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Quantized Neural Networks (QNNs) use low bit-width fixed-point numbers forrepresenting weight parameters and activations, and are often used inreal-world applications due to their saving of computation resources andreproducibility of results.  Batch Normalization (BN) poses a challenge for QNNs for requiring floatingpoints in reciprocal operations, and previous QNNs either require computing BNat high precision or revise BN to some variants in heuristic ways.  In this work, we propose a novel method to quantize BN by converting anaffine transformation of two floating points to a fixed-point operation withshared quantized scale, which is friendly for hardware acceleration and modeldeployment.  We confirm that our method maintains same outputs through rigoroustheoretical analysis and numerical analysis. Accuracy and efficiency of ourquantization method are verified by experiments at layer level on CIFAR andImageNet datasets.  We also believe that our method is potentially useful in other problemsinvolving quantization.

Optimal Quantization for Batch Normalization in Neural Network Deployments and Beyond