{"id":"06bd19a5-845f-490c-aab1-b0e6fb21f838","arxiv_id":"2608.00989","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"Block-level Gaussian mirror statistics give a mostly sound linear FDR method, but the neural Permutation SHAP variant proves null symmetry only by assuming the fitted model already ignores null groups.","lead":"This paper extends Gaussian mirror false-discovery control from single features to blocks of sub-features, using matrix perturbations for linear models and Permutation SHAP derivatives for neural networks. The linear construction is largely sound, but the neural FDR proof assumes away the core difficulty and simulations often miss the target FDR.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3 assumes the fitted model already ignores the null group; this is exactly what training on augmented mirror inputs must establish, so the neural FDR claim is circular.","rationale":"The reader identified the same load-bearing concern: Theorem 3's proof assumes the null at the model level, i.e., the fitted nonlinear model does not depend on the null group, but the paper provides no argument that training on augmented mirror inputs yields this property. This is indeed the critical gap. The proof of Theorem 3 (Appendix C.7) explicitly starts with 'there exists a measurable function g such that f(x)=g(x_-j)', which is exactly the property needed for null symmetry of PSGM statistics. In the actual pipeline, f is trained on U_j, V_j, X_-j, and the fitted f may depend on null blocks through the random perturbations or through spurious correlations. The paper's Section 7 limitation admits this possibility. The simulation results in Tables 2–4 show FDR above the target in most neural rows, consistent with the theoretical gap. The linear contribution (Theorem 1, GGM) appears sound: the block-orthogonality algebra is correct and the mirror statistic is symmetric under the grouped null. The high-dimensional linear extension (Theorem 2) is plausible under sure screening and data-splitting. Therefore the reader's REJECT is appropriate for the paper as a whole, since the central model-agnostic neural FDR claim is not established. I see no reason to change the verdict; the concern is decisive.","tokens_in":31513,"tokens_out":3466,"duration_ms":38241,"concrete_test":"Run the LSTM simulation in Table 2 (n=2500, p=300, m=5, weak signal) with all 300 groups null (β=0). Train the PSGM model exactly as described, compute mirror statistics M_j for all null groups, and test whether the empirical distribution is symmetric about zero (e.g., signed-rank test on M_j, or compare #{j: M_j > t} with #{j: M_j < -t} across thresholds). If the distribution is shifted or asymmetric, Theorem 3's premise fails. As a secondary check, compute the average permutation-SHAP derivative bψ_j for null groups without mirror augmentation; a nonzero mean would show the fitted model depends on null groups.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central advertised claim is FDR control for LSTM/GRU/Transformer models via PSGM. The proof of Theorem 3 (Appendix C.7) begins: 'We interpret the null at the model level: there exists a measurable function g such that f(x)=g(x_-j).' This is an assumption about the fitted model f, not a consequence of the data-generating null β_j=0. In the actual procedure, f is trained on augmented inputs [U_j, V_j, X_-j] with U_j,V_j = X_j ± eZ_j G_j. Under a true null group, y does not depend on X_j, but nothing prevents the trained network from fitting U_j/V_j or spurious correlations; indeed G_j is selected by a finite-sample kernel objective that does not guarantee conditional independence U_j ⟂ V_j | W_j in finite samples. Theorem 3 applies only when f is fixed and independent of group j; it does not show that training produces such f. Theorem 5 similarly assumes eZ_j,λ odd and bG_j even in Z_j, and swap-equivariance, without deriving these properties from the training/optimization procedure. The paper's own Section 7 limitation states null symmetry 'may be weakened if the network learns spurious correlations or assigns systematic directional importance to null grouped features,' which is precisely the gap. The experiments corroborate this: in Tables 2–4, PSGM FDR exceeds the nominal 0.1 in most neural rows, reaching 0.283 in one Transformer row. Thus the model-agnostic neural FDR control is not established as stated; only the linear GGM construction is supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes group-level FDR-controlled feature selection for grouped and sequential models. For grouped linear models, it constructs block mirror variables X_j^± = X_j ± eZ_j G_j with matrix-valued perturbations, proves null symmetry of the resulting block mirror statistic (Theorem 1), and gives a two-stage screen-then-mirror high-dimensional extension (Theorem 2). For neural models, it optimizes a kernel conditional-dependence objective to choose G_j, trains a network on augmented mirror inputs, and uses smoothed Permutation SHAP derivatives as block-level importance scores; Theorems 3 and 5 are claimed to give asymptotic symmetry and hence FDR control. Experiments cover grouped linear models, LSTM/GRU/Transformer architectures, and a CausalRivers real-data application.","tokens_in":31860,"tokens_out":10954,"duration_ms":134043,"significance":"If the neural claim were established, the framework would be a useful extension of mirror-statistic FDR control to grouped and sequential deep models, and it would be genuinely model-agnostic. Credit is due for the clean linear construction (Theorem 1), which requires no covariate-distribution specification and yields a parameter-free matrix-valued perturbation, and for Proposition 4, which shows Permutation SHAP derivatives reduce to the linear coefficient vector. The experiments are broad. However, the paper's headline neural FDR guarantee is not proved: the proofs assume the very property that the training procedure must deliver, and the reported simulations show FDR often exceeding the nominal level. The linear part alone is a moderate, well-executed contribution, but the manuscript as a whole does not support the neural claims as stated.","major_comments":[{"comment":"The proof of Theorem 3 begins: 'We interpret the null at the model level: there exists a measurable function g such that f(x)=g(x_-j).' This is an assumption about the fitted model, not a consequence of the data-generating null β_j=0. In Algorithm 3, f is trained on augmented inputs [U_j, V_j, X_-j], and nothing in the training procedure prevents the network from using U_j or V_j through spurious correlations. Thus Theorem 3 does not establish null symmetry for the actual PSGM pipeline. Section 7 concedes this: 'Null symmetry of PSGM mirror statistics may be weakened if the network learns spurious correlations or assigns systematic directional importance to null grouped features.' The empirical FDRs in Tables 2–4, e.g., 0.283 for Transformer strong high-dimensional, are consistent with this gap. This is the central load-bearing issue for the neural FDR claim.","section":"Theorem 3 / Appendix C.7 / Section 7"},{"comment":"Theorem 5 assumes eZ_{j,λ} is odd in Z_j, bG_j is even in Z_j, and the downstream importance map is swap-equivariant. Oddness of eZ_{j,λ} follows from linearity in Z_j, but the evenness of bG_j is not derived: bG_j is a minimizer of I^K_j(G_j)^2, and no invariance argument is given for the objective or for the selection rule. More importantly, swap-equivariance of the full pipeline—including training a neural network with stochastic optimization and random initialization—is asserted rather than proven. These are conditions, not consequences of Algorithm 4. Hence the high-dimensional neural symmetry-safe claim is unsupported.","section":"Theorem 5 / Appendix C.10 / Section 4.3"},{"comment":"Even if the model-level null were granted, Theorem 3 proves only marginal asymptotic symmetry of each individual sub-feature derivative estimator. The mirror statistic M_j = sign(<ψ_j^+, ψ_j^->)(||ψ_j^+||+||ψ_j^-||) requires joint distributional symmetry or exchangeability of the plus and minus derivative vectors. Appendix C.7 does not establish joint asymptotic normality or exchangeability of (ψ_j^+, ψ_j^-). Thus null symmetry of M_j does not follow from the stated theorem even under its own assumptions.","section":"Theorem 3 / Section 4.1"},{"comment":"The paper claims FDR control for the low-dimensional Group Gaussian Mirror, but no theorem proves that the mirror threshold τ_q controls FDR. Theorem 1 establishes null symmetry of M_j, and the text says 'we use the same mirror thresholding and selection rule as in 2.1 to perform FDR Control,' but no grouped analogue of the Gaussian Mirror FDR lemma is stated or proved. Since the grouped statistics are correlated across j, a formal argument is needed. The low-dimensional linear FDR claim is therefore not fully supported as written.","section":"Section 3.2 / end of Theorem 1"}],"minor_comments":[{"comment":"The notation in Theorem 3 does not distinguish the plus and minus branch estimators ψ^+ and ψ^-, even though the mirror statistic uses both. This should be made explicit.","section":"Theorem 3 / Appendix C.7"},{"comment":"No standard errors or confidence intervals are reported. With 50 repetitions, the binomial standard error at FDR 0.1 is about 0.042, so some deviations are interpretable, but reporting uncertainty would help the reader.","section":"Tables 2–4"},{"comment":"The regularity conditions are stated only as 'under some regularity conditions.' For a theorem carrying the paper's neural FDR claim, these conditions should be listed precisely.","section":"Theorem 3"}],"recommendation":"reject","confidential_remarks":"The linear Group Gaussian Mirror construction is a solid contribution and could be publishable on its own. The neural PSGM claim, however, has a load-bearing circularity: Theorem 3 assumes the fitted model already ignores the null group, which is precisely what training on augmented mirror inputs must establish. The paper's own limitations section effectively concedes the gap, and the simulation FDRs exceed the nominal level in several neural rows. I would not oppose a resubmission that either proves a symmetry guarantee for the actual training pipeline or explicitly reframes the neural method as a heuristic without an FDR theorem."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read it. The linear half is genuinely useful; the neural half is sold with a theorem that assumes the conclusion.\n\nThe new material is the grouped linear extension: block-level mirror variables with matrix-valued perturbations and a block statistic built from the two fitted coefficient vectors. The low-dimensional derivation in Theorem 1 is clean — the block-orthogonality algebra goes through, the symmetry argument is honest, and the GLS whitening in Proposition 2 is a nice addition. The high-dimensional screen-then-mirror version (Theorem 2) is plausible under sure-screening and data-splitting assumptions. The linear experiments look decent: FDR is near the target with full power in most settings, and the method clearly beats Group Lasso as an FDR procedure. The Permutation SHAP derivative is a real modeling idea, and the reduction to the linear coefficient in Proposition 4 is neat. The citation of prior work is fair; this is a natural escalation from Gaussian Mirror and Neural Gaussian Mirror.\n\nThe soft spot is load-bearing and it is the neural half. Theorem 3 starts from 'there exists g such that f(x)=g(x_-j)' — that is, it assumes the fitted model ignores the null group. But in the actual algorithm, the network is trained on the augmented mirror inputs, and the whole question is whether training yields a model with that property. The kernel objective is built to make the two mirror branches conditionally independent of each other, not to stop the network from fitting spurious dependence on the null block. So the theorem is circular on the central claim. Theorem 5 still assumes odd/even structure and swap-equivariance instead of deriving them from the training dynamics. The simulations back up the concern: PSGM FDR exceeds the nominal 0.1 in most neural rows of Tables 2–4, reaching 0.283 for one Transformer setting. The paper's own Section 7 admits exactly this, noting null symmetry 'may be weakened if the network learns spurious correlations.' The honest summary is that the model-agnostic neural FDR guarantee is not established.\n\nMinor: the high-dimensional time-series chunking leans on mixing-type asymptotic independence that isn't examined in the experiments, and I don't see code or data shipped.\n\nWho should read this: anyone working on grouped FDR in linear lagged models — the GGM construction is worth their time. The neural part is a useful cautionary example of how to set up these claims. I'd send it to peer review; the linear contribution is solid, and the neural gap is precisely what referees should wrestle with. My own recommendation: use the linear method, don't lean on the neural guarantees.","headline":"Linear grouped Gaussian mirror is a real, defensible extension; the neural PSGM FDR control is not established — Theorem 3 assumes the fitted model already ignores the null group.","tokens_in":32358,"tokens_out":3062,"would_cite":true,"duration_ms":30336,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62J05","62H15","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Block-level Gaussian mirrors and Permutation SHAP derivatives extend FDR control to grouped and sequential features.","keywords":["FDR control","grouped feature selection","Gaussian Mirror","Permutation SHAP","sequential neural networks","mirror statistics","high-dimensional inference","time series models"],"falsifier":"Generate a grouped dataset with a known null block, train an LSTM, GRU, or Transformer on the mirror-augmented inputs, and compute the PSGM mirror statistic for that null block over many noise realizations and sample sizes. If the empirical distribution of $M_j$ is not symmetric about zero, for example if $\\sup_{t>0} |P(M_j > t) - P(M_j < -t)|$ does not go to zero as $n$ grows, the central symmetry claim fails.","tokens_in":31322,"feed_emoji":"🧩","tokens_out":6769,"duration_ms":65673,"temperature":0.7,"pith_summary":"The paper claims that false-discovery-rate control can be moved from one-feature-one-weight testing to grouped-feature testing, where one original feature is represented by a block of lags, recurrent states, or attention sub-features. For grouped linear models it constructs block-level mirror variables and proves the resulting block mirror statistics are symmetric under the grouped null, yielding FDR control in both low and high dimensions. For sequential neural networks it uses derivatives of Permutation SHAP values as block-level importance scores, selects the matrix-valued perturbation through a kernel-based conditional-dependence objective, and proves asymptotic symmetry of the smoothed derivative estimator under a fixed fitted nonlinear model. If correct, this gives practitioners a model-agnostic way to select grouped features with controlled FDR in lagged and attention-based models, without specifying the covariate distribution.","feed_headline":"Grouped features get FDR control via block mirror statistics","feed_subtitle":"Block mirrors and Permutation SHAP derivatives bring FDR control to LSTM, GRU, and Transformer models.","key_machinery":"The engine is the block-level mirror construction: for each grouped feature $j$, form mirror copies $X_j^\\pm = X_j \\pm \\widetilde{Z}_j G_j$ and combine their fitted importance vectors through the block mirror statistic $M_j$. In the linear case the perturbation is fixed by residualized block orthogonality, with $G_j = (R_j^\\top R_j)^{1/2}$ for the residualized group block $R_j$, making the two mirror coefficient vectors independent under the null. In the neural case the perturbation matrix is chosen by minimizing the kernel conditional-dependence score $I_j^K(G_j)^2$, and the importance vector is $\\psi_j(x) = \\nabla_{x_j} \\Phi_j(x)$, the derivative of the Permutation SHAP value with respect","core_discovery":"The central claim is that a grouped null hypothesis $H_{0,j}: \\beta_j = 0$ can be tested with a mirror statistic built from two perturbed copies of the whole feature block, $X_j^\\pm = X_j \\pm \\widetilde{Z}_j G_j$, where $\\widetilde{Z}_j$ is a normalized Gaussian noise block and $G_j$ an $m\\times m$ perturbation matrix. Under a grouped linear model, the two fitted coefficient vectors $\\widehat{\\beta}_j^+$ and $\\widehat{\\beta}_j^-$ are independent centered Gaussian vectors with equal covariance under the null, so the block statistic $M_j = \\operatorname{sign}(\\langle \\widehat{\\beta}_j^+, \\widehat{\\beta}_j^-\\rangle)(\\|\\widehat{\\beta}_j^+\\|_2 + \\|\\widehat{\\beta}_j^-\\|_2)$ is symmetric about zero","pith_inferences":["Editorial inference: the neural FDR guarantee rests on a model-level null assumption that is not proved for networks trained on the mirror-augmented data; a direct empirical check would be to test sign symmetry of the PSGM statistic on simulated null blocks while varying network depth, regularization, and attention structure.","Editorial inference: the same block-mirror machinery could be combined with other swap-equivariant attribution maps, suggesting the essential role of Permutation SHAP here is to provide a symmetric block-level importance signal rather than a uniquely necessary one.","Editorial inference: the framework works best with sparse support and moderate block size; for dense supports or very long lag windows, the separation between null and non-null mirror statistics may weaken, and future procedures could adapt by pairing the group mirror with group knockoffs or more conservative thresholding."],"forward_implications":["If the linear results are correct, grouped lag models can be first screened by Group Lasso on one data chunk and then mirrored on a second, yielding asymptotic FDR control for the selected feature blocks.","For LSTM, GRU, and Transformer models, the framework provides feature selection whose FDR is controlled at the target level when the fitted model does not depend on null blocks.","Because the method is model-agnostic and does not require specifying the covariate distribution, it applies to any architecture for which Permutation SHAP derivatives can be computed.","The grouped null answers the scientific question for lagged time series and attention models: whether a feature contributes anywhere across its block, not whether a single sub-weight is zero.","Empirically, the method maintains FDR control and often improves power relative to baselines, particularly when signals are spread across correlated feature blocks."],"supporting_citations":[{"why":"Establishes the Gaussian Mirror mechanism and the scalar sign-symmetry property that the block-level construction generalizes.","marker":"[54]"},{"why":"Supplies the mirror threshold formula that turns symmetric statistics into FDR control.","marker":"[8]"},{"why":"Introduces the RKHS conditional-dependence objective that the neural version adapts to matrix-valued perturbations.","marker":"[53]"},{"why":"Defines SHAP values, whose group-level Permutation SHAP is the basis for the neural importance score.","marker":"[34]"},{"why":"Provides permutation-sampling estimation of SHAP values used by the Monte Carlo estimator.","marker":"[38]"},{"why":"Supplies the screen-then-mirror two-stage strategy adopted for high-dimensional grouped linear models.","marker":"[12]"},{"why":"Group Lasso is the default first-stage grouped screener, and its non-polyhedral selection event motivates the two-stage design.","marker":"[56]"},{"why":"Establishes the sure-screening property assumed for the first-stage screening in the high-dimensional theorem.","marker":"[52]"},{"why":"Provides the mixing condition used to treat two chronological data chunks as asymptotically independent in time-series settings.","marker":"[55]"}],"fun_headline_variants":["Block mirrors and SHAP derivatives control FDR for feature groups","FDR control for grouped features without distribution assumptions","Model-agnostic group FDR via Gauss mirror and Permutation SHAP","Grouped features get reliable FDR control in LSTM, GRU, Transformer"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The neural guarantee assumes the fitted model is null at the model level, meaning $f(x)=g(x_{-j})$ for a null group $j$; for a network trained on the mirror-augmented inputs, the paper does not prove that the fitted network avoids dependence on null blocks, so null symmetry of PSGM statistics is assumed rather than established.","fun_headline_variants_meta":{"raw":{"variants":["Block mirrors and SHAP derivatives control FDR for feature groups","FDR control for grouped features without distribution assumptions","Model-agnostic group FDR via Gauss mirror and Permutation SHAP","Grouped features get reliable FDR control in LSTM, GRU, Transformer"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000632,"raw_usage":{"total_tokens":2761,"prompt_tokens":759,"completion_tokens":2002,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":503,"completion_tokens_details":{"reasoning_tokens":1927}},"tokens_in":503,"tokens_out":2002,"duration_ms":15094,"temperature":1.0,"reasoning_tokens":1927,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:35:24.749220+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate a grouped dataset with a known null block, train an LSTM, GRU, or Transformer on the mirror-augmented inputs, and compute the PSGM mirror statistic for that null block over many noise realizations and sample sizes. If the empirical distribution of $M_j$ is not symmetric about zero, for example if $\\sup_{t>0} |P(M_j > t) - P(M_j < -t)|$ does not go to zero as $n$ grows, the central symmetry claim fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the Gaussian Mirror mechanism and the scalar sign-symmetry property that the block-level construction generalizes."},{"cited_title":"J., Fan, Y ., Janson, L., and Lv, J","cited_arxiv_id":null,"evidence_quote":"Supplies the mirror threshold formula that turns symmetric statistics into FDR control."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the RKHS conditional-dependence objective that the neural version adapts to matrix-valued perturbations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines SHAP values, whose group-level Permutation SHAP is the basis for the neural importance score."},{"cited_title":"Sampling Permutations for Shapley Value Estimation","cited_arxiv_id":"2104.12199","evidence_quote":"Provides permutation-sampling estimation of SHAP values used by the Monte Carlo estimator."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the screen-then-mirror two-stage strategy adopted for high-dimensional grouped linear models."},{"cited_title":"and Lin, Y","cited_arxiv_id":null,"evidence_quote":"Group Lasso is the default first-stage grouped screener, and its non-polyhedral selection event motivates the two-stage design."},{"cited_title":"and Huang, J","cited_arxiv_id":null,"evidence_quote":"Establishes the sure-screening property assumed for the first-stage screening in the high-dimensional theorem."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the mixing condition used to treat two chronological data chunks as asymptotically independent in time-series settings."}],"review_version":1}