  Recent works within machine learning have been tackling inputs of
ever-increasing size, with cybersecurity presenting sequence classification
problems of particularly extreme lengths. In the case of Windows executable
malware detection, inputs may exceed $100$ MB, which corresponds to a time
series with $T=100,000,000$ steps. To date, the closest approach to handling
such a task is MalConv, a convolutional neural network capable of processing up
to $T=2,000,000$ steps. The $\mathcal{O}(T)$ memory of CNNs has prevented
further application of CNNs to malware. In this work, we develop a new approach
to temporal max pooling that makes the required memory invariant to the
sequence length $T$. This makes MalConv $116\times$ more memory efficient, and
up to $25.8\times$ faster to train on its original dataset, while removing the
input length restrictions to MalConv. We re-invest these gains into improving
the MalConv architecture by developing a new Global Channel Gating design,
giving us an attention mechanism capable of learning feature interactions
across 100 million time steps in an efficient manner, a capability lacked by
the original MalConv CNN. Our implementation can be found at
https://github.com/NeuromorphicComputationResearchProgram/MalConv2
