# MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task

arXiv: https://arxiv.org/abs/2402.18603 · HTML: https://mlsanity.com/paper/2402.18603/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 62 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 30 of 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://mlsanity.com/paper/2102.03334/) (2021)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [FLAVA: A Foundational Language And Vision Alignment Model](https://mlsanity.com/paper/2112.04482/) (2021)
- [SimVLM: Simple Visual Language Model Pretraining with Weak Supervision](https://mlsanity.com/paper/2108.10904/) (2021)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Image as a Foreign Language: BEiT Pretraining for All Vision and Vision-Language Tasks](https://mlsanity.com/paper/2208.10442/) (2022)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [PaLI-X: On Scaling up a Multilingual Vision and Language Model](https://mlsanity.com/paper/2305.18565/) (2023)
- [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)
- [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)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)

## Built on by (most cited first, 13 of 13)

- [ChatSR: Multimodal Large Language Models for Scientific Formula Discovery](https://mlsanity.com/paper/2406.05410/) (2024)
- [Generative Pre-Trained Transformer for Symbolic Regression Base In-Context Reinforcement Learning](https://mlsanity.com/paper/2404.06330/) (2024)
- [SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discovery](https://mlsanity.com/paper/2506.06176/) (2025)
- [ViSymRe: Vision Multimodal Symbolic Regression](https://mlsanity.com/paper/2412.11139/) (2024)
- [Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression](https://mlsanity.com/paper/2602.08885/) (2026)
- [DN-CL: Deep Symbolic Regression against Noise via Contrastive Learning](https://mlsanity.com/paper/2406.14844/) (2024)
- [Neuro-Symbolic Multitasking: A Unified Framework for Discovering Generalizable Solutions to PDE Families](https://mlsanity.com/paper/2602.11630/) (2026)
- [Multi-Modal Learning meets Genetic Programming: Analyzing Alignment in Latent Space Optimization](https://mlsanity.com/paper/2604.08324/) (2026)
- [FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression](https://mlsanity.com/paper/2605.12704/) (2026)
- [UniSymNet: A Unified Symbolic Network Guided by Transformer](https://mlsanity.com/paper/2505.06091/) (2025)
- [EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification](https://mlsanity.com/paper/2606.07915/) (2026)
- [ERBench: A Benchmark and Testsuite for Equation Discovery Algorithms](https://mlsanity.com/paper/2606.09276/) (2026)
- [SNIP++: Fine-Grained Symbolic-Numerical Alignment for Symbolic Regression](https://mlsanity.com/paper/2609.31965/) (2026)

## Abstract (arXiv)

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great challenge for artificial intelligence. This field is called symbolic regression (SR). Symbolic regression was originally formulated as a combinatorial optimization problem, and Genetic Programming (GP) and Reinforcement Learning algorithms were used to solve it. However, GP is sensitive to hyperparameters, and these two types of algorithms are inefficient. To solve this problem, researchers treat the mapping from data to expressions as a translation problem. And the corresponding large-scale pre-trained model is introduced. However, the data and expression skeletons do not have very clear word correspondences as the two languages do. Instead, they are more like two modalities (e.g., image and text). Therefore, in this paper, we proposed MMSR. The SR problem is solved as a pure multi-modal problem, and contrastive learning is also introduced in the training process for modal alignment to facilitate later modal feature fusion. It is worth noting that to better promote the modal feature fusion, we adopt the strategy of training contrastive learning loss and other losses at the same time, which only needs one-step training, instead of training contrastive learning loss first and then training other losses. Because our experiments prove training together can make the feature extraction module and feature fusion module wearing-in better. Experimental results show that compared with multiple large-scale pre-training baselines, MMSR achieves the most advanced results on multiple mainstream datasets including SRBench. Our code is open source at https://github.com/1716757342/MMSR