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Block Floating Point (BFP) can efficiently support quantization for DeepNeural Network (DNN) training by providing a wide dynamic range via a sharedexponent across a group of values. In this paper, we propose a Fast First,Accurate Second Training (FAST) system for DNNs, where the weights,activations, and gradients are represented in BFP. FAST supports matrixmultiplication with variable precision BFP input operands, enabling incrementalincreases in DNN precision throughout training. By increasing the BFP precisionacross both training iterations and DNN layers, FAST can greatly shorten thetraining time while reducing overall hardware resource usage. Our FASTMultipler-Accumulator (fMAC) supports dot product computations under multipleBFP precisions. We validate our FAST system on multiple DNNs with differentdatasets, demonstrating a 2-6$\times$ speedup in training on a single-chipplatform over prior work based on \textbf{mixed-precision or block} floatingpoint number systems while achieving similar performance in validationaccuracy.

FAST: DNN Training Under Variable Precision Block Floating Point with Stochastic Rounding