Less is More: Efficient Black-box Attribution via Minimal Interpretable Subset Selection
Pith reviewed 2026-05-22 21:26 UTC · model grok-4.3
The pith
Reformulating black-box attribution as submodular subset selection identifies key input regions more faithfully using fewer samples.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
LiMA reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, a submodular function is designed to quantify subset importance and capture their impact on decision outcomes. Then, a bidirectional greedy search algorithm efficiently ranks input sub-regions by importance, identifying both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors.
What carries the argument
The submodular function that quantifies subset importance together with the bidirectional greedy search algorithm for ranking and selecting minimal interpretable input regions.
If this is right
- Provides faithful interpretations with fewer regions across eight foundation models.
- Achieves an average 36.3 percent improvement in Insertion and 39.6 percent in Deletion metrics.
- Runs 1.6 times faster than naive greedy search for attribution.
- Yields 86.1 percent higher average highest confidence when explaining reasons for model prediction errors.
Where Pith is reading between the lines
- The bidirectional search might be adapted to locate minimal subsets that preserve or remove specific model behaviors for targeted debugging.
- If the submodular scoring generalizes, the same machinery could apply to other discrete inputs such as tokenized text sequences.
- Identifying least-important regions could support data pruning experiments that test whether removing them leaves model accuracy intact.
Load-bearing premise
The submodular function designed to quantify subset importance accurately captures the true impact on decision outcomes without requiring post-hoc tuning or data-specific adjustments.
What would settle it
On a new set of foundation models or image datasets, the insertion and deletion faithfulness scores of LiMA would fail to exceed those of prior attribution methods while using fewer regions.
Figures
read the original abstract
To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes LiMA, a black-box attribution method that reformulates identifying influential input regions as a submodular subset selection optimization problem. It introduces a custom submodular function to quantify subset importance for model decisions and a bidirectional greedy search algorithm to efficiently find both most- and least-important regions while defining an optimal attribution boundary. Experiments on eight foundation models report average gains of 36.3% on Insertion and 39.6% on Deletion metrics versus baselines, 1.6x speedup over naive greedy search, and 86.1% higher confidence on error explanations, with code released.
Significance. If the submodular function is verifiably monotone submodular and the empirical gains are robust, the approach could advance efficient, faithful black-box explanations for discrete inputs like images by using fewer regions and providing both positive and negative attributions. The code release and multi-model evaluation are positive factors supporting reproducibility and generalization claims.
major comments (3)
- [§3 (submodular function definition)] The design of the submodular function (abstract and §3) is asserted to quantify subset importance and capture decision impact, yet no formal proof of monotonicity or the diminishing-returns property is supplied, nor is there empirical verification on the model output surface. This is load-bearing because the bidirectional greedy algorithm's (1-1/e) approximation guarantee depends on it; without verification the reported metric gains and 'optimal attribution boundary' become purely empirical rather than theoretically supported.
- [§4 (experiments)] Experimental results (abstract and §4) report average improvements of 36.3% Insertion / 39.6% Deletion and 1.6x speedup without error bars, standard deviations, or statistical significance tests across the eight models. This weakens the strength of the generalization and efficiency claims.
- [§4 (experiments and algorithm)] No ablation is presented on the bidirectional search versus standard greedy or on how parameters of the submodular function were selected (abstract states 'design a submodular function' but provides no tuning details or sensitivity analysis). This leaves open whether the gains are driven by the specific search procedure or by implicit data-specific adjustments.
minor comments (2)
- [Abstract] Abstract contains grammatical issues ('which aim to identify' should be 'which aims to identify'; repeated 'on average' in the error-explanation sentence).
- [§3] Notation for the submodular function and the bidirectional search steps could be clarified with explicit pseudocode or a small worked example to improve readability.
Simulated Author's Rebuttal
We appreciate the referee's thorough review and valuable suggestions for improving the theoretical and empirical aspects of our work. Below, we provide point-by-point responses to the major comments.
read point-by-point responses
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Referee: [§3 (submodular function definition)] The design of the submodular function (abstract and §3) is asserted to quantify subset importance and capture decision impact, yet no formal proof of monotonicity or the diminishing-returns property is supplied, nor is there empirical verification on the model output surface. This is load-bearing because the bidirectional greedy algorithm's (1-1/e) approximation guarantee depends on it; without verification the reported metric gains and 'optimal attribution boundary' become purely empirical rather than theoretically supported.
Authors: We recognize that the absence of a formal proof for the monotonicity and diminishing returns properties of our submodular function, as well as empirical verification, limits the theoretical support for the approximation guarantee. We will revise Section 3 to include a formal mathematical proof establishing these properties and add empirical analysis verifying the submodular behavior on the model outputs. This will strengthen the connection between the algorithm's guarantees and the reported performance improvements. revision: yes
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Referee: [§4 (experiments)] Experimental results (abstract and §4) report average improvements of 36.3% Insertion / 39.6% Deletion and 1.6x speedup without error bars, standard deviations, or statistical significance tests across the eight models. This weakens the strength of the generalization and efficiency claims.
Authors: We agree that reporting without error bars or statistical tests reduces the robustness of our claims. In the revised version, we will update the experimental results in Section 4 to include error bars, standard deviations across the eight models, and statistical significance tests to validate the average improvements of 36.3% on Insertion and 39.6% on Deletion, as well as the speedup. revision: yes
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Referee: [§4 (experiments and algorithm)] No ablation is presented on the bidirectional search versus standard greedy or on how parameters of the submodular function were selected (abstract states 'design a submodular function' but provides no tuning details or sensitivity analysis). This leaves open whether the gains are driven by the specific search procedure or by implicit data-specific adjustments.
Authors: We will incorporate ablations in the revised manuscript to compare the bidirectional greedy search against the standard greedy algorithm, quantifying the efficiency benefits. Additionally, we will provide details on the selection of parameters for the submodular function and include a sensitivity analysis to demonstrate that the performance gains are not due to data-specific tuning. revision: yes
Circularity Check
No significant circularity in derivation chain
full rationale
The paper reformulates black-box attribution as a submodular subset selection optimization problem and introduces a custom submodular function plus bidirectional greedy search as explicit algorithmic contributions. Performance claims (36.3% Insertion / 39.6% Deletion gains, 1.6x speed-up) are obtained by direct comparison against external baselines on eight foundation models rather than by algebraic reduction of fitted parameters or self-citations. No load-bearing step equates a derived quantity to its own inputs by construction, and the central optimization framework remains independent of the reported empirical outcomes.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption A submodular function can be defined that accurately quantifies the importance of input subsets for model decisions.
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel echoes?
echoesECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.
We construct our objective function ... F(S) = λ1 scons + λ2 scolla + λ3 sconf + λ4 seff (Eq. 8). Lemma 1 (Diminishing returns) ... Lemma 2 (Monotonically non-decreasing).
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IndisputableMonolith/Foundation/BranchSelection.leanbranch_selection unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
Bidirectional greedy search algorithm ... optimality bound F(S) ≥ (1-1/e-ε) F(S*) (Theorem 1)
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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