Incremental Sparse Tensor Format for Maximizing Efficiency in Tensor-Vector Multiplications

Current state-of-the-art sparse tensor formats achieve memory-efficient representations but often require extensive indexing or precomputation, thus limiting their flexibility and efficiency. We propose Bit-IF (Incremental Sparse Fibers with Bit Encoding), a format that only records index increments encoded by a compact bit array. This mode-independent approach allows for an arbitrary index traversal during tensor-vector multiplications (TVM), enabling the usage of space-filling curves. Bit-IF’s design characteristics significantly reduce memory overhead, improve data locality, and eliminate the need for multiple tensor copies or mode-specific preprocessing before performing a TVM. Our analysis and initial comparative studies show that Bit-IF reduces memory consumption and TVM computation time compared to COO-based approaches. The applicability of this method could be extended to other tensor operations, such as tensor-matrix and Khatri-Rao products.