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While neural networks have been remarkably successful in a wide array ofapplications, implementing them in resource-constrained hardware remains anarea of intense research. By replacing the weights of a neural network withquantized (e.g., 4-bit, or binary) counterparts, massive savings in computationcost, memory, and power consumption are attained. To that end, we generalize apost-training neural-network quantization method, GPFQ, that is based on agreedy path-following mechanism. Among other things, we propose modificationsto promote sparsity of the weights, and rigorously analyze the associatederror. Additionally, our error analysis expands the results of previous work onGPFQ to handle general quantization alphabets, showing that for quantizing asingle-layer network, the relative square error essentially decays linearly inthe number of weights -- i.e., level of over-parametrization. Our result holdsacross a range of input distributions and for both fully-connected andconvolutional architectures thereby also extending previous results. Toempirically evaluate the method, we quantize several common architectures withfew bits per weight, and test them on ImageNet, showing only minor loss ofaccuracy compared to unquantized models. We also demonstrate that standardmodifications, such as bias correction and mixed precision quantization,further improve accuracy.

Post-training Quantization for Neural Networks with Provable Guarantees