גבול נוקלאורי-טוב לדיזר סקאלרי-קוונטיזציה של תוצרי מטריצות

תקציר מקורי באנגליתarXiv:2609.05641v1 Announce Type: cross Abstract: 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 $E_{\rm lead} \ge (c_A+c_B)/K \Vert AB\Vert_*^2$, where $K$ is the