Walking Noise: Understanding Implications of Noisy Computations on Classification Tasks

Machine learning methods like neural networks are extremely successful and popular in a variety of applications, however, they come at substantial computational costs, accompanied by high energy demands. In contrast, hardware capabilities are limited and there is evidence that technology scaling is stuttering, therefore, new approaches to meet the performance demands of increasingly complex model architectures are required. As an unsafe optimization, noisy computations are more energy efficient, and given a fixed power budget also more time efficient. However, any kind of unsafe optimization requires counter measures to ensure functionally correct results. This work considers noisy computations in an abstract form, and gears to understand the implications of such noise on the accuracy of neural-network-based classifiers as an exemplary workload. We propose a methodology called "Walking Noise" that allows to assess the robustness of different layers of deep architectures by means of a so-called "midpoint noise level" metric. We then investigate the implications of additive and multiplicative noise for different classification tasks and model architectures, with and without batch normalization. While noisy training significantly increases robustness for both noise types, we observe a clear trend to increase weights and thus increase the signal-to-noise ratio for additive noise injection. For the multiplicative case, we find that some networks, with suitably simple tasks, automatically learn an internal binary representation, hence becoming extremely robust. Overall this work proposes a method to measure the layer-specific robustness and shares first insights on how networks learn to compensate injected noise, and thus, contributes to understand robustness against noisy computations.