Overparameterized neural networks implement associative memory

Identifying computational mechanisms for memorization and retrieval of data is a long-standing problem at the intersection of machine learning and neuroscience. Our main finding is that standard overparameterized deep neural networks trained using standard optimization methods implement such a mechanism for real-valued data. We provide empirical evidence that 1) overparameterized autoencoders store training samples as attractors and thus iterating the learned map leads to sample recovery, and that 2) the same mechanism allows for encoding sequences of examples and serves as an even more efficient mechanism for memory than autoencoding. Theoretically, we prove that when trained on a single example, autoencoders store the example as an attractor. Lastly, by treating a sequence encoder as a composition of maps, we prove that sequence encoding provides a more efficient mechanism for memory than autoencoding.