# Bootstrapping OTS-Funcimg Pre-training Model (Botfip) -- A Comprehensive Symbolic Regression Framework

arXiv: https://arxiv.org/abs/2401.09748 · HTML: https://mlsanity.com/paper/2401.09748/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [MaPLe: Multi-modal Prompt Learning](https://mlsanity.com/paper/2210.03117/) (2022)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [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)
- [Multimodal Prompting with Missing Modalities for Visual Recognition](https://mlsanity.com/paper/2303.03369/) (2023)
- [Causal Attention for Vision-Language Tasks](https://mlsanity.com/paper/2103.03493/) (2021)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Neural Symbolic Model for Space Physics](https://mlsanity.com/paper/2503.07994/) (2025)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)

## Abstract (arXiv)

In the field of scientific computing, many problem-solving approaches tend to focus only on the process and final outcome, even in AI for science, there is a lack of deep multimodal information mining behind the data, missing a multimodal framework akin to that in the image-text domain. In this paper, we take Symbolic Regression(SR) as our focal point and, drawing inspiration from the BLIP model in the image-text domain, propose a scientific computing multimodal framework based on Function Images (Funcimg) and Operation Tree Sequence (OTS), named Bootstrapping OTS-Funcimg Pre-training Model (Botfip). In SR experiments, we validate the advantages of Botfip in low-complexity SR problems, showcasing its potential. As a MED framework, Botfip holds promise for future applications in a broader range of scientific computing problems.