Universality and Individuality in Recurrent Networks extended to Biologically inspired networks

Abstract: Activities in the motor cortex are found to be dynamical in nature. Modeling these activities and comparing them with neural recordings helps in understanding the underlying mechanism for the generation of these activities. For this purpose, Recurrent Neural networks or RNNs, have emerged as an appropriate tool. A clear understanding of how the design choices associated with these networks affect the learned dynamics and internal representation still remains elusive. A previous work exploring the dynamical properties of discrete time RNN architectures (LSTM, UGRNN, GRU, and Vanilla) such as the fixed point topology and the linearised dynamics remains invariant when trained on 3 bit Flip- Flop task. In contrast, they show that these networks have unique representational geometry. The goal for this work is to understand if these observations also hold for networks that are more biologically realistic in terms of neural activity. Therefore, we chose to analyze rate networks that have continuous dynamics and biologically realistic connectivity constraints and on spiking neural networks, where the neurons communicate via discrete spikes as observed in the brain. We reproduce the aforementioned study for discrete architectures and then show that the fixed point topology and linearized dynamics remain invariant for the rate networks but the methods are insufficient for finding the fixed points of spiking networks. The representational geometry for the rate networks and spiking networks are found to be different from the discrete architectures but very similar to each other. Although, a small subset of discrete architectures (LSTM) are observed to be close in representation to the rate networks. We show that although these different network architectures with varying degrees of biological realism have individual internal representations, the underlying dynamics while performing the task are universal. We also observe that some discrete networks have close representational similarities with rate networks along with the dynamics. Hence, these discrete networks can be good candidates for reproducing and examining the dynamics of rate networks.