  This paper considers the problem of neural decoding from parallel neural
measurements systems such as micro-electrocorticography ($\mu$-ECoG). In
systems with large numbers of array elements at very high sampling rates, the
dimension of the raw measurement data may be large. Learning neural decoders
for this high-dimensional data can be challenging, particularly when the number
of training samples is limited. To address this challenge, this work presents a
novel neural network decoder with a low-rank structure in the first hidden
layer. The low-rank constraints dramatically reduce the number of parameters in
the decoder while still enabling a rich class of nonlinear decoder maps. The
low-rank decoder is illustrated on $\mu$-ECoG data from the primary auditory
cortex (A1) of awake rats. This decoding problem is particularly challenging
due to the complexity of neural responses in the auditory cortex and the
presence of confounding signals in awake animals. It is shown that the proposed
low-rank decoder significantly outperforms models using standard dimensionality
reduction techniques such as principal component analysis (PCA).
