Measuring and Controlling Solution Degeneracy across Task-Trained Recurrent Neural Networks

Task-trained recurrent neural networks (RNNs) are versatile models of dynamical processes widely used in machine learning and neuroscience. While RNNs are easily trained to perform a wide range of tasks, the nature and extent of the degeneracy in the resultant solutions (i.e., the variability across trained RNNs) remain poorly understood. Here, we provide a unified framework for analyzing degeneracy across three levels: behavior, neural dynamics, and weight space. We analyzed RNNs trained on diverse tasks across machine learning and neuroscience domains, including N-bit flip-flop, sine wave generation, delayed discrimination, and path integration. Our key finding is that the variability across RNN solutions, quantified on the basis of neural dynamics and trained weights, depends primarily on network capacity and task characteristics such as complexity. We introduce information-theoretic measures to quantify task complexity and demonstrate that increasing task complexity consistently reduces degeneracy in neural dynamics and generalization behavior while increasing degeneracy in weight space. These relationships hold across diverse tasks and can be used to control the degeneracy of the solution space of task-trained RNNs. Furthermore, we provide several strategies to control solution degeneracy, enabling task-trained RNNs to learn more consistent or diverse solutions as needed. We envision that these insights will lead to more reliable machine learning models and could inspire strategies to better understand and control degeneracy observed in neuroscience experiments.