Reduce memory usage of forced alignment on CPU

[MahmoudAshraf97]

In the forced alignment c++ code, backPtr is an int8 tensor while only storing the values 0,1, and 2 which can be effectively stored using only 2 bits instead of 8, and since the backPtr tensor size is log_probs_len * (targets_length * 2 + 1), it can grow to unmanageable sizes in audio files that exceed 2 hours.
By using two std::vector<bool> to represent the two bits needed for backPtr we guarantee that the results are exactly the same while lowering memory usage since std::vector<bool> should use 1 bit to represent a boolean.
Best case scenario is memory usage drops to 25%, worst case scenario memory usage doubles if a boolean is represented using 1 byte.

From my experiments, the new code can handle longer audio files without running out of memory. I also noticed that on average, only 1-targets_length/log_probs_length of the backPtr array is used (depending on the inputs) so further memory savings can be gained if we used a shape that reduces unused elements.

log_probs.shape (1,50000,32)
targets.shape (1,25000)
# new code
12.2 s ± 63 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
# original
12.3 s ± 170 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

edit:
I implemented a better structure for the backPtr tensor that still uses two boolean vectors but the numbers of elements are greatly reduced to achieve better memory efficiency.
The new structure is similar to a sparse matrix or a list of lists, instead of initializing a complete trellis matrix, we initialize the elements which are only going to be used which is approximated by the formula in the code (deduced empirically and tested thorougly). We also create two new arrays for indexing purposes.

[pytorch-bot]

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[vadimkantorov]

I used this compression trick in my Python CTC-based forced alignment: https://github.com/vadimkantorov/ctc/blob/master/ctc.py

And this compression indeed works and helps

[MahmoudAshraf97]

since torchaudio is no longer maintained, I've created a library that builds upon this code and improves it here
it's around 50% faster with 5x less memory usage, it also supports all CTC models from hugging face. The MMS alignment model used by torch audio is hosted here