A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products
We consider the problem of minimizing error in quantized matrix multiplication $C=AB$. Scalar quantization of the factors introduces rounding errors whose scale depends on the maximum absolute entries -- the ranges -- of their rows and columns. These ranges determine the quantization grid steps. To reduce the error, we optimize over product-preserving transformations that alter the factor ranges and grid steps without changing $C$. Specifically, we seek the smallest leading expected squared error over invertible inner changes of basis and orthogonal outer rotations. Under independent, zero-mean subtractive dither noise on an unbounded lattice, we prove the output-only bound $E_{\rm lead} ...
| Authors | Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara et al. |
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| Primary category | cs.IT |
| Published | 4 September 2026 |
| Last updated at source | 4 September 2026 |
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