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almostsuremath.com | ||
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qchu.wordpress.com
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| | | | | (Part I of this post ishere) Let $latex p(n)$ denote the partition function, which describes the number of ways to write $latex n$ as a sum of positive integers, ignoring order. In 1918 Hardy and Ramanujan proved that $latex p(n)$ is given asymptotically by $latex \displaystyle p(n) \approx \frac{1}{4n \sqrt{3}} \exp \left( \pi \sqrt{ \frac{2n}{3}... | |
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terrytao.wordpress.com
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| | | | | Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ... | |
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francisbach.com
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| | | | | [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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www.josephamccullough.com
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| | | [AI summary] A blog post announces new miniatures releases from Frostgrave Fireheart, including the Barbarian II box, available for purchase. | ||
