Determine whether the cross-problem control removes stylistic effects

Determine the extent to which the cross-problem control in Shared Residual Distillation removes stylistic effects from peer-induced residuals, while accounting for possible effects introduced by the control trajectory’s own content.

Background

Shared Residual Distillation compares same-problem peer-conditioned predictions with a trajectory from another problem, using the latter as a control intended to remove generic distributional shifts caused by adding solution text. The paper explicitly notes that this control may not cleanly isolate problem-specific information: stylistic effects may persist, and the control’s content may itself alter the residual directions used to construct the distillation target. Characterizing the extent of these effects remains unresolved.