Neural Structure Embedding for Symbolic Regression via Continuous Structure Search and Coefficient Optimization
arXiv:2603.22429v1 Announce Type: new Abstract: Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational cost, unstable performance, and limited scalability to large equation spaces. To address these challenges, we propose SRCO, a unified embedding-driven framework for symbolic regression that transforms symbolic structures into a continuous, optimizable representation space. The framework consists of three key components: (1) structure embedding: we first generate a large pool of exploratory equations using traditional symbolic regression algorithms and train a Transformer model to compress symbolic structures into a continuous embedding space; (2) continuous structure search: the embedding space enables efficient exploration using gradient-based or sampling-based optimization, significantly reducing the
arXiv:2603.22429v1 Announce Type: new Abstract: Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational cost, unstable performance, and limited scalability to large equation spaces. To address these challenges, we propose SRCO, a unified embedding-driven framework for symbolic regression that transforms symbolic structures into a continuous, optimizable representation space. The framework consists of three key components: (1) structure embedding: we first generate a large pool of exploratory equations using traditional symbolic regression algorithms and train a Transformer model to compress symbolic structures into a continuous embedding space; (2) continuous structure search: the embedding space enables efficient exploration using gradient-based or sampling-based optimization, significantly reducing the cost of navigating the combinatorial structure space; and (3) coefficient optimization: for each discovered structure, we treat symbolic coefficients as learnable parameters and apply gradient optimization to obtain accurate numerical values. Experiments on synthetic and real-world datasets show that our approach consistently outperforms state-of-the-art methods in equation accuracy, robustness, and search efficiency. This work introduces a new paradigm for symbolic regression by bridging symbolic equation discovery with continuous embedding learning and optimization.
Executive Summary
This article proposes a novel framework, SRCO, for symbolic regression that leverages continuous structure search and coefficient optimization. By embedding symbolic structures into a continuous representation space using a Transformer model, SRCO enables efficient exploration of the combinatorial structure space. Experiments on synthetic and real-world datasets demonstrate the approach's superiority in equation accuracy, robustness, and search efficiency. The framework's ability to bridge symbolic equation discovery with continuous embedding learning and optimization introduces a new paradigm for symbolic regression, with potential applications in various fields such as physics, engineering, and finance. However, the approach's scalability and interpretability require further investigation.
Key Points
- ▸ SRCO transforms symbolic structures into a continuous, optimizable representation space using a Transformer model.
- ▸ Continuous structure search enables efficient exploration of the combinatorial structure space, reducing computational cost and improving stability.
- ▸ Coefficient optimization treats symbolic coefficients as learnable parameters, allowing for accurate numerical value estimation.
Merits
Strength in Disguise
SRCO's use of continuous structure search and coefficient optimization mitigates the combinatorial explosion problem in traditional symbolic regression, leading to improved performance and scalability.
Interpretability
The framework's ability to generate human-interpretable equations makes it a valuable tool for various applications, including physics, engineering, and finance.
Demerits
Scalability Limitations
The approach's scalability remains a concern, as the size of the embedding space and the computational cost of training the Transformer model may increase exponentially with the size of the symbolic structure space.
Interpretability Concerns
The continuous embedding space may compromise the interpretability of the discovered equations, making it challenging to understand the underlying relationships between variables.
Expert Commentary
The proposed SRCO framework represents a significant advancement in the field of symbolic regression, leveraging continuous structure search and coefficient optimization to improve performance and scalability. While the approach shows promise, its scalability and interpretability require further investigation. The use of neural embeddings in SRCO is a novel application of techniques from natural language processing and machine learning, highlighting the need for continued collaboration between researchers in these fields. As the field of symbolic regression continues to evolve, SRCO's contributions will likely have a lasting impact on the development of new methods and applications.
Recommendations
- ✓ Future research should focus on addressing the scalability limitations of SRCO, including the development of more efficient optimization algorithms and the exploration of alternative representation spaces.
- ✓ Investigations into the interpretability of the discovered equations are necessary to ensure that the framework's benefits are not compromised by a lack of understanding.
Sources
Original: arXiv - cs.LG
