The F1 loss matrix has rank s^2-s+2, and every convex calibrated surrogate for it requires at least Omega(s^2) prediction dimension.
Embedding dimension of polyhedral losses
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Exact Rank and Convex Calibration Dimension Lower Bounds for the Multi-Label F1 Loss
The F1 loss matrix has rank s^2-s+2, and every convex calibrated surrogate for it requires at least Omega(s^2) prediction dimension.