Linear RNNs and RWKV are examples of RNNs on deep sequences:
https://srush.github.io/annotated-s4/
HiPPO was brilliant - instead of working with the raw sequence, you work with its weighted laplace transform, and instead of actually computing the laplace transform you find the rule to update it when new data is added. Furthermore, we can 'band limit' the Laplace transform (similar to PCA) to keep only the 'most important' information while still preserving most of the information in the sequence - this is a common and quite effective compression technique.
Any 'fast' transformer is going to be working with some kind of sampling or aggregation or compression of the long sequence. Sampling is ultimately going to be too noisy, and standard aggregations are going to be too coarse. So the thing to bet on is better compression techniques, which is what the S4/RWKV group are ultimately working on.
This is similar to basic compression you get with PCA or Fourier transforms. These transforms re fully invertible, until you drop the less significant components. Dropping less-significant components lets you reconstruct some degraded version of the input, and the transform makes it easy to pick the right components to drop.
The current versions of RWKV slowly go insane when exposed to sequences that are too long, because the state slowly diverges over time as you increase past the context length of the training session. They are experimenting with ways to avoid this though: https://github.com/Blealtan/RWKV-LM-LoRA/tree/dev-infctx