Unfolding recurrence by Green's functions for optimized reservoir computing
This work addresses a fundamental problem in neuroscience and machine learning by linking recurrent and feed-forward networks, offering insights for optimizing reservoir computing, though it appears incremental in its methodological approach.
The paper tackled the challenge of understanding how recurrence and non-linearities in cortical networks contribute to function by presenting a solvable recurrent network model that transforms recurrent dynamics into an effective feed-forward structure using perturbative methods, resulting in optimized time-series classifiers with strong potential performance gains.
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical understanding, it remains unclear how the interplay of recurrence and non-linearities in recurrent cortical networks contributes to their function. The purpose of this work is to present a solvable recurrent network model that links to feed forward networks. By perturbative methods we transform the time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels. The resulting analytical expressions allow us to build optimal time-series classifiers from random reservoir networks. Firstly, this allows us to optimize not only the readout vectors, but also the input projection, demonstrating a strong potential performance gain. Secondly, the analysis exposes how the second order stimulus statistics is a crucial element that interacts with the non-linearity of the dynamics and boosts performance.