Towards Theoretically Inspired Neural Initialization Optimization

TL;DR

This paper introduces GradCosine, a theoretically motivated metric for neural initialization, and proposes NIO, an automated method to optimize initial weights, improving performance across various architectures and datasets.

Contribution

The paper presents a novel differentiable metric, GradCosine, and an automated initialization optimization algorithm, NIO, for neural networks, reducing reliance on handcrafted initializations.

Findings

NIO improves classification accuracy on CIFAR-10, CIFAR-100, and ImageNet.

GradCosine correlates with training and test performance.

NIO enables training large vision Transformers without warmup.

Abstract

Automated machine learning has been widely explored to reduce human efforts in designing neural architectures and looking for proper hyperparameters. In the domain of neural initialization, however, similar automated techniques have rarely been studied. Most existing initialization methods are handcrafted and highly dependent on specific architectures. In this paper, we propose a differentiable quantity, named GradCosine, with theoretical insights to evaluate the initial state of a neural network. Specifically, GradCosine is the cosine similarity of sample-wise gradients with respect to the initialized parameters. By analyzing the sample-wise optimization landscape, we show that both the training and test performance of a network can be improved by maximizing GradCosine under gradient norm constraint. Based on this observation, we further propose the neural initialization optimization (NIO) algorithm. Generalized from the sample-wise analysis into the real batch setting, NIO is able to automatically look for a better initialization with negligible cost compared with the training time. With NIO, we improve the classification performance of a variety of neural architectures on CIFAR-10, CIFAR-100, and ImageNet. Moreover, we find that our method can even help to train large vision Transformer architecture without warmup.