Title: Dataset on Hub re-downloads every time?
State: closed

### Describe the bug

Hi, I have a dataset on the hub [here](https://huggingface.co/datasets/manestay/borderlines). It has 1k+ downloads, which I sure is mostly just me and my colleagues working with it. It should have far fewer, since I'm using the same machine with a properly set up HF_HOME variable. However, whenever I run the below function `load_borderlines_hf`, it downloads the entire dataset from the hub and then does the other logic:
https://github.com/manestay/borderlines/blob/4e161f444661e2ebfe643f3fe149d9258d63a57d/run_gpt/lib.py#L80

Let me know what I'm doing wrong here, or if it's a bug with the `datasets` library itself. On the hub I have my data stored in CSVs, but several columns are lists, so that's why I have the code to map splitting on `;`. I looked into dataset loading scripts, but it seemed difficult to set up. I have verified that other `datasets` and `models` on my system are using the cache properly (e.g. I have a 13B parameter model and large datasets, but those are cached and don't redownload).

__EDIT: __ as pointed out in the discussion below, it may be the `map()` calls that aren't being cached properly. Supposing the `load_dataset()` retrieve from the cache, then it should be the case that the `map()` calls also retrieve from the cached output. But the `map()` commands re-execute sometimes.

### Steps to reproduce the bug

1. Copy and paste the function from [here](https://github.com/manestay/borderlines/blob/4e161f444661e2ebfe643f3fe149d9258d63a57d/run_gpt/lib.py#L80) (lines 80-100)
2. Run it in Python `load_borderlines_hf(None)`
3. It completes successfully, downloading from HF hub, then doing the mapping logic etc.
4. If you run it again after some time, it will re-download, ignoring the cache

### Expected behavior

Re-running the code, which calls `datasets.load_dataset('manestay/borderlines', 'territories')`, should use the cached version

### Environment info


- `datasets` version: 2.16.1
- Platform: Linux-5.14.21-150500.55.7-default-x86_64-with-glibc2.31
- Python version: 3.10.13
- `huggingface_hub` version: 0.20.3
- PyArrow version: 15.0.0
- Pandas version: 1.5.3
- `fsspec` version: 2023.10.0

Comments: The caching works as expected when I try to reproduce this locally or on Colab...hi @mariosasko , Thank you for checking. I also tried running this again just now, and it seems like the `load_dataset()` caches properly (though I'll double check later).

I think the issue might be in the caching of the function output for `territories.map(lambda row: {'Claimants': row['Claimants'].split(';')})`. My current run re-ran this, even though I have run this many times before, and as demonstrated by loading from cache, the loaded dataset is the same.

I wonder if the issue stems from using CSV output. Do you recommend changing to Parquet, and if so, is there an easy way to take the already uploaded data on the Hub and reformat?This issue seems similar to https://github.com/huggingface/datasets/issues/6184 (`dill` serializes objects defined outside the `__main__` module by reference). You should be able to work around this limitation by defining the lambdas outside of `load_borderlines_hf` (as module variables) and then setting their `__module__` attribute's value to `None` to force serializing them by value, e.g., like this: 
```python
split_Claimants_row = lambda row: {'Claimants': row['Claimants'].split(';')}
split_Claimants_row.__module__ = None
```Thank you, I'll give this a try. Your fix makes sense to me, so this issue can be closed for now.

Unrelated comment -- for "Downloads last month" on the hub page, I'm assuming for this project that each downloaded CSV is 1 download? The dataset consists of 51 CSVs, so I'm trying to see why it's incrementing so quickly (1125 2 days ago, 1246 right now).This doc explains how we count "Downloads last month": https://huggingface.co/docs/hub/datasets-download-stats