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Quantized Neural Networks (QNNs) are often used to improve network efficiencyduring the inference phase, i.e. after the network has been trained. Extensiveresearch in the field suggests many different quantization schemes. Still, thenumber of bits required, as well as the best quantization scheme, are yetunknown. Our theoretical analysis suggests that most of the training process isrobust to substantial precision reduction, and points to only a few specificoperations that require higher precision. Armed with this knowledge, wequantize the model parameters, activations and layer gradients to 8-bit,leaving at a higher precision only the final step in the computation of theweight gradients. Additionally, as QNNs require batch-normalization to betrained at high precision, we introduce Range Batch-Normalization (BN) whichhas significantly higher tolerance to quantization noise and improvedcomputational complexity. Our simulations show that Range BN is equivalent tothe traditional batch norm if a precise scale adjustment, which can beapproximated analytically, is applied. To the best of the authors' knowledge,this work is the first to quantize the weights, activations, as well as asubstantial volume of the gradients stream, in all layers (including batchnormalization) to 8-bit while showing state-of-the-art results over theImageNet-1K dataset.

Scalable Methods for 8-bit Training of Neural Networks