# Controllable Neural Symbolic Regression arXiv: https://arxiv.org/abs/2304.10336 ยท HTML: https://mlsanity.com/paper/2304.10336/ ## Key facts - Cited by 20 papers in the map (data through 14 Oct 2026). - Builds on 25 of its 43 references that are in the map. - First posted on arXiv 20 Apr 2023. ## Builds on (most cited first, 25 of 25) - [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017) - [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022) - [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022) - [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014) - [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019) - [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020) - [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019) - [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021) - [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022) - [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021) - [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020) - [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017) - [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020) - [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021) - [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021) - [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022) - [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022) - [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022) - [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021) - [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019) - [Evolving symbolic density functionals](https://mlsanity.com/paper/2203.02540/) (2022) - [What is my math transformer doing? -- Three results on interpretability and generalization](https://mlsanity.com/paper/2211.00170/) (2022) - [Complexity Measures for Multi-objective Symbolic Regression](https://mlsanity.com/paper/2109.00238/) (2021) - [Symbolic Expression Transformer: A Computer Vision Approach for Symbolic Regression](https://mlsanity.com/paper/2205.11798/) (2022) - [Discovering ordinary differential equations that govern time-series](https://mlsanity.com/paper/2211.02830/) (2022) ## Built on by (most cited first, 20 of 20) - [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023) - [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025) - [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024) - [A Neural Symbolic Model for Space Physics](https://mlsanity.com/paper/2503.07994/) (2025) - [ChatSR: Multimodal Large Language Models for Scientific Formula Discovery](https://mlsanity.com/paper/2406.05410/) (2024) - [AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge](https://mlsanity.com/paper/2504.01538/) (2025) - [Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression](https://mlsanity.com/paper/2406.00695/) (2024) - [Model-based Policy Optimization using Symbolic World Model](https://mlsanity.com/paper/2407.13518/) (2024) - [A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data](https://mlsanity.com/paper/2507.21873/) (2025) - [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025) - [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025) - [Mixture of Concept Bottleneck Experts](https://mlsanity.com/paper/2602.02886/) (2026) - [Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework](https://mlsanity.com/paper/2402.05306/) (2024) - [DN-CL: Deep Symbolic Regression against Noise via Contrastive Learning](https://mlsanity.com/paper/2406.14844/) (2024) - [Analytical Lyapunov Function Discovery: An RL-based Generative Approach](https://mlsanity.com/paper/2502.02014/) (2025) - [Parsing the Language of Expression: Enhancing Symbolic Regression with Domain-Aware Symbolic Priors](https://mlsanity.com/paper/2503.09592/) (2025) - [Can Test-time Computation Mitigate Reproduction Bias in Neural Symbolic Regression?](https://mlsanity.com/paper/2505.22081/) (2025) - [Neural-Guided Equation Discovery](https://mlsanity.com/paper/2503.16953/) (2025) - [AutoSR: Automatic Symbolic Regression by Searching Research States](https://mlsanity.com/paper/2608.16876/) (2026) - [Synthesizing Physics Formulae with Transformers](https://mlsanity.com/paper/2610.03947/) (2026) ## Abstract (arXiv) In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.