{"id":"85c22aef-e1f0-4104-8498-1305e8e8cf00","arxiv_id":"2607.03351","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"Outcome-adapted representations that preserve outcome prediction while discarding Riesz information strictly reduce asymptotic variance of AutoDML estimators relative to using all covariates.","lead":"The paper shows that AutoDML estimators of causal parameters become more efficient when the shared covariate representation is trained only to predict the outcome and then frozen before learning the Riesz representer. This yields lower asymptotic variance and state-of-the-art accuracy on the IHDP benchmark.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The Reader correctly isolates the representation-error term after Proposition 13 as the weakest link for asymptotic normality of the original target. That condition is strong and is only rigorously controlled under coordinate-projection sure screening (Corollary 14). However, this is not a load-bearing flaw in the central claim: Theorem 6 itself is an exact finite-sample variance comparison that holds whenever the representation preserves the outcome regression and conditional variance, independent of estimation. The paper never claims that neural-net representations automatically satisfy the o_P(n^{-1/2}) rate; it explicitly advises bootstrap when they may not. The empirical results (especially the adaptive bottleneck on IHDP and the bias-variance decomposition on the ASE and missing-outcome designs) stand on their own as evidence that outcome-adapted representations improve finite-sample accuracy. No internal inconsistency, circular argument, or unacknowledged gap appears. Therefore the ACCEPT verdict with high confidence remains appropriate.","tokens_in":35488,"tokens_out":437,"duration_ms":4043,"concrete_test":"Re-run the adaptive-dimensionality-reduction outcome-adapted net on the Kang-Schafer process (c=1.75, n=2000) with 500 bootstrap resamples instead of 200; if the percentile intervals still attain nominal 95% coverage while Gaussian intervals remain undercover, the authors' practical recommendation is confirmed and the representation-error concern is operationally handled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central efficiency claim (Theorem 6) is cleanly proved under the stated conditions and is not threatened by the representation-error caveat that the Reader correctly flags. That caveat is already acknowledged by the authors (Section 4.3 and Discussion), who recommend bootstrap inference precisely when the o_P(n^{-1/2}) rate on representation error cannot be guaranteed. The neural-net experiments (IHDP, ASE, Kang-Schafer) show the practical gains without relying on the sure-screening corollary, so the theoretical soft spot does not undermine the paper's main contribution.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies efficient shared covariate representations for automatic debiased machine learning (AutoDML) of parameters that are continuous linear functionals of an outcome regression. It proves that a permissible representation Z = h(X) that preserves the outcome regression and conditional outcome variance while discarding information about the Riesz representer yields strictly smaller asymptotic variance than the full-covariate AutoDML estimator (Theorem 6), with the gap equal to E[Var(α_P(X)|Z) Var(Y|Z)]. For a broad class of functionals (Lemma 7), the converse holds: Riesz-adapted representations inflate variance (Theorem 8). Motivated by this, the authors define an outcome-adapted AutoDML estimator that first learns a representation via outcome regression, then estimates the Riesz representer on the frozen representation; they establish sample-split asymptotic normality for the representation-dependent functional (Theorem 11) and bound representation error (Proposition 13, Corollary 14). A neural-network implementation freezes the shared trunk after MSE training and applies simple or group-LASSO adaptive dimensionality reduction as an information bottleneck. Experiments on synthetic ATE/ASE/mean-missing-outcome designs and the semi-synthetic IHDP benchmark show efficiency gains over separate nets, RieszNet, and MADNet, with state-of-the-art MAE on IHDP.","tokens_in":35641,"tokens_out":1272,"duration_ms":21613,"significance":"If the efficiency comparison holds, the paper resolves a concrete design question for shared-trunk AutoDML architectures (RieszNet, MADNet, Dragonnet): the shared representation should be outcome-adapted, not Riesz-adapted. This is a clean generalization of the DOPE principle from AIPW/ATE to the full AutoDML class, with transparent variance decompositions rather than ad-hoc multi-objective loss weights. Strengths that raise the contribution: Theorems 6 and 8 are elementary but previously missing; sample-split asymptotics follow standard double-robust arguments under uniform mean-square continuity and product-rate conditions; code and 1000-replication experiments with error bars are provided; the authors correctly flag the representation-error caveat and recommend bootstrap when the o_P(n^{-1/2}) rate cannot be guaranteed. The empirical finding that RieszNet performs best when its Riesz-loss weight is small further supports the theory. The result is of direct practical interest for causal and policy estimation with neural nuisance models.","major_comments":[{"comment":"Section 4.3, condition (2) after Proposition 13, and Corollary 14: asymptotic normality and coverage for the original target ψ(P) (rather than ψ_ĥ(P)) require the representation error to be o_P(n^{-1/2}). This rate is established only for coordinate-projection representations under a uniform sure-screening property. The neural representations used throughout Section 6 are not shown to satisfy (2). The Discussion correctly recommends bootstrap when the rate cannot be justified, but bootstrap consistency is left open. For the central claim that the proposed estimator targets ψ(P) with valid inference, either (i) give conditions under which neural outcome-adapted representations achieve the rate, or (ii) state more prominently that the Gaussian intervals of Corollary 12 cover ψ_ĥ(P) and that bootstrap is the default for ψ(P) in the neural setting.","section":null},{"comment":"Algorithm 1 / Theorem 11 vs Section 6.2: the asymptotic theory is developed under a fixed sample split (I1 for nuisances, I2 for the estimating equation). The IHDP experiment (and the RieszNet weight-sweep) uses the full sample with no splitting. The reported MAE and confidence-interval claims for IHDP are therefore not covered by Theorem 11 or Corollary 12. Either supply a cross-fit or no-split argument, or clearly label the IHDP results as exploratory relative to the sample-split theory.","section":null}],"minor_comments":[{"comment":"Figure 2 caption and Section 6.2: state explicitly that the RieszNet, MADNet, and C-learner numbers are taken from the cited papers rather than re-run under identical seeds/architectures, so that the comparison is not over-interpreted as a fully controlled bake-off.","section":null},{"comment":"Section 5.1 / Figure 3: the two hypotheses about RieszNet (small λ_Riesz and TMLE contributing to outcome-adaptation) are well motivated; a short formal remark that the RieszNet objective with λ_Riesz → 0 recovers the two-step outcome-adapted procedure would tighten the link to Theorem 6.","section":null},{"comment":"Example A.2 (Appendix): the ASE counter-example where a Riesz-adapted representation can improve variance is valuable; a one-sentence pointer in the main text near Theorem 8 would help readers see the scope of the converse result.","section":null},{"comment":"Notation: m_h vs m_ĥ and γ_h,P vs γ_ĥ,P are dense in Section 4; a short notational table or consistent bolding of estimated maps would improve readability.","section":null},{"comment":"Appendix C.1: the group-LASSO λ grid and the 1-SE rule are sensible; reporting the selected dimensions/λ values (or their distribution across replications) for the main experiments would aid reproducibility.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid, well-executed contribution that cleanly answers a design question left open by RieszNet/MADNet. The representation-error and sample-split gaps are real but already partially acknowledged; they do not threaten Theorems 6/8. I would accept after a light revision that makes the inference caveats more prominent for the neural case. Fit for a methods journal in causal inference / semiparametrics is good."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This paper gives a clean answer to a practical question that has been floating around the AutoDML literature: when you share a representation between the outcome regression and the Riesz representer, should that representation be outcome-adapted or Riesz-adapted? Theorems 6 and 8 settle it. If the representation preserves the outcome regression (and the residual variance), the asymptotic variance drops by a non-negative term that is exactly the leftover variation of the Riesz representer; the converse holds for a broad class of functionals that includes ATE, ASE, and missing-outcome means. That is a genuine generalization of the DOPE result from Christgau et al., and the proofs are short and elementary once you have the Riesz representation in hand.\n\nThey then implement the idea with a two-step neural net: train the shared trunk on the MSE loss, freeze it, then train the Riesz branch. An optional group-LASSO bottleneck on the shared layer forces the representation to discard Riesz information. On the usual synthetic and semi-synthetic suites (including the Kang–Schafer stress test and the 1000 IHDP replications) the estimator is competitive or better than RieszNet and MADNet, and the adaptive-bottleneck version is state-of-the-art on IHDP. The code is public and the experiments are thorough.\n\nThe soft spot is exactly the one the authors flag: the representation error |ψ_ĥ − ψ| is only guaranteed to be o_P(n^{-1/2}) under sure-screening variable selection. For neural nets you do not have that guarantee, so the asymptotic normality result is formally for the representation-dependent functional, not necessarily for the original target. They recommend bootstrap intervals when you cannot justify the rate, and the experiments show that bootstrap helps on the hard missing-outcome design. That is a real limitation, but it is not hidden and it does not break the efficiency principle itself.\n\nThis is for people who already use AutoDML or RieszNet-style estimators and want a theoretically justified way to share representations. The math is solid, the experiments are reproducible, and the citation pattern is fair. I would send it to peer review without hesitation.","headline":"Clean efficiency principle for AutoDML plus a simple neural implementation that beats RieszNet/MADNet on the usual benchmarks; the representation-error caveat is real but already flagged by the authors.","tokens_in":36216,"tokens_out":551,"would_cite":true,"duration_ms":5973,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G05","62G20","62P20"],"pacs":[],"model":"grok-4.5","headline":"A shared covariate representation that keeps only what predicts the outcome is asymptotically more efficient for AutoDML estimators than using all covariates.","keywords":["automatic debiased machine learning","Riesz representer","outcome-adapted representation","doubly robust estimation","asymptotic efficiency","neural networks","causal inference"],"falsifier":"On a design where the true outcome depends on a known low-dimensional projection while the Riesz representer depends on additional covariates, replace the outcome-adapted representation by an oracle projection onto those extra covariates and check whether the resulting AutoDML variance rises by the amount predicted by Theorem 6.","tokens_in":36428,"feed_emoji":"📉","tokens_out":689,"duration_ms":5296,"temperature":0.7,"pith_summary":"Many causal parameters can be written as linear functionals of an outcome regression. Automatic debiased machine learning estimates them by also estimating a Riesz representer and plugging both into a doubly robust formula. Existing neural architectures share a representation of the covariates for both tasks, but it was unclear whether that representation should be tuned to the outcome or to the representer. This paper proves that a representation that preserves the outcome regression (and residual variance) while discarding information about the Riesz representer yields a strictly smaller asymptotic variance. The gain is exactly the expected product of the residual variance of the representer given the representation and the residual variance of the outcome. The authors turn the theory into a practical estimator: first learn a representation by outcome regression alone, freeze it, then learn the representer on the reduced features, optionally with an information bottleneck. On synthetic designs the estimator recovers the theoretical efficiency gain; on the IHDP benchmark it attains the lowest mean absolute error among published doubly robust methods.","feed_headline":"Keep only outcome-predictive features for better AutoDML","feed_subtitle":"A shared representation that discards Riesz information cuts asymptotic variance and hits SOTA on IHDP","key_machinery":"Theorem 6 (outcome-adapted efficiency). It supplies the exact variance difference between the full-covariate AutoDML estimator and any outcome-adapted representation, and thereby justifies freezing the shared trunk after the outcome-regression step.","core_discovery":"If a permissible representation Z = h(X) satisfies γ_h,P(Z) = γ_P(X) and Var_P[Y|Z] = Var_P[Y|X], then the asymptotic variance of the AutoDML estimator based on Z is smaller than the variance based on the original covariates by the non-negative quantity E[Var(α_P(X)|Z) Var(Y|Z)]. Maximizing that gap requires discarding as much information about the Riesz representer as possible while still predicting the outcome.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Outcome-adapted AutoDML keeps only outcome-predictive features","Discard Riesz info in shared representation to cut AutoDML variance","Sparse outcome-only covariates yield more efficient AutoDML","AutoDML gains efficiency by ignoring Riesz while predicting Y","Outcome-focused representation beats full-covariate AutoDML"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"The learned representation must keep enough of the outcome signal that the difference between the original target and the representation-dependent functional vanishes faster than one over square-root n; otherwise the final estimator is asymptotically normal only for the wrong functional.","fun_headline_variants_meta":{"raw":{"variants":["Outcome-adapted AutoDML keeps only outcome-predictive features","Discard Riesz info in shared representation to cut AutoDML variance","Sparse outcome-only covariates yield more efficient AutoDML","AutoDML gains efficiency by ignoring Riesz while predicting Y","Outcome-focused representation beats full-covariate AutoDML"]},"model":"grok-4.5","effort":"low","cost_usd":0.004154,"raw_usage":{"total_tokens":1293,"prompt_tokens":805,"num_sources_used":0,"completion_tokens":89,"cost_in_usd_ticks":41540000,"prompt_tokens_details":{"text_tokens":805,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":399,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":805,"tokens_out":89,"duration_ms":3324,"temperature":1.0,"reasoning_tokens":399,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T03:04:51.441686+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"On a design where the true outcome depends on a known low-dimensional projection while the Riesz representer depends on additional covariates, replace the outcome-adapted representation by an oracle projection onto those extra covariates and check whether the resulting AutoDML variance rises by the amount predicted by Theorem 6.","supporting_citations":[],"review_version":1}