  In theoretical neuroscience, recent work leverages deep learning tools to
explore how some network attributes critically influence its learning dynamics.
Notably, initial weight distributions with small (resp. large) variance may
yield a rich (resp. lazy) regime, where significant (resp. minor) changes to
network states and representation are observed over the course of learning.
However, in biology, neural circuit connectivity could exhibit a low-rank
structure and therefore differs markedly from the random initializations
generally used for these studies. As such, here we investigate how the
structure of the initial weights -- in particular their effective rank --
influences the network learning regime. Through both empirical and theoretical
analyses, we discover that high-rank initializations typically yield smaller
network changes indicative of lazier learning, a finding we also confirm with
experimentally-driven initial connectivity in recurrent neural networks.
Conversely, low-rank initialization biases learning towards richer learning.
Importantly, however, as an exception to this rule, we find lazier learning can
still occur with a low-rank initialization that aligns with task and data
statistics. Our research highlights the pivotal role of initial weight
structures in shaping learning regimes, with implications for metabolic costs
of plasticity and risks of catastrophic forgetting.
