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terrytao.wordpress.com | ||
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almostsuremath.com
In today's post, I investigate a simple recurrence relation and show how it is possible to describe its behaviour asymptotically at large times. The relation describing how the series evolves at a time n will depend both on its value at the earlier time n/2 and on whether n is even or odd, which, as... |
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francisbach.com
[AI summary] This text discusses the scaling laws of optimization in machine learning, focusing on asymptotic expansions for both strongly convex and non-strongly convex cases. It covers the derivation of performance bounds using techniques like Laplace's method and the behavior of random minimizers. The text also explains the 'weird' behavior observed in certain plots, where non-strongly convex bounds become tight under specific conditions. The analysis connects theoretical results to practical considerations in optimization algorithms. |
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anuragbishnoi.wordpress.com
Finite geometry is often used to construct graphs with certain extremal properties. For example, the Norm graphs are one of the best-known constructions in extremal graph theory (see this for a geometrical description of these graphs). Similarly, generalized polygons, and their substructures, give various constructions in Ramsey theory, the degrtocee-diameter problem, and the (bipartite) forbidden... |
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dustintran.com
Alireza Makhzani, Jonathon Shlens, Navdeep Jaitly, and Ian Goodfellow. Adversarial Autoencoders. arXiv preprint arXiv:1511.05644, 2015. |
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