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Hold-out Digits experiments show that retaining the input mean or correcting the output bias improves median product error over round-to-nearest in all four tested bit-width and calibration-size settings.
The problem of minimizing error in quantized matrix multiplication is considered and the full-gauge optimum is characterized and the cost of preserving row and column indices is quantized.
The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal. In high dimensions, however, distances co...
An exact finite-dimensional identity is derived for the expected squared product error under independent, zero-mean entrywise errors with known variance fields; it holds exactly for non-overloading subtractive dither and for independent stochastic rounding, and is empirically assess deterministic round-to-nearest (RTN)...
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