Knowledge Tree
Deep Symbolic Regression
Also known as: symbolic regressions, Deep Symbolic Regression, symbolic regression
Facts (17)
Sources
Neuro-Symbolic AI: Explainability, Challenges, and Future Trends arxiv.org Nov 7, 2024 12 facts
procedureThe implicit adjustment process in Deep Symbolic Regression (DSR) provides feedback to the RNN to guide expression generation, relying on gradient descent or optimization algorithms to adjust RNN weights.
claimIn the Deep Symbolic Regression (DSR) method, the internal weights, activation functions, and processed sequences of the Recurrent Neural Network act as an implicit intermediate representation that is not directly oriented to the end user. However, because the symbolic form is output explicitly as a mathematical expression, the process is considered partially explicit and interpretable.
referenceThe paper 'Deep symbolic regression for recurrent sequences' by d’Ascoli et al. (2022) presents a method for deep symbolic regression applied to recurrent sequences.
referenceT. Nathan Mundhenk, Mikel Landajuela, Ruben Glatt, Claudio P. Santiago, Daniel M. Faissol, and Brenden K. Petersen introduced symbolic regression via neural-guided genetic programming population seeding in 2021.
referenceMajumdar et al. (2023) presented Symbolic Regression for PDEs using Pruned Differentiable Programs, published as an arXiv preprint.
referenceNeuro-symbolic AI research is categorized into several domains: mathematics and symbolic regression (e.g., Majumdar et al., 2023; Petersen et al., 2019), logic and knowledge processing including concept/rule learning (e.g., Aspis et al., 2022) and logical reasoning (e.g., Cunnington et al., 2023), and applications such as visual question answering (e.g., Mao et al., 2019), medical (e.g., Jain et al., 2023), communication (e.g., Thomas and Saad, 2023), programming (e.g., Hu et al., 2022a), recommendation systems (e.g., Carraro, 2023), and security (e.g., Wang et al., 2018).
claimThe logical decision-making part of Deep Symbolic Regression (DSR) consists of two steps: an explicit evaluation process and an implicit adjustment process.
procedurePetersen et al. (2019) proposed the Deep Symbolic Regression (DSR) method to recover mathematical expressions from data. The method proceeds by: (1) representing expressions as node sequences in symbolic expression trees containing mathematical operators and operands; (2) using a Recurrent Neural Network (RNN) to predict the next operator or operand based on the existing sequence; (3) calculating the degree of fit of the generated expression on a specific dataset; and (4) using the fit as feedback to guide the RNN's subsequent generation process.
referenceBrenden K. Petersen, Mikel Landajuela, T. Nathan Mundhenk, Claudio P. Santiago, Soo K. Kim, and Joanne T. Kim developed deep symbolic regression, a method for recovering mathematical expressions from data via risk-seeking policy gradients, in 2019.
procedureThe explicit evaluation process in Deep Symbolic Regression (DSR) calculates the fit or reward of an expression by comparing the expression against data.
referenceBahmani et al. (2024) published the paper 'Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions' in Computer Methods in Applied Mechanics and Engineering, Vol. 422, 116827.
referenceKubalík et al. (2023) developed a neural network approach to symbolic regression designed to create physically plausible data-driven models.
A Comprehensive Review of Neuro-symbolic AI for Robustness ... link.springer.com Dec 9, 2025 3 facts
claimA neuro-symbolic system described in the source text models entities as random variables using Bayesian inference to update beliefs about latent properties, while simultaneously employing symbolic regression to discover the form of force laws, enabling the system to learn physical reasoning from few examples and output a posterior distribution over possible explanations.
claimCurrent research in AI is moving toward more autonomous and generalizable systems through the automation of optimization algorithm discovery and the use of neural-guided genetic programming for symbolic regression.
referenceMundhenk et al. (2021) proposed a method for symbolic regression using neural-guided genetic programming population seeding.
Track: Poster Session 3 - aistats 2026 virtual.aistats.org 2 facts
claimKrzysztof Kacprzyk and Mihaela van der Schaar establish a reconstruction theorem for symbolic regression, which offers potential insights for developing future optimization techniques.
claimSymbolic regression is a machine learning approach aimed at discovering mathematical closed-form expressions that best fit a given dataset.