# Formula-Supervised Visual-Geometric Pre-training

arXiv: https://arxiv.org/abs/2409.13535 · HTML: https://mlsanity.com/paper/2409.13535/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 30 of 33)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [Exploring Plain Vision Transformer Backbones for Object Detection](https://mlsanity.com/paper/2203.16527/) (2022)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022)
- [An End-to-End Transformer Model for 3D Object Detection](https://mlsanity.com/paper/2109.08141/) (2021)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [Masked Discrimination for Self-Supervised Learning on Point Clouds](https://mlsanity.com/paper/2203.11183/) (2022)
- [Pre-training without Natural Images](https://mlsanity.com/paper/2101.08515/) (2021)
- [Virtual Multi-view Fusion for 3D Semantic Segmentation](https://mlsanity.com/paper/2007.13138/) (2020)
- [P2P: Tuning Pre-trained Image Models for Point Cloud Analysis with Point-to-Pixel Prompting](https://mlsanity.com/paper/2208.02812/) (2022)
- [Pri3D: Can 3D Priors Help 2D Representation Learning?](https://mlsanity.com/paper/2104.11225/) (2021)
- [3D-to-2D Distillation for Indoor Scene Parsing](https://mlsanity.com/paper/2104.02243/) (2021)
- [Learning Multi-View Aggregation In the Wild for Large-Scale 3D Semantic Segmentation](https://mlsanity.com/paper/2204.07548/) (2022)
- [ODIN: A Single Model for 2D and 3D Segmentation](https://mlsanity.com/paper/2401.02416/) (2024)
- [Pre-training Vision Transformers with Formula-driven Supervised Learning](https://mlsanity.com/paper/2206.09132/) (2022)
- [Visual Atoms: Pre-training Vision Transformers with Sinusoidal Waves](https://mlsanity.com/paper/2303.01112/) (2023)
- [Invariant Training 2D-3D Joint Hard Samples for Few-Shot Point Cloud Recognition](https://mlsanity.com/paper/2308.09694/) (2023)

## Built on by (most cited first, 3 of 3)

- [Pre-training with 3D Synthetic Data: Learning 3D Point Cloud Instance Segmentation from 3D Synthetic Scenes](https://mlsanity.com/paper/2503.24229/) (2025)
- [Industrial Synthetic Segment Pre-training](https://mlsanity.com/paper/2505.13099/) (2025)
- [IDeaL: Data-Free Multi-Teacher Distillation via Improved Dead Leaves](https://mlsanity.com/paper/2608.24759/) (2026)

## Abstract (arXiv)

Throughout the history of computer vision, while research has explored the integration of images (visual) and point clouds (geometric), many advancements in image and 3D object recognition have tended to process these modalities separately. We aim to bridge this divide by integrating images and point clouds on a unified transformer model. This approach integrates the modality-specific properties of images and point clouds and achieves fundamental downstream tasks in image and 3D object recognition on a unified transformer model by learning visual-geometric representations. In this work, we introduce Formula-Supervised Visual-Geometric Pre-training (FSVGP), a novel synthetic pre-training method that automatically generates aligned synthetic images and point clouds from mathematical formulas. Through cross-modality supervision, we enable supervised pre-training between visual and geometric modalities. FSVGP also reduces reliance on real data collection, cross-modality alignment, and human annotation. Our experimental results show that FSVGP pre-trains more effectively than VisualAtom and PC-FractalDB across six tasks: image and 3D object classification, detection, and segmentation. These achievements demonstrate FSVGP's superior generalization in image and 3D object recognition and underscore the potential of synthetic pre-training in visual-geometric representation learning. Our project website is available at https://ryosuke-yamada.github.io/fdsl-fsvgp/.