证明了卷积网络在时间序列输入下输出服从渐近正态分布，为深度学习提供理论支撑。
Central limit theorems for the outputs of fully convolutional neural networks with time series input
- 基于短程依赖线性过程假设，推导出全卷积网络输出的渐近正态性
- 当时间序列长度趋于无穷时，输出分布收敛至高斯分布，理论成立
- 提出可学习加权全局池化层，提升模型泛化能力，适合时间序列建模者
深度学习广泛应用于时间序列分类与预测任务。尽管实证表现优异，但时间序列领域的理论研究仍不充分。本文证明：若网络输入来自短程依赖的线性过程，则采用全局平均池化（GAP）的全卷积神经网络（FCN）输出在样本量趋于无穷时渐近服从高斯分布。该结论基于经典时间序列理论工具。基于此理论，我们进一步提出一种广义的全局加权池化方法，使用缓慢变化且可学习的系数，以增强模型表达能力。
原文摘要 · Abstract (English)
Deep learning is widely deployed for time series learning tasks such as classification and forecasting. Despite the empirical successes, only little theory has been developed so far in the time series context. In this work, we prove that if the network inputs are generated from short-range dependent linear processes, the outputs of fully convolutional neural networks (FCNs) with global average pooling (GAP) are asymptotically Gaussian and the limit is attained if the length of the observed time series tends to infinity. The proof leverages existing tools from the theoretical time series literature. Based on our theory, we propose a generalization of the GAP layer by considering a global weighted pooling step with slowly varying, learnable coefficients.
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