Memory capacity of neural networks with threshold and ReLU activations
This resolves a foundational theoretical problem in machine learning regarding the memorization capacity of neural networks.
The paper proves that mildly overparametrized neural networks with threshold or mixed threshold and ReLU activations can memorize training data with 100% accuracy, addressing a long-standing open question from 1988.
Overwhelming theoretical and empirical evidence shows that mildly overparametrized neural networks -- those with more connections than the size of the training data -- are often able to memorize the training data with $100\%$ accuracy. This was rigorously proved for networks with sigmoid activation functions and, very recently, for ReLU activations. Addressing a 1988 open question of Baum, we prove that this phenomenon holds for general multilayered perceptrons, i.e. neural networks with threshold activation functions, or with any mix of threshold and ReLU activations. Our construction is probabilistic and exploits sparsity.