Recorded 16 October 2024. Shaowei Lin of the Topos Institute presents "Singular Learning, Relative Information and the Dual Numbers" at IPAM's Theory and Practice of Deep Learning Workshop. Abstract: Relative information (Kullback-Leibler divergence) is a fundamental concept in statistics, machine learning and information theory. In the first half of the talk, I will define conditional relative information, list its axiomatic properties, and describe how it is used in machine learning. For example, according to Sumio Watanabe's Singular Learning Theory, the generalization error of a learning algorithm depends on the structure of algebraic geometric singularities of relative information. In the second half of the talk, I will define the rig category Info of random variables and their conditional maps, as well as the rig category R(e) of dual numbers. Relative information can then be constructed, up to a scalar multiple, via rig monoidal functors from Info to R(e). If time permits, I may discuss how this construction relates to the information cohomology of Baudot, Bennequin and Vigneaux, and to the operad derivations of Bradley. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-theory-and-practice-of-deep-learning/?tab=overview