Characterize the frequency and impact of ties-to-even discrepancies

Characterize the frequency and impact of exact tie events arising from using PRISM’s untied round-to-nearest mode instead of native IEEE ties-to-even rounding in reduced-precision transformer inference.

Background

The experiments use PRISM’s untied round-to-nearest mode, in which exact half-ULP ties round away from zero, rather than native IEEE round-to-nearest, ties-to-even. Although the paper states that exact ties are expected to be rare in continuous floating-point activations, it does not quantify how often they occur or how much they affect inference accuracy. Determining these quantities is necessary for assessing the portability of the reported results to hardware implementing the standard IEEE tie-breaking rule.

References

Non-target operations in these sweeps use PRISM's untied RN at $t=24$, rather than native ties-to-even (RNE); while exact tie events are rare in continuous floating-point activations, their frequency and impact have not been characterized.

— Stochastic Rounding in Low-Precision Transformer Inference: A Variable-Precision Emulation Study of a Small GPT-2  (2610.01889 - Chatelain et al., 1 Oct 2026) in Section 5.5, Limitations