Earlier quoted context omitted.
RNNs provided by common frameworks really do give a matrix back (examples [0, 1]). They're about as stateful as any other object or generator function. [0]: https://pytorch.org/docs/stable/generated/torch.nn.RNN.html [1]: https://docs.nvidia.com/deeplearning/cudnn/api/index.html#cu...
What other statistical machine learning algorithm gives you a state machine as an output? The particular encoding -- matrix or otherwise -- is just an implementation detail.
* hidden Markov models
* autoregressive models
* learned LQR
Sure, some of those have finite memory, but RNNs are practically limited–not as easily quantified.
I see what you're saying about the single-step operation appearing unique, but I also think that RNNs can be viewed through a lens such that they look like "normal" programming concepts like generators and folding iterators.