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We introduce \\emph{Tensor Cache}, a two-level cache that pairs sliding-window softmax attention as a first-level cache (L1) with a fixed-size outer-product fast-weight memory as a second-level cache (L2) fed by KV pairs evicted from the window. Recent tokens remain in exact local attention; evicted pairs are compressed into a per-layer matrix $A$ and read by future queries through a single matrix multiplication, exploiting the linear-attention identity $q_t(k_i \\otimes v_i)=\\langle q_t,k_i\\rangle v_i$. A learned scalar gate fuses the L1 and L2 outputs, and per-head decay and write-rate parameters are trained end-to-end. 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