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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
n_instances: int64
configs: list<item: string>
sizes: list<item: int64>
seeds: int64
restarts_per_instance: int64
max_M_selfadjoint_rel_err: double
max_constant_pres_abs_err: double
max_mass_rel_err: double
min_entry_over_all: double
min_lambda_over_all: double
min_eig_over_all: double
max_eig_over_all: double
max_uniqueness_rel_dev: double
max_plan_rowsum_rel_err: double
max_plan_symmetry_rel_err: double
max_sos_identity_rel_err: double
max_iters: int64
frac_all_axioms_ok: double
n_def43ii_holds: int64
n_def43ii_violated: int64
frac_all_axioms_ok_given_def43ii: double
configs_violating_def43ii: list<item: string>
worst_min_eig_K_rel: double
worst_eig_min_when_def43ii_violated: double
max_selfadj_err_given_def43ii: double
max_const_err_given_def43ii: double
all_ok: bool
runtime_s: double
rows: list<item: struct<config: string, n: int64, seed: int64, iters: int64, min_lambda: double, min_eig_K_rel: double, def43_ii_holds: bool, sym_err: double, const_err: double, mass_err: double, min_entry: double, eig_max: double, eig_min: double, damping_ok: bool, uniqueness_max_rel_dev: double, plan_rowsum_rel_err: double, plan_symmetry_rel_err: double, sos_rel_err: double, all_axioms_ok: bool>>
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
              n_instances: int64
              configs: list<item: string>
              sizes: list<item: int64>
              seeds: int64
              restarts_per_instance: int64
              max_M_selfadjoint_rel_err: double
              max_constant_pres_abs_err: double
              max_mass_rel_err: double
              min_entry_over_all: double
              min_lambda_over_all: double
              min_eig_over_all: double
              max_eig_over_all: double
              max_uniqueness_rel_dev: double
              max_plan_rowsum_rel_err: double
              max_plan_symmetry_rel_err: double
              max_sos_identity_rel_err: double
              max_iters: int64
              frac_all_axioms_ok: double
              n_def43ii_holds: int64
              n_def43ii_violated: int64
              frac_all_axioms_ok_given_def43ii: double
              configs_violating_def43ii: list<item: string>
              worst_min_eig_K_rel: double
              worst_eig_min_when_def43ii_violated: double
              max_selfadj_err_given_def43ii: double
              max_const_err_given_def43ii: double
              all_ok: bool
              runtime_s: double
              rows: list<item: struct<config: string, n: int64, seed: int64, iters: int64, min_lambda: double, min_eig_K_rel: double, def43_ii_holds: bool, sym_err: double, const_err: double, mass_err: double, min_entry: double, eig_max: double, eig_min: double, damping_ok: bool, uniqueness_max_rel_dev: double, plan_rowsum_rel_err: double, plan_symmetry_rel_err: double, sos_rel_err: double, all_axioms_ok: bool>>
              
              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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Theorem 4.1 shows a symmetric smoothing operator with positive coefficients can be rescaled by a diagonal matrix (via a symmetric Sinkhorn iteration) into a diffusion operator that is self-adjoint with respect to a mass-weighted inner product (Theorem 4.1).
unverified
Theorem 4.2 proves that for Gaussian and exponential kernels, the Sinkhorn-normalized operators converge uniformly on bounded domains to continuous diffusion operators as sampling resolution increases (Theorem 4.2).
unverified
The symmetric Sinkhorn algorithm empirically requires only 5 to 10 iterations to reduce normalization error below 0.1% (Section 4/5, empirical convergence results).
unverified
The normalized operators simultaneously satisfy symmetry, mass conservation, entrywise positivity, and spectral damping (eigenvalues in [0,1]), properties not jointly satisfied by standard row- or symmetric-normalization schemes (Theorem 4.1).
unverified
The method is demonstrated on point clouds, sparse voxel grids (jaw bone geometry), and Gaussian mixture models with covariance-aware kernels, showing Laplacian-like smoothing on each irregular data type (Section 5, experiments).
unverified
Shape analysis experiments on the Armadillo mesh show spectral distributions remain consistent across sampling modalities, with eigenvalue divergence appearing only at scales matching sampling resolution, validating the Theorem 4.2 convergence guarantee (Section 5).
unverified
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