# Training neural networks using Metropolis Monte Carlo and an adaptive variant

arXiv: https://arxiv.org/abs/2205.07408 · HTML: https://mlsanity.com/paper/2205.07408/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 73 references that are in the map.
- First posted on arXiv 16 May 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [Capacity and Trainability in Recurrent Neural Networks](https://mlsanity.com/paper/1611.09913/) (2016)
- [Correspondence between neuroevolution and gradient descent](https://mlsanity.com/paper/2008.06643/) (2020)
- [RSO: A Gradient Free Sampling Based Approach For Training Deep Neural Networks](https://mlsanity.com/paper/2005.05955/) (2020)

## Built on by (most cited first, 2 of 2)

- [Nonlinear thermodynamic computing out of equilibrium](https://mlsanity.com/paper/2412.17183/) (2024)
- [Adaptive AI-Driven Material Synthesis: Towards Autonomous 2D Materials Growth](https://mlsanity.com/paper/2410.10885/) (2024)

## Abstract (arXiv)

We examine the zero-temperature Metropolis Monte Carlo algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis Monte Carlo can train a neural net with an accuracy comparable to that of gradient descent, if not necessarily as quickly. The Metropolis algorithm does not fail automatically when the number of parameters of a neural network is large. It can fail when a neural network's structure or neuron activations are strongly heterogenous, and we introduce an adaptive Monte Carlo algorithm, aMC, to overcome these limitations. The intrinsic stochasticity and numerical stability of the Monte Carlo method allow aMC to train deep neural networks and recurrent neural networks in which the gradient is too small or too large to allow training by gradient descent. Monte Carlo methods offer a complement to gradient-based methods for training neural networks, allowing access to a distinct set of network architectures and principles.