# Scaling of hardware-compatible perturbative training algorithms

arXiv: https://arxiv.org/abs/2501.15403 · HTML: https://mlsanity.com/paper/2501.15403/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Builds on (most cited first, 18 of 18)

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- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Hardware-aware training for large-scale and diverse deep learning inference workloads using in-memory computing-based accelerators](https://mlsanity.com/paper/2302.08469/) (2023)
- [Brain-inspired learning in artificial neural networks: a review](https://mlsanity.com/paper/2305.11252/) (2023)
- [Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial](https://mlsanity.com/paper/2311.00537/) (2023)
- [Tensor-Compressed Back-Propagation-Free Training for (Physics-Informed) Neural Networks](https://mlsanity.com/paper/2308.09858/) (2023)
- [Multiplexed gradient descent: Fast online training of modern datasets on hardware neural networks without backpropagation](https://mlsanity.com/paper/2303.03986/) (2023)
- [Demonstrating Hybrid Learning in a Flexible Neuromorphic Hardware System](https://mlsanity.com/paper/1604.05080/) (2016)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)

## Abstract (arXiv)

In this work, we explore the capabilities of multiplexed gradient descent (MGD), a scalable and efficient perturbative zeroth-order training method for estimating the gradient of a loss function in hardware and training it via stochastic gradient descent. We extend the framework to include both weight and node perturbation, and discuss the advantages and disadvantages of each approach. We investigate the time to train networks using MGD as a function of network size and task complexity. Previous research has suggested that perturbative training methods do not scale well to large problems, since in these methods the time to estimate the gradient scales linearly with the number of network parameters. However, in this work we show that the time to reach a target accuracy--that is, actually solve the problem of interest--does not follow this undesirable linear scaling, and in fact often decreases with network size. Furthermore, we demonstrate that MGD can be used to calculate a drop-in replacement for the gradient in stochastic gradient descent, and therefore optimization accelerators such as momentum can be used alongside MGD, ensuring compatibility with existing machine learning practices. Our results indicate that MGD can efficiently train large networks on hardware, achieving accuracy comparable to backpropagation, thus presenting a practical solution for future neuromorphic computing systems.