Measuring Sharpness in Grokking

Neural networks sometimes exhibit grokking, a phenomenon where perfect or near-perfect performance is achieved on a validation set well after the same performance has been obtained on the corresponding training set. In this workshop paper, we introduce a robust technique for measuring grokking, based on fitting an appropriate functional form. We then use this to investigate the sharpness of transitions in training and validation accuracy under two settings. The first setting is the theoretical framework developed by Levi et al. (2023) where closed form expressions are readily accessible. The second setting is a two-layer MLP trained to predict the parity of bits, with grokking induced by the concealment strategy of Miller et al. (2023). We find that trends between relative grokking gap and grokking sharpness are similar in both settings when using absolute and relative measures of sharpness. Reflecting on this, we make progress toward explaining some trends and identify the need for further study to untangle the various mechanisms which influence the sharpness of grokking.