CARGO-VL: Counterfactual Arbitration with Risk-Constrained Group Optimization for Vision-Language Models

Vision-language systems combine images with retrieved text, but these sources can disagree or jointly fail to support an answer. Reliable models must identify the trustworthy source and abstain when neither is adequate. Existing post-training objectives score instances independently and therefore do not enforce coherent behavior under counterfactual evidence changes. We introduce CARGO-VL, a group-relative framework that optimizes matched variants covering aligned, image-correct, text-correct, and both-wrong (A/V/T/N) evidence states as one bundle. Its objective couples condition-wise correctness with transition rewards for answer invariance, source equivariance, and answer-to-abstention switching, while a primal-dual controller balances unsafe answers against excessive deferral. We also contribute XMC (eXtended Modal Conflict), a four-condition conflict training resource, and evaluate transfer on CMC-Bench and Modality-Bias. Across multiple seeds, CARGO-VL improves conflict handling, unsupported-answer avoidance, and modality balance over pointwise baselines. Ablations identify complementary benefits from relational transition signals and adaptive risk control, supporting counterfactual consistency as a practical objective for reliable multimodal evidence arbitration.

Not Every Divergence Should Be Suppressed: Counterfactual Recoverability in On-Policy Distillation

On-policy distillation (OPD) supervises student-visited trajectories, yet divergence-based rules cannot determine whether an erroneous prefix remains correctable. We formulate this decision as counterfactual recoverability and replay each error state through budget-matched teacher-continuation and rollback branches. Based on their relative success, states are categorized as recoverable, irreversible-but-avoidable, or ambiguous, and these labels guide whether training retains, rolls back, or conventionally supervises the corresponding trajectory. On AIME branch diagnostics, the mean continuation-minus-rollback effect is 0.185 for recoverable states and -1.000 for irreversible-but-avoidable states, demonstrating opposite intervention preferences. A branch-derived recoverability proxy achieves an AUC of 1.000, substantially outperforming divergence alone at 0.392. Across frozen evaluations, recoverability-aware control achieves the strongest recorded performance, reaching 0.578 success on held-out AIME2025 compared with 0.517 for the best baseline. It also improves AIME2024-2025 average@32 from 0.2656 to 0.3125 and GPQA-Diamond average@32 from 0.2702 to 0.3070. Component ablations further show that retaining teacher-correctable prefixes provides the largest individual contribution. These findings establish recoverability as an outcome-grounded decision variable for selective supervision in OPD.