The Complexity Dynamics of Grokking

We investigate the phenomenon of generalization through the lens of compression. In particular, we study the complexity dynamics of neural networks to explain grokking, where networks suddenly transition from memorizing to generalizing solutions long after over-fitting the training data. To this end we introduce a new measure of intrinsic complexity for neural networks based on the theory of Kolmogorov complexity. Tracking this metric throughout network training, we find a consistent pattern in training dynamics, consisting of a rise and fall in complexity. We demonstrate that this corresponds to memorization followed by generalization. Based on insights from rate--distortion theory and the minimum description length principle, we lay out a principled approach to lossy compression of neural networks, and connect our complexity measure to explicit generalization bounds. Based on a careful analysis of information capacity in neural networks, we propose a new regularization method which encourages networks towards low-rank representations by penalizing their spectral entropy, and find that our regularizer outperforms baselines in total compression of the dataset.

DITTO: Offline Imitation Learning with World Models

We propose DITTO, an offline imitation learning algorithm which uses world models and on-policy reinforcement learning to addresses the problem of covariate shift, without access to an oracle or any additional online interactions. We discuss how world models enable offline, on-policy imitation learning, and propose a simple intrinsic reward defined in the world model latent space that induces imitation learning by reinforcement learning. Theoretically, we show that our formulation induces a divergence bound between expert and learner, in turn bounding the difference in reward. We test our method on difficult Atari environments from pixels alone, and achieve state-of-the-art performance in the offline setting.