提出新型随机激活函数Br-ReLU，提升LSTM在金融时序数据中的稳定性与预测精度。
Brownian ReLU(Br-ReLU): A New Activation Function for a Long-Short Term Memory (LSTM) Network
- 基于布朗运动设计随机激活函数，自适应处理负输入
- 在苹果、标普500等数据上实现更低的均方误差和更高的决定系数
- 特别适合噪声大、非平稳的金融时间序列建模任务
深度学习模型在序列数据建模中表现优异，但传统激活函数如ReLU、LeakyReLU和PReLU在处理噪声大、非平稳的金融时间序列时常出现梯度不稳问题。本文提出布朗运动诱导的随机激活函数BrownianReLU，增强长短期记忆网络（LSTM）中的梯度传播与学习稳定性。通过蒙特卡洛模拟，该函数对负输入提供平滑自适应响应，缓解了“死区ReLU”问题。在苹果公司、GCB及标普500金融时间序列，以及LendingClub贷款数据分类任务上的实验表明，其均方误差持续更低，决定系数（R²）更高，显示更强的预测准确性和泛化能力。尽管分类任务中ROC-AUC指标受限，但激活函数选择显著影响准确率与敏感性的权衡，其中BrownianReLU与其他优选函数均展现出实际意义的性能优势。
原文摘要 · Abstract (English)
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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