  Approaches to predicting neuronal spike responses commonly use a Poisson
learning objective. This objective quantizes responses into spike counts within
a fixed summation interval, typically on the order of 10 to 100 milliseconds in
duration; however, neuronal responses are often time accurate down to a few
milliseconds, and Poisson models struggle to precisely model them at these
timescales. We propose the concept of a spike distance function that maps
points in time to the temporal distance to the nearest spike. We show that
neural networks can be trained to approximate spike distance functions, and we
present an efficient algorithm for inferring spike trains from the outputs of
these models. Using recordings of chicken and frog retinal ganglion cells
responding to visual stimuli, we compare the performance of our approach to
that of Poisson models trained with various summation intervals. We show that
our approach outperforms the use of Poisson models at spike train inference.
