# NeuSOGA3D: A Neuro-Symbolic Framework for Explainable 3D Geometric Reconstruction

arXiv: https://arxiv.org/abs/2609.20323 · HTML: https://mlsanity.com/paper/2609.20323/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [CAD-Llama: Leveraging Large Language Models for Computer-Aided Design Parametric 3D Model Generation](https://mlsanity.com/paper/2505.04481/) (2025)
- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [NS3D: Neuro-Symbolic Grounding of 3D Objects and Relations](https://mlsanity.com/paper/2303.13483/) (2023)
- [Lexicon3D: Probing Visual Foundation Models for Complex 3D Scene Understanding](https://mlsanity.com/paper/2409.03757/) (2024)
- [Text-to-CadQuery: A New Paradigm for CAD Generation with Scalable Large Model Capabilities](https://mlsanity.com/paper/2505.06507/) (2025)
- [Img2CAD: Conditioned 3D CAD Model Generation from Single Image with Structured Visual Geometry](https://mlsanity.com/paper/2410.03417/) (2024)
- [CADOps-Net: Jointly Learning CAD Operation Types and Steps from Boundary-Representations](https://mlsanity.com/paper/2208.10555/) (2022)
- [OpenECAD: An Efficient Visual Language Model for Editable 3D-CAD Design](https://mlsanity.com/paper/2406.09913/) (2024)
- [SceneCOT: Eliciting Grounded Chain-of-Thought Reasoning in 3D Scenes](https://mlsanity.com/paper/2510.16714/) (2025)
- [Distilling Neuro-Symbolic Programs into 3D Multi-modal LLMs](https://mlsanity.com/paper/2606.01215/) (2026)
- [OmniCAD: A Large-Scale Benchmark for 3D Spatial Reasoning in Robotics Assemblies](https://mlsanity.com/paper/2608.22637/) (2026)
- [Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations](https://mlsanity.com/paper/2609.01408/) (2026)

## Abstract (arXiv)

Three-dimensional reconstruction from unorganized point clouds remains a challenging problem in computer vision, geometric modeling, and computer-aided design. While neural implicit methods achieve impressive reconstruction accuracy, geometry is typically encoded in latent representations that limit interpretability and reuse within engineering workflows. We present NeuSOGA3D (Neuro-Symbolic Observation-Guided Geometric Abstraction in 3D), a hybrid framework that combines learned perceptual priors inherited from NeuSOGA with explicit symbolic geometric reasoning. The method projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations from the resulting observations, and fuses them through shape-preserving constructive solid geometry operations to generate a coarse visual hull. Additional geometric detail is recovered through cross-sectional decomposition and volumetric reconstruction using Partial Shape-Preserving Splines. Unlike conventional neural implicit approaches, NeuSOGA3D progressively transforms observations into explicit symbolic entities, including control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments on all forty categories of the ModelNet40 benchmark demonstrate the ability of the framework to recover structurally meaningful and CAD-compatible geometric representations from diverse point-cloud observations. The results highlight the potential of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.