Lightcap/symplectic-inside-outside-atlas

Inside-Outside Ambiguity Atlas

A controlled ambiguity benchmark for exact CFG/PCFG parsing. The dataset is built for the paper Symplectic Inside--Outside Atlas for Ambiguous Grammars and is intended for chart-level diagnostics, ambiguity stress tests, weighted deduction experiments, and parser-evaluation studies.

The main point is simple: parse count alone does not determine ambiguity geometry. Two examples can have the same number of parses while concentrating uncertainty in different spans, spreading it across the chart, or responding differently to PCFG weight perturbations.

Atlas Diagnostics

Regime separation. Each violin summarizes one controlled ambiguity family. The left panel shows the canonical defect, while the middle and right panels show span entropy and chart-wide spread. The separation of adversarial and structured families illustrates why parse count should be paired with chart-geometry diagnostics.

Shock phase map. Points are grammar/string instances embedded by posterior span entropy and canonical defect. The background intensity tracks the median response of the log partition function under a small PCFG temperature perturbation, exposing ambiguity regimes rather than a single monotone difficulty curve.

Matched-count counterexample. The two heatmaps have matched length and nearly matched log parse count, but their posterior span mass is distributed differently. This is the dataset's intended use case: holding parse count fixed while testing whether a parser is sensitive to where ambiguity lives in the chart.

Rare-Event Findings

The full-atlas tail analysis is kept as tables rather than preview figures. Cells are grouped by ambiguity family, span-entropy band, log-partition shock band, and length band. Detailed outputs are in analysis/full_phase_pockets.csv, analysis/sample_stability.csv, and analysis/family_high_defect_rates.csv.

Rank	Family	Entropy band	Shock band	Length band	Rows	High-defect rate	Lift
1	adversarial cfg	3.9	0	10	483,200	0.538	10.76x
2	adversarial cfg	3.6	0	10	483,200	0.315	6.29x
3	adversarial cfg	3.2	0	5	483,200	0.070	1.39x

Sample rows	Mean top-pocket Jaccard	Mean recovered pockets
5,000	0.870	23.25
20,000	0.906	23.75
50,000	0.923	24.00
100,000	0.962	24.50
250,000	0.971	24.62

In this run, the strongest high-defect tail is concentrated in adversarial CFG cells. Small samples recover much of the top-k tail ordering, while the full atlas provides stable cell counts and family-level rates for downstream audits.

What Is In A Row?

Each row is one generated grammar/string instance with exact chart statistics:

• unweighted CKY log parse count
• weighted log partition value log_z
• log-inside/log-outside projected coordinates z0_* and z1_*
• posterior span masses span_mass_*
• span entropy, spread index, and critical span
• ambiguity-family label
• canonical defect ||A^T Omega A - Omega|| / ||Omega||

No language-model inference is used. The data come from batched CKY inside--outside parsing over controlled weighted grammars.

Example

from datasets import load_dataset

ds = load_dataset(
    "Lightcap/symplectic-inside-outside-atlas",
    data_files="data/atlas_shard_*.parquet",
    split="train",
)

cols = [
    "sentence",
    "ambiguity_geometry_label",
    "length",
    "log_parse_count",
    "span_entropy",
    "spread_index",
    "canonical_defect",
]

print(ds.select_columns(cols).to_pandas().head())

A typical use is to compare parser behavior under matched parse count:

import pandas as pd

df = ds.to_pandas()
df["parse_bin"] = df["log_parse_count"].round(2)
pair = (
    df.groupby(["length", "parse_bin"])
      .filter(lambda g: g["ambiguity_geometry_label"].nunique() > 1)
      .sort_values("spread_index")
)

Suggested Uses

• stress-test symbolic, neural, and hybrid parsers by ambiguity family
• evaluate whether grammar induction creates localized or distributed ambiguity
• study chart-level uncertainty beyond parse count and sentence length
• mine rare high-defect phase pockets that are unstable under small samples
• benchmark weighted deduction implementations with exact inside/outside traces
• build figures for manuscripts on ambiguity geometry and parsing difficulty

Citation

Paper arXiv identifier is pending. Until the arXiv ID is assigned, cite the dataset and manuscript as:

@misc{alpay2026symplectic_atlas_dataset,
  title  = {Inside--Outside Ambiguity Atlas},
  author = {Alpay, Faruk and Kilictas, Bugra},
  year   = {2026},
  publisher = {Hugging Face},
  howpublished = {\url{https://huggingface.co/datasets/Lightcap/symplectic-inside-outside-atlas}}
}

@misc{alpay2026symplectic_inside_outside,
  title  = {Symplectic Inside--Outside Atlas for Ambiguous Grammars},
  author = {Alpay, Faruk and Kilictas, Bugra},
  year   = {2026},
  eprint = {arXiv:placeholder},
  archivePrefix = {arXiv},
  primaryClass = {cs.CL}
}

Reproducibility

Run configuration, shard metadata, and upload history are in dataset_manifest.json and RUN_LOG.md.