Towards a More General Understanding of the Algorithmic Utility of Recurrent Connections
Authors: Larsen Brett W. , Druckmann Shaul 
Published: March 2021

Lateral and recurrent connections are ubiquitous in biological neural circuits. Yet while the strong computational abilities of feedforward networks have been extensively studied, our understanding of the role and advantages of recurrent computations that might explain their prevalence remains an important open challenge. Foundational studies by Minsky and Roelfsema argued that computations that require propagation of global information for local computation to take place would likely particularly benefit from the sequential, parallel nature of processing in recurrent networks. Such “tag propagation” algorithms perform repeated, local propagation of information and were originally introduced in the context of detecting connectedness, a task that is challenging for feedforward networks. Here, we advance the understanding of the utility of lateral and recurrent computation by first performing a large-scale empirical study of neural architectures for the computation of connectedness to explore feedforward solutions more fully and establish robustly the importance of recurrent architectures. In addition, we highlight a tradeoff between computation time and performance and demonstrate hybrid feedforward/recurrent models that perform well even in the presence of varying computational time limitations. We then generalize tag propagation architectures to multiple, interacting propagating tags, and demonstrate that these are efficient computational substrates for more general computations of connectedness by introducing and solving an abstracted biologically inspired decision-making task. Our work thus clarifies and expands the set of computational tasks that can be solved efficiently by recurrent computation, yielding hypotheses for structure in population activity that may be present in such tasks.

Author Summary

In striking contrast to the majority of current-day artificial neural network research which primarily uses feedforward architectures, biological brains make extensive use of lateral and recurrent connections, raising the possibility that this difference makes a fundamental contribution to the gap in computational power between real neural circuits and artificial neural networks. Thus, despite the challenge of making effective comparisons between different network architectures, developing a more detailed understanding of the computational role played by such connections is a pressing need. Here, we leverage the computational capabilities of large-scale machine learning to robustly explore how differences in architectures affect a network’s ability to learn tasks that require propagation of global information. We first focus on the task of determining whether two pixels are connected in an image which has an elegant and efficient recurrent solution: propagate a connected label or tag along paths. Inspired by this solution, we show that it can be generalized in many ways, including propagating multiple tags at once and changing the computation performed on the result of the propagation. Strikingly, this simple expansion of the tag propagation network is sufficient to solve a crucial abstraction to temporal connectedness at the core of many decision-making problems, which we illustrate for a an abstracted competitive foraging task Our results shed light on the set of computational tasks that can be solved efficiently by recurrent computation and how these solutions may relate to the structure of neural activity.