  The machine learning community has become increasingly interested in the
energy efficiency of neural networks. The Spiking Neural Network (SNN) is a
promising approach to energy-efficient computing, since its activation levels
are quantized into temporally sparse, one-bit values (i.e., "spike" events),
which additionally converts the sum over weight-activity products into a simple
addition of weights (one weight for each spike). However, the goal of
maintaining state-of-the-art (SotA) accuracy when converting a non-spiking
network into an SNN has remained an elusive challenge, primarily due to spikes
having only a single bit of precision. Adopting tools from signal processing,
we cast neural activation functions as quantizers with temporally-diffused
error, and then train networks while smoothly interpolating between the
non-spiking and spiking regimes. We apply this technique to the Legendre Memory
Unit (LMU) to obtain the first known example of a hybrid SNN outperforming SotA
recurrent architectures -- including the LSTM, GRU, and NRU -- in accuracy,
while reducing activities to at most 3.74 bits on average with 1.26 significant
bits multiplying each weight. We discuss how these methods can significantly
improve the energy efficiency of neural networks.
