Sparse tensors are vectors, matrices, and higher-dimensional generalizations with many zeros. They are crucial in various fields such as scientific computing, signal processing, and deep learning due to their efficiency in storage, computation, and power. Despite their benefits, handling sparse tensors manually or through existing libraries is often cumbersome, error-prone, nonportable, and does not scale with the combinatorial explosion of sparsity patterns, data types, operations, and targets.  Research largely focuses on sparse storage formats—data structures that compactly store nonzeros and allow efficient operations that avoid redundancies such as x+0=x and x*0=0. This enables scaling to larger sizes or solving same sizes with fewer resources. No single sparse format is optimal; the best choice depends on the nonzero distribution, operations, and target architecture. The Universal Sparse Tensor (UST) decouples a tensor’s sparsity from its memory storage representation.…