Grokking Applied to Chaotic Iterates of the Logistic Map
Donkoh, Felix · Digital Commons - East Tennessee State University (East Tennessee State University) · 2025
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.