# Ornstein-Uhlenbeck Adaptation as a Mechanism for Learning in Brains and Machines

arXiv: https://arxiv.org/abs/2410.13563 · HTML: https://mlsanity.com/paper/2410.13563/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 74 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Learning and Planning in Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2006.16318/) (2020)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Constrained Parameter Inference as a Principle for Learning](https://mlsanity.com/paper/2203.13203/) (2022)
- [Efficient Deep Learning with Decorrelated Backpropagation](https://mlsanity.com/paper/2405.02385/) (2024)
- [Correlations Are Ruining Your Gradient Descent](https://mlsanity.com/paper/2407.10780/) (2024)
- [Gradient-Free Training of Recurrent Neural Networks using Random Perturbations](https://mlsanity.com/paper/2405.08967/) (2024)

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

- [Neuromorphic Intelligence](https://mlsanity.com/paper/2509.11940/) (2025)
- [Intrinsic-Noise Consolidation: A Doob-Barrier-Conditioned Diffusion Turns Analog Device Noise into a Continual-Learning Resource](https://mlsanity.com/paper/2607.06924/) (2026)
- [Noise-based reward-modulated learning](https://mlsanity.com/paper/2503.23972/) (2025)
- [A Unified Perspective on Optimization in Machine Learning and Neuroscience: From Gradient Descent to Neural Adaptation](https://mlsanity.com/paper/2510.18812/) (2025)
- [DecNefSimulator: A Modular, Interpretable Framework for Decoded Neurofeedback Simulation Using Generative Models](https://mlsanity.com/paper/2511.14555/) (2025)
- [A Noise Optimum in Rehearsal-Free Continual Learning: Isolation, Mechanism, and Scope](https://mlsanity.com/paper/2609.20162/) (2026)

## Abstract (arXiv)

Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and complex information flow makes its implementation in biological and neuromorphic systems challenging. This has motivated the exploration of alternative learning mechanisms that can operate locally and do not rely on exact gradients. In this work, we introduce a novel approach that leverages noise in the parameters of the system and global reinforcement signals. Using an Ornstein-Uhlenbeck process with adaptive dynamics, our method balances exploration and exploitation during learning, driven by deviations from error predictions, akin to reward prediction error. Operating in continuous time, Orstein-Uhlenbeck adaptation (OUA) is proposed as a general mechanism for learning dynamic, time-evolving environments. We validate our approach across diverse tasks, including supervised learning and reinforcement learning in feedforward and recurrent systems. Additionally, we demonstrate that it can perform meta-learning, adjusting hyper-parameters autonomously. Our results indicate that OUA provides a viable alternative to traditional gradient-based methods, with potential applications in neuromorphic computing. It also hints at a possible mechanism for noise-driven learning in the brain, where stochastic neurotransmitter release may guide synaptic adjustments.