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Description
🚀 Feature
It should be possible to somehow cache the traced graphs in torch_xla.experimental.scan so we don't trace on every call.
Motivation
Today torch_xla.experimental.scan and scan_layers traces the user function with both AOTAutograd (to get the backward) and with LazyTensor (to lower them to HLO). AOTAutograd is very slow and we can easily become tracing bound. For example, python3 examples/train_decoder_only_base.py takes 1min30s but python3 examples/train_decoder_only_base.py scan.decoder_with_scan.DecoderWithScan takes 4min.
Pitch
We could wait for torch.scan to support autograd (c.f. #7901 (comment)) which will take a long time. In the meantime, we can implement some simple caching based on the id of the input function/module.
The caching should be opt-in because it's only sound if the function is pure. We can add a assume_pure=True argument to scan so that it only uses the caching when the user confirms that their function is pure.