  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.
