# PINs: Progressive Implicit Networks for Multi-Scale Neural Representations

arXiv: https://arxiv.org/abs/2202.04713 · HTML: https://mlsanity.com/paper/2202.04713/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 9 Feb 2022.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural Scene Graphs for Dynamic Scenes](https://mlsanity.com/paper/2011.10379/) (2020)
- [CodeNeRF: Disentangled Neural Radiance Fields for Object Categories](https://mlsanity.com/paper/2109.01750/) (2021)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [Learning to Infer Implicit Surfaces without 3D Supervision](https://mlsanity.com/paper/1911.00767/) (2019)
- [DI-Fusion: Online Implicit 3D Reconstruction with Deep Priors](https://mlsanity.com/paper/2012.05551/) (2020)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)

## Built on by (most cited first, 19 of 19)

- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Disorder-invariant Implicit Neural Representation](https://mlsanity.com/paper/2304.00837/) (2023)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [Robust Camera Pose Refinement for Multi-Resolution Hash Encoding](https://mlsanity.com/paper/2302.01571/) (2023)
- [Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting](https://mlsanity.com/paper/2410.23159/) (2024)
- [Streamable Neural Fields](https://mlsanity.com/paper/2207.09663/) (2022)
- [Learning Large-scale Neural Fields via Context Pruned Meta-Learning](https://mlsanity.com/paper/2302.00617/) (2023)
- [How to Train Neural Field Representations: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2312.10531/) (2023)
- [Attention Beats Linear for Fast Implicit Neural Representation Generation](https://mlsanity.com/paper/2407.15355/) (2024)
- [Progressive Multi-scale Light Field Networks](https://mlsanity.com/paper/2208.06710/) (2022)
- [PIP: Positional-encoding Image Prior](https://mlsanity.com/paper/2211.14298/) (2022)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [I-INR: Iterative Implicit Neural Representations](https://mlsanity.com/paper/2504.17364/) (2025)
- [Continuous Levels of Detail for Light Field Networks](https://mlsanity.com/paper/2309.11591/) (2023)
- [Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features](https://mlsanity.com/paper/2603.01028/) (2026)
- [T-MLP: Tailed Multi-Layer Perceptron for Level-of-Detail Signal Representation](https://mlsanity.com/paper/2509.00066/) (2025)
- [SAND: Spatially Adaptive Network Depth for Fast Sampling of Neural Implicit Surfaces](https://mlsanity.com/paper/2604.25936/) (2026)
- [Texture-preserving implicit neural representation for Cone beam CT truncated reconstruction](https://mlsanity.com/paper/2606.06039/) (2026)
- [CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting](https://mlsanity.com/paper/2609.18554/) (2026)

## Abstract (arXiv)

Multi-layer perceptrons (MLP) have proven to be effective scene encoders when combined with higher-dimensional projections of the input, commonly referred to as textitpositional encoding. However, scenes with a wide frequency spectrum remain a challenge: choosing high frequencies for positional encoding introduces noise in low structure areas, while low frequencies result in poor fitting of detailed regions. To address this, we propose a progressive positional encoding, exposing a hierarchical MLP structure to incremental sets of frequency encodings. Our model accurately reconstructs scenes with wide frequency bands and learns a scene representation at progressive level of detail textitwithout explicit per-level supervision. The architecture is modular: each level encodes a continuous implicit representation that can be leveraged separately for its respective resolution, meaning a smaller network for coarser reconstructions. Experiments on several 2D and 3D datasets show improvements in reconstruction accuracy, representational capacity and training speed compared to baselines.