gpu-runtime | library allows running CUDA applications | GPU library

The reason the JAX code compiles slowly is that during JIT compilation JAX unrolls loops. So in terms of XLA compilation, your function is actually very large: you call rnn_jax.apply() 1000 times, and compilation times tend to be roughly quadratic in the number of statements.

By contrast, your pytorch function uses no Python loops, and so under the hood it is relying on vectorized operations that run much faster.

Any time you use a for loop over data in Python, a good bet is that your code will be slow: this is true whether you're using JAX, torch, numpy, pandas, etc. I'd suggest finding an approach to the problem in JAX that relies on vectorized operations rather than relying on slow Python looping.