Split the Labor: Separating Evidence Interpretation from Decision Aggregation

Rule-based reasoning, as in eligibility checks and contract reviews, requires language models to assess evidence against individual conditions and combine their judgments under explicit rules. Errors in evidence assessment can leave a decision unchanged, but misinterpreting or overlooking decision-critical evidence can reverse it. Identifying such evidence allows more capable models to focus on checking the corresponding condition judgments, supporting accurate and safe decisions. Recognizing the evidence's criticality requires understanding how evidence affects a condition judgment and how that judgment affects the decision. To achieve the goal, we propose a INTERvention-based imPACT learning framework (InterPact), which enables counterfactual verification of evidence criticality in rule-governed decisions. Specifically, its evidence intervention constructor generates training pairs for a propagation verifier by editing case facts with a frozen language model while holding rules and non-target conditions fixed. Human-reviewed labels record the resulting condition and decision changes, while complete state-to-decision mappings supervise consequences beyond the observed edit. During training, the verifier weights learned conditional decision predictions by evidence-based condition probabilities through a fixed composition operation, propagating decision-change supervision into the base model. At inference, the trained base model directly judges criticality from the original case and target evidence, without human or stronger-model supervision. On single-case evidence criticality verification over adapted rule-governed decision cases, InterPact achieves 68.28% accuracy, outperforming all six baselines. These results support learned decision sensitivity as a basis for prioritizing evidence checks.

In many review workflows the verdict is the only thing retained. The passages behind it are not marked, because that annotation costs far more than recording the decision. We measure how much of that evidence a small language model can recover when it is post-trained on the verdicts alone, with no human evidence labels at any stage. On ContractNLI the human evidence spans are held out until evaluation. Matching the recorded verdict and agreeing with those spans are not the same thing: across six systems the two scores are only weakly related and rank the systems differently, so accuracy is a poor guide when the citations have to be reviewable. Label-only training on the bare verdict reaches accuracy 0.896 and span F1 0.564. Rejection sampling, which keeps a generated trace only when its verdict matches the record and then picks one by an automatic source-grounding score, reaches 0.797 and 0.556, against 0.747 and 0.493 before training. Verbatim citation rises from 0.597 to 0.729 under label-only training and to 0.701 under rejection sampling. One seed on one corpus cannot say which method is better, but both improve the evidence without anyone annotating it.

Despite increasing reliance on LLMs that reason with external evidence supplied by tools, retrieval-augmented generation, other agents, and users, how LLMs integrate such evidence into decisions they have already begun to form remains largely unclear. We present a distributional theory in which evidence shifts the receiver's distribution of initial answers, driven by a receiver prior weight and a candidate evidence tilt, leading to three predictions. First, candidates more probable to the receiver are more persuasive. Second, receivers more readily integrate characteristic errors of their own than foreign errors from different sources. Third, identical evidence can improve weaker models and harm stronger ones. We confirm these over ten million trials, twelve LLMs from four families, and eight domains, four of them scientific discovery tasks in the physical and life sciences: quantum mechanics, physics, genetics, and molecular biology. The law also yields a receiver-relative reliability frontier: receiver-congruent errors depress performance more steeply than random errors of the same rate. LLMs also integrate candidates even after internally verifying their invalidity (93-100% with propositional constraints; up to 99.4% on held-out physical and life-sciences reasoning), demonstrating evidence integration is a receiver-specific control policy over existing distributions, determined by receiver properties rather than scalar trust in the evidence source. Causal interventions show candidate integration is implemented late in the network, as a structured sequence of steps admitting external candidate answers, promoting them, and transporting them into the answer state. Representations of verification are decodable but have little causal impact on answers. A J-lens decomposition shows the state underlying verbalized verification is fully dissociable from that underlying candidate integration.