On the Long-Term Memory of Deep Recurrent Networks
Yoav Levine, Or Sharir et al.
arXiv 2017 · 2017
On the Long-Term Memory of Deep Recurrent Networks analyzes Recurrent Arithmetic Circuits, Start-End separation rank, grid tensors, and Tensor Network constructions to quantify how depth affects temporal expressivity. The main result proves depth-2 RACs achieve Start-End separation rank on the order of the multiset coefficient (min{M,R} + T/2 − 1 choose T/2), while depth-1 RACs are limited to rank min{R, M^{T/2}}.