We analyze deep ReLU neural networks trained with mini-batch stochastic gradient decent and weight decay. We prove that the source of the SGD noise is an implicit low rank constraint across all of the weight matrices within the network. Furthermore, we show, both theoretically and empirically, that when training a neural network using Stochastic Gradient Descent (SGD) with a small batch size, the resulting weight matrices are expected to be of small rank. Our analysis relies on a minimal set of assumptions and the neural networks may include convolutional layers, residual connections, as well as batch normalization layers.
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Taming the Noisy Gradient: Train Deep Neural Networks with Small Batch Sizes
Deep learning architectures are usually proposed with millions of parameters, resulting in a memory issue when training deep neural networks with stochastic gradient descent type methods using large batch sizes. However, training with small batch sizes tends to produce low quality solution due to the large variance of stochastic gradients. In this paper, we tackle this problem by proposing a new framework for training deep neural network with small batches/noisy gradient. During optimization, our method iteratively applies a proximal type regularizer to make loss function strongly convex. Such regularizer stablizes the gradient, leading to better training performance. We prove that our algorithm achieves comparable convergence rate as vanilla SGD even with small batch size. Our framework is simple to implement and can be potentially combined with many existing optimization algorithms. Empirical results show that our method outperforms SGD and Adam when batch size is small. Our implementation is available at https://github.com/huiqu18/TRAlgorithm.
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- Award ID(s):
- 1855759
- PAR ID:
- 10108626
- Date Published:
- Journal Name:
- The Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI)
- Page Range / eLocation ID:
- 4348 to 4354
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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