Information-Gain Rewards over Diversity-Pruned Tests: GT-Anchored Verifier Co-Training for Reliable Code Generation
Abstract: Self-play methods that co-train a single language model as both coder and test author promise to move code-generation RL beyond fixed test suites, but they suffer from two coupled pathologies: permissiveness collapse, where pass-rate rewards are maximised by trivial, non-discriminative tests, and concentration bias, where i.i.d. sampled tests cluster on modal inputs and inflate estimator variance. We introduce CoVer (Co-trained Coder and Verifier), a single-policy GRPO framework that addresses both failure modes. First, an information-gain (IG) reward scores each self-generated test by the mutual information between its pass/fail vector and a graded, ground-truth-anchored correctness signal y [0, 1] m, gated by the sign of their covariance so that only positively discriminative tests receive reward. Second, a three-stage diversity-aware selection step prunes a candidate pool to a behaviourally non-redundant suite (invalidity, input-string, execution-profile filtering), raising the effective sample size of the IG estimator at fixed execution budget. On five benchmarks (LiveBench, MBPP, LiveCodeBench, CodeContests, Code-Forces), CoVer raises one-shot pass@1 by +5.8 points at 7B and +7.1 points at 14B over the Qwen2.5-Instruct backbone, and achieves the highest macro-average among all compared methods at both scales. As a drop-in backbone inside the CodeT ranking pipeline, CoVer-7B adds +3.5 points, demonstrating the dual benefit of co-training for both generation and selection.