  Efficient machine learning implementations optimized for inference in
hardware have wide-ranging benefits depending on the application from lower
inference latencies to higher data throughputs to more efficient energy
consumption. Two popular techniques for reducing computation in neural networks
are pruning, removing insignificant synapses, and quantization, reducing the
precision of the calculations. In this work, we explore the interplay between
pruning and quantization during the training of neural networks for ultra low
latency applications targeting high energy physics use cases. However,
techniques developed for this study have potential application across many
other domains. We study various configurations of pruning during
quantization-aware training, which we term \emph{quantization-aware pruning}
and the effect of techniques like regularization, batch normalization, and
different pruning schemes on multiple computational or neural efficiency
metrics. We find that quantization-aware pruning yields more computationally
efficient models than either pruning or quantization alone for our task.
Further, quantization-aware pruning typically performs similar to or better in
terms of computational efficiency compared to standard neural architecture
optimization techniques. While the accuracy for the benchmark application may
be similar, the information content of the network can vary significantly based
on the training configuration.
