# Spatial Functa: Scaling Functa to ImageNet Classification and Generation

arXiv: https://arxiv.org/abs/2302.03130 · HTML: https://mlsanity.com/paper/2302.03130/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 40)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [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)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)

## Built on by (most cited first, 30 of 57)

- [Graph Metanetworks for Processing Diverse Neural Architectures](https://mlsanity.com/paper/2312.04501/) (2023)
- [Neural Functional Transformers](https://mlsanity.com/paper/2305.13546/) (2023)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Online Adaptation of Language Models with a Memory of Amortized Contexts](https://mlsanity.com/paper/2403.04317/) (2024)
- [Scale Equivariant Graph Metanetworks](https://mlsanity.com/paper/2406.10685/) (2024)
- [Grounding Continuous Representations in Geometry: Equivariant Neural Fields](https://mlsanity.com/paper/2406.05753/) (2024)
- [Space-Time Continuous PDE Forecasting using Equivariant Neural Fields](https://mlsanity.com/paper/2406.06660/) (2024)
- [Monomial Matrix Group Equivariant Neural Functional Networks](https://mlsanity.com/paper/2409.11697/) (2024)
- [Locality-Aware Generalizable Implicit Neural Representation](https://mlsanity.com/paper/2310.05624/) (2023)
- [CINA: Conditional Implicit Neural Atlas for Spatio-Temporal Representation of Fetal Brains](https://mlsanity.com/paper/2403.08550/) (2024)
- [How to Train Neural Field Representations: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2312.10531/) (2023)
- [Implicit-Zoo: A Large-Scale Dataset of Neural Implicit Functions for 2D Images and 3D Scenes](https://mlsanity.com/paper/2406.17438/) (2024)
- [Manifold Diffusion Fields](https://mlsanity.com/paper/2305.15586/) (2023)
- [Fit Pixels, Get Labels: Meta-learned Implicit Networks for Image Segmentation](https://mlsanity.com/paper/2510.04021/) (2025)
- [Generative Neural Fields by Mixtures of Neural Implicit Functions](https://mlsanity.com/paper/2310.19464/) (2023)
- [ASMR: Activation-sharing Multi-resolution Coordinate Networks For Efficient Inference](https://mlsanity.com/paper/2405.12398/) (2024)
- [Latent-INR: A Flexible Framework for Implicit Representations of Videos with Discriminative Semantics](https://mlsanity.com/paper/2408.02672/) (2024)
- [MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fields](https://mlsanity.com/paper/2502.14401/) (2025)
- [End-to-End Implicit Neural Representations for Classification](https://mlsanity.com/paper/2503.18123/) (2025)
- [Attention Beats Linear for Fast Implicit Neural Representation Generation](https://mlsanity.com/paper/2407.15355/) (2024)
- [Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees](https://mlsanity.com/paper/2410.18153/) (2024)
- [GaussianVision: Vision-Language Alignment from Compressed Image Representations using 2D Gaussian Splatting](https://mlsanity.com/paper/2509.22615/) (2025)
- [Improved Positional Encoding for Implicit Neural Representation based Compact Data Representation](https://mlsanity.com/paper/2311.06059/) (2023)
- [SCENT: Robust Spatiotemporal Learning for Continuous Scientific Data via Scalable Conditioned Neural Fields](https://mlsanity.com/paper/2504.12262/) (2025)
- [PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling](https://mlsanity.com/paper/2506.12790/) (2025)
- [Picasso: Holistic Scene Reconstruction with Physics-Constrained Sampling](https://mlsanity.com/paper/2602.08058/) (2026)
- [ARC: Anchored Representation Clouds for High-Resolution INR Classification](https://mlsanity.com/paper/2503.15156/) (2025)
- [CINeMA: Conditional Implicit Neural Multi-Modal Atlas for a Spatio-Temporal Representation of the Perinatal Brain](https://mlsanity.com/paper/2506.09668/) (2025)
- [Unified all-atom molecule generation with neural fields](https://mlsanity.com/paper/2511.15906/) (2025)
- [Neural Modulation Fields for Conditional Cone Beam Neural Tomography](https://mlsanity.com/paper/2307.08351/) (2023)

## Abstract (arXiv)

Neural fields, also known as implicit neural representations, have emerged as a powerful means to represent complex signals of various modalities. Based on this Dupont et al. (2022) introduce a framework that views neural fields as data, termed *functa*, and proposes to do deep learning directly on this dataset of neural fields. In this work, we show that the proposed framework faces limitations when scaling up to even moderately complex datasets such as CIFAR-10. We then propose *spatial functa*, which overcome these limitations by using spatially arranged latent representations of neural fields, thereby allowing us to scale up the approach to ImageNet-1k at 256x256 resolution. We demonstrate competitive performance to Vision Transformers (Steiner et al., 2022) on classification and Latent Diffusion (Rombach et al., 2022) on image generation respectively.