Datasets:

arcadia-impact
/

mean-field-xor-repro-2026-06-29

Error code:   DatasetGenerationError
Exception:    CastError
Message:      Couldn't cast
eval_loss: double
seed: int64
width: int64
losses: list<item: struct<step: int64, loss: double, elapsed: double>>
  child 0, item: struct<step: int64, loss: double, elapsed: double>
      child 0, step: int64
      child 1, loss: double
      child 2, elapsed: double
lr: double
steps: int64
scale: string
batch: int64
eff_lr: double
to
{'losses': List({'step': Value('int64'), 'loss': Value('float64'), 'elapsed': Value('float64')}), 'width': Value('int64'), 'steps': Value('int64'), 'batch': Value('int64'), 'lr': Value('float64'), 'eff_lr': Value('float64'), 'seed': Value('int64'), 'scale': Value('string')}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
                  for key, table in generator:
                                    ^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
                  for item in generator(*args, **kwargs):
                              ~~~~~~~~~^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
                  self._cast_table(pa_table, json_field_paths=json_field_paths),
                  ~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
                  pa_table = table_cast(pa_table, self.info.features.arrow_schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
                  raise CastError(
                  ...<3 lines>...
                  )
              datasets.table.CastError: Couldn't cast
              eval_loss: double
              seed: int64
              width: int64
              losses: list<item: struct<step: int64, loss: double, elapsed: double>>
                child 0, item: struct<step: int64, loss: double, elapsed: double>
                    child 0, step: int64
                    child 1, loss: double
                    child 2, elapsed: double
              lr: double
              steps: int64
              scale: string
              batch: int64
              eff_lr: double
              to
              {'losses': List({'step': Value('int64'), 'loss': Value('float64'), 'elapsed': Value('float64')}), 'width': Value('int64'), 'steps': Value('int64'), 'batch': Value('int64'), 'lr': Value('float64'), 'eff_lr': Value('float64'), 'seed': Value('int64'), 'scale': Value('string')}
              because column names don't match
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
                  parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
                                                                        ~~~~~~~~~~~~~~~~~~~~~~~~~^
                      builder, max_dataset_size_bytes=max_dataset_size_bytes
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  )
                  ^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
                  builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
                  ~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1683, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ~~~~~~~~~~~~~~~~~~~~~~~~~~^
                      gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                  ):
                  ^
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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losses list	width int64	steps int64	batch int64	lr float64	eff_lr float64	seed int64	scale string
[ { "step": 0, "loss": 1.0036742687225342, "elapsed": 0.13739752769470215 }, { "step": 500, "loss": 0.9342653751373291, "elapsed": 0.5521457195281982 }, { "step": 1000, "loss": 0.7329516410827637, "elapsed": 0.916205644607544 }, { "step": 1500, "loss": 0.5661819...	16	60,000	4,096	0.0005	0.0005	0	meanfield
[ { "step": 0, "loss": 1.1561672687530518, "elapsed": 0.1318376064300537 }, { "step": 500, "loss": 0.4235398769378662, "elapsed": 0.5130698680877686 }, { "step": 1000, "loss": 0.2866777777671814, "elapsed": 0.8851196765899658 }, { "step": 1500, "loss": 0.2428734...	2,048	60,000	4,096	0.0005	0.0005	0	ntk
[ { "step": 0, "loss": 1.0000845193862915, "elapsed": 0.13401389122009277 }, { "step": 500, "loss": 0.9228320717811584, "elapsed": 0.5302345752716064 }, { "step": 1000, "loss": 0.771371603012085, "elapsed": 0.9073035717010498 }, { "step": 1500, "loss": 0.6442194...	2,048	60,000	4,096	0.0005	0.0005	1	meanfield
[ { "step": 0, "loss": 1.0002570152282715, "elapsed": 0.14290547370910645 }, { "step": 500, "loss": 0.9298369884490967, "elapsed": 0.5214736461639404 }, { "step": 1000, "loss": 0.7781744003295898, "elapsed": 0.9100320339202881 }, { "step": 1500, "loss": 0.655597...	2,048	60,000	4,096	0.0005	0.0005	2	meanfield
[ { "step": 0, "loss": 1.0012304782867432, "elapsed": 0.12584209442138672 }, { "step": 500, "loss": 0.9272105693817139, "elapsed": 0.5977511405944824 }, { "step": 1000, "loss": 0.7669275999069214, "elapsed": 0.9611372947692871 }, { "step": 1500, "loss": 0.647712...	2,048	60,000	4,096	0.0005	0.0005	3	meanfield
[ { "step": 0, "loss": 1.00016188621521, "elapsed": 0.1303105354309082 }, { "step": 500, "loss": 0.9282854795455933, "elapsed": 0.5453689098358154 }, { "step": 1000, "loss": 0.7770320177078247, "elapsed": 0.9191069602966309 }, { "step": 1500, "loss": 0.657481312...	2,048	60,000	4,096	0.0005	0.0005	0	meanfield

Mean-field XOR cloverleaf reproduction

Reproduction of the experiment in Dmitry Vaintrob, "Mean field sequence: an introduction" (LessWrong, 2026-04-04).

2-layer width-2048 net trained on continuous XOR (y = sign(x1)*sign(x2), x ~ U([-1,1]^2))
Hardtanh activation, Adam optimizer, 60k steps batch 4096, lr 5e-4
Mean-field output scaling f = (1/N) sum a_i sigma(...) → reproduces the cloverleaf
3 seeds + NTK-scaling + width-16 controls included
Hardware: 1× RTX 4090 (RunPod), ~5 minutes of GPU time total

Plot summary in notebook.html. Scripts: train_xor.py, plot_cloverleaf.py, plot_compare.py, self_consistency.py (attempted but not used — see notebook §5).

Git commit: 8b745fc913d46162890253f0d9a93ee04803b89b (local).

Downloads last month: 111

Total file size:

1.62 MB