Large step sizes are necessary to learn the "threshold neuron" of a ReLU network

Large step sizes are necessary to learn the "threshold neuron" of a ReLU network

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate.

Enhancing the computational efficiency of on-device Deep Neural Networks (DNNs) remains a significant challengein mobile and edge computing. As we aim to execute increasingly complex tasks with constrained computational resources, much of the research has focused on compressing neural network structures and optimizing systems. Although many studies have focused on compressing neural network structures and parameters or optimizing underlying systems, there has been limited attention on optimizing the fundamental building blocks of neural networks: the neurons. In this study, we deliberate on a simple but important research question: Can we design artificial neurons that offer greater efficiency than the traditional neuron paradigm? Inspired by the threshold mechanisms and the excitation-inhibition balance observed in biological neurons, we propose a novel artificial neuron model, Threshold Neurons. Using Threshold Neurons, we can construct neural networks similar to those with traditional artificial neurons, while significantly reducing hardware implementation complexity. Our extensive experiments validate the effectiveness of neural networks utilizing Threshold Neurons, achieving substantial power savings of 7.51x to 8.19x and area savings of 3.89x to 4.33x at the kernel level, with minimal loss in precision. Furthermore, FPGA-based implementations of these networks demonstrate 2.52x power savings and 1.75x speed enhancements at the system level. The source code will be made available upon publication.

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al. (ICLR 2021), which exhibit startling new phenomena (the "edge of stability" or "unstable convergence") and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks. For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons (i.e., neurons with a non-zero first-layer bias). This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

Given such a classification task in most cases it is not too difficult to devise a network architecture that is capable of learning the input-output relation as represented by a number of training examples.

Given such a classification task in most cases it is not too difficult to devise a network architecture that is capable of learning the input-output relation as represented by a number of training examples.

Given such a classification task in most cases it is not too difficult to devise a network architecture that is capable of learning the input-output relation as represented by a number of training examples.