Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
12-2025
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Rodney Keaton, Robert A. Beeler
Abstract
This thesis investigates grokking, the delayed transition from memorization to generalization in neural networks trained on deterministic chaotic data. Using an integer–arithmetic discretization of the logistic map, yn+1 =( a yn(p − yn))/ p 2 , bounded aperiodic sequences were generated across control parameters α ranging from 3.0 to 4.0. Transformer-based models displayed characteristic grokking curves. In periodic and chaotic regimes, validation accuracy rose suddenly after long plateaus, while at the Feigenbaum boundary (α ≈ 3.57) generalization failed completely. Increasing data diversity restored learning in chaotic domains, and explicit α–conditioning enabled a single network to generalize across all regimes. A bifurcation diagram of model-predicted data reproduced the main features of the true logistic map, confirming that the network captured the underlying dynamics. These results link delayed generalization in deep learning to structural transitions in deterministic chaos.
Document Type
Thesis - unrestricted
Recommended Citation
Donkoh, Felix, "Grokking Applied to Chaotic Iterates of the Logistic Map" (2025). Electronic Theses and Dissertations. Paper 4613. https://dc.etsu.edu/etd/4613
Copyright
Copyright by the authors.
