{"id":"3f2d14d3-93b3-49ce-897e-8117cf080e98","arxiv_id":"2502.10311","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"ExplainReduce selects a small subset of local explanations that act as a global surrogate, matching the fidelity of the full explanation set on many problems.","lead":"This paper introduces ExplainReduce, a procedure that compresses hundreds of local explanations of a black-box model into a few representative proxy models that can serve as a global explanation. The approach is model-agnostic and applies to both regression and classification, with experiments suggesting five proxies often match the fidelity of hundreds of explanations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Test-fidelity results depend on an unvalidated Euclidean nearest-neighbor gating rule; the proxy set alone is not shown to be a deployable surrogate.","rationale":"The paper does something useful: it formalizes explanation reduction as a submodular optimization problem, gives greedy algorithms with guarantees, and shows on twelve datasets that small proxy sets match or beat the full set on training coverage/fidelity and on NN-gated test fidelity. The theoretical guarantees around Problems 1-3 are standard (Nemhauser et al. 1978) and the empirical comparisons to submodular pick, GLocalX, and the IP approach are informative. The weakest point is not the optimization itself but the bridge from a set of proxy models to a working surrogate on new data. Section 5's Euclidean nearest-neighbor gating is the only mechanism that produces test-fidelity numbers, and it is neither learned nor justified from the optimization. The paper even acknowledges in Section 6 that the method ignores the spatial distribution of data with respect to proxy association. This matters because the abstract's headline claim ('as few as five explanations can faithfully emulate the closed-box model') is a claim about deployment, not just about a readable set of models. The inconsistency in Algorithm 2 between y_i and \\hat{y}_i strengthens the concern: if the implementation uses raw labels for the mapping while the loss matrix uses closed-box predictions, the training map is not aligned with the explanation objective. The proposed test, comparing NN gating to oracle and learned gating, would separate proxy-set quality from gating quality and tell us whether the headline result is robust. This is consistent with the reader's conditional verdict, so no verdict change is needed; the concern is exactly the condition that must be met.","tokens_in":32130,"tokens_out":10224,"duration_ms":103792,"concrete_test":"Recompute the main test-fidelity experiments (e.g., Gas Turbine and Jets, k=5) under three assignment rules: (i) the paper's Euclidean-NN; (ii) an oracle that, for each test item, selects the proxy with minimum loss to the closed-box prediction; and (iii) a learned gating function, e.g., a multiclass classifier trained on (x_i, map[i]) using the corrected \\hat{y}_i-based map. If (i) is close to (ii) and (iii), the NN heuristic is adequate; if (i) is substantially worse, the five-proxy claim depends on an unvalidated heuristic and the paper should be revised to include a proper gating mechanism for novel items.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that five proxies 'faithfully emulate the closed-box model' is established only through a test-time assignment that is not part of the ExplainReduce optimization. Section 5 states that each novel item is assigned to the proxy of its nearest training item in Euclidean feature space. This nearest-neighbor gating is a heuristic: it is not learned, not derived from the loss matrix, and not evaluated against alternatives. The reported test fidelity therefore conflates the quality of the proxy set with the quality of this Euclidean-NN gating. If the gating misassigns test items, the same five proxies could show much worse fidelity in practice, and the abstract's 'faithfully emulate' claim would overstate what ExplainReduce delivers. The paper itself acknowledges in Section 6 that the method 'has no consideration of the spatial distribution of the data with respect to which proxy was associated with each item.' In addition, Algorithm 2's mapping step uses y_i (original labels) rather than \\hat{y}_i (closed-box predictions) in the argmin, inconsistent with the loss matrix definition L_ij=ell(g_i(x_j),\\hat{y}_j); if the implementation follows the pseudocode, the training map itself is optimized against the wrong target. Because the test-time gating is the only mechanism that turns a set of five models into a surrogate, this is the weakest link in the empirical support for the headline result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ExplainReduce, a model-agnostic procedure that reduces a large set of local surrogate explanations to a small 'proxy set' of simple models that can serve as a generative global explanation for a closed-box model. The reduction is formalized as three optimization problems (maximum coverage, minimum average loss, and a balanced joint utility), each approximated by greedy submodular maximization with standard (1-1/e)-type guarantees. The empirical study covers twelve datasets, several XAI methods (LIME, SHAP, SLISEMAP, SmoothGrad, LORE), and comparisons with submodular pick, GLocalX, and an IP-based aggregation method. The central claim is that as few as five proxies can faithfully emulate the closed-box model on test data.","tokens_in":32430,"tokens_out":5404,"duration_ms":53204,"significance":"If the empirical claim is fully established, ExplainReduce would be a practically useful, model-agnostic tool for compressing hundreds of local explanations into a compact global surrogate, with clear computational advantages over IP-based and rule-merging baselines. The theoretical component is standard but correct: the submodularity arguments for the coverage, loss-reduction, and balanced objectives are sound, and the experimental breadth is substantial. The main weakness is that the test-fidelity evaluation depends on an ad hoc Euclidean nearest-neighbor assignment for novel items, so the headline generalization claim is not supported as cleanly as the abstract states. Nevertheless, the optimization framework and the overall empirical picture are strong enough that the concerns are addressable within the manuscript's scope.","major_comments":[{"comment":"The test-fidelity evaluation relies on a nearest-neighbor mapping that is not part of ExplainReduce. Section 5 states that 'each novel item is assigned to a proxy corresponding to the training item that is closest in the feature space using Euclidean distance,' but this gating rule is not learned, not derived from the loss matrix, and not compared against alternatives. Consequently, the reported test fidelity is a joint property of the proxy set and this Euclidean-NN heuristic, not of the proxy set alone. The abstract's claim that 'as few as five explanations can faithfully emulate the closed-box model' is therefore stronger than the evidence supports; the paper itself acknowledges in Section 6 that the method has no consideration of the spatial distribution of the data with respect to proxy assignment. I recommend that the authors report train and test fidelity separately, evaluate at least one alternative assignment rule (for example, direct loss-based assignment on a validation set, or a classifier trained on the training proxy assignments), and qualify the headline claim to refer to the proxy set together with the assignment rule used to deploy it.","section":"Section 5, Figs. 5 and 8"},{"comment":"The mapping step in Algorithm 2 computes map[i] = arg min_{j in S_c} ell(g_j(x_i), y_i), using the original labels y_i, whereas the loss matrix L_ij = ell(g_i(x_j), hat y_j) and the fidelity metric are defined with respect to the closed-box predictions hat y_j. If the implementation follows the pseudocode, the training-time mapping is optimized against the wrong target; if the implementation uses hat y_i, the pseudocode should be corrected. This is a correctness ambiguity in a load-bearing part of the evaluation pipeline, and it should be clarified in the manuscript.","section":"Algorithm 2, Section 4.2"},{"comment":"The main quantitative claims are presented as single runs without error bars or repeated-seed variation. For example, Figures 5 and 8 assert that k=5 proxies reach or surpass the fidelity of the full explanation set, but the reader cannot assess the variability of this conclusion across dataset splits or XAI initialization randomness. Since the paper makes a precise numerical claim ('as few as five'), reporting at least mean and standard deviation over several repetitions, or stating that each curve is a single fixed split, would materially strengthen the empirical support.","section":"Figs. 5-8 and Appendix C"}],"minor_comments":[{"comment":"The abstract contains formatting errors: 'includelime,shap, andslisemap' is missing spaces around the method names.","section":"Abstract"},{"comment":"The caption says 'different datasets are depicted as rows, with the XAI methods used to produce the initial local explanations shown as rows'; the repetition of 'rows' makes the intended layout unclear.","section":"Figure 6 caption"},{"comment":"In the proof of supermodularity of the loss function, the line 'Since M_A >= M_B, then -M_A <= min(0, ell_v - M_B)' is not generally valid as written; the claimed inequality Delta(A,v) <= Delta(B,v) is true but requires a short case analysis. Please rephrase the proof step.","section":"Appendix H, Lemma 1 proof"},{"comment":"The phrase 'we set the default number of subsamples to n=500' reuses the symbol n, which is already used for the size of the dataset D; use a distinct notation such as n_G or |G| for the number of local explanations.","section":"Section 5.2.1"},{"comment":"The column headers such as 'G. Maxc A. ratio' and 'G. Min Loss A. ratio' are difficult to parse; spell out 'greedy max coverage' and 'approximation ratio' or use a separate legend.","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"The central optimization framework is sound and the experimental campaign is extensive, but the paper's headline claim is currently supported by a test-time assignment heuristic that is external to the method. This is fixable with additional experiments or a carefully qualified claim, so I do not see it as grounds for rejection. One point to watch in revision is that the pseudocode/target mismatch in Algorithm 2 should be resolved explicitly, since it affects the reproducibility of the reported mappings."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: ExplainReduce is a solid, useful aggregation method for local explanations, with a genuine generalization over prior work and a broad empirical study. The main weakness is the out-of-sample mapping: test fidelity is measured through a Euclidean nearest-neighbor heuristic that is not part of the optimization, so the \"five proxies suffice\" claim is not fully established as a deployable surrogate. Still, the paper is worth serious refereeing.\n\nWhat's new: prior aggregation methods (submodular pick, GLocalX, Li et al.) are tied to specific explanation types or classification. ExplainReduce gives a unified formulation—max coverage, min loss, and a balanced objective—with standard greedy submodular guarantees, and works with any generative local explainer on regression or classification. The experiments are extensive: 12 datasets, several explainers (LIME, SHAP, SmoothGrad, SLISEMAP, LORE), comparison to three prior aggregation methods. The finding that k=5 proxies often match the fidelity of the full set of hundreds is interesting and likely useful.\n\nSoft spots: (1) The test-fidelity evaluation assigns each novel item to the proxy of its nearest training item in Euclidean space. That mapping is a heuristic, not derived from the loss matrix, and not compared to alternatives. The paper admits this in Section 6, but the headline claim rests on it. It would be easy to test other mappings (e.g., choose the proxy that actually minimizes loss on the test point, or learn a classifier for proxy assignment), and the sensitivity should be reported. (2) Algorithm 2 maps training items using the original labels y_i, while the loss matrix and fidelity use closed-box predictions \\hat{y}_i. This is likely a typo, but it should be fixed; if the implementation actually uses \\hat{y}_i, the pseudocode is misleading. (3) Main figures lack error bars; some appendix tables have them, but the central plots would be stronger with variability shown. (4) Code availability is not clear from the arXiv version despite the text claiming supplementary code.\n\nThe theory is standard Nemhauser et al., correctly applied; no issue there. The citation pattern is fine; self-citations to SLISEMAP are relevant but not load-bearing.\n\nBottom line: this is a practical contribution for XAI practitioners. The core idea holds up; the out-of-sample gating needs more scrutiny before the strong \"faithful emulation\" claim is accepted. I'd send it to review, with a request for the mapping analysis and code.","headline":"Solid, useful aggregation method for local explanations; the 'five proxies suffice' claim rests on an unvalidated nearest-neighbor gating rule, but the work deserves serious refereeing.","tokens_in":32915,"tokens_out":2428,"would_cite":true,"duration_ms":22798,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T05","68W25","90C27"],"pacs":[],"model":"deepseek-v4-flash","headline":"A handful of local surrogate models, selected greedily to maximize coverage or minimize loss, can replace a large explanation set and match the closed-box model's fidelity, coverage, and stability on test data.","keywords":["explainable artificial intelligence","local explanations","global explanations","proxy models","submodular maximization","explanation aggregation","model-agnostic interpretability","greedy algorithms"],"falsifier":"Construct a closed-box model on a high-dimensional or discontinuous feature space—for example, a random forest with many axis-aligned thresholds—where neighboring points in Euclidean distance frequently land on opposite sides of decision boundaries. If ExplainReduce's five-proxy set then fails to reach the full explanation set's test fidelity, or if test fidelity drops sharply when the nearest-neighbor assignment is replaced with an oracle mapping from the true best local model, the claimed generalization would be contradicted.","tokens_in":31964,"feed_emoji":"📉","tokens_out":3679,"duration_ms":37129,"temperature":0.7,"pith_summary":"The paper claims that the many local explanations produced by methods like LIME, SHAP, or SLISEMAP are largely redundant, and that a small subset of them can act as a global explanation of a closed-box model. It introduces ExplainReduce, which frames the reduction as an optimization problem balancing fidelity, coverage, and interpretability, and solves it with greedy algorithms that carry a worst-case approximation guarantee. Experiments across twelve regression and classification datasets show that as few as five proxy models often match or beat the test-set fidelity of a full set of hundreds of local explanations. If right, this gives practitioners a compact, human-readable way to summarize what a black-box model is doing without sacrificing accuracy.","feed_headline":"Five explanations match hundreds in explaining a black-box model","feed_subtitle":"ExplainReduce shrinks large sets of local surrogates to a small proxy set that keeps fidelity, coverage, and stability.","key_machinery":"The central object is the proxy set selection problem, formalized through a loss matrix $L_{ij} = \\ell(g_i(x_j), \\hat{y}_j)$ and a coverage threshold $\\varepsilon$. The objective functions—coverage $C(S,\\varepsilon)$, average loss $L(S)$, and balanced utility $U(S) = \\lambda C(S,\\varepsilon) + (1-\\lambda)(L_{\\text{base}}-L(S))/L_{\\text{base}}$—are monotone submodular set functions. The greedy algorithm 'reduce' iteratively adds the explanation with the highest marginal gain, and its performance is bounded by the submodular maximization guarantee. For unseen test items, the paper assigns each item to the proxy of its nearest training item in Euclidean feature space.","core_discovery":"ExplainReduce's central claim is that a large set of local explanations can be reduced to a small 'proxy set' of simple models that serves as a generative global explanation. The reduction is formalized as three optimization problems: maximum coverage, minimum average loss, and a balanced joint utility combining both. Each objective is monotone submodular, so the standard greedy algorithm achieves at least a $(1-1/e)$ approximation to the optimal proxy set. Empirically, the balanced variant reaches or surpasses the full explanation set's fidelity, coverage, and stability with only about five proxies, and does so while being agnostic to the choice of closed-box model and local explanation method.","pith_inferences":["The paper's reliance on Euclidean nearest-neighbor assignment for test items implicitly assumes that the closed-box function is smooth enough that nearby feature-space points share the same best local explanation; on highly discontinuous or high-dimensional functions, the reported test fidelity may not transfer.","The proxy-selection view could be adapted for concept-drift monitoring by tracking how the selected proxy set changes over time, since a shift in the most representative local models would signal a change in the closed-box function's behavior.","For explanation methods that output feature attributions rather than generative surrogates, one could first fit a generative model to the attributions and then apply ExplainReduce, extending its scope beyond the methods tested in the paper.","The balanced utility formulation could be tuned per application, e.g., prioritizing coverage in safety-critical settings or fidelity in high-stakes prediction, with the greedy guarantee preserved for any $\\lambda \\in [0,1]$."],"forward_implications":["Users of XAI methods can obtain a global view of a closed-box model by inspecting only a handful of simple models instead of reading hundreds of local explanations.","ExplainReduce works across regression and classification, and with local explanation methods that produce generative surrogates, including LIME, SHAP, SLISEMAP, SmoothGrad, and LORE.","The greedy algorithms find proxy sets in seconds, whereas the integer-programming baseline and GLocalX take hundreds to thousands of seconds on the same tasks.","Proxy sets enable downstream uses such as clustering data by model behavior, outlier detection, and building an interpretable surrogate for the closed-box model.","Test-set fidelity plateaus at small $k$, so a user can set $k$ around five and still get a faithful and interpretable global explanation."],"supporting_citations":[{"why":"Supplies the $(1-1/e)$ approximation guarantee for greedy maximization of monotone submodular functions, which underpins all three reduction objectives.","marker":"Nemhauser et al. (1978)"},{"why":"Introduces LIME and the submodular pick baseline that ExplainReduce is compared against for global explanation aggregation.","marker":"Ribeiro et al., 2016"},{"why":"Provides SHAP as a local explanation method used in the experiments and as a source of local linear surrogate models.","marker":"Lundberg and Lee, 2017"},{"why":"Introduces SLISEMAP and motivates the observation that neighboring local explanations are often nearly interchangeable, forming the basis for the redundancy claim.","marker":"Björklund et al., 2023"},{"why":"Defines SmoothGrad, another local explanation generator tested as input for the reduction procedure.","marker":"Smilkov et al., 2017"},{"why":"Provides the definitions of fidelity and instability used to evaluate the proxy sets.","marker":"Guidotti et al., 2018"},{"why":"Introduces GLocalX, a rule-based local-to-global aggregation method used as a baseline in the comparison.","marker":"Setzu et al., 2021"},{"why":"Proposes the integer-programming 'max spherical coverage' aggregation method, the main optimization-based baseline ExplainReduce is compared against.","marker":"Li et al. (2022)"}],"fun_headline_variants":["Five surrogates replace hundreds of local explanations","Global explanation from just five local proxies","Five proxy models capture a black box's full behavior","Reduce hundreds of local explanations to five that work"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The test-time evaluation assumes that a novel item can be mapped to the right proxy simply by taking the closest training item in Euclidean feature space, which only works if the closed-box model's local behavior changes smoothly between neighboring points.","fun_headline_variants_meta":{"raw":{"variants":["Five surrogates replace hundreds of local explanations","Global explanation from just five local proxies","Five proxy models capture a black box's full behavior","Reduce hundreds of local explanations to five that work"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000821,"raw_usage":{"total_tokens":3531,"prompt_tokens":821,"completion_tokens":2710,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":2661}},"tokens_in":437,"tokens_out":2710,"duration_ms":17241,"temperature":1.0,"reasoning_tokens":2661,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T18:34:36.804719+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a closed-box model on a high-dimensional or discontinuous feature space—for example, a random forest with many axis-aligned thresholds—where neighboring points in Euclidean distance frequently land on opposite sides of decision boundaries. If ExplainReduce's five-proxy set then fails to reach the full explanation set's test fidelity, or if test fidelity drops sharply when the nearest-neighbor assignment is replaced with an oracle mapping from the true best local model, the claimed generalization would be contradicted.","supporting_citations":[{"cited_title":", Lee , S.-I","cited_arxiv_id":null,"evidence_quote":"Provides SHAP as a local explanation method used in the experiments and as a source of local linear surrogate models."},{"cited_title":", Guidotti , R","cited_arxiv_id":null,"evidence_quote":"Introduces GLocalX, a rule-based local-to-global aggregation method used as a baseline in the comparison."}],"review_version":1}