and their solutions, including the use of strong duality, semidefinite programming (SDP) relaxations, and efficient algorithms. It highlights the importance of these problems in machine learning and optimization, particularly for non-convex problems where strong duality holds. The post also mentions the equivalence between certain non-convex problems and their convex relaxations, such as SDP, and provides examples of when these relaxations are tight or not. Key concepts include the role of eigenvalues in quadratic optimization, the use of Lagrange multipliers, and the application of methods like Newton-Raphson for solving these problems. The author also acknowledges contributions... | |
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www.jeremykun.com
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| | | | | This post is a sequel to Formulating the Support Vector Machine Optimization Problem. The Karush-Kuhn-Tucker theorem Generic optimization problems are hard to solve efficiently. However, optimization problems whose objective and constraints have special structure often succumb to analytic simplifications. For example, if you want to optimize a linear function subject to linear equality constraints, one can compute the Lagrangian of the system and find the zeros of its gradient. More generally, optimizing... | |
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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... | |
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magenta.withgoogle.com
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| | | When a painter creates a work of art, she first blends and explores color options on an artist's palette before applying them to the canvas. This process is ... | ||
