Pith. sign in

REVIEW 5 major objections 5 minor 2 cited by

Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A reinforcement-learning fine-tuning loop that rewards a pretrained equation generator for numerical fit substantially improves the recovery of symbolic equations on physics and dynamics benchmarks.

desk verdict Fine-tuning a pretrained SR transformer with PPO-style R2 rewards works on benchmarks, but the paper overclaims structural recovery and lacks reproducibility details. read the letter →

arxiv 2505.15572 v1 pith:EF4W3ZLN submitted 2025-05-21 cs.LG cs.AI

Wangyang Ying , Haoyue Bai , Nanxu Gong , Xinyuan Wang , Sixun Dong , Haifeng Chen , Yanjie Fu This is my paper
classification cs.LGcs.AI
keywords symbolicregressiondata-to-equationreinforcementlearningfine-tuningfoundationmodelstransformerencoder-decoderpolicygradientR2rewarddomainadaptation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to close the gap between what a pretrained symbolic-regression transformer learns on generic synthetic tables and what domain-specific data actually look like. It proposes REEL, a reinforcement-learning fine-tuning loop that keeps the pretrained model's parameters as a starting policy, generates candidate equations, scores them by how well they fit sampled training points, and updates the policy with a clipped policy-gradient objective plus a KL penalty toward the original model. The reported payoff is large: the share of equations recovered with test R² above 0.99 rises from 0.815 to 0.908 on Feynman, from 0.357 to 0.857 on Strogatz, and from 0.000 to 0.088 on Black-box, with average R² and noise robustness also improving. Sympathetically read, this shows that a token-level pretrained generator can be steered by numerical semantics rather than retrained from scratch.

What carries the argument

The load-bearing mechanism is the reward-coupled policy update: sample a bag of rows from the target table, decode an equation under the current policy, parse and evaluate it, compute a smoothed R² score (or -1 for invalid equations), and update the decoder with a clipped importance-ratio objective ρ·r together with a KL-divergence penalty to the frozen pretrained model. The relative endorsement ratio ρ compares the fine-tuned policy's token likelihoods with the foundation model's, so high-quality equations that the fine-tuned model now favors are reinforced while the KL term prevents over-departure. Data bag sampling plays the role of trajectory diversity, letting the agent see many subspaces of the same table within the transformer's input limits.

What would settle it

Take the Strogatz benchmark, fine-tune REEL with the published bag size, then evaluate the fine-tuned policy on a held-out split of equations (or on added label noise at level 0.1); if the share of equations with test R² above 0.99 does not exceed the E2E baseline's 0.357 while the training-bag R² is high, the reward proxy is overfitting the bags rather than driving generalization.

Watch

Extended reading notes

Core claim

On its own terms, the paper discovers that a pretrained transformer for data-to-equation (symbolic regression) can be adapted to a target dataset by treating equation generation as a reinforcement-learning policy and using the coefficient of determination R² of the generated equation on sampled data bags as the reward. The resulting method, REEL, improves the E2E backbone under both beam search and stochastic sampling on three benchmarks; the strongest configuration, REEL-Sampling, lifts the proportion of equations with test R² above 0.99 to 0.908 on Feynman, 0.857 on Strogatz, and 0.088 on the harder Black-box collection, and maintains higher average R² than the unadapted model. The authors attribute the gain to reward-driven exploration: the policy is pushed toward expressions that are numerically correct on the task data, not merely token-likely, while the KL regularization keeps it from drifting too far from pretraining.

Load-bearing premise

The method hinges on the reward: R² computed on a bag of 200 randomly sampled training points is assumed to be a reliable proxy for how well the generated equation will generalize to held-out test points, even when labels are noisy; if a bag misrepresents the data, the policy could overfit the bags and the reported test gains would not hold.

Editorial extensions

If this is right

  • If the central claim holds, domain-specific equation discovery can be obtained by fine-tuning one pretrained generator per dataset, instead of running expensive genetic-programming searches at inference time.
  • The same reward-driven loop should transfer to other pretrained symbolic-regression backbones and other numerical fitness metrics, since the framework only needs a policy and a reward oracle.
  • The large jump on Strogatz (0.357 to 0.857) suggests that reward fine-tuning is especially effective when the pretrained distribution is far from the target domain, not just as a small correction.
  • Because inference time stays low after fine-tuning, the method points to a deployment pattern where training cost is paid once and repeated symbolic predictions are cheap, suitable for high-frequency scientific discovery.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the bag-sampling mechanism can be tested directly by ablating bag size and number of bags, since the authors' framing makes trajectory diversity a load-bearing component rather than a minor implementation detail.
  • Beyond the paper: the same RL loop could adapt a fine-tuned policy not just to one dataset but to a family of equations sharing physical structure, turning the fine-tuned model into a reusable prior for an entire domain.
  • Beyond the paper: the reward function is plug-in, so adding parsimony or dimensional-consistency penalties could push generated equations closer to the true symbolic form; the case studies show the model still emits constants and extra terms, so a complexity-aware reward is a natural extension.
  • Beyond the paper: the claim that noise robustness comes from policy smoothing could be probed by comparing REEL on corrupted labels against an ensemble of pointwise-trained models, a comparison the paper does not isolate.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper introduces REEL, a reinforcement-learning fine-tuning method for adapting pretrained transformer-based symbolic regression models (specifically E2E) to domain-specific datasets. It samples multiple bootstrap bags of 200 training points per equation, generates equations with the current policy, computes a smoothed R2 reward for each complete equation, and updates the policy with a clipped likelihood-ratio objective plus KL regularization toward the pretrained model. Experiments on the Feynman, Strogatz, and Black-box benchmarks report consistent gains over the E2E backbone in average test R2 and in the proportion of equations reaching R2>0.99, competitive accuracy with SRBench genetic-programming baselines at lower inference time, and robustness to label noise. Appendices contain the training algorithm, hyperparameter sensitivity, complexity analysis, and case studies.

Significance. If the reported results are reliable, REEL provides a useful recipe for adapting symbolic-regression foundation models to domain-specific data with numerical feedback, an important problem for scientific discovery. The paper uses standard benchmarks, evaluates on held-out points, and releases code, which are strengths. The main contributions—using downstream fitness as reward and regularizing with a frozen reference policy—are reasonable and of interest to the symbolic-regression community. However, the current experimental reporting lacks repeated trials and a validation protocol, and the paper does not yet establish that the improved R2 reflects equation recovery rather than interpolation; these issues need to be resolved before the interpretability and domain-adaptation claims can be accepted.

major comments (5)
  1. [Section 4.1, Appendix B] It is unclear whether a single shared REEL model is fine-tuned on all equations of a benchmark or a separate model is trained per equation. The sentence "we train on each equation instance separately to ensure reward consistency and optimization stability" suggests per-equation models; if so, the gains in Table 1 are per-equation overfitting results rather than evidence of domain adaptation, and the comparison with E2E (which is not fine-tuned per equation) is not apples-to-apples. Please clarify the training setup and, if one model per equation is used, report the total training cost and reconsider the domain-adaptation claim.
  2. [Appendix D, Table 1] No standard errors, confidence intervals, or number of seeds are reported, and the hyperparameters (β=0.2, ϵ=0.2, N=128, bag size 200, 10 epochs, lr 5e-5) appear to be selected using the evaluation datasets, since the sensitivity analysis in Figure 6 is reported on Strogatz performance. This makes it impossible to assess whether the large reported differences are reliable or partly due to selection. Please add mean and standard deviation over at least 5 seeds and describe a validation protocol (e.g., a held-out subset of equations for hyperparameter selection) or provide a fixed default configuration.
  3. [Section 3.2, Eq. (2), Table 2] The reward is R2 computed on a stochastically sampled bag of 200 points, and the case study shows REEL-generated equations with R2 0.95–1.0 that are structurally different from the ground truth (e.g., "Cx0(C + Ccos(Cx1 + Cx2 + Cx1x2)) + C" vs "2x0(1 − cos(x1x2))"). This demonstrates that high R2 does not imply recovery of the underlying equation and raises the concern that the reported test-R2 gains reflect interpolation in the input space rather than meaningful symbolic discovery. Since the paper motivates REEL by interpretability and "mathematical semantics", please add structural metrics (exact-match rate, symbolic edit distance, complexity-weighted success rate) or explicitly limit the claims to numerical fitness rather than equation recovery.
  4. [Section 3.3.1, Eqs. (3)–(5)] The ratio ρ compares the fine-tuned policy to the frozen pretrained model, not to the policy from the previous update, so the clipped surrogate in Eq. (4) is not the standard PPO objective and the meaning of the clip range is different. Moreover, the objective has no baseline or advantage normalization, so gradient estimates can have high variance over the 10 fine-tuning epochs. Please justify this objective theoretically or empirically (e.g., comparison with a REINFORCE baseline and with a standard PPO variant).
  5. [Section 4.4] In the noise-robustness experiment, it is not stated whether the added Gaussian noise is applied only to the training labels used for reward computation or also to the test labels. If the test labels are noisy, the R2 ceiling decreases with noise level and the comparison to E2E needs that ceiling to be reported; if the test labels are clean, please state so explicitly, because training on noisy y and evaluating on clean y is a different and more favorable setting.
minor comments (5)
  1. [Eq. (2), Section 4.1] The summation index in Eq. (2) is written as "i−1" instead of "i=1"; similarly, the R2 formula in Section 4.1 uses ˜y in the denominator instead of y.
  2. [Eq. (1), Algorithm 1] Eq. (1) selects actions by arg max, while Algorithm 1 samples a1:T ∼ πθ; please clarify that sampling is used during training and beam or argmax decoding at evaluation.
  3. [Appendix B] The appendix states that the REEL code is publicly released but no repository URL is provided.
  4. [Table 2] All constants are collapsed to "C", which makes it difficult to verify whether the shown expressions are actually equivalent to the true equations; please display fitted constant values or use distinct symbols.
  5. [Section 4.1] The metric name "R2 > 0.99" is used both as a threshold and as a proportion; consider renaming it to "Success@0.99" for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper finetunes a pretrained symbolic regression model with R2 rewards on training bags and evaluates on disjoint test points, a standard train/test setup.

full rationale

This is an empirical method paper. The central claim is that reinforcement-learning finetuning with a numerical fitness reward improves a pretrained Data2Eqn foundation model. The reward in Eq. (2) is R2 computed on sampled training subsets, while the reported performance metrics (R2 and R2 > 0.99) are computed on a disjoint 25% held-out test split, as stated in Section 4.1: 'We split the datapoints of each equation into training and testing datapoints at a ratio of 75% and 25%, respectively. The finetuning datasets are sampled from the training datapoints, while the test datapoints are used to evaluate model performance.' Thus, the evaluation is not a re-statement of the optimized objective on the same data. No fitted parameter is renamed as a prediction, and no equation derivation reduces by construction to its inputs. The self-citations in the paper appear in related work and broader impact contexts and are not load-bearing for the main empirical claims. The base model E2E [25] is an external, publicly available pretrained model, not an unverified self-citation. Potential concerns such as the sparsity of the 200-point bag reward or structural mismatch in case-study equations are correctness and generalization risks, not circularity. The paper is self-contained as an empirical comparison, so the circularity score is 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central empirical contribution rests on a set of hand-chosen hyperparameters (beta, epsilon, bag size, number of bags, epochs, learning rate) and on assumptions about the adequacy of R2 computed on small sampled bags as a reward signal, the usefulness of the pretrained E2E policy as an initialization, and the representativeness of the selected benchmarks. No new physical entities are introduced.

free parameters (6)
  • KL regularization coefficient beta = 0.2
    Chosen via sensitivity analysis (Appendix D) to balance policy stability and adaptation; affects the objective L = L_clip + beta * L_kl.
  • PPO clip range epsilon = 0.2
    Chosen via sensitivity analysis (Appendix D) to limit policy update magnitude.
  • Number of sampled instance bags N = 128
    Number of trajectory training subsets per equation; chosen by hand in Appendix B.
  • Bag size (rows per subset) = 200
    Number of input points in each trajectory training subset; aligned with E2E pretraining input length <= 200.
  • Fine-tuning epochs = 10
    RL update epochs per equation; chosen in Appendix B.
  • Learning rate = 5e-5
    AdamW learning rate for fine-tuning; chosen in Appendix B.
assumptions (4)
  • domain assumption The pretrained E2E transformer provides a policy prior that can be meaningfully fine-tuned with RL on small data subsets.
    The entire method assumes the pretrained model's token distribution is a useful starting point; invoked in Section 3.3.1 'The Agent'.
  • domain assumption R2 on a sampled 200-point bag is a reliable reward signal for equation quality and generalizes to unseen points.
    Eq. (2) defines reward as R2 on the training subset; the method optimizes this reward, and test performance is assumed to follow.
  • standard math The clipped importance-ratio policy gradient (PPO-style surrogate) converges to an improved policy on each task.
    The loss in Eq. (4) is a standard PPO clipped surrogate; convergence relies on standard RL assumptions, though no formal convergence proof is given.
  • domain assumption Benchmark datasets (Feynman, Strogatz, Black-box) with input dimensionality <= 10 are representative of the intended domain-specific Data2Eqn applications.
    Section 4.1 and Appendix B select these datasets; the paper excludes higher-dimensional black-box datasets, which is a stated constraint inherited from E2E.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback." pith.science (2026). https://pith.science/paper/EF4W3ZLN

@misc{pith2026250515572,
  author       = {Pith},
  title        = {Pith review of: Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EF4W3ZLN}},
  note         = {Machine review of arXiv:2505.15572}
}
read the original abstract

The data-to-equation (Data2Eqn) task aims to discover interpretable mathematical equations that map observed values to labels, offering physical insights and broad applicability across academic and industrial domains. Genetic programming and traditional deep learning-based approaches suffer from search inefficiency and poor generalization on small task-specific datasets. Foundation models showed promise in this area, but existing approaches suffer from: 1) They are pretrained on general-purpose data distributions, making them less effective for domain-specific tasks; and 2) their training objectives focus on token-level alignment, overlooking mathematical semantics, which can lead to inaccurate equations. To address these issues, we aim to enhance the domain adaptability of foundation models for Data2Eqn tasks. In this work, we propose a reinforcement learning-based finetuning framework that directly optimizes the generation policy of a pretrained model through reward signals derived from downstream numerical fitness. Our method allows the model to adapt to specific and complex data distributions and generate mathematically meaningful equations. Extensive experiments demonstrate that our approach improves both the accuracy and robustness of equation generation under complex distributions.

Figures

Figures reproduced from arXiv: 2505.15572 by the authors.

Figure 1
Figure 1. Framework Overview. Given a domain-specific dataset, we first sample diverse instance [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Reward as￾signment: we reinforce it when the finetuned model generates high￾quality equations. Policy Learning [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Performance comparison of REEL and all SRBench algorithms for Feynman and Strogatz [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Robustness to noise, where the perfor￾mances are shown for various target noise levels. To evaluate the robustness of REEL to noise, we conduct experiments by injecting varying levels of Gaussian noise into the values y of the in￾put tables during training. These noisy…
Figure 5
Figure 5. Figure 5: Complexity and Scalability Analysis of REEL. (a) Comparison of training time on the [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Hyperparameter sensitivity analysis. (a) [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Teaching Time Series to See and Speak: Forecasting with Aligned Visual and Textual Perspectives

    cs.LG 2025-06 reject novelty 5.0 of 10

    TimesCLIP aligns image-based and text-based views of the same time series via contrastive learning to improve forecasting accuracy on several benchmarks, but the full multimodal model is not used on two of the six lon...

  2. LLM-ML Teaming: Integrated Symbolic Decoding and Gradient Search for Valid and Stable Generative Feature Transformation

    cs.LG 2025-06 conditional novelty 4.0 of 10

    A product-of-experts decoder that blends a fine-tuned LLM's token probabilities with a gradient-searched sequence decoder produces more valid and stable feature transformations than either alone.

Reference graph

Works this paper leans on

63 extracted references · 41 canonical work pages · cited by 2 Pith papers

  1. [1]

    Artificial intelligence in physical sci- ences: Symbolic regression trends and perspectives

    Dimitrios Angelis, Filippos Sofos, and Theodoros E Karakasidis. Artificial intelligence in physical sci- ences: Symbolic regression trends and perspectives. Archives of Computational Methods in Engineering, 30(6):3845–3865, 2023

    work page 2023

  2. [2]

    Multiple regression genetic programming

    Ignacio Arnaldo, Krzysztof Krawiec, and Una-May O’Reilly. Multiple regression genetic programming. In Proceedings of the 2014 annual conference on genetic and evolutionary computation, pages 879–886, 2014

    work page 2014

  3. [3]

    Gorec: a generative cold-start recommendation framework

    Haoyue Bai, Min Hou, Le Wu, Yonghui Yang, Kun Zhang, Richang Hong, and Meng Wang. Gorec: a generative cold-start recommendation framework. In Proceedings of the 31st ACM international conference on multimedia, pages 1004–1012, 2023

    work page 2023

  4. [4]

    Multimodality invariant learning for multimedia-based new item recommendation

    Haoyue Bai, Le Wu, Min Hou, Miaomiao Cai, Zhuangzhuang He, Yuyang Zhou, Richang Hong, and Meng Wang. Multimodality invariant learning for multimedia-based new item recommendation. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 677–686, 2024

    work page 2024

  5. [5]

    Neural symbolic regression that scales

    Luca Biggio, Tommaso Bendinelli, Alexander Neitz, Aurelien Lucchi, and Giambattista Parascandolo. Neural symbolic regression that scales. InInternational Conference on Machine Learning, pages 936–945. Pmlr, 2021

    work page 2021

  6. [6]

    Operon c++: an efficient genetic pro- gramming framework for symbolic regression

    Bogdan Burlacu, Gabriel Kronberger, and Michael Kommenda. Operon c++: an efficient genetic pro- gramming framework for symbolic regression. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, GECCO ’20, page 1562–1570, New York, NY , USA, 2020. As- sociation for Computing Machinery. ISBN 9781450371278. doi: 10.1145/337792...

    arXiv 2020

  7. [7]

    Comparison of experimental designs for simulation-based symbolic regression of manufacturing systems

    Birkan Can and Cathal Heavey. Comparison of experimental designs for simulation-based symbolic regression of manufacturing systems. Computers & Industrial Engineering, 61(3):447–462, 2011

    work page 2011

  8. [8]

    William La Cava, Patryk Orzechowski, Bogdan Burlacu, Fabrício Olivetti de França, Marco Virgolin, Ying Jin, Michael Kommenda, and Jason H. Moore. Contemporary symbolic regression methods and their relative performance, 2021. URL https://arxiv.org/abs/2107.14351

    arXiv 2021

Show all 63 references
  1. [9]

    Multi-model approach for stock price prediction and trading recommendations

    Zhenrui Chen, Zhibo Dai, Huiyan Xing, Junyu Chen, Menghao Huo, and Kuan Lu. Multi-model approach for stock price prediction and trading recommendations. Preprints, May 2025. doi: 10.20944/ preprints202501.1003.v3. URL https://doi.org/10.20944/preprints202501.1003.v3

    2025

  2. [10]

    Assessment of the effect of the financial crisis on agents’ expectations through symbolic regression

    Oscar Claveria, Enric Monte, and Salvador Torra. Assessment of the effect of the financial crisis on agents’ expectations through symbolic regression. Applied Economics Letters, 24(9):648–652, 2017

    2017

  3. [11]

    Discovering symbolic models from deep learning with inductive biases

    Miles Cranmer, Alvaro Sanchez Gonzalez, Peter Battaglia, Rui Xu, Kyle Cranmer, David Spergel, and Shirley Ho. Discovering symbolic models from deep learning with inductive biases. Advances in neural information processing systems, 33:17429–17442, 2020

    2020

  4. [12]

    Interaction–transformation evolutionary algorithm for symbolic regression

    Fabricio Olivetti de Franca and Guilherme Seidyo Imai Aldeia. Interaction–transformation evolutionary algorithm for symbolic regression. Evolutionary computation, 29(3):367–390, 2021

    2021

  5. [13]

    Deep symbolic regression for recurrence prediction

    Stéphane d’Ascoli, Pierre-Alexandre Kamienny, Guillaume Lample, and Francois Charton. Deep symbolic regression for recurrence prediction. In International Conference on Machine Learning, pages 4520–4536. PMLR, 2022

    2022

  6. [14]

    Evolutionary large language model for automated feature transformation

    Nanxu Gong, Chandan K Reddy, Wangyang Ying, Haifeng Chen, and Yanjie Fu. Evolutionary large language model for automated feature transformation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 16844–16852, 2025. 10

    2025

  7. [15]

    Unsupervised feature transformation via in-context generation, generator-critic llm agents, and duet-play teaming

    Nanxu Gong, Xinyuan Wang, Wangyang Ying, Haoyue Bai, Sixun Dong, Haifeng Chen, and Yanjie Fu. Unsupervised feature transformation via in-context generation, generator-critic llm agents, and duet-play teaming. arXiv preprint arXiv:2504.21304, 2025

    2025 arXiv

  8. [16]

    Neuro-symbolic embedding for short and effective feature selection via autoregressive generation

    Nanxu Gong, Wangyang Ying, Dongjie Wang, and Yanjie Fu. Neuro-symbolic embedding for short and effective feature selection via autoregressive generation. ACM Transactions on Intelligent Systems and Technology, 16(2):1–21, 2025

    2025

  9. [17]

    Gustafson, E.K

    S. Gustafson, E.K. Burke, and N. Krasnogor. On improving genetic programming for symbolic regression. In 2005 IEEE Congress on Evolutionary Computation, volume 1, pages 912–919 V ol.1, 2005. doi: 10.1109/CEC.2005.1554780

    2005

  10. [18]

    Shape- constrained multi-objective genetic programming for symbolic regression

    Christian Haider, Fabricio Olivetti de Franca, Bogdan Burlacu, and Gabriel Kronberger. Shape- constrained multi-objective genetic programming for symbolic regression. Applied Soft Computing, 132: 109855, 2023

    2023

  11. [19]

    Double correction framework for denoising recommendation

    Zhuangzhuang He, Yifan Wang, Yonghui Yang, Peijie Sun, Le Wu, Haoyue Bai, Jinqi Gong, Richang Hong, and Min Zhang. Double correction framework for denoising recommendation. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1062–1072, 2024

    2024

  12. [20]

    Deep generative symbolic regression

    Samuel Holt, Zhaozhi Qian, and Mihaela van der Schaar. Deep generative symbolic regression. arXiv preprint arXiv:2401.00282, 2023

    2023 arXiv

  13. [21]

    Reinforcement feature transformation for polymer property performance prediction

    Xuanming Hu, Dongjie Wang, Wangyang Ying, and Yanjie Fu. Reinforcement feature transformation for polymer property performance prediction. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages 4538–4545, 2024

    2024

  14. [22]

    Ct-patchtst: Channel-time patch time-series transformer for long-term renewable energy forecasting

    Menghao Huo, Kuan Lu, Yuxiao Li, and Qiang Zhu. Ct-patchtst: Channel-time patch time-series transformer for long-term renewable energy forecasting. arXiv preprint arXiv:2501.08620, 2025. URL https://arxiv.org/abs/2501.08620

    2025

  15. [23]

    Enhancing customer contact efficiency with graph neural networks in credit card fraud detection workflow

    Menghao Huo, Kuan Lu, Qiang Zhu, and Zhenrui Chen. Enhancing customer contact efficiency with graph neural networks in credit card fraud detection workflow. arXiv preprint arXiv:2504.02275, 2025. URL https://arxiv.org/abs/2504.02275

    2025

  16. [24]

    Bayesian symbolic regression.arXiv preprint arXiv:1910.08892, 2019

    Ying Jin, Weilin Fu, Jian Kang, Jiadong Guo, and Jian Guo. Bayesian symbolic regression.arXiv preprint arXiv:1910.08892, 2019

    1910 arXiv

  17. [25]

    End-to- end symbolic regression with transformers

    Pierre-Alexandre Kamienny, Stéphane d’Ascoli, Guillaume Lample, and François Charton. End-to- end symbolic regression with transformers. Advances in Neural Information Processing Systems, 35: 10269–10281, 2022

    2022

  18. [26]

    Integration of neural network-based symbolic regression in deep learning for scientific discovery

    Samuel Kim, Peter Y Lu, Srijon Mukherjee, Michael Gilbert, Li Jing, Vladimir ˇCeperi´c, and Marin Soljaˇci´c. Integration of neural network-based symbolic regression in deep learning for scientific discovery. IEEE transactions on neural networks and learning systems, 32(9):416...

    2020

  19. [27]

    Inference of compact nonlinear dynamic models by epigenetic local search

    William La Cava, Kourosh Danai, and Lee Spector. Inference of compact nonlinear dynamic models by epigenetic local search. Engineering Applications of Artificial Intelligence, 55:292–306, 2016

    2016

  20. [28]

    Epsilon-lexicase selection for regression

    William La Cava, Lee Spector, and Kourosh Danai. Epsilon-lexicase selection for regression. In Proceedings of the Genetic and Evolutionary Computation Conference 2016, pages 741–748, 2016

    2016

  21. [29]

    Learning concise representations for regression by evolving networks of trees

    William La Cava, Tilak Raj Singh, James Taggart, Srinivas Suri, and Jason H Moore. Learning concise representations for regression by evolving networks of trees. arXiv preprint arXiv:1807.00981, 2018

    2018 arXiv

  22. [30]

    A flexible symbolic regression method for constructing interpretable clinical prediction models

    William G La Cava, Paul C Lee, Imran Ajmal, Xiruo Ding, Priyanka Solanki, Jordana B Cohen, Jason H Moore, and Daniel S Herman. A flexible symbolic regression method for constructing interpretable clinical prediction models. NPJ Digital Medicine, 6(1):107, 2023

    2023

  23. [31]

    Sehf: A summary-enhanced hierarchical framework for financial report sentiment analysis

    Haozhou Li, Qinke Peng, Xinyuan Wang, Xu Mou, and Yonghao Wang. Sehf: A summary-enhanced hierarchical framework for financial report sentiment analysis. IEEE Transactions on Computational Social Systems, 11(3):4087–4101, 2023. 11

    2023

  24. [32]

    Sade: A speaker-aware dual encoding model based on diagbert for medical triage and pre-diagnosis

    Haozhou Li, Xinyuan Wang, Hongkai Du, Wentong Sun, and Qinke Peng. Sade: A speaker-aware dual encoding model based on diagbert for medical triage and pre-diagnosis. In ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 127...

    2024

  25. [33]

    Pth and the regulation of mesenchymal cells within the bone marrow niche

    Hanghang Liu, Linyi Liu, and Clifford J Rosen. Pth and the regulation of mesenchymal cells within the bone marrow niche. Cells, 13(5):406, 2024

    2024

  26. [34]

    Edta enhances stromal cell–derived factor 1α–induced migration of dental pulp cells by up-regulating chemokine receptor 4 expression

    Linyi Liu, Sha Leng, Junli Yue, Qian Lu, Weizhe Xu, Xiaowei Yi, Dingming Huang, and Lan Zhang. Edta enhances stromal cell–derived factor 1α–induced migration of dental pulp cells by up-regulating chemokine receptor 4 expression. Journal of Endodontics, 45(5):599–605, 2019

    2019

  27. [35]

    Calorie restriction in mice impairs cortical but not trabecular peak bone mass by suppressing bone remodeling

    Linyi Liu, Phuong T Le, J Patrizia Stohn, Hanghang Liu, Wangyang Ying, Roland Baron, and Clifford J Rosen. Calorie restriction in mice impairs cortical but not trabecular peak bone mass by suppressing bone remodeling. Journal of Bone and Mineral Research, 39(8):1188–1199, 2024

    2024

  28. [36]

    Ffx: Fast, scalable, deterministic symbolic regression technology

    Trent McConaghy. Ffx: Fast, scalable, deterministic symbolic regression technology. In Genetic Programming Theory and Practice IX, pages 235–260. Springer, 2011

    2011

  29. [37]

    Symbolic regression via neural-guided genetic programming population seeding

    T Nathan Mundhenk, Mikel Landajuela, Ruben Glatt, Claudio P Santiago, Daniel M Faissol, and Brenden K Petersen. Symbolic regression via neural-guided genetic programming population seeding. arXiv preprint arXiv:2111.00053, 2021

    2021 arXiv

  30. [38]

    Symbolic regression via deep reinforcement learning enhanced genetic programming seeding

    Terrell Mundhenk, Mikel Landajuela, Ruben Glatt, Claudio P Santiago, Brenden K Petersen, et al. Symbolic regression via deep reinforcement learning enhanced genetic programming seeding. Advances in Neural Information Processing Systems, 34:24912–24923, 2021

    2021

  31. [39]

    Olson, William La Cava, Patryk Orzechowski, Ryan J

    Randal S. Olson, William La Cava, Patryk Orzechowski, Ryan J. Urbanowicz, and Jason H. Moore. Pmlb: A large benchmark suite for machine learning evaluation and comparison, 2017. URL https: //arxiv.org/abs/1703.00512

    2017 arXiv

  32. [40]

    Deep symbolic regression: Recovering mathematical expressions from data via risk- seeking policy gradients

    Brenden K Petersen, Mikel Landajuela, T Nathan Mundhenk, Claudio P Santiago, Soo K Kim, and Joanne T Kim. Deep symbolic regression: Recovering mathematical expressions from data via risk- seeking policy gradients. arXiv preprint arXiv:1912.04871, 2019

    1912 arXiv

  33. [41]

    Age-fitness pareto optimization

    Michael D Schmidt and Hod Lipson. Age-fitness pareto optimization. In Proceedings of the 12th annual conference on Genetic and evolutionary computation, pages 543–544, 2010

    2010

  34. [42]

    Transformer-based planning for symbolic regression

    Parshin Shojaee, Kazem Meidani, Amir Barati Farimani, and Chandan Reddy. Transformer-based planning for symbolic regression. Advances in Neural Information Processing Systems, 36:45907– 45919, 2023

    2023

  35. [43]

    Symbolic physics learner: Discovering governing equations via monte carlo tree search

    Fangzheng Sun, Yang Liu, Jian-Xun Wang, and Hao Sun. Symbolic physics learner: Discovering governing equations via monte carlo tree search. arXiv preprint arXiv:2205.13134, 2022

    2022 arXiv

  36. [44]

    Ai feynman: A physics-inspired method for symbolic regression

    Silviu-Marian Udrescu and Max Tegmark. Ai feynman: A physics-inspired method for symbolic regression. Science Advances, 6(16):eaay2631, 2020

    2020

  37. [45]

    Ai feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity, 2020

    Silviu-Marian Udrescu, Andrew Tan, Jiahai Feng, Orisvaldo Neto, Tailin Wu, and Max Tegmark. Ai feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity, 2020. URL https: //arxiv.org/abs/2006.10782

    2020 arXiv

  38. [46]

    Semantically-based crossover in genetic programming: application to real-valued symbolic regression

    Nguyen Quang Uy, Nguyen Xuan Hoai, Michael O’Neill, Robert I McKay, and Edgar Galván-López. Semantically-based crossover in genetic programming: application to real-valued symbolic regression. Genetic Programming and Evolvable Machines, 12:91–119, 2011

    2011

  39. [47]

    Symbolicgpt: A generative transformer model for symbolic regression

    Mojtaba Valipour, Bowen You, Maysum Panju, and Ali Ghodsi. Symbolicgpt: A generative transformer model for symbolic regression. arXiv preprint arXiv:2106.14131, 2021

    2021 arXiv

  40. [48]

    Scalable genetic pro- gramming by gene-pool optimal mixing and input-space entropy-based building-block learning

    Marco Virgolin, Tanja Alderliesten, Cees Witteveen, and Peter AN Bosman. Scalable genetic pro- gramming by gene-pool optimal mixing and input-space entropy-based building-block learning. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 1041–1048, 2017. 12

    2017

  41. [49]

    Linear scaling with and within semantic backpropagation-based genetic programming for symbolic regression

    Marco Virgolin, Tanja Alderliesten, and Peter AN Bosman. Linear scaling with and within semantic backpropagation-based genetic programming for symbolic regression. In Proceedings of the genetic and evolutionary computation conference, pages 1084–1092, 2019

    2019

  42. [50]

    Towards data-centric ai: A comprehensive survey of traditional, reinforcement, and generative approaches for tabular data transformation

    Dongjie Wang, Yanyong Huang, Wangyang Ying, Haoyue Bai, Nanxu Gong, Xinyuan Wang, Sixun Dong, Tao Zhe, Kunpeng Liu, Meng Xiao, et al. Towards data-centric ai: A comprehensive survey of traditional, reinforcement, and generative approaches for tabular data transformation. arXiv...

    2025 arXiv

  43. [51]

    Lcmdc: Large-scale chinese medical dialogue corpora for automatic triage and medical consultation

    Xinyuan Wang, Haozhou Li, Dingfang Zheng, and Qinke Peng. Lcmdc: Large-scale chinese medical dialogue corpora for automatic triage and medical consultation. arXiv preprint arXiv:2410.03521, 2024

    2024 arXiv

  44. [52]

    Knockoff-guided feature selection via a single pre-trained reinforced agent

    Xinyuan Wang, Dongjie Wang, Wangyang Ying, Rui Xie, Haifeng Chen, and Yanjie Fu. Knockoff-guided feature selection via a single pre-trained reinforced agent. arXiv preprint arXiv:2403.04015, 2024

    2024 arXiv

  45. [53]

    Llm-enhanced user-item interactions: Leveraging edge information for optimized recommendations

    Xinyuan Wang, Liang Wu, Liangjie Hong, Hao Liu, and Yanjie Fu. Llm-enhanced user-item interactions: Leveraging edge information for optimized recommendations. arXiv preprint arXiv:2402.09617, 2024

    2024 arXiv

  46. [54]

    A successful hybrid deep learning model aiming at promoter identification

    Ying Wang, Qinke Peng, Xu Mou, Xinyuan Wang, Haozhou Li, Tian Han, Zhao Sun, and Xiao Wang. A successful hybrid deep learning model aiming at promoter identification. BMC bioinformatics, 23(Suppl 1):206, 2022

    2022

  47. [55]

    Symbolic regression in materials science.MRS Communications, 9(3):793–805, 2019

    Yiqun Wang, Nicholas Wagner, and James M Rondinelli. Symbolic regression in materials science.MRS Communications, 9(3):793–805, 2019

    2019

  48. [56]

    Self-optimizing feature generation via categorical hashing representation and hierarchical reinforcement crossing

    Wangyang Ying, Dongjie Wang, Kunpeng Liu, Leilei Sun, and Yanjie Fu. Self-optimizing feature generation via categorical hashing representation and hierarchical reinforcement crossing. In 2023 IEEE International Conference on Data Mining (ICDM), pages 748–757. IEEE, 2023

    2023

  49. [57]

    Topology-aware reinforcement feature space reconstruction for graph data

    Wangyang Ying, Haoyue Bai, Kunpeng Liu, and Yanjie Fu. Topology-aware reinforcement feature space reconstruction for graph data. arXiv preprint arXiv:2411.05742, 2024

    2024 arXiv

  50. [58]

    Feature selection as deep sequential generative learning

    Wangyang Ying, Dongjie Wang, Haifeng Chen, and Yanjie Fu. Feature selection as deep sequential generative learning. ACM Transactions on Knowledge Discovery from Data, 18(9):1–21, 2024

    2024

  51. [59]

    Revolutionizing biomarker discovery: Leveraging generative ai for bio-knowledge-embedded continuous space exploration

    Wangyang Ying, Dongjie Wang, Xuanming Hu, Ji Qiu, Jin Park, and Yanjie Fu. Revolutionizing biomarker discovery: Leveraging generative ai for bio-knowledge-embedded continuous space exploration. In Proceedings of the 33rd ACM International Conference on Information and Knowledg...

    2024

  52. [60]

    Unsupervised generative feature transformation via graph contrastive pre-training and multi-objective fine-tuning

    Wangyang Ying, Dongjie Wang, Xuanming Hu, Yuanchun Zhou, Charu C Aggarwal, and Yanjie Fu. Unsupervised generative feature transformation via graph contrastive pre-training and multi-objective fine-tuning. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery ...

    2024

  53. [61]

    A survey on data-centric ai: Tabular learning from reinforcement learning and generative ai perspective

    Wangyang Ying, Cong Wei, Nanxu Gong, Xinyuan Wang, Haoyue Bai, Arun Vignesh Malarkkan, Sixun Dong, Dongjie Wang, Denghui Zhang, and Yanjie Fu. A survey on data-centric ai: Tabular learning from reinforcement learning and generative ai perspective. arXiv preprint arXiv:2502.08828, 2025

    2025 arXiv

  54. [62]

    Deep learning and symbolic regression for discovering parametric equations

    Michael Zhang, Samuel Kim, Peter Y Lu, and Marin Soljaˇci´c. Deep learning and symbolic regression for discovering parametric equations. IEEE Transactions on Neural Networks and Learning Systems, 2023. A Algorithm: Reinforcement Finetuning for Learning-centric Foundation Model...

    2023

  55. [63]

    To simplify the notations, we replace the constant with ’C’ in the equations

    0.8736 REEL Generation (Cx 0 + C)(Cx 1 + C)(Cx 4 + C)( C(x2−x3) x2x3 ) + C 1.0000 True Equation x0sin2( x2 x1 2 ) sin2( x1 2 ) - E2E Generation Cx 0(cos(cx2) + C(x1cos2(Cx 2)) 0.5225 REEL Generation Cx 0(1 − sin2(Cx 2x1 + Cx 2 1)) 0.9673 complex structures such as nested nonli...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.