Resolve whether specialized-hardware reachability should be Boolean or continuous

Determine whether the specialized-hardware reachability quantity $mathrm{reached}(d)$ should remain a Boolean dispatch indicator or be reformulated as a continuous degree in $[0,1]$, and derive how the chosen formulation composes with the time and energy prediction equations.

Background

The A100 experiment detects nonzero tensor-core activity but only partial utilization, approximately 20.7% of peak, rather than a simple fully reached or not reached outcome. This creates a modeling ambiguity: a Boolean variable captures whether specialized hardware is dispatched at all, whereas a continuous variable could represent the degree of engagement. The paper explicitly leaves unresolved both the appropriate representation and the corresponding reformulation of the time and energy models.

References

This paper does not resolve that tension: whether to keep $\mathrm{reached}(d)$ boolean with a principled dispatch-fraction threshold, or restate it as a continuous quantity in $[0,1]$ and re-derive how it composes with Equations~(\ref{eq:reached-time})--(\ref{eq:reached-energy}), is left as a concrete, real-data-motivated question for the remaining ensemble.

— Closing the Prediction Gap: Completing Machine Shape So That Predicted Time, Power, Energy, and Mapping Match What Real Hardware Does  (2610.03197 - Mullin et al., 2 Oct 2026) in Section 8, “Real-Hardware Validation: NCSA Delta A100,” immediately following the reachability measurements