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A plethora of recent research has focused on improving the memory footprintand inference speed of deep networks by reducing the complexity of (i)numerical representations (for example, by deterministic or stochasticquantization) and (ii) arithmetic operations (for example, by binarization ofweights).  We propose a stochastic binarization scheme for deep networks that allows forefficient inference on hardware by restricting itself to additions of smallintegers and fixed shifts. Unlike previous approaches, the underlyingrandomized approximation is progressive, thus permitting an adaptive control ofthe accuracy of each operation at run-time. In a low-precision setting, wematch the accuracy of previous binarized approaches. Our representation isunbiased - it approaches continuous computation with increasing sample size. Ina high-precision regime, the computational costs are competitive with previousquantization schemes. Progressive stochastic binarization also permitslocalized, dynamic accuracy control within a single network, thereby providinga new tool for adaptively focusing computational attention.  We evaluate our method on networks of various architectures, alreadypretrained on ImageNet. With representational costs comparable to previousschemes, we obtain accuracies close to the original floating pointimplementation. This includes pruned networks, except the known special case ofcertain types of separated convolutions. By focusing computational attentionusing progressive sampling, we reduce inference costs on ImageNet further by afactor of up to 33% (before network pruning).

Progressive Stochastic Binarization of Deep Networks