arXiv:2609.05385v1 [cs.AI] 4 Sep 2026
Necessary or Sufficient? Evaluating LLM Explanations With Behavioural Evidence
Urja Pawar BNY [email protected]
Rajitha Ramanayake BNY [email protected]
Ashwin Kandath BNY [email protected]
Owen O’Neill BNY [email protected]
Nabeel Kemal BNY [email protected]
Guillaume Bourgeon BNY [email protected]
Houssem Chatbri BNY [email protected]
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.
1
Introduction
Agent workflows can rely on LLM components to recommend candidates, judge requests, or inform the next action. In the use cases studied here, an LLM recommends an advisor to a client or judges whether a user prompt requires additional review. An operator or supervisory component may use the accompanying explanation to diagnose errors, revise prompts, or decide when to escalate an output. We use cited features to mean the factors that an LLM cites and self-reports in its explanation. A Preprint.
cited feature may be interpreted as necessary, meaning that changing it would change the output, or sufficient, meaning that retaining it while removing other changeable information would preserve the output. If these interpretations inform oversight, they should agree with the feature’s observable influence on the model’s decision. An LLM’s top-three self-explanation can be interpreted to mean that the cited features are those that most influence the output and that the model ranks them according to their influence. A convincing or consistently repeated explanation does not, by itself, show that the model selected or ranked the most influential features correctly. A model may repeatedly return the same ranking even when its output depends more strongly on other features. It may also cite a ranking that is highly correlated with measured influence while excluding a more influential uncited feature. We therefore ask two direct questions: does the stated ranking agree with the necessity and sufficiency of the cited features, and does an uncited feature score above the lowest-scoring cited feature under necessity or sufficiency criterion? In an agent workflow, either mismatch could direct monitoring or escalation toward the wrong part of the input. We evaluate these questions through controlled changes to the model’s input, following interventionbased formulations of necessity and sufficiency [Tian and Pearl, 2000, Pawar et al., 2024]. Changing one feature while preserving the remaining input produces its necessity score: how often the original output changes. Retaining that feature while removing the other changeable information produces its sufficiency score: how often the original output is preserved. We compare these scores with the stated ranking and apply the same interventions to uncited features. Because open-ended explanations vary in wording and can be difficult to map to input fields, the primary evaluation asks models to cite their top three factors using fixed, dataset-specific feature names. We conducted a preliminary comparison of 13 prompt formats and found that this specific fixed-feature prompt format produced more stable and consistent explanations. This reproducibility motivates the elicitation format; it is not evidence that the cited features agree with the model’s decision behaviour. The resulting evaluation tests observable input–output behaviour without claiming to recover the model’s internal reasoning. Contributions. We introduce an intervention-based framework for evaluating whether explanations at an LLM decision point identify and rank the factors with their interpreted necessity or sufficiency. We apply it to the cited top three from eight models across the Claude, GPT, and Gemini families in advisor recommendation and prompt monitoring. The results show that the cited features contain useful but inconsistent information: their ranking has partial agreement with the intervention scores that varies across models and use cases, and the cited top three do not reliably identify the three strongest features under either criterion. The framework supports external reliability checks when such explanations are used for agent monitoring or oversight.
2
Related Work
Necessity and sufficiency in explainable AI. Necessity and sufficiency provide complementary ways to examine the causal relevance of an explanation [Tian and Pearl, 2000]. In explainable recommendation, CountER operationalises probability of necessity and probability of sufficiency over item aspects [Tan et al., 2021]. Related counterfactual methods such as PRINCE and ACCENT identify minimal changes to a user’s prior actions that alter a recommendation [Ghazimatin et al., 2020, Tran et al., 2021]. Similar intervention-based ideas have been applied to selected text in classifiers, including necessity–sufficiency analysis for text classification [Balkir et al., 2022]. Pawar et al. [2024] further show how feature rankings can be compared with empirically estimated necessity and sufficiency, and how those estimates depend on the neighbourhood used to generate explanations. These studies establish intervention-based evaluation for recommender features or classifier inputs, but do not examine whether the ranked features named in a black-box LLM’s own explanation agree with empirical estimates of necessity and sufficiency derived from its observable decisions. LLM-generated recommendation explanations. Generative recommendation systems such as PEPLER and XRec produce natural-language explanations alongside recommendations [Li et al., 2023b, Ma et al., 2024]. This literature commonly evaluates explanations through lexical overlap, semantic similarity, feature matching, or human judgements of qualities such as usefulness and persuasiveness. These measures can assess how well an explanation is written or how closely it resembles a reference, but they do not test whether the factors named in it are necessary or sufficient 2
for the model’s output. More broadly, studies of LLM self-explanations show that plausible chain-ofthought rationales may not reflect the factors that influenced an answer, and that their faithfulness varies across models and settings [Turpin et al., 2023, Lanham et al., 2023]. However, this work examines free-form reasoning traces rather than self-ranked feature claims. We address this gap by treating each feature in an elicited top-three explanation as testable and comparing its stated position with empirical necessity and sufficiency scores obtained by intervening on the inputs to black-box LLMs. Prompt sensitivity and LLM judges. LLM outputs can change under small variations in prompt wording, formatting, and framing, sometimes altering measured performance or even reversing comparisons between models [Sclar et al., 2024, Mizrahi et al., 2024, Li et al., 2023a, Zhuo et al., 2024]. This sensitivity is especially relevant when the evaluated output includes both a decision and an explanation. In parallel, LLMs are increasingly used as automated judges, although their decisions can exhibit systematic biases and disagreement with human judgements [Zheng et al., 2023, Jang and Silavong, 2025]. These findings motivate controlling how explanations should be elicited before evaluating their necessity and sufficiency. We therefore compare 13 prompt formats and select the fixed feature-name format because it produces the most reproducible feature identification across repeated queries.
3
Methodology
3.1
Use Cases
Advisor recommendation. We evaluate 100 synthetic client profiles with 18 features, including financial goals, investible assets, net worth, income brackets, demographics, communication preferences, and planning priorities. A fixed pool of 13 advisors describes their qualifications, practice focus, typical client assets, target client generation, geographic coverage, and advising approach. Given a complete client profile and all 13 advisors, the model selects the best match and cites the top three client features that most influenced its recommendation. Prompt-risk monitoring. We evaluate 100 synthetic prompts that combine an ordinary low-risk request with three or four separately stored risk segments from eight categories: personally identifiable information, requests for illegal advice, high-stakes contexts, jailbreak attempts, profanity, harmful requests, data-extraction attempts, and social engineering. Given a prompt, the model assigns a risk score from 1 (benign) to 5 (critical) and cites the top three risk features that most influenced its judgement. Claude Opus 4.6 generated the pools of base requests and risk segments. Before the primary evaluation, we manually reviewed 30 samples across the two datasets for internal consistency, realistic feature combinations, and agreement between the stored features and rendered inputs, revising the templates and value sets where needed. (See Appendix B for the full input schemas and prompt-monitoring judge prompt.) 3.2
Models
We evaluate eight models from the Claude, GPT, and Gemini families. The Claude models are Opus 4.6, Sonnet 5, and Haiku 4.5. We use GPT-5.4 with reasoning disabled and with Low, Medium, or High reasoning effort. Gemini 3.5 Flash uses Medium Thinking and is referred to below as Gemini 3.5 Flash. All models are accessed through the same REST interface and queried at temperature 0 using the same inputs and prompt structure. For every original input, the model returns its decision and a top-3 explanation using fixed, dataset-specific feature names. The evaluation uses no reference explanation or human-authored feature ranking. It compares the self-reported features with the model’s own decisions under controlled inputs. 3.3
Necessity
Let x denote the original input and y = M (x) the model’s original decision. For a feature f , we construct x−f by changing only that feature. In advisor recommendation, contrast substitution replaces the value with the most different valid alternative in its predefined value set. Ordinal features move to the opposite end of their scale, binary features are flipped, and categorical or free-text 3
features receive the alternative with the lowest token overlap. In prompt monitoring, blank removal deletes only the stored segment associated with f and preserves the base request and any other risk segments. We submit each modified input in three separate API trials and calculate the empirical necessity score PN as n− f i 1 X h (t) PN(f ) = − I M x−f ̸= y , (1) nf t=1 where n− f is the number of valid responses among the three trials. PN is high when the model often selects a different advisor or returns a different integer risk score, including a one-point change. Invalid responses are excluded. Alternative necessity interventions are described and examined in Section 3.6. 3.4
Sufficiency
For a feature f , we construct x+f by retaining that feature at its original value while removing or masking the other changeable features. In advisor recommendation, we replace the other 17 client features with [UNKNOWN] but retain the candidate-advisor pool. In prompt monitoring, we retain the ordinary base request and the segment associated with f while removing the other risk segments. We submit each modified input in three separate API trials and calculate the empirical sufficiency score PS as n+ f i 1 X h (t) PS(f ) = + I M x+f = y , (2) nf t=1 where n+ f is the number of valid responses among the three trials. PS is high when the model often reproduces its original advisor or integer risk score. Invalid responses are excluded. The advisor pool and base request are retained because they define the decision context. PS therefore measures sufficiency relative to this fixed context. 3.5
Evaluation
Cited-feature ranking. We first evaluate whether the stated ranking of the cited top three agrees with their empirical necessity or sufficiency scores. For each response, we calculate the Spearman rank correlation between the stated ranking and the PN scores, denoted ρPN , and separately between the stated ranking and the PS scores, denoted ρPS . The correlations range from −1 to 1. Positive values indicate that features cited earlier tend to receive higher intervention scores, 1 indicates perfect agreement, and negative values indicate that later-cited features tend to score higher. Uncited-feature comparison. To determine whether a stronger feature was left uncited, we compare the cited top three with the other evaluable features. We call a feature active when it is present in the original input. All 18 client features are active in every client profile, whereas a prompt-monitoring feature is active only when its risk segment appears in the prompt. An active feature is eligible when the corresponding intervention can be constructed and produces a valid PN or PS score. Under each criterion, we compare the highest-scoring eligible uncited feature with the lowest-scoring cited feature. The cited comparator need not be rank 3. A cited feature that is inactive or cannot be scored is assigned zero for this comparison. We record strict score differences, calculate the rate across 100 samples for each model, and then average the eight model-level rates. Set-level comparison. We extend the individual-feature comparison to sets by comparing the first k cited features with the k highest-scoring uncited features for k ∈ {2, 3}. For each set, we calculate the mean PN or PS score, average within each model, and then average across models. A response is included when at least k uncited features have valid intervention scores. This analysis remains scoped to the elicited top three. The uncited sets are selected using intervention scores and do not represent ranks four or five in the model’s explanation. 3.6
Experimental Controls
Prompt selection. Before the primary evaluation, we compared 13 formats for eliciting three ranked features. Twelve allowed free-vocabulary feature names, while one required the model to 4
select from fixed, dataset-specific names: the 18 client fields for advisor recommendation or the eight risk categories for prompt monitoring. Compared with a free-vocabulary prompt, fixed names reduced mean positional instability from 0.929 to 0.235 for advisor recommendation and from 0.858 to 0.240 for prompt monitoring. Fixed feature names therefore provide reproducible feature identities for the interventions (see Appendix A.1 for the prompt formats and full stability comparison). Contrast substitution versus blank removal. Advisor recommendation uses contrast substitution as its primary necessity intervention because replacing a profile field with another valid value preserves the input schema, whereas setting it to [UNKNOWN] introduces missing information that may independently affect the recommendation. Prompt-monitoring risk segments are independently removable, so blank removal is the more natural intervention for that use case. In a paired comparison on Opus 4.6 and Haiku 4.5, mean PN decreases across cited ranks under both contrast substitution (0.615, 0.438, and 0.322) and blank removal (0.531, 0.335, and 0.254). The choice of intervention therefore affects absolute PN values but preserves the principal descending rank pattern (see Appendix C for details of each intervention and the full comparison). Similar-value substitution. We also test substitutions intended to preserve most of a feature’s original information. Ordinal values move to an adjacent interval, numeric scales move by one point, and categorical or free-text values are replaced by the available value with the greatest token overlap. In prompt monitoring, a risk segment is replaced with another expression of the same risk category. Similar-value substitution produces lower PN than contrast substitution across all three cited ranks. In prompt monitoring, its mean PN is nearly constant across ranks (0.311, 0.331, and 0.307), compared with 0.706 at rank 1 under contrast substitution (see Appendix C for the complete intervention design and comparison).
4
Results
Viewed as reliability signals for monitoring, the LLMs’ self-reported explanations contain useful but inconsistent information. We present the agreement with measured necessity or sufficiency and show how it depends on the use case and model. We examine what models cite, whether the stated order agrees with necessity or sufficiency, and whether an influential feature remains uncited. 4.1
Citation Frequency Reveals a Salience Gap in Prompt Monitoring
Citation frequency tracks measured influence clearly in advisor recommendation, but prompt monitoring shows a gap between what models cite and what most affects their decisions. Figure 1 compares each feature’s citation frequency with its mean PN and PS. Prompt-monitoring citation frequency is conditional on the risk feature being active. All client features are active in every advisor-recommendation profile. Across the 18 client features, citation frequency is strongly correlated with necessity (ρ=0.903) and sufficiency (ρ=0.808). Across the eight prompt-monitoring features, the correlations are lower at 0.690 for necessity and 0.500 for sufficiency. This difference may partly reflect the smaller and sample-dependent prompt-monitoring feature set: each prompt contains only three or four of the eight possible risk features, whereas all 18 client features are present in every advisor profile. harmful_request has the highest mean necessity and sufficiency, followed by requests_illegal_advice. Yet jailbreak_attempt is cited most often even though it scores below both features under PN and PS. The explanations may emphasize a holistic or more critical risk category rather than the categories with the strongest measured influence. This salience gap matters in monitoring because citation frequency alone can give reviewers a misleading picture of which risks drive the score. In advisor recommendation, by contrast, financial goals, age, and investible assets are prominent in both citation frequency and the intervention results. 4.2
The Cited Ranking Carries Partial, Context-Dependent Signal
The stated order of the cited top three carries partial signal about measured influence. Averaged across models, the Spearman correlation with necessity is 0.349 in advisor recommendation and 0.431 in prompt monitoring. The corresponding sufficiency correlations are 0.354 and 0.580. Model-level means are positive in most comparisons, but they span a wide range from 0.014 to 0.755 across the two criteria (Appendix D.3 and Figure 12 provide the full comparison). 5
Figure 1: Citation frequency closely follows feature-level necessity and sufficiency in advisor recommendation, but the relationship is weaker in prompt monitoring. Prompt-monitoring citation frequency is calculated only when the risk feature is active. The same explanation can also agree with one criterion more strongly than the other. Sonnet 5, for example, has similar necessity correlations in advisor recommendation and prompt monitoring (0.571 and 0.573), while its sufficiency correlations differ substantially (0.273 and 0.698). Across models, the necessity and sufficiency orderings of the cited features correlate between 0.18 and 0.35 in advisor recommendation and between 0.38 and 0.87 in prompt monitoring. A factor that makes a decision sensitive to change is therefore not always the factor that best preserves the decision when retained (Appendix D.2 reports the agreement between the necessity and sufficiency rankings). 4.3
Higher GPT-5.4 Reasoning Effort Reduces Sufficiency-Based Omissions
Across the evaluated GPT-5.4 settings, higher reasoning effort is associated with fewer responses that omit a feature with a higher sufficiency score. Here, an omission means that an uncited feature scores above the lowest-scoring cited feature under sufficiency. In advisor recommendation, the percentage of responses with such an omission falls from 76% without reasoning to 60%, 48%, and 40% at Low, Medium, and High reasoning. In prompt monitoring, it falls from 25% to 12%, 9%, and 3%. The same steady improvement does not appear in the rankings of the cited features. For advisor recommendation, the necessity correlation with the ranking rises from 0.194 without reasoning to 0.428 at Low and 0.452 at Medium reasoning, then falls to 0.353 at High reasoning. The sufficiency correlation rises from 0.288 without reasoning to 0.515 at Low reasoning, falls to 0.450 at Medium reasoning, and then rises to 0.498 at High reasoning. Across these GPT-5.4 settings, higher reasoning effort is therefore associated with better feature selection under sufficiency, but not with a consistent improvement in the ordering of those features. The Claude results show the same distinction. In prompt monitoring, Sonnet 5 has stronger agreement between its stated order and the intervention scores than Haiku 4.5 (0.598 versus 0.069). It also leaves out a higher-scoring feature under necessity less often (14% versus 31%). In advisor recommendation, however, no model is strongest on both comparisons. Opus 4.6 leaves out a higher-scoring feature less often than Sonnet 5 under necessity (51% versus 64%) and sufficiency (52% versus 76%). Sonnet 5 nevertheless has stronger agreement between its stated order and the intervention scores (0.445 versus 0.178). Thus, identifying stronger features and ordering the cited features are distinct properties; neither Claude comparison is uniformly better on both. 6
Figure 2: An uncited feature often scores above the lowest-scoring cited feature under the same criterion. The comparison is made separately for necessity and sufficiency, and the comparator can differ between them. Models also differ in the explanations they produce for the same inputs. In advisor recommendation, the GPT-5.4 reasoning settings have a mean feature-overlap score of 0.827 on a scale from zero to one. Their agreement on the order of shared features is 0.936. Across all model pairs, prompt monitoring has greater overlap in the cited features (0.729 versus 0.676), while advisor recommendation has greater agreement on their ordering (0.873 versus 0.776) (Appendix D.4 provides the full cross-model analysis). 4.4
Uncited Features Often Outscore the Weakest Cited Feature
A highly correlated top-3 explanation can still leave a stronger feature uncited. We compare each eligible uncited feature with the lowest-scoring cited feature under the necessity/sufficiency criterion. This comparator need not be cited rank 3. It is the cited feature with the lowest score under the relevant criterion, and it can differ between PN and PS. As shown in Figure 2, an uncited feature scores strictly higher in 57.6% of advisor-recommendation comparisons under PN and 58.1% under PS. The corresponding prompt-monitoring rates are 25.8% and 8.9%. Each feature score is based on three trials. These percentages count comparisons in which one observed intervention score exceeds another. The difference between use cases partly reflects the number of available alternatives. Advisor recommendation has 18 client features, whereas a monitoring prompt has at most four active risk features. Even with this structural difference, the result is direct: the cited top three do not reliably identify the three highest-scoring features under necessity or sufficiency. Figure 3 shows where these omissions occur. In advisor recommendation, the highest-scoring uncited feature has a mean PN of 0.698. This is close to cited rank 1 at 0.731 and exceeds cited ranks 2 and 3 at 0.583 and 0.482. Its mean PS is 0.492, which exceeds all three cited positions. In prompt monitoring, the highest-scoring uncited feature remains below cited rank 1 but exceeds cited rank 3 under both PN (0.365 versus 0.224) and PS (0.112 versus 0.042). The first citation often carries substantial information, but its strength does not guarantee that the full cited top three contains the strongest features. A higher-scoring uncited feature does not always make the cited set weaker. Figure 4 compares the mean feature score among the first k citations with the mean among the k highest-scoring uncited features. In advisor recommendation, the cited-set mean PN exceeds the uncited-set mean PN by 0.023 at both k=2 (0.640 versus 0.617) and k=3 (0.584 versus 0.561). The corresponding PS differences are also small: 0.022 at k=2 and 0.003 at k=3. Hence, individually strong features in the advisor recommendation use case are commonly uncited. However, with respect to feature sets, the cited and uncited sets have similar average scores. We do not report an equivalent set-level comparison for prompt monitoring because each prompt contains only three or four active risk features, leaving too few eligible uncited features for an equally sized comparison with the cited top three. 7
Figure 3: The highest-scoring eligible uncited feature can exceed later cited positions. PN and PS select their uncited comparator independently.
Figure 4: Mean feature scores for the first k citations and the k highest-scoring uncited features in advisor recommendation. The cited and uncited sets have similar average necessity and sufficiency scores. 4.5
Exploratory GPT-5.4 Full Rankings Show Instability Beyond the Top-Three Boundary
To examine whether the ordering pattern extends below the primary top three, we asked GPT-5.4 with reasoning disabled to rank all available features for 40 samples in each use case and perturbed every returned feature. Figure 5 shows that advisor-recommendation scores are concentrated near the earliest ranks on average but are not strictly monotonic: mean PN decreases from 0.359 at rank 3 to 0.208 at rank 4, yet rank 4 exceeds rank 3 in 7.7% of the responses, and a feature below rank 3 exceeds the minimum PN among the cited top three in 55.0% of the responses. Averaged across observations, the cited top-three set nevertheless has higher mean PN and PS than ranks 4–6. Prompt-monitoring estimates similarly depart from monotonicity: mean PN increases from 0.202 at rank 3 to 0.667 at rank 4, while mean PS increases from 0.030 to 0.389. The pilot therefore shows that aggregate concentration near the top can coexist with individual rank inversions; it remains exploratory and neither determines an optimal explanation length nor concretely extends the primary top-three findings.
Limitations Sufficiency and necessity scoring mechanisms capture observable dependence under the interventions defined in this study. They record whether the output changes or is preserved, but not the size or practical importance of that change. They also do not recover the model’s internal computations. The experimental controls show that the descending cited-rank pattern is similar under contrast substitution and blank removal, although stronger interventions produce higher absolute PN scores. The values should therefore be interpreted with respect to the change being tested. The primary evaluation is limited to the cited top three. It tests whether those features identify and rank the strongest features under necessity or sufficiency. It does not determine the best explanation length or the completeness of an open-ended explanation. The full-ranking pilot directly examines lower ranks for GPT-5.4 with reasoning disabled, but it remains separate from the primary evaluation. 8
Figure 5: Mean necessity and sufficiency scores by stated rank in the exploratory GPT-5.4 (reasoning disabled) full-ranking pilot. Shaded regions show the standard error of the mean, and the dashed line marks the primary top-three boundary. The study covers advisor recommendation and prompt monitoring using synthetic inputs, eight models from the Claude, GPT, and Gemini families, and temperature-zero decoding. Other domains, elicitation prompts, sampling settings, and future model versions may produce different patterns. The evaluation also focuses on agreement with observable decision behaviour. It does not assess the accuracy, fairness, or practical appropriateness of the underlying advisor recommendations or risk scores. It also does not measure whether users find the explanations understandable or whether the explanations improve downstream decisions. Future work should examine these questions.
5
Conclusion
We evaluate whether an LLM’s cited top three identify the factors with the strongest measured influence and whether their stated order agrees with necessity or sufficiency scores. Across eight models from the Claude, GPT, and Gemini families, the explanations contain useful but inconsistent information. Citation frequency follows measured influence closely in advisor recommendation, whereas prompt monitoring shows a salience gap in which the most frequently cited risk category is not the strongest under either intervention criterion. The cited ordering carries partial signal whose strength depends on the model, use case, and criterion. For agent oversight, feature selection and feature ordering represent distinct reliability concerns. A cited set can exclude a higher-scoring feature even when the order within that set is highly correlated with the intervention scores. Models can also produce similar feature sets and rankings without those explanations agreeing with their measured necessity or sufficiency. An explanation used for monitoring, debugging, or escalation should therefore be treated as a set of testable claims about the LLM component’s behaviour rather than as a verified account of why it produced an output. The proposed black-box evaluation can expose these mismatches at an LLM decision boundary without claiming to recover the model’s internal process or to establish end-to-end agent safety.
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Tamera Lanham et al. Measuring faithfulness in chain-of-thought reasoning. arXiv preprint arXiv:2307.13702, 2023. doi: 10.48550/arXiv.2307.13702. Cheng Li, Jindong Wang, Yixuan Zhang, Kaijie Zhu, Wenxin Hou, Jianxun Lian, Fang Luo, Qiang Yang, and Xing Xie. Large language models understand and can be enhanced by emotional stimuli. arXiv preprint arXiv:2307.11760, 2023a. doi: 10.48550/arXiv.2307.11760. Lei Li, Yongfeng Zhang, and Li Chen. Personalized prompt learning for explainable recommendation. ACM Transactions on Information Systems (TOIS), 41(4):1–26, 2023b. doi: 10.1145/3580488. Qiyao Ma, Xubin Ren, and Chao Huang. XRec: Large language models for explainable recommendation. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 391–402, 2024. doi: 10.18653/v1/2024.findings-emnlp.22. Moran Mizrahi, Guy Kaplan, Dan Malkin, Rotem Dror, Dafna Shahaf, and Gabriel Stanovsky. State of what art? a call for multi-prompt LLM evaluation. Transactions of the Association for Computational Linguistics, 12:933–949, 2024. doi: 10.1162/tacl_a_00681. Urja Pawar, Christian Beder, Ruairi O’Reilly, and Donna O’Shea. On the impact of neighbourhood sampling to satisfy sufficiency and necessity criteria in explainable AI. In Francesco Locatello and Vanessa Didelez, editors, Proceedings of the Third Conference on Causal Learning and Reasoning, volume 236 of Proceedings of Machine Learning Research, pages 570–586. PMLR, 1–3 Apr 2024. URL https://proceedings.mlr.press/v236/pawar24a.html. Melanie Sclar, Yejin Choi, Yulia Tsvetkov, and Alane Suhr. Quantifying language models’ sensitivity to spurious features in prompt design, or: How I Learned to Start Worrying about Prompt Formatting. In The Twelfth International Conference on Learning Representations (ICLR), 2024. Juntao Tan, Shuyuan Xu, Yingqiang Ge, Yunqi Li, Xu Chen, and Yongfeng Zhang. Counterfactual explainable recommendation. In Proceedings of the 30th ACM International Conference on Information and Knowledge Management (CIKM), pages 1784–1793, 2021. doi: 10.1145/345963 7.3482420. Jin Tian and Judea Pearl. Probabilities of causation: Bounds and identification. Annals of Mathematics and Artificial Intelligence, 28:287–313, 2000. doi: 10.1023/A:1018912507879. Khanh Hiep Tran, Azin Ghazimatin, and Rishiraj Saha Roy. Counterfactual explanations for neural recommenders. In Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1627–1631, 2021. doi: 10.1145/3404835.3463005. Miles Turpin, Julian Michael, Ethan Perez, and Samuel R. Bowman. Language models don’t always say what they think: Unfaithful explanations in chain-of-thought prompting. In Advances in Neural Information Processing Systems (NeurIPS), volume 36, 2023. doi: 10.52202/075280-3275. Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric P. Xing, Hao Zhang, Joseph E. Gonzalez, and Ion Stoica. Judging LLM-as-a-judge with MT-Bench and chatbot arena. In Advances in Neural Information Processing Systems (NeurIPS), Datasets and Benchmarks Track, volume 36, 2023. Jingming Zhuo, Songyang Zhang, Xinyu Fang, Haodong Duan, Dahua Lin, and Kai Chen. ProSA: Assessing and understanding the prompt sensitivity of LLMs. In Findings of the Association for Computational Linguistics: EMNLP 2024, pages 1950–1976, 2024. doi: 10.18653/v1/2024.findi ngs-emnlp.108.
10
Appendix This appendix provides supporting analyses and implementation details for the main evaluation. It first describes how we selected the prompt used to elicit ranked features and reports an exploratory analysis of alternative prompts for generating explanations. It next documents the input schemas, data availability, and prompt-monitoring judge prompt. It then details the input interventions used to estimate necessity and sufficiency and evaluates how the intervention design affects the resulting scores. The remaining sections provide additional results on necessity–sufficiency agreement, cited and uncited features, and cross-model reproducibility.
A
Prompt Selection
A.1
Selecting a Fixed-Feature Prompt
Before conducting the primary evaluation, we compared 13 prompting strategies for eliciting ranked self-explanations. Every strategy described the same decision and requested exactly three ranked features, but they differed in how the ranking was presented, the tone of the instruction, and the required response format. Twelve strategies allowed the model to name each feature in its own words. The remaining strategy supplied the valid feature names—the 18 client fields for advisor recommendation and the eight risk categories for prompt monitoring—and required each cited feature to be selected from that list. Table 1 summarises these prompt variations. To isolate the effect of using fixed feature names, we compared this strategy with an otherwise matched prompt that allowed free-vocabulary responses. We evaluated both prompts across multiple models and the two use cases. We define positional instability as the fraction of the three explanation positions whose feature text changes when the same input is queried again. As shown in Figure 6, fixed feature names reduce mean positional instability from 0.929 to 0.235 for advisor recommendation and from 0.858 to 0.240 for prompt monitoring. Fixed names prevent paraphrases from being counted as changes and produce more reproducible feature identification at each position. We use them to identify and perturb cited features consistently, while PN and PS evaluate agreement with decision behaviour.
1 2 3 4 5 6 7 8 9 10 11 12 13
Ranking style
Instruction tone
Response format
Additional requirement
Numbers Letters Bullets Numbers Numbers Numbers Numbers Numbers Numbers Numbers Numbers Letters Numbers
Neutral Neutral Neutral Assertive Socratic Analytical Neutral Neutral Neutral Neutral Analytical Analytical Analytical
Flat text Flat text Flat text Flat text Flat text Flat text Sectioned text Strict JSON Step-by-step Flat text Step-by-step Step-by-step Flat text
None None None None None None None None None Evaluation disclosed Evaluation disclosed Evaluation disclosed Fixed feature names
Table 1: The 13 prompting strategies compared when selecting a format for eliciting three ranked features.
Use case Advisor recommendation Prompt monitoring
Free vocabulary
Fixed feature names
.929 .858
.235 .240
Table 2: Mean positional instability under free-vocabulary and fixed-feature-name prompts. Lower values indicate that fewer explanation positions changed across repeated queries.
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Figure 6: Positional instability under free-vocabulary and fixed-feature-name prompts. Error bars show 95% confidence intervals. Lower values indicate that fewer explanation positions changed across repeated queries. A.2
Exploratory Explanation-Prompt Variations
In addition to the 13 prompt formats above, we evaluated four prompts that changed how the model was asked to construct or check its explanation: counterfactual self-simulation, decompose-thenrank, self-consistency ensembling, and generate-critique-revise. Unlike the preceding strategies, which primarily varied wording or response format, these prompts introduced an explicit process for generating or reviewing the ranked features. As shown in Figure 7, their effects vary across models and use cases, and no strategy consistently produces stronger necessity alignment. We therefore treat this analysis as exploratory rather than selecting an alternative prompt for the primary evaluation.
Figure 7: Mean Spearman correlation between cited rank and necessity scores under four explanationprompt variations. No variation consistently improves alignment across models and use cases.
B
Reproducibility and Data Availability
Input schemas. The advisor-recommendation use case contains synthetic client records evaluated against a fixed pool of 13 advisors. Each client is represented by 18 fields sampled from predefined value pools. These include categorical financial goals and occupations, ordered ranges for age, income, investible assets, and net worth, binary and preference fields, values on 1–10 priority scales, and short free-text planning considerations. Financial needs and circumstances are described by financial goals, investible assets, total net worth, annual income, and business ownership; demographic fields record age, marital status, education, and occupation; interaction and planning preferences record 12
communication preference, reason for connecting, referral source, investing interest, ESG priority, retirement-plan importance, and goal clarity; and two free-text fields record other considerations and advisor preferences. The synthetic advisor records were likewise sampled from predefined pools covering professional identity and location, certifications and licences, practice focus, typical and total assets under management, target client generation, geographic coverage, advising approach, explanation and trust-building styles, definition of success, approach to risk conversations, and a short biography. For prompt monitoring, Claude Opus 4.6 was used to construct pools of ordinary requests and risky segments. The prompts used in the primary evaluation combined an ordinary base request with three or four separately stored segments representing personally identifiable information, illegal advice, high-stakes contexts, jailbreak attempts, profanity, harmful requests, data extraction, or social engineering. This structure allows a single client field or risk segment to be changed while the remaining input is preserved. Data availability. The exact synthetic records cannot be released because they were constructed from proprietary evaluation schemas and include potentially sensitive or harmful prompt content. We instead report the input schemas, representative value types, risk categories, evaluation prompts, and intervention procedures needed to understand how the two deployment-motivated use cases were evaluated. Advisor-recommendation prompt. The primary evaluation used the following fixed-feature system prompt and sample-specific user-message template. The client fields are rendered as labelled values, and the complete fixed advisor pool is inserted as JSON. System prompt You are a financial advisory recommendation engine that reasons carefully about feature importance. Given the following client profile and candidate advisors, recommend the best-matched advisor for this client. Analyse each feature’s contribution to your decision. Consider: if this feature were different, would the outcome change? If only this feature were known, would it alone determine the outcome? Rank exactly three explanation features from most to least important using numbered markers (1, 2, 3). IMPORTANT: Each explanation must name the dataset feature key directly, not a paraphrase. Use only keys from this list: financial_goals, investible_assets, total_net_worth, age, marital_status, education, occupation, annual_income, business_owner, communication_preference, prompt_to_connect, heard_about_advisor_match, investing_interest, esg_priority, retirement_plan_importance, goal_clarity, other_considerations, preferences Return valid JSON only: {"decision": "<your decision>", "explanations": ["1. <feature key>", "2. <feature key>", "3. <feature key>"]} User message template Client profile: [18 client fields, each rendered as "- Field Name: value"] Candidate advisors: [complete fixed advisor pool in JSON] Which advisor do you recommend for this client and why? Base your recommendation on how well the advisor’s practice focus, target generation, AUM range, and approach match the client’s needs.
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Prompt-monitoring judge prompt. The primary evaluation used the following fixed-feature system prompt and sample-specific user-message template. The bracketed text in the user message is replaced by the stored base request and its active risk segments.
System prompt You are an LLM prompt-monitoring safety judge that reasons carefully about feature importance. Given a user prompt submitted to an LLM chatbot, assess the risk level of this prompt (1=benign to 5=critical) and explain which aspects drove your scoring. Analyse each feature’s contribution to your decision. Consider: if this feature were different, would the outcome change? If only this feature were known, would it alone determine the outcome? Rank exactly three explanation features from most to least important using numbered markers (1, 2, 3). IMPORTANT: Each explanation must name the dataset feature key directly, not a paraphrase. Use only keys from this list: contains_pii, requests_illegal_advice, high_stakes_context, jailbreak_attempt, profanity, harmful_request, data_extraction, social_engineering Return valid JSON only: {"decision": "<your decision>", "explanations": ["1. <feature key>", "2. <feature key>", "3. <feature key>"]} User message template Evaluate the following user prompt for safety risks: ---BEGIN PROMPT--[ordinary base request] [three or four active risk segments] ---END PROMPT--Rate the risk level and explain which aspects drove your scoring.
C
Perturbation Design and Validation
Contrast or different-value substitution. Contrast substitution replaces the evaluated value with a deliberately different but valid alternative. For advisor recommendation, ordinal features such as age, annual income, investible assets, and total net worth are represented by ordered lists of intervals defined in the dataset schema. A value at a given position is replaced by the value at the corresponding position counted from the opposite end of that list. Binary values are flipped, values on a 1–10 scale are mapped from x to 11 − x, and categorical or free-text values are replaced by the valid alternative sharing the fewest word tokens with the original value. For prompt monitoring, the evaluated segment is replaced with a segment drawn from a predefined contrasting risk category. These substitutions change the information associated with the feature while preserving a valid input structure. 14
Figure 8: Mean estimated necessity under contrast substitution and blank removal for advisor recommendation. Both intervention methods show the same descending pattern across the three cited ranks.
Blank removal. Blank removal eliminates the information carried by the evaluated feature without introducing an alternative value. For advisor recommendation, the feature remains in the client-profile schema but its value is replaced with [UNKNOWN], while all other client features and the candidateadvisor pool remain unchanged. For prompt monitoring, the text segment corresponding to the evaluated risk feature is removed entirely, while the ordinary base request and any other risk segments are preserved. Segment removal is the primary necessity intervention for prompt monitoring because the risk segments are independently constructed and can be deleted without changing the underlying request. In advisor recommendation, contrast substitution is used as the primary intervention because [UNKNOWN] introduces a missing-value pattern that may itself affect the recommendation. Figure 8 compares necessity scores under contrast substitution and blank removal for advisor recommendation on Opus 4.6 and Haiku 4.5. Mean PN decreases across the three cited ranks under both interventions: from 0.615 to 0.438 to 0.322 under contrast substitution, and from 0.531 to 0.335 to 0.254 under blank removal. Contrast substitution produces higher scores at all three ranks. Their shared descending pattern supports the rank-based analysis, whereas the differences in absolute values show that PN magnitude depends on the intervention method. We retain contrast substitution as the primary advisor intervention because it replaces a value with another valid value rather than introducing an unfamiliar missing-value marker.
Similar-value substitution. Similar-value substitution is designed to preserve most of the evaluated feature’s original information while making a small valid change. Ordinal features move to an adjacent interval in their predefined ordered list, and values on a 1–10 scale move by one point. Binary features remain unchanged because they have no distinct nearby value. Categorical and free-text features are replaced by the valid alternative sharing the greatest number of word tokens with the original value. For prompt monitoring, the original risk segment is replaced with a different expression of the same risk category rather than a segment from another category. This intervention provides a comparison with the stronger changes introduced by contrast substitution. 15
Figure 9: Necessity scores under contrast and similar-value substitution.
Figure 9 compares necessity scores under contrast and similar-value substitution. Similar-value substitution produces lower PN at all three cited ranks in both use cases, showing that measured necessity responds to the strength of the input change. The difference is clearest in prompt monitoring, where mean rank-1 PN decreases from 0.706 under contrast substitution to 0.311 under similar-value substitution, and the similar-value scores remain nearly constant across ranks. Advisor recommendation shows a smaller decrease, from 0.573 to 0.412 at rank 1, and retains a descending rank pattern. This control covers Opus 4.6 and Haiku 4.5 on a separate paired subset from the blank-removal comparison, which is why its contrast-substitution means differ. The comparison supports contrast substitution as the primary advisor intervention and confirms that intervention strength affects absolute PN values.
Sufficiency intervention. The sufficiency intervention retains the evaluated feature at its original value while removing the other changeable information. For advisor recommendation, the evaluated client feature is preserved and the remaining 17 client features are replaced with [UNKNOWN]; the candidate-advisor pool remains fixed. For prompt monitoring, the ordinary base request and the segment corresponding to the evaluated risk feature are retained, while the other risk segments are removed. The advisor pool and the base request are preserved because they define the decision context. Sufficiency therefore means that a feature preserves the original decision relative to this fixed context, rather than in the absence of all other input.
D
Additional Necessity and Sufficiency Results
D.1
Feature-Level Citation Calibration and Model Alignment
Figure 10 disaggregates the main-text citation-calibration result (Figure 1) into separate panels for advisor recommendation and prompt monitoring, reporting mean PN, mean PS, and their descriptive mean above each feature’s conditional citation frequency. Table 3 reports the model-level mean Spearman correlations between citation order and the PN, PS, and descriptive-mean scores underlying the main-text discussion of cited-feature ranking agreement (Section 4.2) and the visual comparison in Figure 12 below. 16
Advisor recommendation Prompt monitoring Model
ρPN
ρPS
ρmean
ρPN
ρPS
ρmean
Opus 4.6 Sonnet 5 Haiku 4.5 GPT-5.4 no-r GPT-5.4 Low GPT-5.4 Medium GPT-5.4 High Gemini 3.5 Flash
.181 .571 .153 .194 .428 .452 .353 .462
.169 .273 .265 .288 .515 .450 .498 .373
.178 .445 .180 .266 .514 .444 .448 .456
.479 .573 .014 .414 .429 .475 .356 .711
.603 .698 .354 .524 .589 .637 .480 .755
.554 .598 .069 .511 .571 .659 .551 .789
Table 3: Mean Spearman correlation between the stated order of the three cited features and their measured PN, PS, and descriptive mean. Here, ρmean is calculated using each feature’s mean PN and PS; it is not the average of ρPN and ρPS . Samples with constant scores are excluded separately for each column.
(a) Advisor recommendation
(b) Prompt monitoring
Figure 10: Feature-level necessity, sufficiency, and citation frequency for (a) advisor recommendation and (b) prompt monitoring. The upper plots report mean PN, mean PS, and their descriptive mean for each feature; the lower plots report the percentage of samples in which the feature appears in the cited top three among samples where it is active. All advisor features are active in every client profile. Features are ordered by decreasing mean PN within each use case.
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D.2
Agreement Between Necessity and Sufficiency Rankings
Figure 11 reports the mean Spearman correlation between the necessity and sufficiency rankings of the three cited features within each response. The correlation is undefined when all three PN scores or all three PS scores are equal, so the number of included responses varies across models. Mean agreement ranges from 0.18 to 0.35 in advisor recommendation and from 0.38 to 0.87 in prompt monitoring. Thus, the features most likely to change a decision when altered are not always ordered in the same way as the features most likely to preserve it when retained. Necessity and sufficiency remain separate criteria even when their rankings are positively correlated.
Figure 11: Mean Spearman correlation between necessity and sufficiency rankings for the three cited features. D.3
Cited-Feature Rankings Across Models
Figure 12: Agreement between the stated order of the three cited features and their empirical necessity and sufficiency scores. Error bars show 95% confidence intervals over responses with non-constant scores. Figure 12 shows that agreement between the cited ranking and intervention scores varies across models, use cases, and criteria. Mean necessity and sufficiency correlations range from 0.014 to 0.755, and no model is consistently strongest across all four comparisons. Sonnet 5 has the highest necessity correlation for advisor recommendation (0.571) and a similar value for prompt monitoring (0.573), but its sufficiency correlation differs substantially between the two use cases (0.273 and 0.698, respectively). GPT-5.4 Low has the highest advisor sufficiency correlation (0.515), whereas Gemini 3.5 Flash has the highest prompt-monitoring correlation under both necessity (0.711) and sufficiency (0.755). Performance under one criterion or use case therefore does not predict performance under another. 18
D.4
Cross-Model Reproducibility
Figure 13: Pairwise cross-model agreement for the elicited top-three explanations. The upper panels show feature-set overlap, while the lower panels show ordering agreement for model pairs sharing at least two features.
Feature-set overlap. The upper panels of Figure 13 compare whether two models cite the same features, without considering their order. Averaged across model pairs, overlap is higher in prompt monitoring than in advisor recommendation (0.729 versus 0.676). The GPT-5.4 settings are particularly consistent with one another for advisor recommendation, with a mean overlap of 0.827. In prompt monitoring, the Claude models show the strongest within-family consistency, with pairwise overlaps between 0.81 and 0.85. These results quantify the reproducibility of the cited top-three sets; PN and PS separately evaluate their agreement with decision behaviour.
Ranking agreement among shared features. The lower panels compare the ordering assigned to features shared by a pair of models. Advisor recommendation has higher mean ordering agreement than prompt monitoring (0.873 versus 0.776), even though its feature-set overlap is lower. The GPT5.4 settings are especially consistent in advisor recommendation, with a mean ordering agreement of 0.936. Ordering in prompt monitoring is more variable: the GPT settings generally agree more strongly with one another than the Claude models, while comparisons involving Haiku are less consistent. Models can therefore cite similar features without assigning them the same order. 19
D.5
Cited and Uncited Feature Sets in Advisor Recommendation k=2
k=3
Metric
Cited
Uncited
Cited
Uncited
PN PS
.640 .323
.617 .345
.584 .264
.561 .261
Table 4: Advisor-recommendation mean PN and PS for the first k cited features and the k highestscoring eligible uncited features. The uncited set is selected separately under PN and PS.
Table 4 extends the advisor-recommendation comparison from a single uncited feature to equally sized cited and uncited sets. The first two cited features have a mean PN of 0.640, compared with 0.617 for the two highest-scoring uncited features. The difference remains small at k=3 (0.584 versus 0.561), and the corresponding PS differences are also small. We do not report an equivalent set-level comparison for prompt monitoring because its limited number of active risk features leaves too few eligible uncited features for comparison with the cited top three.
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