# NCoder -- A Quantum Field Theory approach to encoding data

arXiv: https://arxiv.org/abs/2402.00944 · HTML: https://mlsanity.com/paper/2402.00944/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Building Quantum Field Theories Out of Neurons](https://mlsanity.com/paper/2112.04527/) (2021)
- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Bayesian Renormalization](https://mlsanity.com/paper/2305.10491/) (2023)
- [Decomposing neural networks as mappings of correlation functions](https://mlsanity.com/paper/2202.04925/) (2022)
- [The Inverse of Exact Renormalization Group Flows as Statistical Inference](https://mlsanity.com/paper/2212.11379/) (2022)
- [Renormalization in the neural network-quantum field theory correspondence](https://mlsanity.com/paper/2212.11811/) (2022)
- [Learning from Topology: Cosmological Parameter Estimation from the Large-scale Structure](https://mlsanity.com/paper/2308.02636/) (2023)
- [Far from Asymptopia](https://mlsanity.com/paper/2205.03343/) (2022)

## Built on by (most cited first, 8 of 8)

- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [Wilsonian Renormalization of Neural Network Gaussian Processes](https://mlsanity.com/paper/2405.06008/) (2024)
- [Fermions and Supersymmetry in Neural Network Field Theories](https://mlsanity.com/paper/2511.16741/) (2025)
- [Towards Worst-Case Guarantees with Scale-Aware Interpretability](https://mlsanity.com/paper/2602.05184/) (2026)
- [Grokking vs. Learning: Same Features, Different Encodings](https://mlsanity.com/paper/2502.01739/) (2025)
- [Quantum Topological Graph Neural Networks for Detecting Complex Fraud Patterns](https://mlsanity.com/paper/2512.03696/) (2025)
- [Lecture Notes on Statistical Physics and Neural Networks](https://mlsanity.com/paper/2605.06394/) (2026)
- [Optimal Pruning for Neural Architectures using Fisher Information Distances](https://mlsanity.com/paper/2609.16129/) (2026)

## Abstract (arXiv)

In this paper we present a novel approach to interpretable AI inspired by Quantum Field Theory (QFT) which we call the NCoder. The NCoder is a modified autoencoder neural network whose latent layer is prescribed to be a subset of n-point correlation functions. Regarding images as draws from a lattice field theory, this architecture mimics the task of perturbatively constructing the effective action of the theory order by order in an expansion using Feynman diagrams. Alternatively, the NCoder may be regarded as simulating the procedure of statistical inference whereby high dimensional data is first summarized in terms of several lower dimensional summary statistics (here the n-point correlation functions), and subsequent out-of-sample data is generated by inferring the data generating distribution from these statistics. In this way the NCoder suggests a fascinating correspondence between perturbative renormalizability and the sufficiency of models. We demonstrate the efficacy of the NCoder by applying it to the generation of MNIST images, and find that generated images can be correctly classified using only information from the first three n-point functions of the image distribution.