Brownian ReLU(Br-ReLU): A New Activation Function for a Long-Short Term Memory (LSTM) Network

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Main Authors: Awiakye-Marfo, George, Agbosu, Elijah, Barns, Victoria Mawuena, Gyamerah, Samuel Asante
Format: Preprint
Published: 2026
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author Awiakye-Marfo, George
Agbosu, Elijah
Barns, Victoria Mawuena
Gyamerah, Samuel Asante
author_facet Awiakye-Marfo, George
Agbosu, Elijah
Barns, Victoria Mawuena
Gyamerah, Samuel Asante
contents Deep learning models are effective for sequential data modeling, yet commonly used activation functions such as ReLU, LeakyReLU, and PReLU often exhibit gradient instability when applied to noisy, non-stationary financial time series. This study introduces BrownianReLU, a stochastic activation function induced by Brownian motion that enhances gradient propagation and learning stability in Long Short-Term Memory (LSTM) networks. Using Monte Carlo simulation, BrownianReLU provides a smooth, adaptive response for negative inputs, mitigating the dying ReLU problem. The proposed activation is evaluated on financial time series from Apple, GCB, and the S&P 500, as well as LendingClub loan data for classification. Results show consistently lower Mean Squared Error and higher $R^2$ values, indicating improved predictive accuracy and generalization. Although ROC-AUC metric is limited in classification tasks, activation choice significantly affects the trade-off between accuracy and sensitivity, with Brownian ReLU and the selected activation functions yielding practically meaningful performance.
format Preprint
id arxiv_https___arxiv_org_abs_2601_16446
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Brownian ReLU(Br-ReLU): A New Activation Function for a Long-Short Term Memory (LSTM) Network
Awiakye-Marfo, George
Agbosu, Elijah
Barns, Victoria Mawuena
Gyamerah, Samuel Asante
Machine Learning
Computational Finance
Deep learning models are effective for sequential data modeling, yet commonly used activation functions such as ReLU, LeakyReLU, and PReLU often exhibit gradient instability when applied to noisy, non-stationary financial time series. This study introduces BrownianReLU, a stochastic activation function induced by Brownian motion that enhances gradient propagation and learning stability in Long Short-Term Memory (LSTM) networks. Using Monte Carlo simulation, BrownianReLU provides a smooth, adaptive response for negative inputs, mitigating the dying ReLU problem. The proposed activation is evaluated on financial time series from Apple, GCB, and the S&P 500, as well as LendingClub loan data for classification. Results show consistently lower Mean Squared Error and higher $R^2$ values, indicating improved predictive accuracy and generalization. Although ROC-AUC metric is limited in classification tasks, activation choice significantly affects the trade-off between accuracy and sensitivity, with Brownian ReLU and the selected activation functions yielding practically meaningful performance.
title Brownian ReLU(Br-ReLU): A New Activation Function for a Long-Short Term Memory (LSTM) Network
topic Machine Learning
Computational Finance
url https://arxiv.org/abs/2601.16446