# Fermions and Supersymmetry in Neural Network Field Theories

arXiv: https://arxiv.org/abs/2511.16741 · HTML: https://mlsanity.com/paper/2511.16741/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 28 of 28)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Infinite attention: NNGP and NTK for deep attention networks](https://mlsanity.com/paper/2006.10540/) (2020)
- [Non-Gaussian processes and neural networks at finite widths](https://mlsanity.com/paper/1910.00019/) (2019)
- [Asymptotics of Wide Networks from Feynman Diagrams](https://mlsanity.com/paper/1909.11304/) (2019)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Predicting the outputs of finite deep neural networks trained with noisy gradients](https://mlsanity.com/paper/2004.01190/) (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)
- [Nonperturbative renormalization for the neural network-QFT correspondence](https://mlsanity.com/paper/2108.01403/) (2021)
- [Finite size corrections for neural network Gaussian processes](https://mlsanity.com/paper/1908.10030/) (2019)
- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Effective Theory of Transformers at Initialization](https://mlsanity.com/paper/2304.02034/) (2023)
- [A Correspondence Between Random Neural Networks and Statistical Field Theory](https://mlsanity.com/paper/1710.06570/) (2017)
- [Towards quantifying information flows: relative entropy in deep neural networks and the renormalization group](https://mlsanity.com/paper/2107.06898/) (2021)
- [Structures of Neural Network Effective Theories](https://mlsanity.com/paper/2305.02334/) (2023)
- [The Inverse of Exact Renormalization Group Flows as Statistical Inference](https://mlsanity.com/paper/2212.11379/) (2022)
- [Conformal Fields from Neural Networks](https://mlsanity.com/paper/2409.12222/) (2024)
- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [Applications of Statistical Field Theory in Deep Learning](https://mlsanity.com/paper/2502.18553/) (2025)
- [NCoder -- A Quantum Field Theory approach to encoding data](https://mlsanity.com/paper/2402.00944/) (2024)
- [Wilsonian Renormalization of Neural Network Gaussian Processes](https://mlsanity.com/paper/2405.06008/) (2024)
- [Quantum Mechanics and Neural Networks](https://mlsanity.com/paper/2504.05462/) (2025)
- [TASI Lectures on Physics for Machine Learning](https://mlsanity.com/paper/2408.00082/) (2024)

## Built on by (most cited first, 6 of 6)

- [Conformal Defects in Neural Network Field Theories](https://mlsanity.com/paper/2512.07946/) (2025)
- [Virasoro Symmetry in Neural Network Field Theories](https://mlsanity.com/paper/2512.24420/) (2025)
- [Topological Effects in Neural Network Field Theory](https://mlsanity.com/paper/2604.02313/) (2026)
- [Spinning Conformal Correlators from Neural Networks](https://mlsanity.com/paper/2608.15001/) (2026)
- [Deep neural networks as lattice gauge theories](https://mlsanity.com/paper/2608.19331/) (2026)
- [Machine learning for the LHC physics program: a 2025-2026 stocktake](https://mlsanity.com/paper/2609.32874/) (2026)

## Abstract (arXiv)

We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac spinor at infinite width and a four fermion interaction at finite width. Yukawa couplings are introduced by breaking the statistical independence of the output weights for the fermionic and bosonic fields. A large class of interacting supersymmetric quantum mechanics and field theory models are introduced by super-affine transformations on the input that realize a superspace formalism.