Identity Crisis: Memorization and Generalization under Extreme Overparameterization
This work addresses the problem of understanding inductive biases in neural network architectures for researchers in machine learning, though it is incremental in exploring extreme overparameterization scenarios.
The authors investigated how overparameterized networks memorize or generalize from a single training example on an identity-mapping task, finding that convolutional networks (CNNs) can generalize with up to 10 layers while fully-connected networks (FCNs) often fail even with 60k examples, and deeper CNNs tend to memorize by growing patterns from boundaries.
We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize the reconstruction error. The trained networks stereotypically take one of two forms: the constant function (memorization) and the identity function (generalization). We formally characterize generalization in single-layer FCNs and CNNs. We show empirically that different architectures exhibit strikingly different inductive biases. For example, CNNs of up to 10 layers are able to generalize from a single example, whereas FCNs cannot learn the identity function reliably from 60k examples. Deeper CNNs often fail, but nonetheless do astonishing work to memorize the training output: because CNN biases are location invariant, the model must progressively grow an output pattern from the image boundaries via the coordination of many layers. Our work helps to quantify and visualize the sensitivity of inductive biases to architectural choices such as depth, kernel width, and number of channels.