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

• URL: http://arxiv.org/abs/2601.16446v1
• Date: Fri, 23 Jan 2026 04:53:16 GMT
• Title: Brownian ReLU(Br-ReLU): A New Activation Function for a Long-Short Term Memory (LSTM) Network
• Authors: George Awiakye-Marfo, Elijah Agbosu, Victoria Mawuena Barns, Samuel Asante Gyamerah,
• Abstract summary: BrownianReLU is an activation function induced by Brownian motion that enhances gradient propagation and learning stability.<n>BrownianReLU is evaluated on financial time series from Apple, GCB, and the S&P 500, as well as LendingClub loan data for classification.<n>Results show consistently lower Mean Squared Error and higher $R2$ values, indicating improved predictive accuracy and generalization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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