# ViSymRe: Vision Multimodal Symbolic Regression

arXiv: https://arxiv.org/abs/2412.11139 · HTML: https://mlsanity.com/paper/2412.11139/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 80 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Multimodal Learning with Transformers: A Survey](https://mlsanity.com/paper/2206.06488/) (2022)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Deep multi-scale video prediction beyond mean square error](https://mlsanity.com/paper/1511.05440/) (2015)
- [MM-LLMs: Recent Advances in MultiModal Large Language Models](https://mlsanity.com/paper/2401.13601/) (2024)
- [Multimodal Deep Learning](https://mlsanity.com/paper/2301.04856/) (2023)
- [Multimodal Compact Bilinear Pooling for Visual Question Answering and Visual Grounding](https://mlsanity.com/paper/1606.01847/) (2016)
- [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)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Resnet in Resnet: Generalizing Residual Architectures](https://mlsanity.com/paper/1603.08029/) (2016)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [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)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Deep Audio-Visual Learning: A Survey](https://mlsanity.com/paper/2001.04758/) (2020)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)

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

- [Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations](https://mlsanity.com/paper/2604.08863/) (2026)
- [EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification](https://mlsanity.com/paper/2606.07915/) (2026)

## Abstract (arXiv)

Extracting interpretable equations from observational datasets to describe complex natural phenomena is one of the core goals of artificial intelligence. This field is known as symbolic regression (SR). In recent years, Transformer-based paradigms have become a new trend in SR, addressing the well-known problem of inefficient search. However, the modal heterogeneity between datasets and equations often hinders the convergence and generalization of these models. In this paper, we propose ViSymRe, a Vision Symbolic Regression framework, to explore the positive role of visual modality in enhancing the performance of Transformer-based SR paradigms. To overcome the challenge where the visual SR model is untrainable in high-dimensional scenarios, we present Multi-View Random Slicing (MVRS). By projecting multivariate equations into 2-D space using random affine transformations, MVRS avoids common defects in high-dimensional visualization, such as variable degradation, non-linear interaction missing, and exponentially increasing sampling complexity, enabling ViSymRe to be trained with low computational costs. To support dataset-only deployment of ViSymRe, we design a dual-vision pipeline architecture based on generative techniques, which reconstructs visual features directly from the datasets via an auxiliary Visual Decoder and automatically suppresses the attention weights of reconstruction noise through a proposed Biased Cross-Attention feature fusion module, ensuring that subsequent processes are not affected by noisy modalities. Ablation studies demonstrate the positive contribution of visual modality to improving model convergence level and enhancing various SR metrics. Furthermore, evaluation results on mainstream benchmarks indicate that ViSymRe achieves competitive performance compared to baselines, particularly in low-complexity and rapid-inference scenarios.