  This paper presents a mixed-computation neural network processing approach
for edge applications that incorporates low-precision (low-width) Posit and
low-precision fixed point (FixP) number systems. This mixed-computation
approach employs 4-bit Posit (Posit4), which has higher precision around zero,
for representing weights with high sensitivity, while it uses 4-bit FixP
(FixP4) for representing other weights. A heuristic for analyzing the
importance and the quantization error of the weights is presented to assign the
proper number system to different weights. Additionally, a gradient
approximation for Posit representation is introduced to improve the quality of
weight updates in the backpropagation process. Due to the high energy
consumption of the fully Posit-based computations, neural network operations
are carried out in FixP or Posit/FixP. An efficient hardware implementation of
a MAC operation with a first Posit operand and FixP for a second operand and
accumulator is presented. The efficacy of the proposed low-precision
mixed-computation approach is extensively assessed on vision and language
models. The results show that, on average, the accuracy of the
mixed-computation is about 1.5% higher than that of FixP with a cost of 0.19%
energy overhead.
