# Necessary or Sufficient? Evaluating LLM Explanations With Behavioural Evidence > Source: > Published: 2026-09-08 14:41:23+00:00 # Computer Science > Artificial Intelligence [Submitted on 4 Sep 2026] # Title:Necessary or Sufficient? Evaluating LLM Explanations With Behavioural Evidence [View PDF](/pdf/2609.05385v1) [HTML (experimental)](https://arxiv.org/html/2609.05385v1) Abstract:LLM decision components that can operate within agent workflows often produce action-relevant recommendations or judgements together with explanations. Operators may use the named factors to monitor a system, diagnose errors, or decide when to escalate an output. Such use assumes that the explanations agree with the component's observable decision behaviour. We test two interpretations of the named factors: necessity, meaning that changing a factor would change the output, and sufficiency, meaning that retaining it while removing other changeable information would preserve the output. We evaluate these interpretations in two synthetic use cases: recommending advisors to clients and judging prompts for harmfulness or risk. Models return an output and the top three factors that most influenced it. Controlled black-box interventions estimate a necessity score for each factor by measuring how often changing it changes the output, and a sufficiency score by measuring how often retaining it preserves the output. Across eight models from the Claude, GPT, and Gemini families, the mean Spearman correlations between the cited ranking and the necessity and sufficiency scores are 0.349 and 0.354 for advisor recommendation, and 0.431 and 0.580 for prompt monitoring. Furthermore, an uncited factor scores above the lowest-scoring cited factor in 57.6% of advisor responses under necessity and 58.1% under sufficiency; the corresponding prompt-monitoring rates are 25.8% and 8.9%. The cited top three contain useful information but do not reliably identify the three factors with the strongest measured influence under necessity or sufficiency. The framework provides a black-box reliability check for explanations used in agent oversight while remaining scoped to individual LLM decisions. ### References & Citations Loading... # Bibliographic and Citation Tools Bibliographic Explorer *(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer)) Connected Papers *(*[What is Connected Papers?](https://www.connectedpapers.com/about)) Litmaps *(*[What is Litmaps?](https://www.litmaps.co/)) scite Smart Citations *(*[What are Smart Citations?](https://www.scite.ai/)) # Code, Data and Media Associated with this Article alphaXiv *(*[What is alphaXiv?](https://alphaxiv.org/)) CatalyzeX Code Finder for Papers *(*[What is CatalyzeX?](https://www.catalyzex.com)) DagsHub *(*[What is DagsHub?](https://dagshub.com/)) Gotit.pub *(*[What is GotitPub?](http://gotit.pub/faq)) Hugging Face *(*[What is Huggingface?](https://huggingface.co/huggingface)) ScienceCast *(*[What is ScienceCast?](https://sciencecast.org/welcome)) # Demos # Recommenders and Search Tools Influence Flower *(*[What are Influence Flowers?](https://influencemap.cmlab.dev/)) CORE Recommender *(*[What is CORE?](https://core.ac.uk/services/recommender)) # arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).