Robust error bounds for quantised and pruned neural networks

Abstract: With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to move towards decentralisation with the data and algorithms stored, and even trained, locally on devices. The device hardware becomes the main bottleneck for model capability in this set-up, creating a need for slimmed down, more efficient neural networks. Neural network pruning and quantisation are two methods that have been developed for this, with both approaches demonstrating impressive results in reducing the computational cost without sacrificing significantly on model performance. However, the understanding behind these reduction methods remains underdeveloped. To address this issue, a semi-definite program is introduced to bound the worst-case error caused by pruning or quantising a neural network. The method can be applied to many neural network structures and nonlinear activation functions with the bounds holding robustly for all inputs in specified sets. It is hoped that the computed bounds will provide certainty to the performance of these algorithms when deployed on safety-critical systems.