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Jonathan Cornford

cornforj@mila.quebec
Postdoctorat - McGill University
Superviseur⋅e principal⋅e
Blake Richards

Publications

How connectivity structure shapes rich and lazy learning in neural circuits
Yuhan Helena Liu
Aristide Baratin
Jonathan Cornford
Stefan Mihalas
Eric Todd SheaBrown
Guillaume Lajoie
In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learn… (voir plus)ing 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 generally has 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.
2024-01-16
ICLR.cc/2024/Conference (poster)
doi.org
openreview.net
Synaptic Weight Distributions Depend on the Geometry of Plasticity
Roman Pogodin
Jonathan Cornford
Arna Ghosh
Gauthier Gidel
Guillaume Lajoie
Blake Richards
A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic … (voir plus)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.
2024-01-16
ICLR.cc/2024/Conference (spotlight)
doi.org
openreview.net
Learning better with Dale’s Law: A Spectral Perspective
Pingsheng Li
Jonathan Cornford
Arna Ghosh
Blake Richards
openreview.net
Learning to live with Dale's principle: ANNs with separate excitatory and inhibitory units
Jonathan Cornford
Damjan Kalajdzievski
Marco Leite
Amélie Lamarquette
Dimitri Michael Kullmann
Blake Richards
The units in artificial neural networks (ANNs) can be thought of as abstractions of biological neurons, and ANNs are increasingly used in ne… (voir plus)uroscience research. However, there are many important differences between ANN units and real neurons. One of the most notable is the absence of Dale's principle, which ensures that biological neurons are either exclusively excitatory or inhibitory. Dale's principle is typically left out of ANNs because its inclusion impairs learning. This is problematic, because one of the great advantages of ANNs for neuroscience research is their ability to learn complicated, realistic tasks. Here, by taking inspiration from feedforward inhibitory interneurons in the brain we show that we can develop ANNs with separate populations of excitatory and inhibitory units that learn just as well as standard ANNs. We call these networks Dale's ANNs (DANNs). We present two insights that enable DANNs to learn well: (1) DANNs are related to normalization schemes, and can be initialized such that the inhibition centres and standardizes the excitatory activity, (2) updates to inhibitory neuron parameters should be scaled using corrections based on the Fisher Information matrix. These results demonstrate how ANNs that respect Dale's principle can be built without sacrificing learning performance, which is important for future work using ANNs as models of the brain. The results may also have interesting implications for how inhibitory plasticity in the real brain operates.
2021-01-12
ICLR.cc/2021/Conference (poster)
doi.org
openreview.net