Overparameterized Neural Networks Implement Associative Memory
This addresses a fundamental problem in machine learning and neuroscience for understanding memory mechanisms, but it appears incremental as it builds on existing overparameterized network concepts.
The paper tackles the problem of computational mechanisms for memorization and retrieval in neural networks, showing that overparameterized deep networks trained with standard methods implement associative memory for real-valued data, with sequence encoding proving more efficient than autoencoding.
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. Empirically, we show that: (1) overparameterized autoencoders store training samples as attractors, and thus, iterating the learned map leads to sample recovery; (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.