  Recurrent neural networks are widely used for modeling spatio-temporal
sequences in both nature language processing and neural population dynamics.
However, understanding the temporal credit assignment is hard. Here, we propose
that each individual connection in the recurrent computation is modeled by a
spike and slab distribution, rather than a precise weight value. We then derive
the mean-field algorithm to train the network at the ensemble level. The method
is then applied to classify handwritten digits when pixels are read in
sequence, and to the multisensory integration task that is a fundamental
cognitive function of animals. Our model reveals important connections that
determine the overall performance of the network. The model also shows how
spatio-temporal information is processed through the hyperparameters of the
distribution, and moreover reveals distinct types of emergent neural
selectivity. To provide a mechanistic analysis of the ensemble learning, we
first derive an analytic solution of the learning at the
infinitely-large-network limit. We then carry out a low-dimensional projection
of both neural and synaptic dynamics, analyze symmetry breaking in the
parameter space, and finally demonstrate the role of stochastic plasticity in
the recurrent computation. Therefore, our study sheds light on mechanisms of
how weight uncertainty impacts the temporal credit assignment in recurrent
neural networks from the ensemble perspective.
