Memorization in Overparameterized Autoencoders
This addresses the problem of understanding generalization in overparameterized neural networks for researchers, though it is incremental as it builds on existing memorization studies.
The paper demonstrates that overparameterized autoencoders memorize training data by constraining learned functions around examples, proving that single-layer autoencoders project data onto the training span and deep ones converge to examples through local contractivity.
The ability of deep neural networks to generalize well in the overparameterized regime has become a subject of significant research interest. We show that overparameterized autoencoders exhibit memorization, a form of inductive bias that constrains the functions learned through the optimization process to concentrate around the training examples, although the network could in principle represent a much larger function class. In particular, we prove that single-layer fully-connected autoencoders project data onto the (nonlinear) span of the training examples. In addition, we show that deep fully-connected autoencoders learn a map that is locally contractive at the training examples, and hence iterating the autoencoder results in convergence to the training examples. Finally, we prove that depth is necessary and provide empirical evidence that it is also sufficient for memorization in convolutional autoencoders. Understanding this inductive bias may shed light on the generalization properties of overparametrized deep neural networks that are currently unexplained by classical statistical theory.