Bridging Lottery Ticket and Grokking: Understanding Grokking from Inner Structure of Networks

Gouki Minegishi, Yusuke Iwasawa, Yutaka Matsuo

Keywords: Grokking, Lottery ticket, Generalization, Representation

Abstract:

Grokking is the intriguing phenomenon of delayed generalization: networks ini-
tially memorize training data with perfect accuracy but poor generalization, then
transition to a generalizing solution with continued training. While reasons for this
delayed generalization, such as weight norms and sparsity, have been discussed,
the influence of network structure, particularly the role of subnetworks, remains
underexplored. In this work, we link the grokking phenomenon to the lottery ticket
hypothesis to investigate the impact of inner network structures. We demonstrate
that using lottery tickets obtained at the generalizing phase (termed ‘grokking
tickets’) significantly reduces delayed generalization on various tasks, including
multiple modular arithmetic, polynomial regression, sparse parity, and MNIST.
Through a series of controlled experiments, our findings reveal that neither small
weight norms nor sparsity alone account for the reduction of delayed generalization;
instead, the presence of a good subnetwork structure is crucial. Analyzing the
transition from memorization to generalization, we observe that rapid changes
in subnetwork structures, measured by the Jaccard distance, correlate strongly
with improvements in test accuracy. We further show that pruning techniques
can accelerate the grokking process, transforming a memorizing network into a
generalizing one without updating the weights. Finally, we confirm the emergence
of periodic inner-structures, indicating that the model discovers internally good
structures (generalizing structures) suited for the task.

Primary Area: interpretability and explainable AI

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Submission Number: 10415