  The majority of the research on the quantization of Deep Neural Networks
(DNNs) is focused on reducing the precision of tensors visible by high-level
frameworks (e.g., weights, activations, and gradients). However, current
hardware still relies on high-accuracy core operations. Most significant is the
operation of accumulating products. This high-precision accumulation operation
is gradually becoming the main computational bottleneck. This is because, so
far, the usage of low-precision accumulators led to a significant degradation
in performance. In this work, we present a simple method to train and fine-tune
high-end DNNs, to allow, for the first time, utilization of cheaper, $12$-bits
accumulators, with no significant degradation in accuracy. Lastly, we show that
as we decrease the accumulation precision further, using fine-grained gradient
approximations can improve the DNN accuracy.
