Matching Numerical Supervision to the Output Interface in Symbolic Regression

Neural symbolic regressors pass coefficient placeholders or predicted constants to numerical solvers. We show that this output interface can reverse conclusions about numerical supervision. In scale-augmented Flash-ANSR continuation, role targets favor placeholder requests, whereas literal targets favor constant requests. Independent confirmation on 256 newly generated families and three training seeds yields interactions of $-6.23$ and $-7.44$ percentage points at $R^2\ge .99$ and $R^2\ge .999$, with both multiplicity-adjusted intervals excluding zero. Exploratory paired comparisons show that the interaction varies with continuation exposure. Balanced 50/50 continuation provides a shared-checkpoint training response: it improves the weaker pairings by $3.17$ and $3.06$ points, reaching observed coverage within $0.70$ points of the respective specialists. Controlled interventions distinguish boundary supervision, numerical context, and optimizer initialization. Fixed-history probes locate immediate format steering at coefficient entry; fixed-pool replays show that predicted coefficients carry useful initialization information across candidate expressions. Together, these findings identify the generation–refinement interface as a design axis for numerical supervision and support balanced exposure when both output capabilities are required.