To Control FDR, Constrain FNR: A Reversed Conformal Risk Training Framework

In safety-critical image segmentation, controlling the False Discovery Rate (FDR) is essential. However, existing post-hoc Conformal Risk Control (CRC) for non-monotonic metrics like FDR yields overly conservative predictions, severely degrading model utility. While Conformal Risk Training (CRT) could theoretically mitigate this by embedding calibration into the training loop, it is fundamentally inapplicable to FDR. The inherent non-monotonicity of FDR violates the prerequisites for implicit differentiation, rendering the standard bi-level optimization intractable. To break this mathematical deadlock, we propose Reversed Conformal Risk Training (R-CRT). R-CRT employs a task reversal mechanism: it minimizes a differentiable surrogate of FDR while enforcing the strictly monotonic False Negative Rate (FNR) as a proxy constraint, thereby restoring the validity of implicit gradients. Extensive experiments on medical datasets demonstrate that R-CRT successfully trains highly effective models that significantly outperform baseline methods while maintaining strict, distribution-free FDR guarantees.