Title: Fix sliced ConcatenationTable pickling with mixed schemas vertically
State: closed

A sliced + pickled ConcatenationTable could end up with a different schema than the original schema, if the slice only contains blocks with only a subset of the columns.

This can lead to issues when saving datasets from a concatenation of datasets with mixed schemas

Reported in https://discuss.huggingface.co/t/datasetdict-save-to-disk-with-num-proc-1-seems-to-hang-with-error/75595

Comments:
The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/datasets/pr_6715). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

<details>
<summary>Show benchmarks</summary>

PyArrow==8.0.0

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.005294 / 0.011353 (-0.006059) | 0.003598 / 0.011008 (-0.007411) | 0.062798 / 0.038508 (0.024290) | 0.027479 / 0.023109 (0.004370) | 0.247146 / 0.275898 (-0.028752) | 0.272103 / 0.323480 (-0.051377) | 0.002979 / 0.007986 (-0.005007) | 0.002701 / 0.004328 (-0.001628) | 0.049384 / 0.004250 (0.045134) | 0.041562 / 0.037052 (0.004510) | 0.269924 / 0.258489 (0.011435) | 0.290749 / 0.293841 (-0.003092) | 0.028285 / 0.128546 (-0.100261) | 0.010464 / 0.075646 (-0.065183) | 0.207000 / 0.419271 (-0.212272) | 0.036186 / 0.043533 (-0.007347) | 0.254524 / 0.255139 (-0.000615) | 0.274843 / 0.283200 (-0.008356) | 0.020044 / 0.141683 (-0.121638) | 1.119223 / 1.452155 (-0.332931) | 1.156557 / 1.492716 (-0.336159) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.092014 / 0.018006 (0.074008) | 0.297349 / 0.000490 (0.296859) | 0.000205 / 0.000200 (0.000005) | 0.000048 / 0.000054 (-0.000006) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.018617 / 0.037411 (-0.018794) | 0.061879 / 0.014526 (0.047354) | 0.072877 / 0.176557 (-0.103680) | 0.121850 / 0.737135 (-0.615286) | 0.074686 / 0.296338 (-0.221653) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.281204 / 0.215209 (0.065995) | 2.728688 / 2.077655 (0.651033) | 1.469659 / 1.504120 (-0.034461) | 1.355306 / 1.541195 (-0.185889) | 1.350598 / 1.468490 (-0.117892) | 0.563669 / 4.584777 (-4.021108) | 2.377177 / 3.745712 (-1.368535) | 2.767402 / 5.269862 (-2.502460) | 1.720188 / 4.565676 (-2.845489) | 0.062594 / 0.424275 (-0.361681) | 0.005004 / 0.007607 (-0.002603) | 0.333017 / 0.226044 (0.106972) | 3.354543 / 2.268929 (1.085615) | 1.840031 / 55.444624 (-53.604593) | 1.545548 / 6.876477 (-5.330929) | 1.569858 / 2.142072 (-0.572214) | 0.642680 / 4.805227 (-4.162547) | 0.117463 / 6.500664 (-6.383201) | 0.042472 / 0.075469 (-0.032997) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.977436 / 1.841788 (-0.864351) | 11.285982 / 8.074308 (3.211673) | 9.441848 / 10.191392 (-0.749544) | 0.140773 / 0.680424 (-0.539650) | 0.013783 / 0.534201 (-0.520418) | 0.292304 / 0.579283 (-0.286979) | 0.275011 / 0.434364 (-0.159353) | 0.339094 / 0.540337 (-0.201244) | 0.447593 / 1.386936 (-0.939343) |

</details>
PyArrow==latest

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.005258 / 0.011353 (-0.006095) | 0.003539 / 0.011008 (-0.007469) | 0.049920 / 0.038508 (0.011412) | 0.029789 / 0.023109 (0.006680) | 0.277187 / 0.275898 (0.001288) | 0.296817 / 0.323480 (-0.026663) | 0.004133 / 0.007986 (-0.003852) | 0.002679 / 0.004328 (-0.001649) | 0.048999 / 0.004250 (0.044749) | 0.044087 / 0.037052 (0.007034) | 0.290359 / 0.258489 (0.031870) | 0.319572 / 0.293841 (0.025731) | 0.030248 / 0.128546 (-0.098298) | 0.010453 / 0.075646 (-0.065194) | 0.058734 / 0.419271 (-0.360537) | 0.051216 / 0.043533 (0.007683) | 0.278667 / 0.255139 (0.023528) | 0.298792 / 0.283200 (0.015592) | 0.019131 / 0.141683 (-0.122552) | 1.131814 / 1.452155 (-0.320340) | 1.167208 / 1.492716 (-0.325508) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.088316 / 0.018006 (0.070309) | 0.297143 / 0.000490 (0.296653) | 0.000207 / 0.000200 (0.000007) | 0.000048 / 0.000054 (-0.000006) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.022457 / 0.037411 (-0.014954) | 0.075251 / 0.014526 (0.060726) | 0.086747 / 0.176557 (-0.089809) | 0.124975 / 0.737135 (-0.612161) | 0.087320 / 0.296338 (-0.209019) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.292339 / 0.215209 (0.077130) | 2.860196 / 2.077655 (0.782541) | 1.599058 / 1.504120 (0.094938) | 1.476104 / 1.541195 (-0.065091) | 1.509109 / 1.468490 (0.040619) | 0.564056 / 4.584777 (-4.020721) | 2.388870 / 3.745712 (-1.356842) | 2.582356 / 5.269862 (-2.687506) | 1.726033 / 4.565676 (-2.839644) | 0.061788 / 0.424275 (-0.362487) | 0.005021 / 0.007607 (-0.002586) | 0.345644 / 0.226044 (0.119600) | 3.384000 / 2.268929 (1.115071) | 1.946591 / 55.444624 (-53.498033) | 1.693485 / 6.876477 (-5.182992) | 1.790300 / 2.142072 (-0.351773) | 0.654637 / 4.805227 (-4.150590) | 0.116271 / 6.500664 (-6.384393) | 0.040710 / 0.075469 (-0.034759) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 1.007367 / 1.841788 (-0.834421) | 11.868065 / 8.074308 (3.793757) | 10.146212 / 10.191392 (-0.045180) | 0.128902 / 0.680424 (-0.551522) | 0.015259 / 0.534201 (-0.518942) | 0.288087 / 0.579283 (-0.291196) | 0.281516 / 0.434364 (-0.152848) | 0.325755 / 0.540337 (-0.214583) | 0.424814 / 1.386936 (-0.962122) |

</details>
</details>

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