TensorPrism: Rethinking Sparse High-Order Tensor Acceleration via Co-Occurrence Graph

Sparse high-order tensors are a key computational primitive across diverse domains, including large language models, scientific computing, recommendation systems, and multi-dimensional signal processing. Existing work primarily relies on tensor contraction to unfold high-order tensors into twodimensional sparse-dense matrix multiplications (SpMM), enabling direct reuse of well-studied SpMM optimization techniques. A complementary line of research adopts tensor-native approaches, which operate directly on the multi-dimensional tensor structure to improve data locality. However, both unfoldingbased and tensor-native techniques are inefficient to fully exploit data reuse in sparse high-order tensor computations, due to (1) the expansion of matrix dimensions and (2) missed reuse opportunities across different tensor modes. In this paper, we posit that matricization dismantles high-dimensional data reuse, erasing the correlations among nonzero elements across multiple tensor modes. We propose TensorPrism, a novel acceleration framework for sparse high-order tensor computation based on a co-occurrence graph abstraction. The central idea is to transform a high-order tensor into a co-occurrence graph that captures nonzero correlations across all tensor dimensions. Building on this abstraction, TensorPrism introduces three key designs. First, we formulate a co-occurrence graph representation that redefines dataflow and tiling to improve data reuse. Second, we introduce a new dataflow strategy that enhances reuse opportunities across tensor modes. Finally, we provide an efficient accelerator design tailored to the graph-based computation. Our evaluation shows that TensorPrism delivers performance speedups of $2.22 \times, 2.40 \times, 1.71 \times$, and $1.76 \times$ over state-of-the-art designs SPADE [1], HotTiles [2], GSpTC [3], and TCP [4], respectively.