# Is This Evidence Decision-Critical? Learning to Verify Rule-Governed Decisions

arXiv: https://arxiv.org/abs/2609.39608 · HTML: https://mlsanity.com/paper/2609.39608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 23 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Learning the Difference that Makes a Difference with Counterfactually-Augmented Data](https://mlsanity.com/paper/1909.12434/) (2019)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [ContractNLI: A Dataset for Document-level Natural Language Inference for Contracts](https://mlsanity.com/paper/2110.01799/) (2021)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [ContextCite: Attributing Model Generation to Context](https://mlsanity.com/paper/2409.00729/) (2024)
- [Interpretation of Natural Language Rules in Conversational Machine Reading](https://mlsanity.com/paper/1809.01494/) (2018)
- [A Closer Look at the Intervention Procedure of Concept Bottleneck Models](https://mlsanity.com/paper/2302.14260/) (2023)
- [R2-Guard: Robust Reasoning Enabled LLM Guardrail via Knowledge-Enhanced Logical Reasoning](https://mlsanity.com/paper/2407.05557/) (2024)
- [Belief Revision: The Adaptability of Large Language Models Reasoning](https://mlsanity.com/paper/2406.19764/) (2024)
- [ConditionalQA: A Complex Reading Comprehension Dataset with Conditional Answers](https://mlsanity.com/paper/2110.06884/) (2021)
- [RuleArena: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios](https://mlsanity.com/paper/2412.08972/) (2024)
- [Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs](https://mlsanity.com/paper/2502.02362/) (2025)
- [Reasoning Elicitation in Language Models via Counterfactual Feedback](https://mlsanity.com/paper/2410.03767/) (2024)
- [Counterfactual Concept Bottleneck Models](https://mlsanity.com/paper/2402.01408/) (2024)
- [PairCFR: Enhancing Model Training on Paired Counterfactually Augmented Data through Contrastive Learning](https://mlsanity.com/paper/2406.06633/) (2024)
- [Learning Concept Bottleneck Models from Mechanistic Explanations](https://mlsanity.com/paper/2603.07343/) (2026)
- [DeltaLogic: Minimal Premise Edits Reveal Belief-Revision Failures in Logical Reasoning Models](https://mlsanity.com/paper/2604.02733/) (2026)

## Abstract (arXiv)

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.