{"id":"3db6f36a-de5c-4019-9d52-196be2544f75","arxiv_id":"2505.21901","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A linear genetic programming method with tunable terminals, tunable functions, and a final linear regression step improves fish biomass prediction from Raman spectra and ranks second on SRBench.","lead":"This paper introduces LGP-TP, a linear genetic programming method with tunable primitives for symbolic regression, and applies it to predict fish biomass from Raman spectra. If the results hold, it offers a compact, interpretable alternative to black-box models for spectral analysis in food production.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported significance tests treat ten repeated six-fold CV runs as independent samples; this pseudoreplication can make p-values anticonservative.","rationale":"The reader's weakest assumption (measurement-level leakage across folds) is probably not the true weak point: the text explicitly says each fold contains \"6 or 7 fish samples\", indicating fish-level grouping, which prevents the same fish from appearing in both training and test sets within a run. However, the reader also flagged unclear multiple-testing correction, and that is close to the more serious issue I see: repeated six-fold CV runs are correlated because the same fish are re-split across runs, yet the paper treats the ten runs as independent replicates in Wilcoxon and Friedman tests. This pseudoreplication can make p-values too small, directly affecting the significance-based components of the central claim and the ablation result. The descriptive \"best mean rank\" claim may remain, but the inferential superiority claims need a valid cluster-level test. Since the paper already needs clarifications and re-analysis, keeping the reader's CONDITIONAL verdict is appropriate; my concern does not push toward rejection but strengthens the need for the requested verification.","tokens_in":15182,"tokens_out":9463,"duration_ms":98947,"concrete_test":"Run a cluster-permutation test at the fish level for the key contrast LGP-TP vs basic LGP: randomly permute the 39 fish labels (or use one bootstrap by fish) and recompute the difference in mean test R2 across the ten CV runs; repeat 10,000 times to get a null distribution. If the resulting p-value is >0.05 or the 95% CI contains 0, the significant-improvement claim is unsupported. Additionally, recompute pairwise per-target Wilcoxon p-values with Bonferroni-Holm over ten targets and seven methods to see whether the \"significantly worse on 4 targets\" counts survive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim (\"significantly better\" than baselines, ablation p=0.019) is supported by Wilcoxon/Friedman tests computed over ten repeated six-fold CV runs. Those runs are not independent: each rerun re-splits the same 39 fish / 117 spectra, so the same fish appears in test sets multiple times and the R2 values used in the tests are correlated. The paper does not state a fish-level or cluster-level correction, and the sentence mentioning \"with the Bonferroni correction\" is ambiguous about whether the pairwise Wilcoxon comparisons across ten targets and seven methods are adjusted at all. The reader's fold-leakage concern is probably not the main issue: Section 2.1 says each fold has \"6 or 7 fish samples\", which strongly indicates fish-level grouping. The load-bearing weakness is statistical: the p=0.019 and per-target p<0.0162 values may not withstand a valid cluster-level test, so the superiority claims are less secure than presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes LGP-TP, a linear genetic programming method with three kinds of tunable primitives (tunable terminals, tunable functions, and a multivariate linear regression function) for symbolic regression on fish biomass Raman spectra. The method is evaluated on ten biomass targets from 117 spectra of 39 fish using ten repeated six-fold cross-validation runs, and compared against six baselines, reporting test R2 values. The paper claims LGP-TP achieves the best overall prediction performance, with compact and interpretable models, and that the tunable primitives are responsible for significant improvements over basic LGP. Generality is further tested on three additional spectral data treatments and on the SRBench symbolic regression benchmark.","tokens_in":15421,"tokens_out":4865,"duration_ms":45177,"significance":"If the central claim holds, LGP-TP offers a practical, interpretable alternative for spectral regression with small, noisy datasets, and the tunable-primitive idea could transfer to other symbolic regression tasks. Strengths of the paper include the use of held-out test folds, a real-world spectral dataset, an ablation study, and an extension to a public benchmark with 122 problems. The authors provide a clear description of the algorithm and make the fish data available on reasonable request. However, the statistical inference supporting the superiority claims is weakened by pseudoreplication in the repeated cross-validation protocol, and several details of the method and comparison require clarification.","major_comments":[{"comment":"The Wilcoxon and Friedman tests in Section 2.3 treat the ten repeated six-fold cross-validation runs as ten independent observations. Because each run re-splits the same 39 fish (117 spectra), and the three measurements of each fish are kept together as implied by Section 2.1, the same fish appears in test folds multiple times across runs, so the R2 values entering the tests are correlated. This pseudoreplication makes the reported p-values (e.g., the ablation p=0.019 and the per-target p<0.0162 thresholds) anticonservative. The authors should re-analyze with a clustering-aware procedure (e.g., cluster bootstrap or permutation at the fish level), or justify why treating the ten runs as independent is valid.","section":"Section 2.3"},{"comment":"The cross-validation splitting is not fully specified: the text says each fold has approximately 20 instances (6 or 7 fish samples) but never states explicitly that the three repeated measurements of each fish are always placed in the same fold. If instances are split at the measurement level, spectra from the same fish would leak across training and test folds and inflate test R2. Please state explicitly that no fish appears in both training and test sets in any fold and describe how the folds are constructed.","section":"Section 2.1"},{"comment":"The description of the statistical adjustments is ambiguous: the sentence 'Friedman's test with a significance level of 0.05 and with the Bonferroni correction and the Wilcoxon rank-sum test with a significance level of 0.05' does not say which family of comparisons the Bonferroni correction applies to, and the threshold p<0.0162 used for per-target comparisons is not derived. Please specify the number of comparisons, the method of correction, and whether the pairwise Wilcoxon tests are adjusted across the ten targets, across the seven methods, or both.","section":"Section 2.3"},{"comment":"The baseline methods KNN, MLP, XGB, and RF use default hyperparameters, whereas PLSR and FishCNN use recommended settings. Because the central claim is that LGP-TP achieves the best overall prediction performance, a comparison using untuned defaults for four of the six baselines may not reflect their true capabilities. The authors should either tune all baselines on the training folds (with nested cross-validation) or clearly state that the comparison is against default configurations and discuss the risk that tuned baselines would close the gap.","section":"Section 2.2, Table 1"},{"comment":"The derivatives for the tunable functions contain an error: for ExpoRF, the derivative with respect to omega_1 includes the term (omega_1^2 + 1) x_j^{omega_1 - 1}, which is not the derivative of omega_0 + (omega_1^2 + 1) x_j + x_j with respect to omega_1; the correct derivative is 2 omega_1 x_j. Since the gradient descent update is used to tune these primitives, the method as described is not reproducible. Please correct the equation and, if the implementation differs, state the exact update used.","section":"Section 4.2.2"}],"minor_comments":[{"comment":"The phrase 'wavenumber range of 1891.58-580.109 (cm−1)' lists the upper bound first, which is easy to misread; consider reordering to 580.109-1891.58 (cm−1). Also, Section 2.6 contains a typo '1064num' that should read '1064nm'.","section":"Section 2.1"},{"comment":"The definition of Fluctuate has a typo: it reads sum_{i=alpha+1}^{beta} |(x_j)_i - (x_j)_i|, likely intended as |(x_j)_i - (x_j)_{i-1}|, since otherwise the term is identically zero. Please correct the formula.","section":"Section 4.2.1"},{"comment":"The model size for LGP-TP in the SRBench comparison is computed by multiplying the number of effective instructions by 2.0, but it is not clear how this factor is chosen or how it aligns with the model-size metric used for other benchmark methods. Please clarify to make the Pareto plot in Figure 5b interpretable.","section":"Section 2.7"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the proposed method is interesting, but the statistical inference issues are load-bearing for the main claim. The pseudoreplication concern can likely be fixed with a re-analysis using cluster-level methods, and the other points are addressable. I recommend major revision rather than rejection, because the core idea and the empirical results are likely sound after the statistical validation is corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate extension of linear genetic programming with a genuinely new set of tunable primitives, and the empirical story on the fish data is mostly believable. But the statistics are sloppier than the paper lets on, and a couple of references are wrong. It deserves a serious referee, not a desk reject.\n\nWhat's new: the three kinds of tunable primitives—window-based linear terminals, residual-approximating functions, and a final multivariate linear regression—are a real combination not present in the cited LGP baseline. The ablation study shows monotone improvement from basic LGP to LGP-TT to LGP-TTF to LGP-TP, which is good evidence that the proposed pieces are doing work. The SRBench result, where LGP-TP ranks second in test R2 while staying small and fast, is impressive and strengthens the generality claim. The interpretability analysis, including the feature-frequency heat maps and the compact program sizes, is a genuine asset for the chemometrics audience.\n\nSoft spots, in proportion. First, the ten repeated six-fold CV runs are treated as independent samples in the Friedman and Wilcoxon tests. They are not independent: the same 39 fish recur in the test folds across runs, so the reported p-values, including the ablation p=0.019, are anticonservative. This is not a fatal flaw, but it means the \"significantly better\" claims are less secure than presented. A cluster-level or fish-level analysis is needed. Second, the multiple-testing correction is ambiguous: the paper says \"with the Bonferroni correction\" in one sentence, but it is not clear whether the pairwise Wilcoxon comparisons across ten targets and seven methods are adjusted at all, and the reported threshold p<0.0162 appears without derivation. Third, no code or pseudocode is provided, and the fish data are commercially restricted, so the main experimental result is not directly reproducible. Fourth, the reference list has at least one clear error: reference [4] is about nuclear shapes in 62Cr, unrelated to fish biomass, and reference [11] is about krill oil adulteration rather than SVR on fish spectra. These are minor but should be fixed.\n\nI do not share the reader's worry that spectra from the same fish leak across train and test folds. The text says each fold has \"6 or 7 fish samples,\" which strongly suggests fish-level grouping. The pseudoreplication issue is the real concern, and it is distinct.\n\nWho is this for? Applied GP researchers and spectral chemometrics practitioners. It is a solid applied paper with a novel method and rich empirical comparison. Send it to peer review, but the reviewers should require a cluster-aware significance test and clearer reporting of the multiple-testing procedure before acceptance.","headline":"A genuine, useful extension of LGP with tunable primitives, but the significance testing on the fish data is anticonservative and needs a cluster-level correction before the empirical claims can be trusted.","tokens_in":15917,"tokens_out":1863,"would_cite":true,"duration_ms":19640,"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":"Adding tunable coefficients to genetic programming yields compact models that beat six regressors on fish biomass spectra.","keywords":["linear genetic programming","tunable primitives","symbolic regression","Raman spectroscopy","fish biomass prediction","spectral data analysis","interpretable regression","SRBench"],"falsifier":"Re-run the comparison with six-fold cross-validation in which each fish's three repeated spectra are explicitly assigned to the same fold, then compare mean test $R^2$ and the Friedman/Wilcoxon ranks. If LGP-TP no longer holds the best overall rank or the significant win counts reported in Fig. 2, the empirical claim fails. A second check is to run LGP-TP without the final multivariate linear regression function and see whether the mean-rank gain from LGP-TTF to LGP-TP disappears.","tokens_in":15009,"feed_emoji":"🐟","tokens_out":9381,"duration_ms":83885,"temperature":0.7,"pith_summary":"This paper tries to establish that a linear genetic programming method with tunable primitives (LGP-TP) is a practical, interpretable alternative for predicting fish biomass composition from small, noisy Raman spectral datasets. It frames the task as symbolic regression: evolution searches over short register-based programs while newly added tunable primitives fit their internal coefficients to the data. Across ten biomass targets measured from 39 fish, LGP-TP reports the best overall mean rank of test $R^2$ among seven methods, including a fish-specific neural network, and the ablation study claims the tunable primitives drive the gain, with LGP-TP significantly outperforming basic LGP ($p=0.019$). If the paper is right, compact human-readable formulas could replace black-box models for spectral quality control while highlighting which spectral peaks actually carry the signal.","feed_headline":"Tuned genetic programs beat six regressors on fish biomass spectra","feed_subtitle":"Compact symbolic models predict ten biomass components from Raman spectra and flag informative peaks.","key_machinery":"The load-bearing machinery is the tunable primitive: a function $T(X,W,\\cdot)$ that takes immediate input values $X$, adjustable coefficients $W$, and, for terminals, two feature indices $\\alpha,\\beta$, and returns a vector meant to approximate the target $Y$. Three kinds are added to a linear genetic programming register machine: tunable terminals that fit linear regression or derived spectral statistics (average, standard deviation, fluctuation, slope, peak, valley, peak location) over a contiguous feature range $x_{\\alpha:\\beta}$; tunable functions that fit residual error of intermediate register values with linear, sine, exponential, or power forms; and a multivariate linear regression function appended at the end that maps several register values to the single output. Coefficients are tuned by least squares for the linear primitives and by normalized gradient descent for the trigonometric, exponential, and power primitives, so genetic search handles symbolic structure while local optimizers set the numbers.","core_discovery":"The paper's central claim is that giving linear genetic programming three kinds of tunable primitives—tunable terminals that fit linear or shape-based features over a wavenumber range, tunable functions that fit residual error at intermediate program points, and a final multivariate linear regression over registers—lets evolution synthesize compact symbolic regressors that predict ten fish biomass components from Raman spectra better than PLSR, KNN, MLP, XGBoost, random forests, and FishCNN. On the paper's own terms, LGP-TP has the best overall mean rank (5.45) in ten runs of six-fold cross-validation, is statistically better than each compared method on at least four of the ten targets, and grows consistently in performance as the three primitive types are added one by one. The same setup transfers to three other spectral preprocessing treatments and, after removing spectral-specific terminals, ranks second in test $R^2$ among the 24 benchmark methods on the SRBench symbolic-regression benchmark while maintaining among the smallest model sizes and shortest training times.","pith_inferences":["Editorial inference: the performance advantage on small noisy datasets may come less from the evolutionary search itself than from the built-in least-squares coefficient fitting, which gives every candidate program a strong local head start; a testable extension would compare LGP-TP against a version with only random coefficients.","Editorial inference: the paper never explicitly states that the six-fold split groups the three repeated measurements of each fish into the same fold, and the reported test $R^2$ would be optimistically biased if spectra from the same fish leaked across training and test folds; reporting the exact split procedure would settle this.","Editorial inference: the same tunable-primitive recipe could be dropped into other high-dimensional, small-sample spectral domains such as soil, food, or pharmaceutical analysis, where interpretability is as valuable as accuracy.","Editorial inference: the shared heat-map pattern across water, protein, and lipids yield suggests one multi-output model might exploit the same spectral peaks for all three targets; an explicit check is whether such a model retains the per-target accuracy of LGP-TP."],"forward_implications":["Fish production lines could estimate water, protein, fat, and seven other biomass components from Raman spectra with compact formulas instead of black-box models, across several spectral preprocessing protocols.","The frequency heat maps identify the first three and the last peaks of the 1891.58–580.109 cm$^{-1}$ range as the informative regions, giving chemists specific wavenumbers to investigate.","The ablation result implies that each of the three tunable-primitive types contributes to the gain, with the final multivariate linear regression function producing the largest jump in mean rank.","The SRBench result suggests the tunable-primitive strategy generalizes beyond spectroscopy to tabular symbolic regression with competitive accuracy, smaller models, and faster training.","Because the synthesized programs are compact and their coefficients are explicit, a domain scientist can read the model and reason about whether the highlighted features make chemical sense."],"supporting_citations":[{"why":"Supplies the linear genetic programming representation, register-based instruction sequences, that LGP-TP extends.","marker":"[12]"},{"why":"Provides the semantic LGP method for symbolic regression that the evolutionary framework builds on.","marker":"[13]"},{"why":"Defines FishCNN, the fish-biomass Raman prediction method that LGP-TP must beat.","marker":"[7]"},{"why":"Defines PLSR, the standard chemometric baseline used in the comparisons.","marker":"[22]"},{"why":"Supplies the previous LGP parameter settings that LGP-TP mostly follows.","marker":"[16]"},{"why":"Supplies the SVR comparison used in the spectral-data-treatment generality experiments.","marker":"[11]"},{"why":"Provides spectral data augmentation used to expand the 117 fish instances to about 5000 training instances.","marker":"[20]"},{"why":"Provides the mix-up linear interpolation strategy used in data augmentation.","marker":"[21]"},{"why":"Defines the SRBench benchmark used to test generality across 122 regression problems.","marker":"[23]"}],"fun_headline_variants":["Tunable genetic programs beat six regressors on fish biomass spectra","Linear GP with tunable primitives wins on fish biomass spectral data","Compact symbolic regressors from tunable GP outperform ML on fish spectra","Tuned genetic programming improves fish biomass prediction from spectra","Fish biomass spectral regression: tunable GP ranks top among seven methods"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported test scores assume that the six cross-validation folds are split by fish rather than by individual measurement, so that spectra from the same fish never appear in both training and test sets; the paper never explicitly states this.","fun_headline_variants_meta":{"raw":{"variants":["Tunable genetic programs beat six regressors on fish biomass spectra","Linear GP with tunable primitives wins on fish biomass spectral data","Compact symbolic regressors from tunable GP outperform ML on fish spectra","Tuned genetic programming improves fish biomass prediction from spectra","Fish biomass spectral regression: tunable GP ranks top among seven methods"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000143,"raw_usage":{"total_tokens":1171,"prompt_tokens":946,"completion_tokens":225,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":137}},"tokens_in":562,"tokens_out":225,"duration_ms":2840,"temperature":1.0,"reasoning_tokens":137,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:20:16.302349+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the comparison with six-fold cross-validation in which each fish's three repeated spectra are explicitly assigned to the same fold, then compare mean test $R^2$ and the Friedman/Wilcoxon ranks. If LGP-TP no longer holds the best overall rank or the significant win counts reported in Fig. 2, the empirical claim fails. A second check is to run LGP-TP without the final multivariate linear regression function and see whether the mean-rank gain from LGP-TTF to LGP-TP disappears.","supporting_citations":[{"cited_title":"& Banzhaf, W","cited_arxiv_id":null,"evidence_quote":"Supplies the linear genetic programming representation, register-based instruction sequences, that LGP-TP extends."},{"cited_title":"& Zhong, J","cited_arxiv_id":null,"evidence_quote":"Provides the semantic LGP method for symbolic regression that the evolutionary framework builds on."},{"cited_title":"Machine Learning for Raman Spectroscopy-based Cyber-Marine Fish Biochemical Composition Analysis","cited_arxiv_id":null,"evidence_quote":"Defines FishCNN, the fish-biomass Raman prediction method that LGP-TP must beat."},{"cited_title":"& Eriksson, L","cited_arxiv_id":null,"evidence_quote":"Defines PLSR, the standard chemometric baseline used in the comparisons."},{"cited_title":"& Zhang, M","cited_arxiv_id":null,"evidence_quote":"Supplies the previous LGP parameter settings that LGP-TP mostly follows."},{"cited_title":"C., Killeen, D","cited_arxiv_id":null,"evidence_quote":"Supplies the SVR comparison used in the spectral-data-treatment generality experiments."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the SRBench benchmark used to test generality across 122 regression problems."}],"review_version":1}