# Training a Hopfield Variational Autoencoder with Equilibrium Propagation

arXiv: https://arxiv.org/abs/2311.15047 · HTML: https://mlsanity.com/paper/2311.15047/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 25 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Hierarchical Associative Memory](https://mlsanity.com/paper/2107.06446/) (2021)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [Equivalence of Equilibrium Propagation and Recurrent Backpropagation](https://mlsanity.com/paper/1711.08416/) (2017)
- [Early Inference in Energy-Based Models Approximates Back-Propagation](https://mlsanity.com/paper/1510.02777/) (2015)

## Built on by (most cited first, 1 of 1)

- [PotentialEP: Backprop-Free Training of CIFAR-Scale Generative Models via Equilibrium Propagation](https://mlsanity.com/paper/2610.14409/) (2026)

## Abstract (arXiv)

On dedicated analog hardware, equilibrium propagation is an energy-efficient alternative to backpropagation. In spite of its theoretical guarantees, its application in the AI domain remains limited to the discriminative setting. Meanwhile, despite its high computational demands, generative AI is on the rise. In this paper, we demonstrate the application of Equilibrium Propagation in training a variational autoencoder (VAE) for generative modeling. Leveraging the symmetric nature of Hopfield networks, we propose using a single model to serve as both the encoder and decoder which could effectively halve the required chip size for VAE implementations, paving the way for more efficient analog hardware configurations.