pith. sign in

arxiv: 2605.29184 · v1 · pith:73QFS7WLnew · submitted 2026-05-27 · 💻 cs.LG · cs.AI

Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback

Evgeny S. Saveliev , Samuel Holt , Nabeel Seedat , David L. Bentley , Jim Weatherall , Mihaela van der Schaar This is my paper

Pith reviewed 2026-06-29 13:00 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords symbolic regressionlarge language modelsinfluence scoresequation discoveryscientific discoverygenomic datamonte carlo tree search
0
0 comments X

The pith

Influence scores let LLMs prune equation terms and surface a DNA methylation link later confirmed in lab experiments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Influence-Guided Symbolic Regression, in which a large language model proposes candidate basis functions for a linear model and each function receives a granular influence score based on its marginal contribution to generalization accuracy. These scores drive an iterative pruning step that removes low-value terms while a Monte Carlo tree search balances exploration of new forms against retention of high-influence components. The resulting process is evaluated on standard symbolic regression benchmarks, pharmacological and epidemiological models, and a high-dimensional genomic dataset. In the genomic case the method proposed a relationship between DNA methylation and RNA Polymerase II pausing that was subsequently supported by wet-lab experimentation.

Core claim

IGSR frames equation discovery as an iterative loop in which an LLM generates candidate basis functions, each is scored by its marginal effect on out-of-sample accuracy, and the scores are used to prune the active set; the pruned set is then explored inside a Monte Carlo tree search. When applied to real genomic measurements this loop identified a previously unreported connection between DNA methylation levels and RNA Polymerase II pausing whose validity was later corroborated by independent laboratory experiments.

What carries the argument

Granular influence scores Δ_j that quantify each candidate basis function's marginal contribution to generalization accuracy and thereby guide term pruning inside an MCTS search.

If this is right

  • The method recovers known functional relationships in pharmacological PKPD models and epidemiological simulations.
  • On LLM-SRBench and similar suites it produces accurate equations while using fewer terms than scalar-feedback baselines.
  • Application to high-dimensional biological data yields hypotheses that can be tested directly in the laboratory.
  • The combination of influence pruning and MCTS maintains a balance between exploring novel functional forms and exploiting high-performing components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same granular scoring approach could be applied to other high-dimensional scientific datasets to generate testable hypotheses without requiring exhaustive manual feature engineering.
  • If influence scores prove stable across modest data perturbations, the pruning step could be reused inside non-linear or kernel-based regression frameworks.
  • Extending the linear-model assumption to allow direct generation of nonlinear terms would enlarge the space of equations the method can discover.

Load-bearing premise

The influence scores computed from marginal contribution to generalization accuracy are stable enough to prune candidate terms without discarding important ones or retaining noise.

What would settle it

Re-running the genomic case study on independent data splits or with different random seeds and obtaining proposed relationships that fail to replicate in subsequent wet-lab tests would show the discovery claim does not hold.

Figures

Figures reproduced from arXiv: 2605.29184 by David L. Bentley, Evgeny S. Saveliev, Jim Weatherall, Mihaela van der Schaar, Nabeel Seedat, Samuel Holt.

Figure 1
Figure 1. Figure 1: Conceptual overview of the Influence-Guided Symbolic Regression (IGSR) framework. The system operates via a Propose-and￾Prune Cycle embedded within a Monte Carlo Tree Search. An LLM agent generates candidate basis functions ψj (x) based on problem context. These terms are evaluated to compute weights wj and per-term influence scores ∆j . A deterministic selector retains terms with the highest influence (or… view at source ↗
Figure 3
Figure 3. Figure 3: Scalability to High-Dimensional Spaces. Total wall￾clock time on the RNA Polymerase dataset (mean ± 95% CI, 10 seeds) is shown as the number of available input features increases. Runtime scales sub-linearly up to the full 263 features, avoiding the combinatorial explosion typical of traditional symbolic search. We also find that on Lung Cancer (with Chemo. & Radio.) dataset, IGSR is more computationally e… view at source ↗
Figure 2
Figure 2. Figure 2: Influence Feedback Improves Convergence. Best test MSE achieved, shown over MCTS nodes expanded (iterations). “Influence Feedback” is full IGSR, and “Basic Feedback” is the ablation where the pruner is guided by a scalar loss value only. Use of per-term influence feedback leads to faster convergence and a lower final MSE. Lung Cancer (with Chemo. & Radio.) dataset, 25 seeds, 95% CIs. These experiments unde… view at source ↗
Figure 4
Figure 4. Figure 4: Cross-seed stability of discovered equation terms on Lung Cancer (with Chemo. & Radio.), 25 seeds. Variables: x = tumor volume, C = chemo. drug concentration, u c = chemo. dosage, d = radiotherapy dose. After canonicalizing variants (e.g. np.log1p → np.log), only 11 unique canonical terms remain. The four highest-frequency terms (84–100%) are all ground-truth (GT) from the known PKPD equations. IGSR’s disc… view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of Structural Fidelity vs. Predictive Accuracy on LLM-SRBench. We plot the Out-of-Distribution (OOD) NMSE (log scale, lower is better, axis reversed such that lower values are to the right) against Term Recall (higher is better) for all method-problem pairs. Markers distinguish the discovery methods, while the colors distinguish the Scientific Domains (Physics, Biology, Material Science, Chem… view at source ↗
Figure 6
Figure 6. Figure 6: SHAP analysis of the IGSR-discovered equation for RNA Polymerase II pausing from Experiment 1. Each “feature” in the SHAP analysis corresponds to a basis function term ψj (x) from the equation. (a) Beeswarm plot showing the distribution of SHAP values for the most important equation terms. Each point is a SHAP value for a term and a sample, colored by the value of the evaluated basis function ψj (x) (red f… view at source ↗
Figure 7
Figure 7. Figure 7: SHAP analysis of the IGSR-discovered equation for RNA Polymerase II pausing from Experiment 2. Analogous to [PITH_FULL_IMAGE:figures/full_fig_p050_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of IGSR Equation Discovery Process. Test MSE achieved versus MCTS nodes expanded for two example IGSR runs (Run A: green, Run B: blue) on the Lung Cancer (with Chemo. & Radio.) dataset. Points A0, A9, A50 for Run A, and B0, B1, B9, B13, B36 for Run B, indicate instances where a new, more accurate equation was discovered. The equations corresponding to these points are detailed below. The equat… view at source ↗
Figure 9
Figure 9. Figure 9: Convergence Efficiency: IGSR vs. GPLearn. Test MSE (mean ± 95% CI over 10 seeds) versus number of major evaluation iterations for IGSR (MCTS expansions) and GPLearn (generations) on the Lung Cancer (with Chemo. & Radio.) dataset. IGSR demonstrates faster convergence to a lower MSE, indicating superior search efficiency. G.6. Investigation of LLM sensitivity Understanding the robustness of IGSR’s advantages… view at source ↗
Figure 10
Figure 10. Figure 10: MSE (± 95% CI error bars) on benchmark datasets for ZeroShot, ZeroOptim, ICL, and IGSR across various base LLMs, including open-weight models. Each subfigure represents a different dataset. IGSR outperforms the other methods across the datasets and base LLMs with few exceptions. Note: The y axis (MSE) scale is logarithmic. For each dataset: the MSE range is different for the ZeroShot baseline, as its perf… view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p066_11.png] view at source ↗
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p067_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Collinearity stress test for influence-based pruning on Lung Cancer (with Chemo. & Radio.), 15 seeds. Variables: x = tumor volume, C = chemo. concentration, u c = chemo. dosage, d = radiotherapy dose. Setup. A 14-term candidate pool mixes the 6 ground-truth basis functions with 4 correlated clones and 4 distractors (a). Each clone vρ of a variable v∈ {C, uc , d} is constructed as vρ = v + sd(v) p ρ−2−1 ε,… view at source ↗
Figure 14
Figure 14. Figure 14: Interaction-only signal recovery under pruning. Setup. Features x1, . . . , x10 iid∼ N (0, 1); targets are pure interaction terms plus noise ε= 0.05 N (0, 1). By construction, the marginal variables (x1, x2, . . . ) carry zero individual linear signal; all predictive power resides in the interaction(s). This tests whether influence-based pruning can recover synergistic terms whose individual constituents … view at source ↗
Figure 15
Figure 15. Figure 15: Pairwise Jaccard similarity of discovered term sets across 25 seeds on Lung Cancer (with Chemo. & Radio.), after canonicalization. Seeds are sorted by validation MSE (shown in parentheses). The dark top-left block (J ≈1) is the near-exact-recovery tier; the lower-right cluster is internally similar but approximates the Gompertz nonlinearity differently. Mean pairwise J = 0.65. 0.0 0.2 0.4 0.6 0.8 1.0 Jacc… view at source ↗
Figure 16
Figure 16. Figure 16: Distribution of pairwise Jaccard similarity over the 300 seed pairs (same data as [PITH_FULL_IMAGE:figures/full_fig_p069_16.png] view at source ↗
read the original abstract

Large Language Models (LLMs) offer a promising avenue for scientific discovery, yet their application to symbolic regression is often constrained by inefficient search strategies and coarse feedback signals. Current methods typically guide LLMs using scalar metrics (e.g., global Mean Squared Error), which fail to identify which components of a proposed equation are driving performance or causing error. We introduce \textit{Influence-Guided Symbolic Regression} (IGSR), a method that frames equation discovery as an iterative two-step process combining diverse term generation with rigorous selection: an LLM generates candidate basis functions $\psi_j(\mathbf{x})$ for a linear model, which are then evaluated using granular influence scores $\Delta_j$. These scores quantify each term's marginal contribution to generalization accuracy, enabling an influence-guided pruning process that systematically refines the model structure. Integrating this mechanism into a Monte Carlo Tree Search (MCTS) enables navigating the combinatorial search space while balancing exploration of novel functional forms with exploitation of high-influence components. We demonstrate IGSR's effectiveness on a diverse suite of benchmarks, including LLM-SRBench, pharmacological PKPD models, an epidemiological simulation, and real-world genomic data. Notably, we validate the framework's capacity for genuine discovery in a case study using a high-dimensional biological dataset, in which IGSR identified a novel relationship between DNA methylation and RNA Polymerase II pausing; a hypothesis that was subsequently supported via wet-lab experimentation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Influence-Guided Symbolic Regression (IGSR), which frames symbolic regression as an iterative LLM-driven process: LLMs generate candidate basis functions ψ_j(x) for a linear model, these are scored by influence scores Δ_j measuring each term's marginal contribution to generalization accuracy, the scores drive pruning of the basis, and the process is embedded in Monte Carlo Tree Search (MCTS) to balance exploration and exploitation. The method is evaluated on LLM-SRBench, PKPD models, an epidemiological simulation, and a high-dimensional genomic dataset; the central discovery claim is that IGSR identified a novel relationship between DNA methylation and RNA Polymerase II pausing that was subsequently corroborated by wet-lab experimentation.

Significance. If the influence scores are shown to be stable and the pruning mechanism demonstrably isolates true signal in noisy genomic data, the work would strengthen the case for granular, component-level feedback in LLM-based scientific discovery pipelines. The wet-lab validation of the genomic finding is a concrete strength that goes beyond synthetic benchmarks and directly addresses the goal of genuine discovery.

major comments (2)
  1. [§4.3] §4.3 (genomic case study) and the description of Δ_j: the discovery claim rests on influence-guided pruning reliably retaining the DNA-methylation term while discarding spurious basis functions, yet no analysis of Δ_j variance under data perturbations, cross-validation folds, or feature correlations (typical of methylation data) is provided; without this, it is impossible to rule out that the retained relationship is an artifact of unstable rankings rather than method-driven signal.
  2. [Method] Method section (definition and use of Δ_j): the marginal-contribution definition of Δ_j is presented as enabling systematic refinement, but no quantitative check (e.g., rank stability across bootstrap samples or ablation of the pruning step) is reported to confirm that the scores are sufficiently accurate to drive reliable MCTS search in high-dimensional regimes.
minor comments (2)
  1. [Abstract] Abstract and §3: pseudocode or explicit formula for computing Δ_j from the linear model is absent, making it difficult for readers to reproduce the influence-guided pruning step.
  2. [Results] Figure captions and tables: several benchmark tables lack error bars or statistical significance tests comparing IGSR against the scalar-MSE baselines, weakening the quantitative claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments regarding the stability and validation of the influence scores Δ_j. These points are well-taken and we outline targeted revisions below to address them directly.

read point-by-point responses

  1. Referee: [§4.3] §4.3 (genomic case study) and the description of Δ_j: the discovery claim rests on influence-guided pruning reliably retaining the DNA-methylation term while discarding spurious basis functions, yet no analysis of Δ_j variance under data perturbations, cross-validation folds, or feature correlations (typical of methylation data) is provided; without this, it is impossible to rule out that the retained relationship is an artifact of unstable rankings rather than method-driven signal.

    Authors: We agree that explicit stability analysis of Δ_j would strengthen the genomic results. In the revised manuscript we will add quantitative experiments reporting the variance of Δ_j under data perturbations, across cross-validation folds, and accounting for feature correlations typical of methylation data. These results will be presented alongside the existing wet-lab validation to demonstrate that the retained DNA-methylation term reflects stable signal. revision: yes

  2. Referee: [Method] Method section (definition and use of Δ_j): the marginal-contribution definition of Δ_j is presented as enabling systematic refinement, but no quantitative check (e.g., rank stability across bootstrap samples or ablation of the pruning step) is reported to confirm that the scores are sufficiently accurate to drive reliable MCTS search in high-dimensional regimes.

    Authors: We concur that additional quantitative checks on Δ_j reliability are warranted for high-dimensional settings. The revision will include (i) rank-stability metrics computed across bootstrap samples and (ii) an ablation comparing MCTS performance with and without the influence-guided pruning step. These additions will confirm that the marginal scores support reliable search. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central discovery claim rests on external wet-lab validation

full rationale

The paper defines influence scores Δ_j from marginal contribution to generalization accuracy and uses them to prune basis functions inside an MCTS loop. However, the load-bearing scientific claim—a novel DNA-methylation / RNA-Pol-II relationship—is presented as having been subsequently confirmed by independent wet-lab experimentation rather than being a quantity defined by the fitted model or by self-citation. No derivation step reduces the reported discovery or performance gain to a quantity that is identical to the method's own inputs by construction. The evaluation protocol is described as external generalization accuracy on held-out data and real biological follow-up, satisfying the criteria for a self-contained, non-circular result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The method rests on two domain assumptions about LLM capability and score reliability plus one invented evaluation object (the per-term influence score); no free parameters are named in the abstract.

axioms (2)
  • domain assumption Large language models can generate candidate basis functions ψ_j(x) that are relevant to the target phenomenon
    The generate step of the two-step process depends on this capability.
  • domain assumption Marginal influence scores Δ_j can be computed that faithfully reflect each term's contribution to generalization accuracy
    The prune step and the entire selection process depend on this property.
invented entities (1)
  • Influence score Δ_j no independent evidence
    purpose: Quantify marginal contribution of each basis function for pruning decisions
    New per-term metric introduced by the method; no independent external validation of the metric itself is described.

pith-pipeline@v0.9.1-grok · 5812 in / 1469 out tokens · 65130 ms · 2026-06-29T13:00:54.833014+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

34 extracted references · 9 canonical work pages

  1. [1]

    A scalable tree boosting system

    ACM, 2016. doi: 10.1145/2939672.2939785. URL https://doi.org/10.1145/2939672.2939785. Chen, T. Q., Rubanova, Y ., Bettencourt, J., and Duve- naud, D. Neural ordinary differential equations. In Bengio, S., Wallach, H. M., Larochelle, H., Grau- man, K., Cesa-Bianchi, N., and Garnett, R. (eds.), Advances in Neural Information Processing Systems 31: Annual Co...

    work page doi:10.1145/2939672.2939785 2016

  2. [2]

    URL https://doi.org/10.1080/00401706.1980.10486199

    doi: 10.1080/00401706.1980.10486199. URL https://doi.org/10.1080/00401706.1980.10486199. Covert, I., Lundberg, S. M., and Lee, S. Understanding global feature contributions with additive importance measures. In Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M., and Lin, H. (eds.),Advances in Neural Information Processing Systems 33: Annual Conference o...

    work page doi:10.1080/00401706.1980.10486199 1980

  3. [3]

    URL https://doi.org/10.18653/v1/2023.acl-industry.4

    doi: 10.18653/V1/2023.ACL-INDUSTRY .4. URL https://doi.org/10.18653/v1/2023.acl-industry.4. Janssen, A., Bennis, F. C., and Mathˆot, R. A. A. Adoption of machine learning in pharmacometrics: An overview of recent implementations and their considerations.Phar- maceutics, 14(9):1814, August 2022. Jonkers, I. and Lis, J. T. Getting up to speed with transcrip...

    work page doi:10.18653/v1/2023.acl-industry 2023

  4. [4]

    URL http://proceedings.mlr.press/v119/kumar20e. html. Lee, M. K., Park, N. H., Lee, S. Y ., and Kim, T. Context-dependent and locus-specific role of H3K36 methylation in transcriptional regulation.Journal of Molecular Biology, 437(1):168796, 2025. ISSN 0022-

    2025

  5. [5]

    Why should I trust you?

    doi: https://doi.org/10.1016/j.jmb.2024.168796. URL https://www.sciencedirect.com/science/article/pii/ S0022283624004182. Controlling Transcription Elonga- tion and Termination. Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., and Wasserman, L. Distribution-free predictive inference for regression.Journal of the American Statistical Associa- tion, 113...

    work page doi:10.1016/j.jmb.2024.168796 2024

  6. [6]

    Why should I trust you?

    doi: 10.1145/2939672.2939778. URL https://doi. org/10.1145/2939672.2939778. Rudin, C. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead.Nature Machine Intelligence, 1(5): 206–215, May 2019. ISSN 2522-5839. doi: 10. 1038/s42256-019-0048-x. URL https://doi.org/10.1038/ s42256-019-0048-x. Rumelha...

    work page doi:10.1145/2939672.2939778 2019

  7. [7]

    black boxes

    ISSN 1476-4687. doi: 10.1038/nature13045. URL https://doi.org/10.1038/nature13045. Yang, X., Han, H., De Carvalho, D. D., Lay, F. D., Jones, P. A., and Liang, G. Gene body methylation can alter gene expression and is a therapeutic target in cancer.Cancer Cell, 26(4):577–590, October 2014. Zamft, B., Bintu, L., Ishibashi, T., and Bustamante, C. Nascent RNA...

    work page doi:10.1038/nature13045 2014

  8. [8]

    reasoning

    prompts an LLM with a natural-language description of the dataset and prediction task and asks it to generate executable Python code that adds new columns, together with free-form textual justifications of their utility. The proposed transformations are accepted only if they improve validation performance of downstream classifiers such as logistic regress...

    2024

  9. [9]

    Fit the full linear model (e.g., OLS) using the training data(Φ train,y train)to obtain the weightsw

  10. [10]

    Calculate the predictions ˆyval and the baseline MSEfull on the validation set(Φ val,y val)

  11. [11]

    change in error if term is removed

    For each termψ j (fromk= 1toM): (a) Calculate the predictions of the model without term j (effectively wj = 0, other wk fixed): ˆyval,−j = ˆyval − ϕval,jwj. (b) Calculate MSE −j using ˆyval,−j. (c) Compute∆ j =MSE −j −MSE full. Computational Cost: • Fitting the initial OLS model: TypicallyO(N trainM2 +M 3)ifN train > MorO(N 2 trainM)ifM > N train. • Calcu...

    2017

  12. [12]

    The top K terms are retained, where K corresponds to the sparsity constraint (the keep n terms hyperparameter)

    Top-K Selection:The candidate terms are ranked in descending order of their aggregate influence scores ∆agg j . The top K terms are retained, where K corresponds to the sparsity constraint (the keep n terms hyperparameter). This is approach we employ in this work

  13. [13]

    prefer these kinds of terms because of scientific reason X

    Threshold Selection:Terms are retained if their aggregate influence score exceeds a specific threshold, ∆agg j > ϵ . This allows the model complexity to adapt dynamically to the signal-to-noise ratio of the discovered terms. This is an alternative approach worth exploring, but we do not investigate it in this work. This approach effectively decouples the ...

  14. [14]

    Propose” agent) and another for refining the set of terms based on evaluation feedback (the “Prune

    controls how many child nodes are attempted to be generated from a parent node during a single expansion step. 27 Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback Variation between these successors arises from the inherent stochasticity in the LLM’s responses to the propose (and, optionally, ...

  15. [15]

    Concatenated with the current candidate terms

  16. [16]

    Propose” Agent:Below is an example response from the LLM acting as the “Propose

    Sent to a LLM term pruner agent that will use various computed signals to decide which terms to keep and which to drop. # Instructions: Given below information, propose some candidate terms. The terms can be any valid numpy expressions. Make use of the dataset and problem description to propose relevant terms. Make sure to use the learnings from the histo...

  17. [17]

    **Inspect every row **

  18. [18]

    keep" or

    **Decide "keep" or "drop" ** for each term using the rule: * Use the heuristic: "delta_k ˜= 0 -> drop", "large delta_k -> keep" and your own judgement

  19. [19]

    DECISION

    **Return** a python dictionary after "DECISION" with exactly the two keys DECISION ‘‘‘ {{ "keep": ["term_a", "term_b", ...], "drop": ["term_c", "term_d", ...] }} ‘‘‘‘ Place each term name in either **keep** or **drop** - never both, never neither. **IMPORTANT:** * Make use of the dataset and problem description to make the best decision. * Make sure to us...

  20. [20]

    - ‘cancer_volume * radiotherapy_dosage‘ (delta = 197.209) is highly impactful

    **Highly influential terms **: - ‘cancer_volume * chemo_concentration‘ (delta = 638.509) is critical. - ‘cancer_volume * radiotherapy_dosage‘ (delta = 197.209) is highly impactful. - ‘np.sqrt(cancer_volume)‘ (delta = 110.587) has substantial influence. - ‘np.log(1 + cancer_volume)‘ (delta = 17.6803)

  21. [21]

    - ‘chemo_dosage‘, ‘radiotherapy_dosage‘: limited delta values

    **Moderately influential / less relevant **: - ‘cancer_volume‘ (delta = 2.7081): core variable, but delta suggests moderate importance. - ‘chemo_dosage‘, ‘radiotherapy_dosage‘: limited delta values

  22. [22]

    These can be ignored safely

    **Negligible**: - Terms involving weighted interactions: e.g., ‘chemo_dosage / (1 + cancer_volume)‘ (delta ˜= 0). These can be ignored safely. --- ### **Analysis for ‘dc_dt‘: **

  23. [23]

    - ‘chemo_dosage‘ (delta = 18.8115): essential for modeling ‘dc_dt‘

    **Highly influential terms **: - ‘np.log(1 + cancer_volume)‘ (delta = 22.3107): critical. - ‘chemo_dosage‘ (delta = 18.8115): essential for modeling ‘dc_dt‘. - ‘np.sqrt(cancer_volume)‘ (delta = 15.8203): quite significant

  24. [24]

    - ‘cancer_volume‘: relevant, but has relatively small delta compared to other terms

    **Moderately influential **: - ‘radiotherapy_dosage‘: important as part of the model. - ‘cancer_volume‘: relevant, but has relatively small delta compared to other terms

  25. [25]

    keep": [

    **Negligible terms **: - Interactions like ‘radiotherapy_dosage / (1 + cancer_volume)‘ (small delta). --- Considering both outputs, I aim to balance interpretability and prioritization based on influence across both equations. Here is the final decision: --- DECISION ‘‘‘ { "keep": [ "cancer_volume * chemo_concentration", # Very high delta for dv_dt "cance...

    work page arXiv 2017

  26. [26]

    These are combined with surviving terms from the previous iteration

    The LLM Propose agent suggests new terms, which may contain c(init) syntax. These are combined with surviving terms from the previous iteration

  27. [27]

    The set of all constantsθfrom all current candidate terms is optimized by minimizingJ(θ)

  28. [28]

    70 Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback

    After optimization, the resulting terms are evaluated on the data splits (train, validation, test). 70 Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback

  29. [29]

    The Prune agent receives the terms (with their optimized c(value) markers), their fitted outer weightsw j, and their per-term influence scores∆ j

    The standard pruning phase proceeds. The Prune agent receives the terms (with their optimized c(value) markers), their fitted outer weightsw j, and their per-term influence scores∆ j

  30. [30]

    Surviving terms, retaining theirc()markers, are passed to the next iteration

    The agent returns keep/drop decisions. Surviving terms, retaining theirc()markers, are passed to the next iteration. This entire cycle is embedded within either the linear iterative refinement or the MCTS search strategy, just as in the standard IGSR framework. G.14.1. PROOF OF CONCEPT EXPERIMENT To provide a clear illustration of the specific advantage o...

    work page arXiv 2023

  31. [31]

    This tests whether a non-linear predictor can extract more value from the discovered symbolic features

    IGSR + XGBoost:The features ψj(x) discovered by IGSR are frozen and used as inputs to an XGBoost regressor. This tests whether a non-linear predictor can extract more value from the discovered symbolic features. 3.OpenFE + Linear Regression:OpenFE is used to generate and select features, followed by a linear predictor. 4.OpenFE + XGBoost:OpenFE is used to...

  32. [32]

    Scalability via Priors:IGSR avoids the combinatorial explosion typical of generative feature engineering by using LLM priors to propose semantically relevant features, making it viable for high-dimensional datasets where traditional methods fail

  33. [33]

    sweet spot

    Inherent Interpretability:By optimizing features specifically for a linear backend, IGSR produces a model that is fully interpretable (f(x) = P wjψj(x)). The results show that this interpretability does not come at the cost of accuracy. Extended comparison against additional AFE baselines.The comparison above focuses on OpenFE as a representative non-LLM ...

    work page arXiv 2025

  34. [34]

    •depth limit:10

    The constant used in the UCT formula to balance exploration and exploitation. •depth limit:10. The maximum depth of the search tree. •rollout is just node reward: True. We utilize Heuristic MCTS where the node’s immediate validation MSE serves as the reward, without performing deep rollouts. 80 Influence-Guided Symbolic Regression: Scientific Discovery vi...

    2024