Relation between two-sided search and T-calibration

Determine whether the observed degradation in solver performance when the hashed target-state ball has radius zero, and the corresponding benefit of increasing the ball radius, are caused by the T-calibration issue in diffusion-based beam search for Rubik’s Cube configurations.

Background

The diffusion-based solver uses a two-sided search: backward beam search is combined with a precomputed ball of radius RR around the goal state. The experiments report that larger hashed-ball radii improve performance and that performance degrades substantially when the radius is zero.

The authors connect this empirical behavior with T-calibration, a procedure that repeatedly reruns inference from shorter effective diffusion times to reduce the bias toward trajectories of the full training length. The proposed relationship is based on observed performance rather than a proved mechanism, so it is stated explicitly as a conjecture.

References

We conjecture that this is related to the issue of T-calibration described in the text.

— Diffusion Models for Cayley Graphs  (2503.05558 - Douglas et al., 7 Mar 2025) in Section 3.1, “Results on the Cube,” paragraph preceding Figure \ref{fig:scoresvsball}