Role of the restoring term in GSM8K collapse

Determine whether the absence of an explicit restoring term proportional to the negative generated sample contributes to the collapse of the V^{+}-V^{-} drift-field formulation on GSM8K when four generated samples are used and generated samples may be attracted to different positive programs.

Background

The paper compares the drift-field coefficient choices (\lambda{+},\lambda{-})=(1,1) and (2,1). Under the original (1,1) choice, the explicit terms proportional to the current generated sample cancel between the attractive and repulsive drifts, leaving no direct restoring force toward the positive solutions. The authors observe that this formulation collapses on GSM8K even with four generated samples, whereas the (2,1) formulation retains an explicit restoring term and trains successfully.

The conjecture concerns the mechanism behind the observed GSM8K failure: with multiple valid programs, different generated samples can be attracted to different positive solutions in the given-positive set and positive queue. Establishing whether the missing restoring term is causally responsible would clarify why the original coefficient choice behaves differently across tasks and sample counts. The paper does not resolve this mechanism theoretically or experimentally.

References

We conjecture that this absence contributes to the collapse of (1,1) on GSM8K even with n=4, where generated samples can be attracted to different positives among the K=12 given ones and the queue.

— ReLaDrift: Recurrent Language Generation via Drifting for Test-Time Scaling  (2610.23225 - Otsuka et al., 16 Oct 2026) in Appendix, Section “Coefficients of the Attractive and Repulsive Drifts,” paragraph “A possible reason: the restoring force toward the positives”