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On the Convergence of the Unadjusted Langevin Algorithm
| | www.randomservices.org
Continuous Distributions
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| | [AI summary] The text covers various topics in probability and statistics, including continuous distributions, empirical density functions, and data analysis. It discusses the uniform distribution, rejection sampling, and the construction of continuous distributions without probability density functions. The text also includes data analysis exercises involving empirical density functions for body weight, body length, and gender-specific body weight.
| | francisbach.com
Scaling laws of optimization - Machine Learning Research Blog
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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.
| | yang-song.net
Generative Modeling by Estimating Gradients of the Data Distribution | Yang Song
2.1 parsecs away

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| | This blog post focuses on a promising new direction for generative modeling. We can learn score functions (gradients of log probability density functions) on a large number of noise-perturbed data distributions, then generate samples with Langevin-type sampling. The resulting generative models, often called score-based generative models, has several important advantages over existing model families: GAN-level sample quality without adversarial training, flexible model architectures, exact log-likelihood ...
| | bartoszmilewski.com
Symmetries and Redundancies | Bartosz Milewski's Programming Cafe
25.1 parsecs away

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| From the outside it might seem like physics and mathematics are a match made in heaven. In practice, it feels more like physicists are given a very short blanket made of math, and when they stretch it to cover their heads, their feet are freezing, and vice versa. Physicists turn reality into numbers. They process...