{"id":"30be6cbe-a4ca-4fd2-a782-888b7b9c8b24","arxiv_id":"2607.08150","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"DeepPySR adds dynamic pruning, exponential Pareto selection, and hierarchical layers to PySR and reports better R²/F1 plus domain-aligned formulas on Feynman and seven real-world datasets.","lead":"DeepPySR extends evolutionary symbolic regression with dynamic feature pruning, an exponential formula-selection score, and multi-layer composition. It aims to make glass-box equations usable on high-dimensional biomedical and social-science data where standard SR fails.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Optimistic multi-config selection without held-out data is the load-bearing soft spot for claimed superiority.","rationale":"The reader correctly isolates the evaluation protocol as the weakest assumption supporting the strongest claim. The paper is otherwise a solid methods-and-benchmarks contribution: three concrete, implementable extensions, multi-domain stress tests including the demanding Raine cohort, public code claims, and candid discussion of compute and exact-recovery limits. No internal inconsistency or fabrication is evident; the concern is classic optimistic selection under small-n CV without nested or external hold-out. That concern is load-bearing precisely because the headline numbers and abstract deltas are what justify “outperforms PySR … on high-dimensional biomedical datasets.” A fixed-config re-run on public tasks is cheap, decisive, and matches the reader’s own acceptance condition. Therefore the CONDITIONAL verdict stands; no upgrade or downgrade is warranted until that check is performed. Agreement with the reader is full on both the soft spot and the recommended path forward.","tokens_in":19726,"tokens_out":672,"duration_ms":6706,"concrete_test":"Re-run the four public headline tasks (body fat, heart disease, student math, wine red) with a single pre-registered config (e.g. T_start=50, T_ramp=100, α=10, ρ=1.5, λ=0.005) fixed before any fold evaluation, identical seeds/operator budget for DeepPySR vs PySR, and report mean±SE R²/F1. If the DeepPySR–PySR gap shrinks below the abstract deltas (or loses significance), the superiority claim is selection-driven.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that DVPS+EPS+multi-layer yields practical superiority over PySR (and baselines) on high-d biomedical tasks rests on Methods §4.6: 5-fold CV over a 27-config grid (T_start ∈ {25,50,75}, T_ramp ∈ {50,100,150}, α ∈ {1,10,50}), with EPS (ρ,λ) scored on the same hall-of-fame fronts, no external held-out set for public data, and “DeepPySR (best)” rows reported in Tables 3–5. Because the grid and EPS selection both use the CV folds that also produce the final metrics, the reported lifts (body fat +0.092 R², heart F1 +0.111, student math +0.016, Raine age-27 +0.215) can be inflated by selection of the lucky configuration rather than by the methods themselves. Wilcoxon n=5 already has low power; nested selection further weakens the inference that the architecture, not search effort, drives the gains. Abstract/table summaries that highlight only the best numbers amplify this.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"DeepPySR extends evolutionary symbolic regression (PySR/SymbolicRegression.jl) with three components aimed at high-dimensional, multicollinear, and imbalanced scientific data: a Dynamic Variable Pruning Schedule (DVPS) that ramps a prune-variable mutation during search (Eqs. 16–17, Alg. 1); Exponential Pareto Selection (EPS) that scores hall-of-fame formulas by R²^ρ·exp(−λ(c−1)) (Eq. 18); and a multi-layer hierarchical composition that discovers latent symbolic subexpressions and substitutes them (Eq. 19). The paper evaluates exact recovery on four Feynman equations and predictive performance plus formula interpretability on seven real-world datasets (body fat, heart disease, wine, student grades, stroke, diabetes, Raine BMI longitudinal with 125 features). Reported gains over PySR include body fat R² 0.794 vs 0.702, heart disease F1 0.898 vs 0.787, student math R² 0.964 vs 0.948, and growing Raine BMI advantage with age, with formulas argued to align with known clinical/epidemiological factors.","tokens_in":20061,"tokens_out":1216,"duration_ms":11528,"significance":"If the gains are attributable to DVPS/EPS/multi-layer rather than extra search effort or optimistic selection, the work would be a useful practical advance for applying evolutionary SR beyond low-d physics benchmarks to biomedical and social data where glass-box equations are valued. Strengths include open code (deeppysr.jl + Python wrapper), multi-dataset evaluation with fold-level means±SE and Wilcoxon tests, convergence curves isolating pruning (Fig. 1), and domain-plausible recovered formulas (e.g., Raine gene–early-BMI interaction, heart-disease risk factors). The integration of pruning inside the evolutionary loop and a tunable, post-hoc Pareto scorer are concrete engineering contributions that address real barriers to SR adoption.","major_comments":[{"comment":"Methods §4.6 and Tables 3–5: The central superiority claims rest on 5-fold CV over a 27-configuration grid (T_start, T_ramp, α) with EPS (ρ, λ) scored on the same hall-of-fame fronts, and no external held-out test set for public datasets. “DeepPySR (best)” rows therefore risk optimistic selection of the lucky configuration rather than a fixed method. Nested selection plus n=5 (Wilcoxon min p=0.031) weakens the inference that DVPS/EPS/multi-layer—not search budget or fold luck—drive the reported lifts (body fat +0.092 R², heart F1 +0.111, Raine age-27 +0.215). A nested CV, fixed default config, or true held-out split is needed to support the abstract/table claims of outperformance.","section":null},{"comment":"§2.1–2.4 and Fig. 1: Ablations isolating DVPS, EPS, and multi-layer are deferred to Supplementary Note S3 and are not quantified in the main text against a matched PySR budget. Convergence curves use identical adaptive parsimony but still leave open whether multi-layer depth and the 27-config search inflate gains. Main-text ablations (or at least a single fixed-config DeepPySR vs PySR column) are load-bearing for attributing gains to the three named contributions rather than overall search effort.","section":null},{"comment":"§4.6 experimental design: SMOTE is applied only to baselines on stroke/diabetes while SR models run without it; the paper argues this is conservative, yet it confounds direct F1/accuracy comparison (Table 4). Either report both with and without SMOTE for all methods or restrict primary claims to metrics that do not depend on this asymmetry (e.g., formula structure and recall at fixed accuracy).","section":null}],"minor_comments":[{"comment":"Abstract and Table 5: Abstract quotes a single Raine BMI R² 0.525 vs 0.370; main text reports age-specific values (0.727–0.425). Clarify whether 0.525 is a mean across ages and report it consistently.","section":null},{"comment":"Eq. (18): The floor max(10^{-4}, R²_i) and the role of r2-weight vs ρ are slightly underspecified relative to the “r2-weight = 1.0” used in the Raine formula; align notation.","section":null},{"comment":"Table 1 vs §2.3: Stroke N is listed as 5,110 in Table 1 but 43,400 in the classification results text; reconcile sample size and preprocessing.","section":null},{"comment":"Fig. 1d–e relationship circle plots are useful but lack a short caption definition of “connection score” and layer colouring in the main text.","section":null},{"comment":"§4.4 multi-layer: Default EPS leaf threshold 2.0 and fixed depth are stated without sensitivity; a brief note on robustness would help.","section":null}],"recommendation":"major_revision","confidential_remarks":"The evaluation design (grid + EPS on the same CV folds, no external test) is the main soft spot; if the authors can add nested CV or a fixed-config comparison, the paper is a solid methods contribution for an applied ML / interpretable-ML venue. Scope fits cs.LG / scientific ML well. No integrity concerns; code availability is a plus."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"DeepPySR is a practical engineering package on top of PySR: a scheduled prune-variable mutation (DVPS), an exponential hall-of-fame scorer (EPS), and a BFS multi-layer composition with local circular-dependency rules. That integration is what is new. The paper does the empirical work carefully enough to be useful.\n\nWhat works: they ship concrete operators and selection rules, run them on four Feynman equations plus seven real datasets (body fat, heart, wines, students, stroke, diabetes, Raine BMI), report fold means ± SE, Wilcoxon tests, convergence curves, and domain-plausible formulas. DVPS is the clearest win—on the 125-feature Raine task the MSE gap versus vanilla PySR is large, and the method keeps rare perinatal variables that impurity selection drops. EPS is cheap and reproducible (scores existing hall-of-fame equations). Multi-layer gives readable ICC decompositions (G2 as Layer-1 anchor for grades; PRS × early zBMI for Raine). Code is claimed public; Feynman recovery is honest (near-exact, not always exact). Biological readings of the Raine formula are post-hoc interpretation, not circular claims of discovery.\n\nSoft spots, in proportion. The load-bearing one is Methods 4.6: 5-fold CV over a 27-config grid (T_start, T_ramp, α), EPS (ρ, λ) chosen on the same fronts, no external held-out set for the public data, and tables that lead with “DeepPySR (best)”. Nested selection can inflate the headline lifts (body fat +0.092 R², heart F1 +0.111, Raine age-27 +0.215). n=5 already has min p=0.031; several PySR comparisons do not clear it. SMOTE only for baselines is deliberate and conservative for SR, but still asymmetric. Abstract/table summaries sometimes emphasize peak numbers over the interpretable (≤40-node) rows. Compute is heavy (70–150 CPU-h per dataset). None of this sinks the contribution; it just means the superiority claims need independent re-runs with fixed seeds and pre-registered configs before treating the deltas as settled.\n\nWho it is for: people who actually want glass-box formulas on messy clinical or cohort tables and already use or consider PySR. Not a theory paper. It deserves a serious referee—methods are clear, experiments are multi-domain, limitations are mostly stated. I would engage: re-run the public tasks, cite the DVPS/EPS pieces if they hold, and treat Raine as a case study rather than a general proof.","headline":"Solid PySR extension for high-d biomedical SR; the real soft spot is optimistic multi-config selection without held-out data, not the algorithms themselves.","tokens_in":20706,"tokens_out":673,"would_cite":true,"duration_ms":7703,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"DeepPySR turns evolutionary symbolic regression into a practical tool for high-dimensional medical and social data by pruning features during search, scoring formulas with an exponential accuracy-complexity rule, and stacking layers to reso","keywords":["symbolic regression","interpretable machine learning","dynamic variable pruning","Pareto selection","hierarchical composition","biomedical prediction","multicollinearity","class imbalance"],"falsifier":"Re-run the same 27-configuration grid and multi-layer pipeline on an independent external cohort for body fat, heart disease, or Raine BMI; if the R^{2}/F1 gaps versus PySR and tree ensembles disappear or reverse under identical operator sets and fold structure, the claimed superiority of DVPS/EPS/multi-layer fails.","tokens_in":20584,"feed_emoji":"🔬","tokens_out":950,"duration_ms":9619,"temperature":0.7,"pith_summary":"Symbolic regression promises glass-box equations instead of black-box models, but it usually fails on real biomedical and social datasets that are high-dimensional, multicollinear, or class-imbalanced. DeepPySR extends evolutionary symbolic regression with three coordinated pieces: a schedule that ramps up pruning of irrelevant variables as search progresses, an exponential score that picks one formula from the Pareto front by jointly rewarding accuracy and penalizing complexity, and a multi-layer architecture that discovers hierarchical intermediate expressions. On physics recovery tasks and seven real-world datasets, the method reports higher accuracy than plain PySR and conventional baselines while returning short formulas that match known clinical and social risk factors. A sympathetic reader would care because the approach aims to make transparent, auditable equations usable where post-hoc explanations of black boxes are unstable or insufficient.","feed_headline":"Symbolic regression that prunes and stacks for real medical data","feed_subtitle":"DeepPySR recovers short equations that beat black-box baselines on body fat, heart disease and BMI","key_machinery":"The Dynamic Variable Pruning Schedule (DVPS) is a mutation whose weight ramps linearly with iteration, replacing variable leaves with constants so the population self-organizes around causal features; Exponential Pareto Selection (EPS) then scores hall-of-fame equations by R^{2}^ρ · exp(−λ(c−1)); multi-layer composition discovers latent symbolic sub-expressions that resolve intraclass correlation.","core_discovery":"Integrating dynamic variable pruning during evolution, exponential Pareto selection of a single formula, and multi-layer hierarchical composition lets symbolic regression handle high-dimensional, multicollinear, and imbalanced real-world data and recover interpretable equations that match or beat both vanilla PySR and standard machine-learning baselines on body-fat, heart-disease, student-performance, and longitudinal BMI prediction tasks.","pith_inferences":["The same pruning-plus-hierarchical pattern could be applied to other observational sciences (epidemiology, ecology, education) where multicollinearity and sparse but causal covariates are the norm.","If EPS reliably sits at the knee of the Pareto front, it may serve as a default selection rule for any evolutionary SR engine, not only this codebase.","The recovered Raine BMI interaction of polygenic score with early BMI trajectory offers a concrete hypothesis that could be tested for mediation or intervention in other birth cohorts.","Fixed layer depth and operator-set dependence remain open limits; automated depth selection or dimensional constraints would be natural next controls."],"forward_implications":["High-dimensional clinical and social datasets can be searched for short analytic formulas without separate pre-selection of features.","A single tunable exponential score can replace manual inspection of Pareto fronts for deploying one communicable equation.","Multi-layer symbolic composition can expose gene–environment and trajectory interactions that single-layer SR and black-box models leave opaque.","Imbalanced classification tasks can be handled by formula structure alone, without synthetic oversampling, while retaining clinical precision.","Domain experts receive equations whose variables and functional form can be checked against known risk factors rather than post-hoc attributions."],"fun_headline_variants":["DeepPySR prunes variables and stacks formulas for real medical data","Dynamic pruning plus Pareto picks beat PySR on body fat and heart risk","Hierarchical symbolic regression recovers short equations on BMI and grades","DeepPySR handles multicollinearity to yield glass-box medical formulas","Pruning and exponential Pareto let SR match baselines on real clinical tasks"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"That five-fold cross-validation over a large internal hyperparameter grid, with no separate held-out cohort on the public datasets, fairly measures how much better the new components generalize than plain PySR.","fun_headline_variants_meta":{"raw":{"variants":["DeepPySR prunes variables and stacks formulas for real medical data","Dynamic pruning plus Pareto picks beat PySR on body fat and heart risk","Hierarchical symbolic regression recovers short equations on BMI and grades","DeepPySR handles multicollinearity to yield glass-box medical formulas","Pruning and exponential Pareto let SR match baselines on real clinical tasks"]},"model":"grok-4.5","effort":"low","cost_usd":0.00265,"raw_usage":{"total_tokens":1029,"prompt_tokens":785,"num_sources_used":0,"completion_tokens":92,"cost_in_usd_ticks":26500000,"prompt_tokens_details":{"text_tokens":785,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":152,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":785,"tokens_out":92,"duration_ms":2568,"temperature":1.0,"reasoning_tokens":152,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T12:14:48.883975+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Re-run the same 27-configuration grid and multi-layer pipeline on an independent external cohort for body fat, heart disease, or Raine BMI; if the R^{2}/F1 gaps versus PySR and tree ensembles disappear or reverse under identical operator sets and fold structure, the claimed superiority of DVPS/EPS/multi-layer fails.","supporting_citations":[],"review_version":1}