# Neural Langevin Machine: a local asymmetric learning rule can be creative

arXiv: https://arxiv.org/abs/2506.23546 · HTML: https://mlsanity.com/paper/2506.23546/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Introduction to Latent Variable Energy-Based Models: A Path Towards Autonomous Machine Intelligence](https://mlsanity.com/paper/2306.02572/) (2023)
- [Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machines](https://mlsanity.com/paper/2105.13889/) (2021)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings](https://mlsanity.com/paper/2305.08459/) (2023)
- [Eight challenges in developing theory of intelligence](https://mlsanity.com/paper/2306.11232/) (2023)
- [Nonequilbrium physics of generative diffusion models](https://mlsanity.com/paper/2405.11932/) (2024)
- [Generative thermodynamic computing](https://mlsanity.com/paper/2506.15121/) (2025)
- [Neural Sampling in Hierarchical Exponential-family Energy-based Models](https://mlsanity.com/paper/2310.08431/) (2023)
- [Statistical physics of learning in high-dimensional chaotic systems](https://mlsanity.com/paper/2306.01477/) (2023)
- [Meta predictive learning model of languages in neural circuits](https://mlsanity.com/paper/2309.04106/) (2023)
- [An optimization-based equilibrium measure describes non-equilibrium steady state dynamics: application to edge of chaos](https://mlsanity.com/paper/2401.10009/) (2024)
- [Generative modeling through internal high-dimensional chaotic activity](https://mlsanity.com/paper/2405.10822/) (2024)
- [How high dimensional neural dynamics are confined in phase space](https://mlsanity.com/paper/2410.19348/) (2024)
- [Synaptic plasticity alters the nature of chaos transition in neural networks](https://mlsanity.com/paper/2412.15592/) (2024)
- [Freezing chaos without synaptic plasticity](https://mlsanity.com/paper/2503.08069/) (2025)

## Built on by (most cited first, 3 of 3)

- [Generative Models on Analog Hardware with Dynamics](https://mlsanity.com/paper/2606.27294/) (2026)
- [Dynamical Learning in Deep Asymmetric Recurrent Neural Networks](https://mlsanity.com/paper/2509.05041/) (2025)
- [Online local learning for generative thermodynamic computing](https://mlsanity.com/paper/2609.15439/) (2026)

## Abstract (arXiv)

Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points are captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that relax to those fixed points for generative learning of a real dataset. We call this type of generative model a neural Langevin machine, which derives an asymmetric and firing-rate-speed-adjusted learning rule requiring only local neural signals, thereby bearing biological relevance in terms of local predictive learning. An out-of-equilibrium regime of the generative process is revealed, together with a memorization-to-generalization transition with increasing training data size. The neuro-inspired machine can also realize a continuous exploration of the phase space for different kinds of generative images and can denoise a corrupted image as well.