Stochastic Rounding Increases Small Singular Values
Over the past half-dozen years, stochastic rounding (SR) has regained significant attention as a quantization scheme for low-precision floating-point arithmetic, with applications spanning numerical analysis and modern machine learning systems. Recent work has shown that SR acts as an implicit regularizer by increasing the smallest singular value of extremely tall-and-thin (or, symmetrically, short-and-fat) matrices. In this work, we substantially sharpen and extend this understanding in two directions. First, we show that the regularization effect of SR is not restricted to extreme aspect ratio regimes: it persists for matrices with constant aspect ratio. Second, we demonstrate that SR d...
| Authors | Linkai Ma, Tingzhou Yu, Petros Drineas |
|---|---|
| Primary category | math.NA |
| Published | 29 May 2026 |
| Last updated at source | 29 May 2026 |
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