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Grokking is an intriguing phenomenon of delayed generalization, where neuralnetworks initially memorize training data with perfect accuracy but exhibitpoor generalization, subsequently transitioning to a generalizing solution withcontinued training. While factors such as weight norms and sparsity have beenproposed to explain this delayed generalization, the influence of networkstructure remains underexplored. In this work, we link the grokking phenomenonto the lottery ticket hypothesis to investigate the impact of internal networkstructures. We demonstrate that utilizing lottery tickets obtained during thegeneralizing phase (termed grokked tickets) significantly reduces delayedgeneralization across various tasks, including multiple modular arithmeticoperations, polynomial regression, sparse parity, and MNIST classification.Through controlled experiments, we show that the mitigation of delayedgeneralization is not due solely to reduced weight norms or increased sparsity,but rather to the discovery of good subnetworks. Furthermore, we find thatgrokked tickets exhibit periodic weight patterns, beneficial graph propertiessuch as increased average path lengths and reduced clustering coefficients, andundergo rapid structural changes that coincide with improvements ingeneralization. Additionally, pruning techniques like the edge-popup algorithmcan identify these effective structures without modifying the weights, therebytransforming memorizing networks into generalizing ones. These resultsunderscore the novel insight that structural exploration plays a pivotal rolein understanding grokking. The implementation code can be accessed via thislink: https://github.com/gouki510/Grokking-Tickets.

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