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Computational neuroscience relies on gradient descent (GD) for training artificial neural network (ANN) models of the brain. The advantage o… (voir plus)f GD is that it is effective at learning difficult tasks. However, it produces ANNs that are a poor phenomenological fit to biology, making them less relevant as models of the brain. Specifically, it violates Dale’s law, by allowing synapses to change from excitatory to inhibitory, and leads to synaptic weights that are not log-normally distributed, contradicting experimental data. Here, starting from first principles of optimisation theory, we present an alternative learning algorithm, exponentiated gradient (EG), that respects Dale’s Law and produces log-normal weights, without losing the power of learning with gradients. We also show that in biologically relevant settings EG outperforms GD, including learning from sparsely relevant signals and dealing with synaptic pruning. Altogether, our results show that EG is a superior learning algorithm for modelling the brain with ANNs.
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 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.
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.
Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale’s Law, which implies that neur… (voir plus)ons must be excitatory (E) or inhibitory (I). Dale’s Law is generally absent from RNNs because simply partitioning a standard network’s units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale’s ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale’s Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale’s Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dale’s ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dale’s ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance. Overall, this work sheds light on a long-standing mystery in neuroscience-inspired AI and computational neuroscience, paving the way for greater alignment between neural networks and biology.
A
bstract
The units in artificial neural networks (ANNs) can be thought of as abstraction… (voir plus)s of biological neurons, and ANNs are increasingly used in neuroscience 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.
