English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we focus on the linear algebra theory behind feedforward (FNN)and recurrent (RNN) neural networks. We review backward propagation, includingbackward propagation through time (BPTT). Also, we obtain a new exactexpression for Hessian, which represents second order effects. We show that for$t$ time steps the weight gradient can be expressed as a rank-$t$ matrix, whilethe weight Hessian is as a sum of $t^{2}$ Kronecker products of rank-$1$ and$W^{T}AW$ matrices, for some matrix $A$ and weight matrix $W$. Also, we showthat for a mini-batch of size $r$, the weight update can be expressed as arank-$rt$ matrix. Finally, we briefly comment on the eigenvalues of the Hessianmatrix.

Feedforward and Recurrent Neural Networks Backward Propagation and Hessian in Matrix Form