# Gradient-Free Training of Recurrent Neural Networks using Random Perturbations

arXiv: https://arxiv.org/abs/2405.08967 · HTML: https://mlsanity.com/paper/2405.08967/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 67 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Decorrelated Batch Normalization](https://mlsanity.com/paper/1804.08450/) (2018)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Gradients without Backpropagation](https://mlsanity.com/paper/2202.08587/) (2022)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [Natural Neural Networks](https://mlsanity.com/paper/1507.00210/) (2015)
- [Brain-Inspired Learning on Neuromorphic Substrates](https://mlsanity.com/paper/2010.11931/) (2020)
- [Fully neuromorphic vision and control for autonomous drone flight](https://mlsanity.com/paper/2303.08778/) (2023)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [GAIT-prop: A biologically plausible learning rule derived from backpropagation of error](https://mlsanity.com/paper/2006.06438/) (2020)
- [Deriving Differential Target Propagation from Iterating Approximate Inverses](https://mlsanity.com/paper/2007.15139/) (2020)
- [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)

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

- [Ornstein-Uhlenbeck Adaptation as a Mechanism for Learning in Brains and Machines](https://mlsanity.com/paper/2410.13563/) (2024)
- [Scaling Recurrent Neural Networks to a Billion Parameters with Zero-Order Optimization](https://mlsanity.com/paper/2505.17852/) (2025)
- [Position: A Dynamical Systems Perspective is Needed to Advance Time Series Modeling](https://mlsanity.com/paper/2602.16864/) (2026)
- [Noise-based Local Learning using Stochastic Magnetic Tunnel Junctions](https://mlsanity.com/paper/2412.12783/) (2024)
- [Noise-based reward-modulated learning](https://mlsanity.com/paper/2503.23972/) (2025)
- [Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach](https://mlsanity.com/paper/2603.21568/) (2026)

## Abstract (arXiv)

Recurrent neural networks (RNNs) hold immense potential for computations due to their Turing completeness and sequential processing capabilities, yet existing methods for their training encounter efficiency challenges. Backpropagation through time (BPTT), the prevailing method, extends the backpropagation (BP) algorithm by unrolling the RNN over time. However, this approach suffers from significant drawbacks, including the need to interleave forward and backward phases and store exact gradient information. Furthermore, BPTT has been shown to struggle to propagate gradient information for long sequences, leading to vanishing gradients. An alternative strategy to using gradient-based methods like BPTT involves stochastically approximating gradients through perturbation-based methods. This learning approach is exceptionally simple, necessitating only forward passes in the network and a global reinforcement signal as feedback. Despite its simplicity, the random nature of its updates typically leads to inefficient optimization, limiting its effectiveness in training neural networks. In this study, we present a new approach to perturbation-based learning in RNNs whose performance is competitive with BPTT, while maintaining the inherent advantages over gradient-based learning. To this end, we extend the recently introduced activity-based node perturbation (ANP) method to operate in the time domain, leading to more efficient learning and generalization. We subsequently conduct a range of experiments to validate our approach. Our results show similar performance, convergence time and scalability compared to BPTT, strongly outperforming standard node and weight perturbation methods. These findings suggest that perturbation-based learning methods offer a versatile alternative to gradient-based methods for training RNNs which can be ideally suited for neuromorphic computing applications