🤖 AI Summary
This study addresses the lack of general design principles linking neural network architecture to computational capacity. By systematically evaluating the computational performance of recurrent neural networks with diverse connectivity patterns on Boolean function tasks through large-scale sampling, the work reveals— for the first time—that local 2-cycles and 3-cycles are critical structural motifs for enhancing computational power. It further demonstrates that introducing a small number of sparse connections and biologically inspired interneuron-like units significantly boosts the performance of large-scale networks. The authors construct a comprehensive performance map linking small-network architectures to Boolean function realization, showing that networks containing short cycles achieve optimal performance. Moreover, network performance can be accurately predicted from structural statistics, offering a theoretical foundation and biologically inspired guidance for future neural architecture design.
📝 Abstract
Understanding how the architecture of neural networks shapes the computations they carry is a central challenge in neuroscience and machine learning. While specific circuit architectures have been linked to particular network computations and theoretical bounds on expressivity of broad classes of networks have been found, we are still missing general principles connecting the structure of finite networks to their computational capabilities. Here, we characterize the computational abilities of recurrent neural networks as a function of their connectivity by training a large collection of different networks to compute a large set of Boolean functions. For small networks, we constructed the complete ``catalogs'' of network-function performance, which revealed that computational capacity varies widely across architectures and that most networks show poor performance, and most functions are hard to compute. However, we show that having local 2- and 3-cycles in a network strongly enhances its computational ability, and networks with such cycles are often the minimal architectures that can solve particular functions. We further show that a small set of structural statistics accurately predict networks' performance. Extending our analysis to large networks showed that typical networks fail even to approximate a randomly selected function. Surprisingly, adding a small number of sparsely connected biologically-inspired interneurons to the network dramatically increases computational capacity. As in small networks, adding short cycles improved networks' capacity, outperforming acyclic or reachability-matched controls. Thus, our results identify local cycles as design principles linking neural connectivity to computational power, and offer a general framework to explore structure-function relations in computing networks.