  This work explores the search for heterogeneous approximate multiplier
configurations for neural networks that produce high accuracy and low energy
consumption. We discuss the validity of additive Gaussian noise added to
accurate neural network computations as a surrogate model for behavioral
simulation of approximate multipliers. The continuous and differentiable
properties of the solution space spanned by the additive Gaussian noise model
are used as a heuristic that generates meaningful estimates of layer robustness
without the need for combinatorial optimization techniques. Instead, the amount
of noise injected into the accurate computations is learned during network
training using backpropagation. A probabilistic model of the multiplier error
is presented to bridge the gap between the domains; the model estimates the
standard deviation of the approximate multiplier error, connecting solutions in
the additive Gaussian noise space to actual hardware instances. Our experiments
show that the combination of heterogeneous approximation and neural network
retraining reduces the energy consumption for multiplications by 70% to 79% for
different ResNet variants on the CIFAR-10 dataset with a Top-1 accuracy loss
below one percentage point. For the more complex Tiny ImageNet task, our VGG16
model achieves a 53 % reduction in energy consumption with a drop in Top-5
accuracy of 0.5 percentage points. We further demonstrate that our error model
can predict the parameters of an approximate multiplier in the context of the
commonly used additive Gaussian noise (AGN) model with high accuracy. Our
software implementation is available under
https://github.com/etrommer/agn-approx.
