Fig. 3: Real-valued matrix inversion examples.
From: I/O-efficient iterative matrix inversion with photonic integrated circuits
a Ideal and encoded weight matrix \({{{{{{\bf{M}}}}}}}_{1}\). MAE Mean absolute error. MAE = \(\frac{1}{16}\sum _{j=1}^{4}\sum _{i=1}^{4}\left|{{{{{{\bf{M}}}}}}}^{{{{{{\rm{encode}}}}}}}\left(i,\, j\right)-{{{{{{\bf{M}}}}}}}^{{{{{{\rm{ideal}}}}}}}(i,\, j)\right|\). b Ideal and measured inverse matrix \({{{{{{\bf{A}}}}}}}_{1}^{{{{{{\boldsymbol{-}}}}}}1}\). \({{{{{{\bf{X}}}}}}}_{j}^{{{{{{\boldsymbol{(}}}}}}0{{{{{\boldsymbol{)}}}}}}}\) is the \({j}^{{th}}\) column of the initial input matrix \({{{{{{\bf{X}}}}}}}^{(0)}\). c Evolution of inversion accuracy of \({{{{{{\bf{A}}}}}}}_{1}\) during convergence. Accuracy = \((1 - || {{{{{{\bf{A}}}}}}}_{{{{{{\rm{meas}}}}}}}^{-1} - {{{{{{\bf{A}}}}}}}_{{{{{{\rm{ideal}}}}}}}^{-1} || / || {{{{{{\bf{A}}}}}}}_{{{{{{\rm{ideal}}}}}}}^{-1} || ) \times 100{\%}\). d Ideal and encoded weight matrix \({{{{{{\bf{M}}}}}}}_{2}\). e Ideal and measured inverse matrix \({{{{{\bf{A}}}}}}_{2}^{-1}\). f Evolution of inversion accuracy of \({{{{{{\bf{A}}}}}}}_{2}\) during convergence.
