AbstractPhil/geometric-vocab

Geometric Vocabulary Embeddings

Dataset Description

This dataset provides geometric "crystal" embeddings for symbolic vocabulary from multiple sources. Each token is embedded as a 5-vertex simplex in n-dimensional space, creating a unique geometric representation.

Dataset Summary

• Sources: unicode, wordnet_eng
• Embedding Dimensions: 19, 22, 24, 25, 29, 500, 2500
• Total Tokens: ~150,000
• Format: Parquet files with optional SafeTensors embeddings

Supported Tasks

• Symbolic representation learning
• Geometric embedding analysis
• Cross-lingual vocabulary alignment
• Character and word-level modeling

Dataset Structure

Data Instances

Each instance contains:

• token_id: Unique identifier for the token
• token: The actual token (character or word)
• definition: Textual definition or description
• volume: Geometric volume of the crystal embedding
• cardinal_id: Cardinal axis identifier
• crystal: 5×d dimensional embedding (5 vertices in d dimensions)
• Additional fields depending on source (e.g., unicode_codepoint, synset_id)

Data Splits

Each configuration has multiple splits based on embedding dimension:

unicode:

• train_19d: 19-dimensional embeddings
• train_22d: 22-dimensional embeddings
• train_24d: 24-dimensional embeddings
• train_25d: 25-dimensional embeddings
• train_29d: 29-dimensional embeddings
• train_500d: 500-dimensional embeddings
• train_2500d: 2500-dimensional embeddings

wordnet_eng:

• train_19d: 19-dimensional embeddings
• train_22d: 22-dimensional embeddings
• train_24d: 24-dimensional embeddings
• train_25d: 25-dimensional embeddings
• train_29d: 29-dimensional embeddings
• train_500d: 500-dimensional embeddings
• train_2500d: 2500-dimensional embeddings

Usage

from datasets import load_dataset

# Load Unicode embeddings at 1024 dimensions
dataset = load_dataset("AbstractPhil/geometric-vocab", "unicode", split="train_1024d")

# Access the crystal embeddings
for item in dataset:
    token = item['token']
    crystal = item['crystal']  # Shape: (5 * dim,) flattened
    # Reshape to (5, dim) for 5 vertices in dim dimensions
    crystal_3d = np.array(crystal).reshape(5, -1)

Dataset Creation

Curation Rationale

This dataset provides deterministic, geometrically-structured embeddings for symbolic vocabulary. The crystal embedding approach ensures:

1. Unique representation for each token
2. Geometric interpretability
3. Deterministic generation from definitions
4. Multi-scale representation (different dimensions)

Source Data

• Unicode: Character names and categories from Unicode standard
• WordNet: Synsets with definitions and examples from WordNet/OMW

Embedding Algorithm

Each token is embedded as a 5-vertex simplex (4-simplex) in n-dimensional space:

1. Generate cardinal axes from token definition
2. Create orthonormal frame
3. Position vertices using geometric constraints
4. Compute volume for quality metrics

Additional Information

Licensing Information

Apache 2.0

Citation Information

@dataset{geometric_vocab_2024,
  title={Geometric Vocabulary Embeddings},
  author={AbstractPhil},
  year={2024},
  publisher={Hugging Face}
}

Contributions

Thanks to the Unicode Consortium and Princeton WordNet for the underlying vocabulary data.