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REVIEW 3 major objections 5 minor 113 references

Rule of Thumb: Explaining Artificial Intelligence Systems using Partial Information

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Fitting one additive model with dropout to an AI's observed input-output pairs yields local feature importance explanations that identify which features most predict its decisions, without needing weights, queries, or mimic models.

desk verdict ROT is a practical, fast additive surrogate for explaining API-only systems, but the paper never verifies how faithfully that surrogate tracks the target system in its headline experiments. read the letter →

arxiv 2608.10766 v1 pith:DXYINX3A submitted 2026-08-11 cs.AI cs.LGstat.ML

Kaivalya Rawal , Daria Onitiu , Brent Mittelstadt , Sandra Wachter , Chris Russell This is my paper · ORCID
classification cs.AIcs.LGstat.ML MSC 68T05
keywords RuleofThumbexplanationsfeatureattributionmodel-agnosticXAIdropoutzero-shotclassificationblack-boxauditingadditivemodelsadversarialrobustness
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces 'Rule of Thumb' (ROT), a post-hoc, per-datapoint explanation method that defines a feature's importance by how much knowing its value should update a prediction of an AI system's behavior, rather than by how much perturbing the input changes the output. ROT fits one additive model to input-output pairs the system has already produced, using dropout over feature subsets so that the fitted per-feature contributions predict the system's output from any subset of features, and these contributions become the explanation. Because it needs only existing predictions, ROT can explain closed systems accessible solely through an API — the setting where perturbation-based explainers such as SHAP and LIME need thousands of extra queries and gradient methods need model weights. The paper demonstrates ROT on zero-shot image and text classification with commercial LLMs, a direct audit of Amazon's proprietary recommender, and scientific-discovery scenarios where features were deliberately made uninformative, reporting that ROT aligns with human annotations at least as well as SHAP, resists adversarial 'fairwashing' attacks that fool SHAP and LIME, and makes each additional explanation nearly free.

What carries the argument

The load-bearing machinery is the all-subsets additive objective, Equation (2): $$L = \sum_{J\subseteq \mathcal{J}}\sum_{x\in X} $p^{{|J|}}$(1-p)^{|\mathcal{J}|-|J|}\,\ell\Bigl[C(x),\, F\Bigl(\sum_{j\in J} f_{\theta_j}(x_j)+G\Bigr)\Bigr],$$ which demands that the system's output $C(x)$ be well estimated from any subset $J$ of revealed features. Minimizing it is equivalent to training the additive model with dropout at probability $p$ on the input features, so the sum over all $2^{|\mathcal{J}|}$ subsets collapses into one stochastic fit. The per-feature functions $f_{\theta_j}$ take a linear form, a linear-plus-mixture-of-Gaussians form, or, for text, a shared linear form over token embeddings; each fitted $f_{\theta_j}(x_j)$ doubles as the signed importance of that feature value. The single global fit, rather than a per-datapoint fit, is what makes the first explanation expensive and every later explanation nearly instantaneous.

What would settle it

Fit ROT to a system with a known interactive decision rule — for example, output flips only when two particular features are both present — using only observed input-output pairs, then check whether the fitted additive model reproduces the system's outputs on held-out inputs and whether the interacting features receive top importance. The paper reports ROT's own held-out prediction accuracy only for the image experiment (97.6 percent) and does not report surrogate fidelity for the judicial, movie, resume, or Amazon settings, so measuring how well the fitted additive model predicts the observed decisions in those settings would settle whether the approximation holds where the claims are made.

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Extended reading notes

Core claim

In the paper's own framing, important inputs are those most predictive of the outputs of an AI system. Given a model $C(\cdot)$ over the full feature set $\mathcal{J}$, ROT seeks additive functions $f_{\theta_j}$ and a global bias $G$ such that $C(x) \approx F\bigl(\sum_{j\in J} f_{\theta_j}(x_j) + G\bigr)$ holds for every subset of features $J$ and every datapoint $x$, and it finds them by minimizing the expected loss over all feature subsets and all datapoints. Dropout makes this exponential-looking objective tractable, and the number of calls to $C$ equals the number of datapoints, independent of the number of features. The fitted value $f_{\theta_j}(x_j)$ is the signed importance of feature $j$ taking value $x_j$, and the feature with the largest $|f_{\theta_j}(x_j)|$ is the one that should most change confidence in the prediction. The paper argues that this predictiveness reading of importance — closer to ablation studies than to sensitivity analysis — is what lets ROT explain zero-shot LLM classification without extra API calls, audit proprietary systems without mimic models, and generate scientific hypotheses without trusting out-of-distribution behavior. In experiments, ROT's token importances align with human annotations about as well as SHAP's (weighted AUROC 0.77 versus 0.74 on judicial texts, 0.72 versus 0.50 for a random baseline on movie reviews), and in the Amazon audit ROT highlights 'sold by amazon' as an important feature, an insight the mimic-based SHAP explanation did not surface.

Load-bearing premise

The load-bearing premise is that the target system's behavior is well approximated by the additive rule — its output given any subset of revealed feature values is roughly the sigmoid (or identity) function of the sum of per-feature contributions; if the system's true decision rule depends on interactions the additive family cannot express, the fitted importances describe the surrogate, not the system.

Editorial extensions

If this is right

  • Zero-shot LLM classification becomes explainable at scale: ROT fits once on predictions the model has already produced, and after the first fit each extra explanation takes under 0.1 milliseconds, where the paper measures roughly 13 million additional ROT explanations per single SHAP explanation on consumer hardware.
  • Proprietary-model audits no longer need a mimic model: ROT explains Amazon's recommendation system directly from scraped observations, yields one consistent importance profile where mimic-based SHAP and LIME disagree with each other, and surfaces 'sold by amazon' as an important feature — a possible self-preferencing signal the mimic-based audit missed.
  • For scientific discovery, ROT correctly dismisses a deliberately uninformative feature: after a transformation makes age statistically uncorrelated with diabetes, ROT assigns it negligible importance while SHAP and LIME find it somewhat important, so hypothesis generation is not misled by perturbations off the data manifold.
  • Adversarial 'fairwashing' attacks fail against ROT: across ten attack experiments designed to hide a sensitive feature behind foil features, ROT recovers the sensitive feature as most important on over 89 percent of datapoints (100 percent in six experiments), while SHAP and LIME succeed on at most 5 percent.
  • ROT matches the access conditions regulators actually have: the EU AI Act's Article 74(12) lets market surveillance authorities use fixed datasets and observe outputs without querying arbitrary inputs, and ROT computes explanations from exactly that kind of access, supporting audits for self-preferencing and adversarial robustness.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • ROT scores predictiveness, not causation: any scientific conclusion drawn from ROT should be cross-checked by measuring how well the additive surrogate predicts the phenomenon model on held-out subsets, a fidelity figure the paper reports only for the image experiment.
  • The non-input-feature trick suggests a log-only audit protocol: to probe whether an opaque system relies on protected attributes, append those attributes to the explanation feature set without changing the model's inputs, fit on historical decisions, and read off their importances — no new query ever required.
  • The worst case for ROT is interaction-heavy decision rules, so a natural stress test is a benchmark whose outputs depend on pairwise or higher-order feature combinations; such a benchmark would map where the additive assumption starts to break.
  • Because the per-datapoint cost is essentially zero after the first fit, ROT could be run as a continuous monitoring layer that re-explains every decision of a live API service, turning explanation from a per-request luxury into an always-on audit signal.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes Rule-of-Thumb (ROT), a post-hoc, model-agnostic local feature-importance method. ROT fits a single additive model—linear or logistic in sums of per-feature learned functions—to observed input/output pairs of a target AI system, using dropout over feature subsets as the training distribution (Eq. (2)). The learned per-feature functions are then presented as local importances. The authors demonstrate ROT on zero-shot LLM classification (judicial, movie, resume, image), on an audit of Amazon's recommendation system without a mimic model, on scientific-discovery scenarios including adversarially manipulated models, and on runtime benchmarks. They claim that ROT is substantially faster than SHAP/LIME and well suited to regulatory auditing.

Significance. ROT addresses a real gap: explaining API-only or historically logged AI systems without additional queries. If surrogate fidelity is adequate, the efficiency gains (a single fit reused for many explanations) and the ability to include non-input features are valuable contributions. Strengths include the released code, the breadth of experimental domains, the comparison of judicial and movie explanations against human annotations, the concrete adversarial-attack and mimic-model experiments, and the reported runtime measurements. The central conceptual claim, however, depends entirely on the additive approximation in Eq. (1), and this dependence is not tested in most of the headline settings. The paper would be a meaningful contribution if the authors can quantify when that approximation holds; in the present form, the central claim is not yet empirically supported.

major comments (3)
  1. [§2.1, Eq. (1)] The method's validity rests on the additive approximation C(x) ≈ F(Σ_{j∈J} f_{θ_j}(x_j) + G) for every feature subset J. Because ROT importances are exactly the fitted f_{θ_j}, any gap between this surrogate and the target system means the explanation describes the surrogate, not the AI. The manuscript never reports surrogate fidelity in the judicial, movie, resume, or Amazon settings; only the image experiment reports ROT test accuracy (Appendix D.1, 97.6%), and that is for the full-feature input only, not for masked subsets. Please report held-out agreement (or loss) between ROT's predictions and C(x) for all used settings, ideally broken down by mask size. Without this, the central claim that ROT "identifies the most relevant features" is unverified.
  2. [§2.1, Eq. (1); §3.3] If the target system has feature interactions, no additive model can satisfy Eq. (1) for all J. A simple example is C(x) = x1 XOR x2 over uniform binary inputs: every singleton-mask prediction is 1/2, so any fitted additive surrogate assigns equal, low importance to both features and fails to indicate that they are jointly decisive. The constructed scenarios in §3.3 are main-effects-like and do not test this failure mode. Please add interaction diagnostics (e.g., fidelity of the surrogate on singleton masks, or comparison with a model that includes pairwise terms) and state more carefully the conditions under which ROT importances are valid.
  3. [§5 vs §2.1] The conclusion states that ROT "does so without making additional assumptions," but §2.1 explicitly says "We make some simplifying assumptions to answer this efficiently," and Eq. (1) is exactly such an assumption. This is internally inconsistent. The paper should either weaken the conclusion or justify why the additive assumption is not an additional assumption relative to existing sensitivity-based methods. The distinction matters because the practical value of ROT depends on whether the assumption holds for the target system.
minor comments (5)
  1. [§3.1.2] The sentence "without access to its weights, ors without making additional API calls" contains a typo: "ors" should be "or".
  2. [§3.3.2 and Appendix D.8] The word "adversial" appears several times and should be "adversarial".
  3. [Table S4] The row labeled "Final Average" reports a negative number of explanations (-6786.2), which appears to be an arithmetic artifact and should be corrected or removed.
  4. [Appendix D.6] The reported 4.9% statistic is stated as a lower bound, but the same paragraph suggests the true value could be as high as 49%; please clarify which number is used in the main text and how the LLM filter's error rate was assessed.
  5. [Eq. (2)] The notation in Eq. (2) is dense and difficult to parse; rewriting the objective as an explicit expectation over randomly masked feature subsets would improve readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: ROT's importance scores are stipulated as fitted additive coefficients and are independently validated against human annotations and constructed ground-truth models.

full rationale

The paper's derivation chain is: define an additive surrogate family (Eq. 1), fit it to observed input–output pairs under feature dropout (Eq. 2), and return the fitted per-feature functions as local importances. Calling the fitted f_theta_j(x_j) an 'importance' is a stipulated definition, not a derived result, and the paper does not present any theorem that would make the largest |f_theta_j(x_j)| equal to a pre-existing, independently defined notion of relevance. The claim is therefore not circular on its own; the independent content lies in the empirical validation. The judicial and movie experiments compare ROT against human segment annotations (Table 1, Section 3.1.2), the adversarial experiments (Section 3.3.2) use externally constructed models from Slack et al. [56] with known sensitive/foil features, and the uninformative-feature experiment (Section 3.3.1) constructs a dataset where age is uncorrelated with the target and checks recovery. These are external falsifiable tests, not rewrites of the objective. The paper does cite prior work by its own authors, notably FairPCA [55] (used to construct the uncorrelated dataset), but that citation is an implementation tool, not a load-bearing premise of ROT's formulation; the uniqueness discussion in Section B.1.2 is an in-paper convexity argument, not an imported theorem. The reader concern that Eq. (1)'s additive-fidelity assumption is unverified in several deployed settings is a correctness/fidelity issue, not a circularity: a poor surrogate would make the explanations uninformative, but it would not make the derivation equivalent to its inputs. No equation was found that equals its own output by construction beyond the ordinary sense in which any fitted regression coefficient is the parameter of the fitted model.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the expressivity of an additive surrogate and on the availability of a logged input-output dataset. The drop-out rate and the choice of feature embedding are free parameters that affect the resulting importances. No new physical or conceptual entities are postulated. The most consequential assumption is that the additive approximation is faithful to the target model, which is not measured in several key experiments.

free parameters (3)
  • Dropout probability p = not reported
    The objective in Eq. (2) weights feature subsets by p to the size of the subset times (1-p) to the remaining size; the chosen value of p controls the relative weighting of small versus large feature subsets and is not stated for any experiment.
  • Importance function family and hyperparameters = linear, linear plus mixture of Gaussians, shared linear over tokens
    Section B selects among functional forms and, for the mixture-of-Gaussians form, chooses the number of components and scales after observing 'better stability', without a principled selection criterion or sensitivity analysis.
  • Embedding model for text and vision features = BERT, ModernBERT, MobileNetV3
    ROT importances are computed on embeddings, and the choice of embedding model changes the feature space and therefore the importances. This is a design choice made separately per experiment.
assumptions (4)
  • domain assumption The AI system's behavior is well-approximated by an additive model of the form F of the sum of per-feature contributions, for any feature subset.
    Eq. (1) in Section 2.1 states this approximation. The paper does not report the fidelity of the fitted ROT model to the target model in most experiments, including judicial, movie, resume, and Amazon audit settings.
  • domain assumption A dataset of observed input-output pairs from the target system is available without the ability to query the system on new synthetic inputs.
    Section 3.2 and Appendix D.5 use scraped data from Amazon, and Section 3.1 uses existing LLM predictions. The 'no additional API calls' property presupposes this logged dataset.
  • standard math Dropout training with Bernoulli masks is a faithful stochastic optimizer of the all-subsets objective.
    Section B.1.1 equates the subset-marginalized objective with dropout. This is standard for i.i.d. Bernoulli masks, but the equivalence is to an expectation, not to a finite-sample optimum.
  • domain assumption The additive decomposition is identifiable, with a unique minimum of the objective.
    The uniqueness claim in Section B.1.2 requires strict convexity and well-posedness. This fails for collinear features and is not established for the non-convex mixture-of-Gaussians parameterization.

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Cite this review

Pith. "Pith review of Rule of Thumb: Explaining Artificial Intelligence Systems using Partial Information." pith.science (2026). https://pith.science/paper/DXYINX3A

@misc{pith2026260810766,
  author       = {Pith},
  title        = {Pith review of: Rule of Thumb: Explaining Artificial Intelligence Systems using Partial Information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DXYINX3A}},
  note         = {Machine review of arXiv:2608.10766}
}
read the original abstract

Explainable Artificial Intelligence (XAI) seeks to explain how an Artificial Intelligence (AI) system arrived at a particular decision. We propose ''Rule of Thumb'' (RoT) explanations, a new approach to XAI based upon a novel formulation that identifies the most relevant features for predicting the behaviour of an AI system, for a particular datapoint. We show how RoT is well-suited to enable XAI in: (a) zero-shot classification using large language models (LLMs), (b) auditing of opaque AI systems without model access, and (c) the use of AI in scientific discovery. Additionally, RoT meets specific requirements from leading AI regulations, provides a familiar interface and visualisations for XAI practitioners, is model-agnostic, and is substantially faster than alternatives. Code available at: https://github.com/KaiRawal/Rule-of-Thumb-Explaining-Artificial-Intelligence-Systems-using-Partial-Information

Figures

Figures reproduced from arXiv: 2608.10766 by the authors.

Figure 1
Figure 1. Examples of local feature importances for zero-shot image classification performed via the OpenAI GPT-4o-mini API. The model is prompted to perform zero-shot classification of pet images into labels ‘Cat’ and ‘Dog’ from a public dataset[3]. ROT is orchestrated to produce positive importances for input features indicative of ‘Cat’, highlighted red, and negative importances for features indicative of ‘Dog’, highlighte… view at source ↗
Figure 2
Figure 2. Resume summaries [10] from an IT-worker (Ebony Robinson, top) and a biology teacher (Matthew Walsh, bottom), that respectively pass and fail our AI filter. The zero-shot resume classification system [10] uses the GPT-4.1-nano API to find suitable candidates for an information technology (IT) role. ROT explanations indicate the predictive value of individual text tokens, visualised here by using deeper colour for gre… view at source ↗
Figure 3
Figure 3. Examples of local feature importance explanations from a Random Forest diabetes prediction system. The AI is trained on the Pima dataset [13] and for a datapoint with feature values: glucose level = 99, age = 30, BMI = 34, etc, predicts a diabetes probability of 0.235. ROT and SHAP explain this differently, but glucose is the most important input feature for both. Standard force plots visualise how individual featur… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Token level explanations for zero-shot text classification with LLMs. A judicial appeal is rejected by an AI system (fine-tuned RoBERTa LLM)[17] making zero-shot predictions. This prediction is explained by ROT and SHAP, with more important text segments highlighted wi…
Figure 5
Figure 5. Figure 5: Word-cloud summary of token importances for zero-shot resume classification. A zero￾shot resume filter system uses the GPT-4.1-nano LLM API to find suitable candidates for an information technology (IT) role. ROT explanations indicate the importance of individual text …
Figure 6
Figure 6. Figure 6: Auditing Amazon’s proprietary recommendation system through mimic models ( [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: ROT explanations do not erroneously find unimportant features to be important. An AI system for diabetes prediction is trained on “Pima Indians data”[13] with a synthetic transformation such that age is uncorrelated with diabetes. For this transformed data, XAI should …
Figure 8
Figure 8. Figure 8: ROT explanations are immune to manipulation from certain adversarial attacks. The adver￾sarial attack misleads explainers into ascribing importance to spurious “foil” features when the underlying AI system actually makes predictions using a “sensitive” demographic feat…
Figure 9
Figure 9. Figure 9: Comparing runtimes for ROT and other explainers from the Judicial Case Outcome Prediction Experiment. While the first ROT explanation takes time, additional explanations are virtually instantaneous, unlike SHAP, LIME, or Integrated Gradients. The time-complexity of SHA…

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    doi: https://doi.org/10.1016/j.jhazmat.2024.133707. URL https://www.sciencedirect. com/science/article/pii/S0304389424002863

    2024

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.