# NAISR: A 3D Neural Additive Model for Interpretable Shape Representation

arXiv: https://arxiv.org/abs/2303.09234 · HTML: https://mlsanity.com/paper/2303.09234/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 101 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 30 of 60)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (2019)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [NASA: Neural Articulated Shape Approximation](https://mlsanity.com/paper/1912.03207/) (2019)
- [NeuMesh: Learning Disentangled Neural Mesh-based Implicit Field for Geometry and Texture Editing](https://mlsanity.com/paper/2207.11911/) (2022)
- [Disentangled Representation Learning for Non-Parallel Text Style Transfer](https://mlsanity.com/paper/1808.04339/) (2018)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [DeVRF: Fast Deformable Voxel Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2205.15723/) (2022)
- [GAN-Control: Explicitly Controllable GANs](https://mlsanity.com/paper/2101.02477/) (2021)
- [NPMs: Neural Parametric Models for 3D Deformable Shapes](https://mlsanity.com/paper/2104.00702/) (2021)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [Causal Interpretability for Machine Learning -- Problems, Methods and Evaluation](https://mlsanity.com/paper/2003.03934/) (2020)

## Built on by (most cited first, 7 of 7)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [NeuralOCT: Airway OCT Analysis via Neural Fields](https://mlsanity.com/paper/2403.10622/) (2024)
- [LucidAtlas: Learning Uncertainty-Aware, Covariate-Disentangled, Individualized Atlas Representations](https://mlsanity.com/paper/2502.08445/) (2025)
- [PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling](https://mlsanity.com/paper/2602.11467/) (2026)

## Abstract (arXiv)

Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. For scientific shape discovery, we propose a 3D Neural Additive Model for Interpretable Shape Representation (textttNAISR) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. textttNAISR is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate textttNAISR with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets: 1) textitStarman, a simulated 2D shape dataset; 2) the ADNI hippocampus 3D shape dataset; and 3) a pediatric airway 3D shape dataset. Our experiments demonstrate that textitStarman achieves excellent shape reconstruction performance while retaining interpretability. Our code is available at hrefhttps://github.com/uncbiag/NAISRhttps://github.com/uncbiag/NAISR.