Initialization and Regularization of Factorized Neural Layers

Mikhail Khodak, Neil A. Tenenholtz, Lester Mackey, Nicolo Fusi

Keywords: model compression, knowledge distillation, multi-head attention, matrix factorization

Abstract: Factorized layers—operations parameterized by products of two or more matrices—occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention architectures. We study how to initialize and regularize deep nets containing such layers, examining two simple, understudied schemes, spectral initialization and Frobenius decay, for improving their performance. The guiding insight is to design optimization routines for these networks that are as close as possible to that of their well-tuned, non-decomposed counterparts; we back this intuition with an analysis of how the initialization and regularization schemes impact training with gradient descent, drawing on modern attempts to understand the interplay of weight-decay and batch-normalization. Empirically, we highlight the benefits of spectral initialization and Frobenius decay across a variety of settings. In model compression, we show that they enable low-rank methods to significantly outperform both unstructured sparsity and tensor methods on the task of training low-memory residual networks; analogs of the schemes also improve the performance of tensor decomposition techniques. For knowledge distillation, Frobenius decay enables a simple, overcomplete baseline that yields a compact model from over-parameterized training without requiring retraining with or pruning a teacher network. Finally, we show how both schemes applied to multi-head attention lead to improved performance on both translation and unsupervised pre-training.

One-sentence Summary: Principled initialization and regularization of factorized neural layers leads to strong performance in compression, knowledge distillation, and language modeling tasks.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Code: [ microsoft/fnl_paper](https://github.com/microsoft/fnl_paper)

Data: [CIFAR-10](https://paperswithcode.com/dataset/cifar-10), [CIFAR-100](https://paperswithcode.com/dataset/cifar-100), [ImageNet](https://paperswithcode.com/dataset/imagenet), [SQuAD](https://paperswithcode.com/dataset/squad)

Community Implementations: [ 6 code implementations](https://www.catalyzex.com/paper/arxiv:2105.01029/code)