{"id":"46987f74-2263-425b-bd15-18c4120ab1d4","arxiv_id":"2505.04775","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"ViaSHAP trains one network whose prediction is the sum of its own learned Shapley values, giving tabular accuracy comparable to XGBoost and built-in, fast Shapley explanations.","lead":"This paper introduces ViaSHAP, a neural network that outputs per-feature Shapley values and makes its prediction by summing them, so one forward pass gives both the answer and the explanation. It reports that a Kolmogorov-Arnold Network version matches XGBoost-level accuracy on 25 tabular datasets and produces Shapley explanations closer to exact values than FastSHAP on tabular data and images.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3.4's exact-Shapley guarantee holds only for raw-sum outputs, but the default classifiers apply sigmoid/softmax; the reported predictions are therefore not covered by the central claim.","rationale":"The paper's central claim is that a single trained network can produce both predictions and their exact Shapley values, with predictions obtained by summation. The proof of that claim is Theorem 3.4, which depends on the unlinked definition ViaSHAP(x) = 1^T φVia(x;θ). The default experimental configuration applies sigmoid or softmax links, and the reported predictive accuracies (Table 1, Table 4) are accuracies of the linked outputs. For a nonlinear link, the output is not 1^T φVia(x;θ), so local accuracy fails and φVia cannot be the Shapley values of the reported prediction. This is not a disagreement with an external consensus; it is an internal inconsistency between the theorem's assumptions and the implementation used for the headline results. The reader's weakest assumption identified precisely this issue, and the paper's own ablation data (Table 12, Table 11) corroborate it: removing the link substantially increases similarity to the KernelSHAP ground truth, while predictive performance remains competitive. Thus the central theoretical guarantee applies to the no-link variant, which is a meaningful contribution, but the paper must either restrict the theorem's claim to pre-link logits and re-evaluate the default-configuration explanation claims, or retrain and report the linked models with a corrected statement. This supports a conditional acceptance with clarification, which matches the reader's verdict; no change to the verdict is needed.","tokens_in":39067,"tokens_out":6573,"duration_ms":69581,"concrete_test":"On a synthetic binary classification dataset with n=3 features, train KANVia with a sigmoid link until convergence. For 100 held-out points, compute the exact Shapley values of the probability output f(x) = sigmoid(1^T φVia(x;θ)) by enumerating all 2^3 coalitions using the same baseline-removal value function, and compare them to φVia(x;θ). If the mean absolute difference exceeds a small tolerance (e.g., 0.01), Theorem 3.4's conclusion does not hold for link-equipped models. Repeat with an identity link; exact equality should hold up to optimizer tolerance, confirming that the theorem's actual scope is the pre-link logits.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 3.4 and its supporting Lemma 3.1 rely on the identity ViaSHAP(x) = 1^T φVia(x;θ). Section 3.1 explicitly allows a link function, and the default experimental configuration uses sigmoid/softmax: ablation J.3 compares 'KANVia (default settings)' against 'KANVia without a link function', confirming that the models whose accuracy is reported in Table 1 apply a link. When a nonlinear link σ is applied, the prediction is σ(1^T φVia(x;θ)), so local accuracy (Property 1) fails: 1^T φVia(x;θ) ≠ σ(1^T φVia(x;θ)). The Shapley values of the game v(S) = σ(1^T φVia(x_S;θ)) are not equal to φVia(x;θ) because Shapley values are not equivariant under monotone transformations. Hence the abstract's claim that predictions are 'derived directly by summation' and Theorem 3.4's claim that φVia computes 'the exact Shapley values of the predictions of ViaSHAP(x)' are unsupported for the default link-equipped models. The paper's own ablation (Table 12) is consistent with this gap: default link models show markedly lower cosine similarity and R² to the KernelSHAP ground truth than the no-link variants. A secondary gap is that Theorem 3.4 concerns the global minimizer of loss (6), whereas training optimizes the dual objective (7) with a prediction-loss term, so even in the no-link case exactness holds only at an idealized optimum of (6) that (7) does not in general reach. The link-function mismatch is the cleaner, directly falsifiable problem.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ViaSHAP, a method that trains a neural network to output both predictions and Shapley-value attributions in a single forward pass. The model produces an n×d matrix of attributions φVia(x;θ); predictions are formed as the column sum 1^T φVia(x;θ), optionally transformed by a link function (sigmoid/softmax). Training uses a dual objective (Eq. 7) that combines a weighted least-squares Shapley loss (Eq. 6) with a prediction loss. The authors prove (Lemmas 3.1–3.3 and Theorem 3.4) that a global minimizer of the Shapley loss computes exact Shapley values of the ViaSHAP prediction, provide epsilon-bounded extensions in Appendices B and C, and evaluate four tabular implementations (KANVia, KANVia-rho, MLPVia, MLPVia-theta) on 25 datasets plus image variants on CIFAR-10. They report competitive tabular AUC versus XGBoost and higher similarity of explanations to KernelSHAP ground truth than FastSHAP.","tokens_in":39424,"tokens_out":6180,"duration_ms":55370,"significance":"If the exact-Shapley claim is established for the actual deployed models, ViaSHAP is a notable contribution: it eliminates post-hoc explanation cost and offers an internal Shapley consistency property. The paper's strengths include a large-scale empirical setup (25 datasets, five seeds), public code, and a careful ablation study covering the link function, the efficiency constraint, and the β hyperparameter. The epsilon-bounded results in Appendices B and C are a useful step toward practice. However, the central theoretical claim currently applies only to the no-link, idealized optimum, so the significance of the work hinges on the revisions described below.","major_comments":[{"comment":"Theorem 3.4 states that φVia(x;θ*) computes the exact Shapley values of the predictions of ViaSHAP(x), but the proof (Lemma 3.1, Appendix A) relies on the identity ViaSHAP(x) = 1^T φVia(x;θ). Section 3.1 explicitly allows a link function σ, and the default experimental configuration applies sigmoid/softmax, as confirmed by Appendix J.3, which compares 'KANVia (default settings)' with 'KANVia without a link function'. Under a nonlinear link, the prediction is σ(1^T φVia(x;θ)), so local accuracy fails: 1^T φVia(x;θ) ≠ σ(1^T φVia(x;θ)). Since Shapley values are not equivariant under monotone transformations, φVia is not the Shapley value of the game v(S) = σ(1^T φVia(x_S;θ)). Consequently, the exact-Shapley guarantee does not cover the models whose predictive performance is reported in Table 1. The paper's own Table 12 shows that the default link-equipped models have markedly lower cosine similarity and R² to the KernelSHAP ground truth than the no-link variants, which is consistent with this gap. Please either present the no-link variant as the main method and state Theorem 3.4 for that setting, or provide a separate analysis for the link case and clarify that the guarantee applies to the pre-link logits only.","section":"§3.1, Eq. (6), Theorem 3.4, Appendix J.3"},{"comment":"The lemmas and Theorem 3.4 are proved for a global minimizer of the Shapley loss L_φ(θ) in Eq. (6), but training uses the dual objective L(θ) in Eq. (7), which adds a prediction-loss term with no guarantee that its optimum coincides with a minimizer of Eq. (6). A model that minimizes Eq. (7) may not satisfy efficiency, missingness, or consistency exactly, and the paper does not quantify the gap between the two optima. Please state the theoretical claim in terms of the actual training objective, or present Theorem 3.4 as an idealized result and add an analysis (theoretical or empirical) of the effect of the prediction term on the Shapley properties.","section":"§3.2, Eq. (7), Theorem 3.4"},{"comment":"The explanation evaluation computes ground truth by running unbiased KernelSHAP on ViaSHAP's own predictions, but Eq. (6) minimizes the same weighted-least-squares objective for which KernelSHAP is an estimator (Section 2.3, Eqs. (3)–(4)). High cosine similarity to this ground truth therefore partly reflects agreement with the training objective rather than an independent validation of the faithfulness of the explanations. For the no-link variant, the reported R² values approach 1.0 on many datasets (Table 12), which may largely follow from construction. A non-self-referential evaluation would use a separate black-box model (e.g., an independently trained XGBoost) as the explained model and compare ViaSHAP's attributions to exact Shapley values of that model, or report removal-based fidelity curves as in the image experiments (Section 4.4).","section":"§4.3, Eq. (6), Tables 2–3"}],"minor_comments":[{"comment":"The final step of the epsilon-bounded missingness proof writes |φVia_i(x;θ)| ≤ 2L_φ(θ) after defining the loss as attaining value ϵ²; since L_φ(θ) = ϵ², the correct bound is 2√L_φ(θ). The conclusion is unaffected, but the displayed inequality is dimensionally inconsistent.","section":"Appendix B"},{"comment":"The abstract states that predictions are 'derived directly by summation,' which is inconsistent with the default use of a sigmoid/softmax link function; please align the wording with the actual default model.","section":"Abstract and §3.1"},{"comment":"The column headers 'Inclusion AUC' and 'Exclusion AUC' are described as being computed using top-1 accuracy; please clarify whether these are areas under the inclusion/exclusion curves or simply the top-1 accuracy values at a fixed threshold, since the numeric range is consistent with accuracy rather than AUC.","section":"Table 5"},{"comment":"The phrase 'Appendex J' should be 'Appendix J'; additionally, the caption of Table 3 omits MLPVia-theta although the table includes four columns.","section":"§4.5"},{"comment":"The displayed formula for the relaxed loss appears to have an unbalanced parenthesis in the notation; please check the bracket structure so that the argument of the outer sum is unambiguous.","section":"Appendix G, Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"This is a borderline case. The link-function gap is serious and affects the main claim, but it is fixable by repositioning the method around the no-link variant, which the ablation shows is both accurate and better aligned with Shapley ground truth. The self-referential explanation benchmark also needs to be addressed. I recommend major revision rather than rejection, as the core idea is promising and the empirical scope is substantial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The punchline: this paper's real contribution is training a single network whose pre-sum components are meant to be Shapley values, so explanations come for free at inference. That is new relative to FastSHAP (post-hoc explainer for a fixed black box) and HarsanyiNet (constrained architecture). The tabular study is substantial, and KANVia matching XGBoost across 25 datasets is a legitimate empirical result. Credit is also due for reporting the link-function and marginal-expectations ablations, since those are precisely the places where their own method struggles.\n\nI checked the stress-test concern and it holds. Theorem 3.4 proves that the global minimizer of the Shapley loss computes exact Shapley values for the raw sum 1^T phi_Via(x). But the default classifiers in Section 3.1 apply sigmoid or softmax, so the predictions whose accuracy is reported are probabilities, not raw sums. Shapley values are not equivariant under monotone transformations, so the theorem does not cover those default models. The ablation in J.3 confirms the gap: cosine similarity to KernelSHAP drops when the link is on. This is not a fatal flaw — you could reframe the method as explaining logits, or train without a link — but the abstract's \"derived directly by summation\" and the theorem's scope need to be corrected. A second, smaller gap is that training optimizes the dual objective (7) with a prediction-loss term, so even in the no-link case the guarantee holds only at an idealized optimum of (6), not at the actual optimum reached by (7). The epsilon-bounded extensions in the appendix are for (6), not (7).\n\nThe explanation evaluation is partly circular. Ground truth is KernelSHAP run on ViaSHAP itself, and Eq (6) is the same weighted least squares objective to which KernelSHAP converges. High cosine similarity to that baseline is thus an internal-consistency check as much as an accuracy claim. It still shows the training objective is being optimized, but it is not an external fidelity benchmark. The FastSHAP comparison is more informative, and the image inclusion/exclusion curves help too. A faithfulness evaluation on an external model would strengthen the story.\n\nMinor: \"quasi-random\" hyperparameter selection is vague. State how beta = 10 and 32 coalitions were actually chosen (random search? on which datasplits?).\n\nRecommendation: send it to peer review. The core idea deserves referee time, the experiments are extensive, and the gaps are addressable with a rescoped theorem and a recalibrated explanation evaluation. It is not ready as is, but it is a serious submission.","headline":"The joint predictor-and-explainer idea is genuinely new and the experiments are solid, but Theorem 3.4 overclaims for the default link-equipped models and the explanation benchmark is partly self-referential.","tokens_in":39980,"tokens_out":3264,"would_cite":false,"duration_ms":35363,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single trained network can simultaneously produce accurate predictions and exact Shapley-value explanations, because the prediction is defined as the sum of the Shapley outputs.","keywords":["Shapley values","explainable AI","Kolmogorov-Arnold Networks","prediction by summation","feature attribution","FastSHAP","tabular data","CIFAR-10"],"falsifier":"Train ViaSHAP on a synthetic linear model with independent features, where the Shapley value of each feature under baseline removal is known in closed form, and compare the learned $\\phi_{\\mathrm{Via}}$ to those values; if, after convergence, the attributions do not satisfy efficiency and match the closed-form values within the paper's bound $2\\sqrt{L_\\phi(\\theta)}$, the global-optimum guarantee is not being attained by gradient training.","tokens_in":38870,"feed_emoji":"📊","tokens_out":8999,"duration_ms":76774,"temperature":0.7,"pith_summary":"The paper proposes ViaSHAP, a training scheme in which a single network outputs a matrix $\\phi_{\\mathrm{Via}}(x;\\theta)$ of per-feature attributions and the prediction is defined by summing those attributions column-wise. This turns the Shapley explanation into the prediction itself, so no post-hoc explainer is needed at inference time. The paper claims that at a global optimum of its dual objective, the learned attributions are exactly the Shapley values of the model's own pre-link predictions, and that the KAN-based implementation is competitive with XGBoost and Random Forests on 25 tabular datasets while producing more accurate Shapley-value approximations than FastSHAP on both tabular data and CIFAR-10. A reader should care because interpretability usually costs extra compute or accuracy; here explanation and prediction are the same artifact, and the reported results suggest that cost can be largely avoided.","feed_headline":"One forward pass gives the prediction and its Shapley values","feed_subtitle":"The KAN version matches XGBoost on tabular data and beats FastSHAP on explanation accuracy.","key_machinery":"The load-bearing object is the attribution matrix $\\phi_{\\mathrm{Via}}(x;\\theta)$ together with the additive identity $1^\\top \\phi_{\\mathrm{Via}}(x;\\theta)$ that defines the prediction before the link function. Since Shapley values are the unique additive attribution satisfying local accuracy, missingness, and consistency, the argument reduces to showing the trained $\\phi_{\\mathrm{Via}}$ satisfies those three properties at the global optimum; the Shapley-weighted least-squares loss in equation (6) is the device that enforces them. The Kolmogorov-Arnold Network (KAN) implementation, built from learnable univariate spline functions, is the architecture that makes the tabular and image results work in practice, while the MLP variant rests on the universal approximation theorem.","core_discovery":"ViaSHAP trains $\\phi_{\\mathrm{Via}}: \\mathcal{X}\\to\\mathbb{R}^{n\\times d}$ so that the model's prediction is $y=\\sigma(1^\\top \\phi_{\\mathrm{Via}}(x;\\theta))$, with $\\sigma$ a link function. The training loss is the prediction loss plus a scaled Shapley-weighted least-squares term that matches the prediction on a masked input $x_S$ against the sum $1_S^\\top \\phi_{\\mathrm{Via}}(x;\\theta)$ of the attributions for the features in $S$. The paper proves three properties of the global minimizer---local accuracy, missingness, and consistency---and then invokes Young's uniqueness theorem to conclude in Theorem 3.4 that $\\phi_{\\mathrm{Via}}(x;\\theta^*)$ computes the exact Shapley values of ViaSHAP's predictions. The exactness is established for the raw additive sum; the default classifiers place the sigmoid or softmax after the sum, so the theorem's guarantee applies to the pre-link logits. Empirically, the Kolmogorov-Arnold implementation ranks first among the compared predictors on tabular AUC, is statistically indistinguishable from XGBoost, exceeds 0.96 AUC on CIFAR-10, and its explanations are closer to converged KernelSHAP values than FastSHAP's are.","pith_inferences":["Because the exact-Shapley theorem covers the raw additive output, a natural extension is to define the game on the probability output after the link function and train with a corresponding objective; the paper leaves this unexplored.","Since prediction and explanation share the same parameters, an adversarial perturbation that changes the explanation must also change the prediction; this suggests concrete adversarial-attack and explanation-robustness tests the paper does not run.","The empirical ground truth is KernelSHAP's Shapley values of ViaSHAP's own pre-link outputs, so the explanation benchmark measures internal consistency with the model rather than alignment with human judgement; a user study would be a separate test.","A direct finite-sample check is to train ViaSHAP on a linear model with independent features, where closed-form Shapley values are known, and verify the learned attributions against them; this would expose how far the global-optimum guarantee holds under gradient training."],"forward_implications":["A single forward pass returns the prediction and its full Shapley explanation, cutting explanation latency from seconds per thousand instances with KernelSHAP to milliseconds with ViaSHAP.","On the 25 tabular datasets tested, KANVia's AUC ranking is statistically indistinguishable from XGBoost and Random Forests, so Shapley-clean explanations need not come at the cost of accuracy.","On CIFAR-10, ViaSHAP variants exceed 0.96 AUC, and their top-feature inclusion/exclusion curves show more faithful attributions than FastSHAP applied to the same models.","Because the prediction is the sum of the attributions, local accuracy holds by construction, so the explanation cannot drift from the model as post-hoc explainers can.","The Shapley regression objective can improve prediction itself: the same KAN architecture trained with the Shapley loss significantly outperforms the architecture trained without it."],"supporting_citations":[{"why":"Defines the Shapley value that the paper claims to compute exactly.","marker":"Shapley, 1953"},{"why":"Establishes uniqueness of the Shapley value among additive, locally accurate, dummy-zero, consistent attributions, completing Theorem 3.4.","marker":"Young, 1985"},{"why":"Provides the Shapley kernel and the weighted least-squares objective from which the training loss is built.","marker":"Lundberg & Lee, 2017"},{"why":"Gives the unbiased KernelSHAP estimator used as the empirical ground truth for explanation accuracy.","marker":"Covert & Lee, 2021"},{"why":"Introduces FastSHAP, the main baseline, and the inclusion/exclusion protocol for image explanations.","marker":"Jethani et al., 2022"},{"why":"Introduces Kolmogorov-Arnold Networks, the architecture of the best-performing ViaSHAP implementation.","marker":"Liu et al., 2024"},{"why":"Universal approximation theorem that justifies the MLP-based variant.","marker":"Hornik et al., 1989"},{"why":"Defines the baseline-removal value function used to mask features during training.","marker":"Sundararajan & Najmi, 2020"}],"fun_headline_variants":["One forward pass gives prediction and exact Shapley values","ViaSHAP: predict and explain in a single forward pass","KAN-based Shapley regression rivals XGBoost, beats FastSHAP","Shapley values without post-hoc cost","Exact Shapley values from one forward pass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The exact-Shapley theorem assumes the training loss reaches a global optimum and that the prediction is the raw additive sum; the reported classifiers apply a sigmoid or softmax after the sum, so the guarantee applies to the pre-link logits, and the explanation benchmark additionally takes KernelSHAP's values for those logits as the ground truth.","fun_headline_variants_meta":{"raw":{"variants":["One forward pass gives prediction and exact Shapley values","ViaSHAP: predict and explain in a single forward pass","KAN-based Shapley regression rivals XGBoost, beats FastSHAP","Shapley values without post-hoc cost","Exact Shapley values from one forward pass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00022,"raw_usage":{"total_tokens":1458,"prompt_tokens":966,"completion_tokens":492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":582,"completion_tokens_details":{"reasoning_tokens":408}},"tokens_in":582,"tokens_out":492,"duration_ms":4373,"temperature":1.0,"reasoning_tokens":408,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:21:57.030834+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train ViaSHAP on a synthetic linear model with independent features, where the Shapley value of each feature under baseline removal is known in closed form, and compare the learned $\\phi_{\\mathrm{Via}}$ to those values; if, after convergence, the attributions do not satisfy efficiency and match the closed-form values within the paper's bound $2\\sqrt{L_\\phi(\\theta)}$, the global-optimum guarantee is not being attained by gradient training.","supporting_citations":[],"review_version":1}