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The dataset generation failed
Error code: DatasetGenerationError
Exception: ArrowInvalid
Message: Schema at index 1 was different:
orid: string
arxiv_id: string
title: string
area: string
authors: list<item: string>
arxiv_url: string
openreview_url: string
text_source: string
full_text: bool
vs
claim: int64
theorem: string
r: int64
rho_n: double
sigma: double
gamma: double
ns: list<item: int64>
trials: struct<200: int64, 400: int64, 800: int64, 1600: int64, 3200: int64>
rows_normal: list<item: struct<n: int64, trials: int64, max_entry: double, se: double, ci_lo: double, ci_hi: double, sqrtn_max: double, gauss_pred: double, ratio_to_gauss_pred: double, gauss_scale_sqrt2logN: double, bound_eq11: double, measured_over_bound: double, eq11_holds_C1: bool, worst_trial: double>>
rows_cauchy: list<item: struct<n: int64, trials: int64, max_entry: double, se: double, ci_lo: double, ci_hi: double, sqrtn_max: double, gauss_pred: double, ratio_to_gauss_pred: double, gauss_scale_sqrt2logN: double, bound_eq11: double, measured_over_bound: double, eq11_holds_C1: bool, worst_trial: double>>
fit_max_entry_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_sqrtn_max_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_cauchy_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
target_exponent: double
fit_ratio_to_gauss_scale_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_gauss_scale_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
residual_exponent_contains_zero: bool
ratio_to_gauss_scale_range: list<item: double>
exponent_agrees_with_minus_half: bool
smallest_C_for_eq11: double
n_where_eq11_first_below_1: double
eq11_holds_all_n_all_seeds_C1: bool
ks_evec: struct<n_sample: int64, sd: double, D: double, p: double>
ks_semicircle: struct<n_eigs: int64, D: double, p: double>
runtime_s: double
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
num_examples, num_bytes = writer.finalize()
~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 781, in finalize
self.write_rows_on_file()
~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 662, in write_rows_on_file
table = pa.concat_tables(self.current_rows)
File "pyarrow/table.pxi", line 6320, in pyarrow.lib.concat_tables
File "pyarrow/error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
return check_status(status)
File "pyarrow/error.pxi", line 92, in pyarrow.lib.check_status
raise convert_status(status)
pyarrow.lib.ArrowInvalid: Schema at index 1 was different:
orid: string
arxiv_id: string
title: string
area: string
authors: list<item: string>
arxiv_url: string
openreview_url: string
text_source: string
full_text: bool
vs
claim: int64
theorem: string
r: int64
rho_n: double
sigma: double
gamma: double
ns: list<item: int64>
trials: struct<200: int64, 400: int64, 800: int64, 1600: int64, 3200: int64>
rows_normal: list<item: struct<n: int64, trials: int64, max_entry: double, se: double, ci_lo: double, ci_hi: double, sqrtn_max: double, gauss_pred: double, ratio_to_gauss_pred: double, gauss_scale_sqrt2logN: double, bound_eq11: double, measured_over_bound: double, eq11_holds_C1: bool, worst_trial: double>>
rows_cauchy: list<item: struct<n: int64, trials: int64, max_entry: double, se: double, ci_lo: double, ci_hi: double, sqrtn_max: double, gauss_pred: double, ratio_to_gauss_pred: double, gauss_scale_sqrt2logN: double, bound_eq11: double, measured_over_bound: double, eq11_holds_C1: bool, worst_trial: double>>
fit_max_entry_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_sqrtn_max_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_cauchy_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
target_exponent: double
fit_ratio_to_gauss_scale_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
fit_gauss_scale_vs_n: struct<slope: double, ci_lo: double, ci_hi: double, stderr: double, intercept: double, r2: double, n_points: int64>
residual_exponent_contains_zero: bool
ratio_to_gauss_scale_range: list<item: double>
exponent_agrees_with_minus_half: bool
smallest_C_for_eq11: double
n_where_eq11_first_below_1: double
eq11_holds_all_n_all_seeds_C1: bool
ks_evec: struct<n_sample: int64, sd: double, D: double, p: double>
ks_semicircle: struct<n_eigs: int64, D: double, p: double>
runtime_s: double
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 datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
text string | status string |
|---|---|
Under the random dot product graph (RDPG) model where P = rho_n * X X^T for latent positions X in R^(n x r), Theorem 3.1 shows trailing eigenvectors associated with zero eigenvalues delocalize, with maximum entry magnitude bounded by r^2 (log n)^(4+6*gamma) / sqrt(n) (Theorem 3.1). | unverified |
Theorem 3.2 shows that when the embedding dimension is over-specified (k>0 extra dimensions), consistent estimation of the latent positions still holds but only at the slower rate n^(-1/4), compared to the n^(-1/2) rate achieved under correct specification (Theorem 3.2). | unverified |
Theorem 3.2 also shows that when the embedding dimension is under-specified (k<0), there is a fundamental lower bound on estimation error of order sqrt(|k| * rho_n), which need not vanish as the network size grows, proving inconsistency (Theorem 3.2). | unverified |
Under correct specification, the adjacency spectral embedding satisfies ||X_hat_{1:r} W - rho_n^{1/2} X_{1:r}||_{2,infty} <~ phi_n, typically achieving the n^{-1/2} rate; over-specification adds an error term of order sqrt(sigma^2 k) * r^2 (log n)^(5+6*gamma) / n^{1/4} (Section 3). | unverified |
Section 3.1 states Conjecture 1, extending the over-/under-specification results from weighted networks to binary networks under relaxed variance conditions (Section 3.1, Conjecture 1). | unverified |
Section 4 presents simulation experiments across multiple noise distributions confirming the theoretical over- and under-specification rates (Section 4). | unverified |
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