Figure 5
From: Downstream network transformations dissociate neural activity from causal functional contributions
Difference between causal contributions and representations in the ESN. (A) The line in teal shows the produced outcome (time series) by the network. Summing the uncovered causal contributions (red in panel B) perfectly reconstructs this outcome. (B) Activity profiles (deep blue) of three exemplar nodes and their corresponding causal contributions are plotted for comparison. Note that node #32 is not completely silent but has a small range of [− 0.0003, 0.007] that, relative to its causal contribution, is visually negligible. Due to the large downstream operations applied by other nodes and the readout layer, the relationship between causal contributions and neural representations (purple) is far less trivial compared to our linear toy examples (see the same plot in Fig. 4). (C) Histogram of the Pearson’s correlation coefficient between every node’s activity profile and its causal contribution. On the right side, three examples with the largest positive, largest negative, and no correlation are plotted. Note that the activity profiles are very similar across these three nodes, while their contributions are far more diverse. Above the histogram, we plotted the ESN’s reservoir architecture as a network. The layout is adjusted to represent the spectrum of coupling between the activity profile of each unit and its contribution. Node size represents nodal degree, i.e., their total number of connections.
