Jonathan Cornford

Yuhan Helena Liu, Aristide Baratin, Jonathan Cornford et al. · uw

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.

Roy Henha Eyono, Daniel Levenstein, Arna Ghosh et al.

Normalization is a critical operation in neural circuits. In the brain, there is evidence that normalization is implemented via inhibitory interneurons and allows neural populations to adjust to changes in the distribution of their inputs. In artificial neural networks (ANNs), normalization is used to improve learning in tasks that involve complex input distributions. However, it is unclear whether inhibition-mediated normalization in biological neural circuits also improves learning. Here, we explore this possibility using ANNs with separate excitatory and inhibitory populations trained on an image recognition task with variable luminosity. We find that inhibition-mediated normalization does not improve learning if normalization is applied only during inference. However, when this normalization is extended to include back-propagated errors, performance improves significantly. These results suggest that if inhibition-mediated normalization improves learning in the brain, it additionally requires the normalization of learning signals.

Roman Pogodin, Jonathan Cornford, Arna Ghosh et al.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.