Learning better with Dale's Law: A Spectral Perspective

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dales Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dales Law is generally absent from RNNs because simply partitioning a standard networks units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dales ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dales 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 Dales Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dales 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 Dales 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.