DISCERN: Decoupling Reasoning and Verification for Reliable Abstention

An external verifier can help a language model abstain from incorrect answers, but its training responses determine which errors it encounters. Can the verifier itself guide the generation of more useful training responses? We propose DISCERN, an answer-supervised chunk-scoring verifier trained through a sparring curriculum. A temporary solver learns to obtain high scores from the current verifier; final-answer labels then distinguish correct responses from errors that received high scores, providing supervision for the next verifier update. Deployment requires no generator weights or logits. On 100 greedy BeyondAIME responses, the final 4B verifier achieves mean-score AUC 0.913. In the continuation comparison on frozen-base BeyondAIME responses, sparring raises mean-score AUC from 0.802 to 0.869, compared with 0.706 for static refresh with an unchanged solver, and lowers expected risk relative to round 1 by 16.5 percentage points at 20% coverage. Same-trace ProcessBench comparisons extend evaluation to GSM8K, MATH, OlympiadBench, and Omni-MATH. Tests with a 30B verifier and external generators broaden the evaluation, while SimpleQA remains difficult. The clearest gains are in mathematical response selection, particularly when accepting only a small fraction of responses.