Gradient descent dynamics in low-rank RNNs reveal hidden learning structure

A recent theoretical study published on arXiv expands the low-rank framework to encompass learning processes in recurrent neural networks. The researchers derive the dynamics of gradient descent within a reduced overlap space, establishing a closed-form system of ordinary differential equations (ODEs) that precisely describes learning for linear RNNs and approaches accuracy for nonlinear RNNs in the large-N Gaussian limit. They differentiate between loss-visible overlaps, which influence network performance and output, and loss-invisible overlaps, which, while not impacting functionality, are essential for characterizing the learning process. This research enhances the theoretical comprehension of learning in low-rank RNNs, connecting network connectivity to its functional outcomes.