  Various animals, including humans, have been suggested to perform Bayesian
inferences to handle noisy, time-varying external information. In performing
Bayesian inference, the prior distribution must be shaped by sampling noisy
external inputs. However, the mechanism by which neural activities represent
such distributions has not yet been elucidated. In this study, we demonstrated
that the neural networks with modular structures including fast and slow
modules effectively represented the prior distribution in performing accurate
Bayesian inferences. Using a recurrent neural network consisting of a main
module connected with input and output layers and a sub-module connected only
with the main module and having slower neural activity, we demonstrated that
the modular network with distinct time scales performed more accurate Bayesian
inference compared with the neural networks with uniform time scales. Prior
information was represented selectively by the slow sub-module, which could
integrate observed signals over an appropriate period and represent input means
and variances. Accordingly, the network could effectively predict the
time-varying inputs. Furthermore, by training the time scales of neurons
starting from networks with uniform time scales and without modular structure,
the above slow-fast modular network structure spontaneously emerged as a result
of learning wherein prior information was selectively represented in the slower
sub-module. These results explain how the prior distribution for Bayesian
inference is represented in the brain, provide insight into the relevance of
modular structure with time scale hierarchy to information processing, and
elucidate the significance of brain areas with slower time scales.
