Causal Influences Decouple From Their Underlying Network Structure In Echo State Networks
Kayson Fakhar, Fatemeh Hadaeghi, Claus Christian Hilgetag · 2022 International Joint Conference on Neural Networks (IJCNN) · 2022
Echo State Networks (ESN) are versatile recurrent neural network models in which the hidden layer remains unaltered during training. Interactions among nodes of this static backbone (the network structure) produce diverse representations (i.e., network dynamics) of the given stimuli that are harnessed by a read-out mechanism to perform computations needed for solving a given task (i.e., behavior). Moreover, ESNs are accessible models of neuronal circuits, since they are relatively inexpensive to train. Therefore, ESNs have become attractive for neuroscientists studying the relationship between neural structure, function, and behavior. For instance, it is not yet clear how distinctive connectivity patterns of brain networks (structure) support effective interactions among their nodes (dynamics) and how these patterns of interactions give rise to computation (behavior). To address this question, we employed an ESN with a biologically inspired structure and used a systematic multi-site lesioning framework to quantify the causal contribution of each node to the network's output, thus providing a causal link between network structure and behavior. We then focused on the structure-function relationship and decomposed the causal influence of each node on all other nodes, using the same lesioning framework. We found that nodes in a properly engineered ESN interact with each other largely irrespective of the network's underlying structure. However, in a network with the same topology where the ESN's leakage rate is non-optimal and the dynamics are diminished, the underlying connectivity patterns determine the node interactions. Our results suggest that causal structure-function relations in ESNs can be decomposed into two components, direct and indirect interactions. The former are based on influences relying on structural connections. The latter describe the effective communication between any two nodes through other intermediate nodes. These widely distributed indirect interactions may crucially contribute to the efficient performance of ESNs.