{"id":"e8b6f227-fbc3-41f5-9127-946fd6bf91a8","arxiv_id":"2505.09660","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Intrinsic causal contributions of input features to a neural network's output can be estimated from observational data via causal normalizing flows, and reduce to Sobol indices when inputs are independent.","lead":"This paper defines a way to measure how much each input feature intrinsically causes a neural network's prediction, separate from influence inherited from other features. It builds a generative model of the inputs and shows the resulting attributions can be identified from observational data, with tests on synthetic and real datasets.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central identifiability result is conditional on a correct, confounder-free causal graph; the real-data graphs are assumed from prior work and GPT-3.5 consultation, and a wrong topological order or hidden confounder changes the recovered noise variables and hence the ICC.","rationale":"The reader's verdict of CONDITIONAL is appropriate, and I agree with the reader's weakest-assumption diagnosis. The mathematical core of the paper is not obviously flawed: given a fixed topological order and causal sufficiency, the CNF identifiability theorem plus the invariance of variance-based conditional expectations under componentwise bijections does establish that ICC is recoverable from P(X,Yhat). The single most load-bearing condition is therefore Assumption 1, which asserts that G is known, acyclic, and confounder-free. The paper does not learn or statistically test G in the real-data experiments; the AutoMPG graph comes with a GPT-3.5 consultation and the COMPAS graph is only inspired by prior work. If the true graph has a different topological order or a latent confounder, the fitted CNF still matches the observational distribution but its U variables are not the causal noises, so Lemma 1 and Theorem 7 no longer connect the computed values to the intended causal quantity. This is an identifiability failure, not a small-sample concern. The proposed test against a permuted-order CNF on synthetic data would settle whether the topological order is actually load-bearing. I would keep the verdict at CONDITIONAL rather than ACCEPT or REJECT, because the theory is plausible but the empirical support and graph validation are insufficient for stronger acceptance.","tokens_in":23309,"tokens_out":20034,"duration_ms":213043,"concrete_test":"On a synthetic SCM with X1 -> X2 and Y = X1 + X2, fit two CNFs with triangular orders (X1,X2) and (X2,X1), both matching P(X) to within the reported Wasserstein tolerance, and compute ICC_Sh for each feature under each fit. If the ICC values or the feature ranking change beyond Monte Carlo error, the recovered noise variables depend on the assumed topological order, so the real-data ICCs rest on the unvalidated graphs; adding a latent-confounder variant tests Assumption 1 directly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The theoretical chain in Sections 4-7 is internally consistent: given Assumption 1 (known acyclic graph, no latent confounders), Lemma 1 lets ICC_To be read off observational conditionals, and Theorem 7's invariance under componentwise reparameterization of U follows from the cited CNF identifiability result. The load-bearing condition is that the CNF's triangular order is a topological order of the true G and that the true SCM is causally sufficient. The real-data graphs do not satisfy this condition in any verified sense: the AutoMPG graph is adopted from Reddy et al. (2023a) and 'validated' by GPT-3.5 consultation (Appendix F), while the COMPAS graph is only 'inspired by' Plecko and Bareinboim (2024). If G has a wrong edge direction or omits a common cause, the fitted CNF can still match P(X) but with noise variables U that are not the true causal noises; the equality phi(Yhat|U_T)=phi(Yhat|do(X_T)) then fails, and the reported ICC values estimate a different quantity. This is an identifiability failure, not a finite-sample issue: no amount of observational data distinguishes the correct graph from an incorrect one under the stated assumptions.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a post-hoc framework for quantifying intrinsic causal contributions (ICC) of input features to the output of a trained neural network. The authors treat the input generation process as a structural causal model (SCM), define ICC through exogenous noise variables, and introduce two aggregation schemes: Shapley-based ICC and a topological-order average ICC_To. They prove efficiency, nullity, symmetry, and sensitivity properties; with a variance-based uncertainty measure they obtain a causal variance decomposition and relate ICC to Sobol indices under independent inputs. To make ICC identifiable from observational data, they fit causal normalizing flows (CNFs) to the input distribution and invoke component-wise identifiability of triangular maps. Experiments on synthetic data, AutoMPG, and COMPAS compare the resulting attributions with GAM, SP-LIME, and permutation feature importance using the PGU metric.","tokens_in":23545,"tokens_out":17658,"duration_ms":179636,"significance":"If the theoretical claims hold, the paper makes a useful contribution: it supplies an identifiability argument (Theorem 7) via existing CNF results, proposes a topological-order averaging scheme that reduces permutation ambiguity, and connects causal ICC with Sobol indices (Theorem 4). The theoretical chain in Sections 3-7 is coherent and, conditional on Assumptions 1 and 2, the central claim is defensible. The paper also creditably avoids overclaiming rung-3 causal semantics by relying on Lemma 1 to read ICC_To from observational conditionals. However, the practical significance depends on the input causal graph being correct and causally sufficient, and the real-data graph assumptions are not verified; this limits the support for the empirical claims in Section 8.","major_comments":[{"comment":"The central identifiability result is conditional on a correct, confounder-free causal graph, but the real-data experiments do not establish that this assumption holds. Appendix F states that the AutoMPG ground-truth graph is unknown, is adopted from Reddy et al. (2023a), and is 'validated through consultations with GPT-3.5'; the COMPAS graph is only 'inspired by' Plecko and Bareinboim (2024). If the topological order or a parent set is misspecified, the fitted CNF can still match P(X), but the recovered noise variables U will not be the true causal noises, so Lemma 1's equality phi(Yhat|U_T) = phi(Yhat|do(X_T)) fails and the reported ICC values estimate a different quantity. No amount of observational data can detect this misspecification under the stated assumptions. The authors should either use datasets with verified causal graphs, perform a sensitivity analysis over plausible graphs, or explicitly reframe the real-data results as illustrative and conditional on assumed graphs; the abstract and Section 8 currently overstate the empirical support.","section":"Section 7 / Assumption 1 / Appendix F"},{"comment":"Algorithm 1 is not executable as written. Step 3 uses undefined variables epsilon_V and epsilon_W, and the expressions N(F_theta(epsilon_V)) and N(F_theta(epsilon_W)) do not match the quantities u_M, u_N, and u_Q defined in steps 1-2. Since this algorithm is the core estimator for ICC_Sh, the pseudocode must be corrected (likely epsilon_V = u_N and epsilon_W = u_Q) before the experiments can be reproduced.","section":"Section 7, Algorithm 1"},{"comment":"The proof of the variance monotonicity inequality is garbled and does not establish the claim. The text invokes the law of total variance and concludes 'E(V(X)) >= E_Y(V(X|Y))', which is not a meaningful comparison, and 'interchanging Y and Z' does not yield Var_Y(E(X|Y)) <= Var_{Y,Z}(E(X|Y,Z)). The inequality itself is true and follows directly from applying the law of total variance to E[X|Y,Z], but the proof as written is invalid. This theorem underpins the positivity/monotonicity of the proposed variance-based ICC and the decomposition in Corollary 3, so the proof needs to be rewritten.","section":"Appendix D, Theorem 2"}],"minor_comments":[{"comment":"The definition of the coalition value phi(Yhat|do(X_T)) := sum_{x_T} phi(Yhat|do(X_T=x_T)) ptilde(x_T) is confusing: the left-hand side notation suggests a single interventional quantity, and the averaging over x_T with ptilde(x_T) should be defined precisely and kept consistent with Lemma 1.","section":"Section 4.1"},{"comment":"The transition from unnormalized to normalized phi should be flagged. As written, the decomposition V(Yhat) = sum_j ICC_To is correct only for the unnormalized convention phi(Yhat|U_I) = V_{U_I}(E(Yhat|U_I)); under the normalized convention introduced immediately afterward, the identity becomes 1 = sum_j ICC_To.","section":"Section 5, Corollary 3"},{"comment":"The overbrace in the telescoping sum reads phi(Yhat|U_V), which should be phi(Yhat|U) or phi(Yhat|U_[p]); this is a typo in a proof of a central property.","section":"Appendix D, Property 1 proof"},{"comment":"The second display in Theorem 4 writes ICC_phi(X_j -> Yhat) without a superscript; since ICC_To and ICC_Sh coincide under independent inputs, the equality should say so explicitly.","section":"Theorem 4, Eq. (7)"},{"comment":"The binomial coefficients in the Property 3 proof use n where the paper elsewhere uses p; please make the notation uniform.","section":"Appendix D, Property 3 proof"},{"comment":"The claim that single-feature classifiers resolve the discrepancy between ICC_To and ICC_Sh in COMPAS is not supported: the reported F1 scores are 0.8972, 0.8964, and 0.8912, which are nearly equal, so this check does not show that recidivism is the most critical feature. Please either remove this sanity check or state explicitly what conclusion it supports.","section":"Section 8, COMPAS analysis"},{"comment":"Algorithm 2's notation x_Q = (x_M-I, x_NI) is ambiguous; please define it elementwise, e.g., x_{Q,i} = x_{M,i} for i not in I and x_{Q,i} = x_{N,i} for i in I.","section":"Appendix E, Algorithm 2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within CLeaR's scope and the theoretical contribution is promising, but the broken pseudocode, the invalid proof of Theorem 2, and the unverified real-data causal graphs are load-bearing issues. Please insist that the authors correct these and replace the GPT-3.5 'validation' in Appendix F with domain literature or a graph sensitivity analysis. A reproducibility package would also materially strengthen the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate adaptation of Janzing et al.'s ICC to neural-network attribution, with a useful identifiability result via causal normalizing flows, but the empirical support is thinner than the theory and the headline real-data attributions rest on assumed causal graphs. Worth sending to a careful referee; it likely comes back with major revisions.\n\nThe genuinely new piece is Theorem 7: if two causal normalizing flows match P(X, Ŷ), they induce equal ICC values, so the CNF-specific noise parametrization does not matter. That is a clean transfer of Xi-Bloem-Reddy componentwise identifiability to the attribution setting, and it makes the framework identifiable rather than heuristic. The topological-ordering average (ICC_To) and the Sobol link are also clearly laid out, with the Owen (2014) relation correctly credited. I also give them credit for flagging the identifiability issue explicitly instead of just running a flow and reading off attributions.\n\nThe soft spots, in order. (1) The load-bearing assumption is the known acyclic no-confounding graph. For AutoMPG the graph comes from Reddy et al. plus a GPT-3.5 consultation; for COMPAS it is only \"inspired by\" Plecko-Bareinboim. Under Assumption 1, an incorrect edge direction or omitted common cause means the recovered U are not the causal noises, and Lemma 1's equality fails. This is not a finite-sample quibble; it is an identifiability boundary of the method. The paper is honest about Assumption 1 but does not seriously validate the graphs used in the headline experiments. (2) The experimental validation is weak. The PGU results have no error bars, no code is released, the effect sizes in Table 2 are modest, and the COMPAS discrepancy argument is suggestive rather than a real test. (3) Presentation issues: the proof of Theorem 2 is garbled, and Algorithm 1 uses undefined epsilon variables. These are fixable, not fatal.\n\nWho benefits: someone working on causal explainability or sensitivity analysis who wants a principled global attribution under a known graph and is willing to treat the causal graph as user input. It deserves a serious referee, not a desk reject, but the experiments need stronger validation and the graph-assumption caveat should move out of the appendix and into the main text.","headline":"A legitimate, mostly sound adaptation of intrinsic causal contributions to neural-network attribution, with a clean identifiability argument, but the real-data results rest on assumed causal graphs and the experiments are thinner than the theory.","tokens_in":24115,"tokens_out":1793,"would_cite":true,"duration_ms":18726,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that the intrinsic causal contribution of each input feature to a trained neural network's output can be computed uniquely from observational data, without interventions, given a known acyclic causal graph over the…","keywords":["intrinsic causal contribution","causal normalizing flow","Sobol' indices","neural network attribution","identifiability","global explanations","structural causal model","Shapley value"],"falsifier":"Fit two differently initialized causal normalizing flows to the same synthetic dataset generated by a known chain SCM A→B→C→Ŷ, compute the ICC of B with each flow, and check that the values agree to Monte Carlo tolerance; then re-run after adding a spurious edge A→C to the supplied graph and measure how much B's attribution moves.","tokens_in":23107,"feed_emoji":"🎯","tokens_out":7003,"duration_ms":62942,"temperature":0.7,"pith_summary":"The paper tries to establish that a trained neural network's input features can be assigned intrinsic causal contributions (ICC): the part of a feature's effect on the network's output that is not merely inherited from its upstream causes. The central claim is that these contributions are identifiable from observational data alone, given a known acyclic causal graph over the inputs, and can be estimated post-hoc by fitting a causal normalizing flow to the input distribution. If this is right, global explanations of model behavior can separate a feature's own causal role from effects it merely passes along, something ordinary Shapley or permutation importance cannot do. The authors also connect variance-based ICC to Sobol' sensitivity indices, and report that ICC-based attributions outperform several existing global explanation methods on a stability measure called PGU.","feed_headline":"Causal feature blame is now computable from data alone","feed_subtitle":"Separates a feature's own causal effect from what it inherits from upstream causes, without running experiments.","key_machinery":"The central object is the causal normalizing flow: a parametric triangular monotone increasing (TMI) map Fθ together with a fully factorized latent noise distribution Pθ, trained to match the observational input distribution. Its role is to recover the exogenous noise variables U behind each input feature, because ICC is defined as the uncertainty reduction in Ŷ from conditioning on those noise variables. Known identifiability results for triangular maps, namely that two matching flows differ only by independent component-wise invertible transformations, make the ICC value invariant across equally good flow fits. A second piece of machinery is Lemma 1, which identifies conditioning on noise with conditioning on observed ancestors and with the corresponding do-intervention, turning a rung-three causal quantity into an observational one.","core_discovery":"The paper treats a neural network as a structural causal model over the input features X and the prediction Ŷ, and defines the intrinsic causal contribution of feature Xj as the change in conditional uncertainty of Ŷ caused by perturbing its exogenous noise Uj, after conditioning on a set I of other noise variables. Symmetrizing over all topological orderings gives ICC_To, and over all permutations gives ICC_Sh; with variance as the uncertainty measure, both decompose the total variance of Ŷ. The key identifiability result (Theorem 7) states that if two causal normalizing flows both match the same observational distribution P(X, Ŷ), their ICC values coincide, because the flows can differ only by component-wise invertible transformations of the exogenous variables, which leave the relevant conditional expectations unchanged. Lemma 1 supplies the bridge from interventions to observation: for a topological ordering, φ(Ŷ|U_T) = φ(Ŷ|X_T) = φ(Ŷ|do(X_T)), so the contributions are computable from observational conditionals. A Monte Carlo algorithm based on the Jansen estimator with randomized quasi-Monte Carlo sampling estimates the required conditional variances.","pith_inferences":["If the identifiability result transfers from variance to other uncertainty measures satisfying the stated axioms, the same flow-based pipeline could produce entropy-based or divergence-based causal attributions without new theory.","Because the graph is assumed rather than learned in the real-world demonstrations, a practical extension is to run the pipeline over a small set of plausible graphs and report the spread in attributions, turning graph uncertainty into an explicit error bar.","The framework could be pointed at fairness questions: the intrinsic contribution of a protected attribute, stripped of effects inherited through mediators, is a concrete, computable target for fairness audits."],"forward_implications":["Post-hoc global attributions can be computed for any trained network from its input data and a known causal graph, with no intervention data or retraining.","Attributions respect causal order: a feature's score is its own added contribution, separate from the effect it inherits from upstream features.","Variance-based ICC gives an exact additive decomposition of the prediction's variance across input features, so attribution scores are comparable and sum in a meaningful way.","When input features are independent, ICC reduces to a Sobol'-index-style variance decomposition, linking explainability to classical global sensitivity analysis.","On the three datasets tested, ICC-based explanations produced smaller prediction-gap-on-perturbation (PGU) values than GAM, SP-LIME, and permutation feature importance, indicating more stable global explanations."],"supporting_citations":[{"why":"Defines intrinsic causal contribution and supplies Lemma 1, the identity that converts noise conditioning into observational and do-conditioning.","marker":"Janzing et al. (2024)"},{"why":"Introduces causal normalizing flows, whose diffeomorphic, causally sufficient SCM class is assumed in Theorem 7.","marker":"Javaloy et al. (2023)"},{"why":"Provides the triangular-map identifiability result that two matching flows differ only by component-wise invertible transformations.","marker":"Xi and Bloem-Reddy (2023)"},{"why":"Establishes the treatment of a trained neural network as an SCM whose hidden layers can be marginalized, the starting point for the paper's causal graph.","marker":"Chattopadhyay et al. (2019)"},{"why":"Connects Sobol' indices to Shapley value, used in the proof that ICC coincides with Sobol' decomposition under independent inputs.","marker":"Owen (2014)"},{"why":"Supplies the variance estimator used in Algorithm 1 to estimate the conditional-uncertainty function φ.","marker":"Jansen (1999)"},{"why":"Provides the synthetic data-generating process and the AutoMPG causal graph used in the experiments.","marker":"Reddy et al. (2023a)"},{"why":"Supplies the COMPAS causal graph used in the real-world experiment.","marker":"Plecko and Bareinboim (2024)"}],"fun_headline_variants":["Feature blame minus inherited bias: now identifiable","Intrinsic causal attribution: identifiable from data alone","Separate a feature's own effect from inherited noise","Causal blame without experiments, via normalizing flows","Blame features, not upstream causes—data-only"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the true cause-effect relationships among the input features are known in advance and involve no hidden common causes; if that graph is misspecified, the attributions silently measure the wrong causal quantity.","fun_headline_variants_meta":{"raw":{"variants":["Feature blame minus inherited bias: now identifiable","Intrinsic causal attribution: identifiable from data alone","Separate a feature's own effect from inherited noise","Causal blame without experiments, via normalizing flows","Blame features, not upstream causes—data-only"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000298,"raw_usage":{"total_tokens":1680,"prompt_tokens":853,"completion_tokens":827,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":469,"completion_tokens_details":{"reasoning_tokens":754}},"tokens_in":469,"tokens_out":827,"duration_ms":7994,"temperature":1.0,"reasoning_tokens":754,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:34:18.281049+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit two differently initialized causal normalizing flows to the same synthetic dataset generated by a known chain SCM A→B→C→Ŷ, compute the ICC of B with each flow, and check that the values agree to Monte Carlo tolerance; then re-run after adding a spurious edge A→C to the supplied graph and measure how much B's attribution moves.","supporting_citations":[{"cited_title":"Causal normalizing flows: from theory to practice","cited_arxiv_id":null,"evidence_quote":"Introduces causal normalizing flows, whose diffeomorphic, causally sufficient SCM class is assumed in Theorem 7."}],"review_version":1}