On the geometry of generalization and memorization in deep neural networks

Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance. To examine the structure of when and where memorization occurs in a deep network, we use a recently developed replica-based mean field theoretic geometric analysis method. We find that all layers preferentially learn from examples which share features, and link this behavior to generalization performance. Memorization predominately occurs in the deeper layers, due to decreasing object manifolds' radius and dimension, whereas early layers are minimally affected. This predicts that generalization can be restored by reverting the final few layer weights to earlier epochs before significant memorization occurred, which is confirmed by the experiments. Additionally, by studying generalization under different model sizes, we reveal the connection between the double descent phenomenon and the underlying model geometry. Finally, analytical analysis shows that networks avoid memorization early in training because close to initialization, the gradient contribution from permuted examples are small. These findings provide quantitative evidence for the structure of memorization across layers of a deep neural network, the drivers for such structure, and its connection to manifold geometric properties.

Untangling in Invariant Speech Recognition

Encouraged by the success of deep neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. Meanwhile, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks. In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network. Finally, we find that the deep representations carry out significant temporal untangling by efficiently extracting task-relevant features at each time step of the computation. Taken together, these findings shed light on how deep auditory models process time dependent input signals to achieve invariant speech recognition, and show how different concepts emerge through the layers of the network.

Label-efficient audio classification through multitask learning and self-supervision

While deep learning has been incredibly successful in modeling tasks with large, carefully curated labeled datasets, its application to problems with limited labeled data remains a challenge. The aim of the present work is to improve the label efficiency of large neural networks operating on audio data through a combination of multitask learning and self-supervised learning on unlabeled data. We trained an end-to-end audio feature extractor based on WaveNet that feeds into simple, yet versatile task-specific neural networks. We describe several easily implemented self-supervised learning tasks that can operate on any large, unlabeled audio corpus. We demonstrate that, in scenarios with limited labeled training data, one can significantly improve the performance of three different supervised classification tasks individually by up to 6% through simultaneous training with these additional self-supervised tasks. We also show that incorporating data augmentation into our multitask setting leads to even further gains in performance.