Central limit theorems for the outputs of fully convolutional neural networks with time series input
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 w...
| Authors | Annika Betken, Giorgio Micali, Johannes Schmidt-Hieber |
|---|---|
| Primary category | stat.ME |
| Published | 31 March 2026 |
| Last updated at source | 31 March 2026 |
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