ignore the bottom for now so if you apply sparse coding to this little spiral data set this is the energy function you get so every line that you you can you can sort of see here is a different linear subspace which is actually the selection of a different column or pair of columns of the W matrix and and the whole thing kind of fits the fits the data right okay the system is trained to just minimize the reconstruction error plus the rigor Iser on the data points and because it's got this regularizer as a consequence it gets high energy to stuff