LoRa

Let’s consider a weight matrix $W$. Typically, the weight matrices in a dense neural networks layers have full-rank. Full-rank means many different things mathematically. I think the easiest explanation of a $d$-dimensional matrix (let’s consider a square matrix $,M \in \mathbb{R}^{d,d}$) being full-rank is one in which the columns could be used to span (hit every point) in $d$-dimensional space. If you consider $d=3$, a matrix like \begin{equation} M = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \end{equation}...

March 24, 2024