Learning continuous updating and control of neural population activities from sparse time samples
Zezhao Wu, Mingsha Zhang, and Ning Qian, bioRxiv, 2026, https://www.biorxiv.org/content/10.64898/2026.09.28.754781v1,
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Abstract
The brain frequently updates or controls its internal representations of
sensory or motor variables over time. An example is transsaccadic updating
of stimuli's retinotopic positions: When the eye moves in one direction, the
positions are updated continuously in the opposite direction, and the process
is controlled by the corollary discharge (CD) of the saccade motor command. We
previously trained neural networks to perform such updating using the desired
time courses of stimuli's positions at every time step. However, this may not
be biologically plausible because, before a system learns to perform the task,
it may not have access to complete time courses and the actual visual
inputs are delayed and thus incorrect. Here we show that by adding the
continuity equation to the loss, we can train neural networks with only
stimuli's pre- and post-saccadic retinotopic positions (without specifying the
intermediate transitions), and with heavily down-sampled time courses.
Moreover, both the connectivity patterns and the CD control signal can be
learned simultaneously. Since the continuity equation can be applied to waves of neural
population activities that are distributed representations of variables, our work
also suggests an advantage of distributed representations which are ubiquitous
in the brain.
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