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arXiv AI By Harun Bayraktar, John Gunnels, Peter Caday

The Missing Fourth Term for the Emulation Tensor Memory Equilibrium (TME) Model: The Residue Deconstruction Cost

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The paper identifies a missing cost term in the Tensor‑Memory Equilibrium (TME) model for emulating fp64 on GPUs: the per‑input deconstruction cost required before matrix multiplication can proceed. By adding this term and calibrating it against cuBLAS, the authors derive a closed‑form operational‑intensity threshold (OI*) below which emulation cannot match native fp64 performance. On an NVIDIA B300 GPU, this threshold is about 0.56 FLOP/B, limiting the speed‑ups of memory‑bound kernels such as GEMV, SpMV, and low‑batch GEMV to 0.3–0.9× native, and reducing the 7‑point stencil speed‑up from 3.1× to 1.8×, while dense GEMM remains unaffected.

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