Property

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. The matrix of pairwise inner products of a set of vectors has a property that constrains what similarity patterns are possible: it is symmetric and positive semi-definite, so its eigenvalues are non-negative and its diagonal entries are the squared lengths of the vectors. ...

Demo note. This note demonstrates what the SciDraft Hugo theme can do for academic and scientific publishing — for research institutions, researchers and students. Its content is demonstration material only: readers should ignore whether the demo content is correct. Convexity of a loss in the parameters is rare in deep learning, but convexity in the scores is not, and the cross-entropy of a softmax has it. The property is what guarantees that the inner optimisation — fitting the output layer, probing a frozen representation — has no local minima to fall into. ...