SparseMap Background

Sparse maps are a way of storing tensor sparsity. Physically speaking, we use the notation \(L(\mathbb{V}\rightarrow \mathbb{U})\) to denote a sparse map, \(L\), which maps from vector space \(\mathbb{V}\) to a vector space \(\mathbb{U}\). In practice each member of \(\mathbb{V}\) will map to a subspace of \(\mathbb{U}\) termed its “domain”. Letting \(v\) be a vector in \(\mathbb{V}\) we denote the domain of \(v\) in \(\mathbb{U}\) as \(\mathbb{U}_{v}\). A member of \(\mathbb{U}_{v}\) is denoted by \(u_v\).