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Long-Term Memory

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}}.