Use pyarrow Tensor dtype

### Feature request

I was going the discussion of converting tensors to lists.
Is there a way to leverage pyarrow's Tensors for nested arrays / embeddings?

For example:
```python
import pyarrow as pa
import numpy as np
x = np.array([[2, 2, 4], [4, 5, 100]], np.int32)
pa.Tensor.from_numpy(x, dim_names=["dim1","dim2"])
```

[Apache docs](https://arrow.apache.org/docs/python/generated/pyarrow.Tensor.html)

Maybe this belongs into the pyarrow features / repo.

### Motivation

Working with big data, we need to make sure to use the best data structures and IO out there

### Your contribution

Can try to a PR if code changes necessary

Labels: name: enhancement

Hi ! We're using the Arrow format for the datasets, and PyArrow tensors are not part of the Arrow format AFAIK:

> There is no direct support in the arrow columnar format to store Tensors as column values.

source: https://github.com/apache/arrow/issues/4802#issuecomment-508494694

@wesm @rok its been around three years. any updates, regarding dataset arrow tensor support? 🙏 I know you must be very busy, would appreciate to learn what is the state of art. I saw the PR is still open [#8510](https://github.com/apache/arrow/pull/8510)

Hey @franz101 & @lhoestq!
There is a plan and a PR to create an [ExtensionArray of Tensors](https://github.com/apache/arrow/pull/8510) of equal sizes as well as a plan to do the same for Tensors of different sizes [ARROW-8714](https://issues.apache.org/jira/browse/ARROW-8714).

The work stalled a little because it was not clear where TensorArray would live. However Arrow community recently agreed to make a [well-known-extension-type document](https://lists.apache.org/thread/sxd5fhc42hb6svs79t3fd79gkqj83pfh) and I would like https://github.com/apache/arrow/pull/8510 to land there and add an implementation to C++/Python + another language. Is that something you would find beneficial to you?

that is a great update, thank you.
it looks like this feature would benefit datasets implementation of [ArrayExtensionArray](https://github.com/huggingface/datasets/blob/9f2ff14673cac1f1ad56d80221a793f5938b68c7/src/datasets/features/features.py#L585-L641). Is that correct @eladsegal @lhoestq?



TensorArray sounds great ! Looking forward to it :)

We've had our own ExtensionArray for fixed shape tensors for a while now, hoping to see something more standardized by the arrow community.

Also super interested in the extension array for tensors of different sizes cc @mariosasko 

[FixedShapeTensor ExtensionType](https://github.com/apache/arrow/pull/8510) was merged and will be in Arrow 12.0.0 (release is planned mid April).


@rok Thanks for keeping us updated! I think it's best to introduce a new feature type that would use this extension type under the hood. I'll create an issue to discuss the design with the community in the coming days.

Also, is there a tentative time frame for the variable-shape Tensor extension type?

@mariosasko please tag me in the discussion, perhaps I can contribute.

As for the [variable shape tensor array](https://github.com/apache/arrow/issues/24868) - I'd be interested in working on it but didn't see much interest in community yet. Are you saying `huggingface/datasets` could use it?

pyarrow 12 is out 🎉, will have a look if I can work on it for the ExtensionArray

I think these two issues need to be fixed first on the Arrow side before adding the tensor feature type here: https://github.com/apache/arrow/issues/35573 and https://github.com/apache/arrow/issues/35599.

@rok We've had a couple of requests for supporting variable-shape tensors on the forum/GH, but I did not manage to find the concrete issues using the search. TF/TFDS (and PyTorch with the `nested_tensor` API) support them, so it makes sense for us to do the same eventually (the Ray project has an [extension](https://github.com/ray-project/ray/blob/42a8d1489b37243f203120899a23d919dc85bf2a/python/ray/air/util/tensor_extensions/arrow.py#L634) type to support this case)

> @rok We've had a couple of requests for supporting variable-shape tensors on the forum/GH, but I did not manage to find the concrete issues using the search. TF/TFDS (and PyTorch with the `nested_tensor` API) support them, so it makes sense for us to do the same eventually (the Ray project has an [extension](https://github.com/ray-project/ray/blob/42a8d1489b37243f203120899a23d919dc85bf2a/python/ray/air/util/tensor_extensions/arrow.py#L634) type to support this case)

That does make sense indeed. We should probably also be careful about memory layout to enable zero-copy interface to TF/PyTorch.

So there is no way we can use [pyarrow.Tensor](https://arrow.apache.org/docs/python/generated/pyarrow.Tensor.html#pyarrow.Tensor) ?

Not with with the Arrow format, and therefore not in `datasets`. But they released a new [FixedShapeTensorArray](https://arrow.apache.org/docs/python/extending_types.html#fixed-size-tensor) to store tensors in Arrow format. We plan to support this in `datasets` at one point !

There is also an open issue to enable the conversion of `pyarrow.Tensor` to `pyarrow.FixedShapeTensorType`: https://github.com/apache/arrow/issues/35068. This way one could indirectly use `pyarrow.Tensor` in Arrow format.

We started a [mailing list discussion](https://lists.apache.org/thread/qc9qho0fg5ph1dns4hjq56hp4tj7rk1k) about potential `VariableShapeTensor` extension array, please check it out and give feedback. For more details here's also a PR https://github.com/apache/arrow/pull/37166.

Kindly ask what's the recent progress?

Short update - the prerequisite C++ work has been merged (https://github.com/apache/arrow/issues/38007) and I'm working on the Python wrapper (https://github.com/apache/arrow/pull/40354) so this will hopefully be out with next release (April-ish)