Physical Sciences and Mathematics Commons^™

Un-Fair Trojan: Targeted Backdoor Attacks Against Model Fairness, Nicholas Furth

Theses

Machine learning models have been shown to be vulnerable against various backdoor and data poisoning attacks that adversely affect model behavior. Additionally, these attacks have been shown to make unfair predictions with respect to certain protected features. In federated learning, multiple local models contribute to a single global model communicating only using local gradients, the issue of attacks become more prevalent and complex. Previously published works revolve around solving these issues both individually and jointly. However, there has been little study on the effects of attacks against model fairness. Demonstrated in this work, a flexible attack, which we call Un-Fair …

Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, William Joseph Mccann

Theses

In this thesis, Stochastic Gradient Descent (SGD), an optimization method originally popular due to its computational efficiency, is analyzed using Markov chain methods. We compute both numerically, and in some cases analytically, the stationary probability distributions (invariant measures) for the SGD Markov operator over all step sizes or learning rates. The stationary probability distributions provide insight into how the long-time behavior of SGD samples the objective function minimum.

A key focus of this thesis is to provide a systematic study in one dimension comparing the exact SGD stationary distributions to the Fokker-Planck diffusion approximation equations —which are commonly used in …