# Polynomial Implicit Neural Representations For Large Diverse Datasets

arXiv: https://arxiv.org/abs/2303.11424 · HTML: https://mlsanity.com/paper/2303.11424/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 64 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 30 of 48)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [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)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)

## Built on by (most cited first, 18 of 18)

- [FINER: Flexible spectral-bias tuning in Implicit NEural Representation by Variable-periodic Activation Functions](https://mlsanity.com/paper/2312.02434/) (2023)
- [Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers](https://mlsanity.com/paper/2405.17527/) (2024)
- [∞-Diff: Infinite Resolution Diffusion with Subsampled Mollified States](https://mlsanity.com/paper/2303.18242/) (2023)
- [FINER++: Building a Family of Variable-periodic Functions for Activating Implicit Neural Representation](https://mlsanity.com/paper/2407.19434/) (2024)
- [MicroDiffusion: Implicit Representation-Guided Diffusion for 3D Reconstruction from Limited 2D Microscopy Projections](https://mlsanity.com/paper/2403.10815/) (2024)
- [Deep Geometric Moments Promote Shape Consistency in Text-to-3D Generation](https://mlsanity.com/paper/2408.05938/) (2024)
- [HOIN: High-Order Implicit Neural Representations](https://mlsanity.com/paper/2404.14674/) (2024)
- [INRetouch: Context Aware Implicit Neural Representation for Photography Retouching](https://mlsanity.com/paper/2412.03848/) (2024)
- [PNeRV: A Polynomial Neural Representation for Videos](https://mlsanity.com/paper/2406.19299/) (2024)
- [Towards the Spectral bias Alleviation by Normalizations in Coordinate Networks](https://mlsanity.com/paper/2407.17834/) (2024)
- [INRFlow: Flow Matching for INRs in Ambient Space](https://mlsanity.com/paper/2412.03791/) (2024)
- [I-INR: Iterative Implicit Neural Representations](https://mlsanity.com/paper/2504.17364/) (2025)
- [Generating visual explanations from deep networks using implicit neural representations](https://mlsanity.com/paper/2501.11784/) (2025)
- [Physics-Informed Chebyshev Polynomial Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2602.01737/) (2026)
- [Talking Head(?) Anime from a Single Image 4: Improved Model and Its Distillation](https://mlsanity.com/paper/2311.17409/) (2023)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations](https://mlsanity.com/paper/2604.02846/) (2026)
- [Texture-preserving implicit neural representation for Cone beam CT truncated reconstruction](https://mlsanity.com/paper/2606.06039/) (2026)

## Abstract (arXiv)

Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding, which accounts for high-frequency information in data. However, the finite encoding size restricts the model's representational power. Higher representational power is needed to go from representing a single given image to representing large and diverse datasets. Our approach addresses this gap by representing an image with a polynomial function and eliminates the need for positional encodings. Therefore, to achieve a progressively higher degree of polynomial representation, we use element-wise multiplications between features and affine-transformed coordinate locations after every ReLU layer. The proposed method is evaluated qualitatively and quantitatively on large datasets like ImageNet. The proposed Poly-INR model performs comparably to state-of-the-art generative models without any convolution, normalization, or self-attention layers, and with far fewer trainable parameters. With much fewer training parameters and higher representative power, our approach paves the way for broader adoption of INR models for generative modeling tasks in complex domains. The code is available at urlhttps://github.com/Rajhans0/PolyINR