TwistEmbed: Non-Commutative Geometry for Word Embeddings

TwistEmbed is a novel approach to generating word embeddings based on non-commutative geometry. Traditional word embedding techniques, such as Word2Vec, GloVe, and FastText, utilize Euclidean geometry and symmetric relationships, which may not capture the full complexity of linguistic structures. TwistEmbed leverages non-commutative algebras, Hilbert spaces, and Dirac operators to create a new framework for modeling word embeddings that accounts for the intricate relationships found in natural language.

Table of Contents

• Introduction
• Features
• Requirements
• Installation
• Usage
• Contributing
• License

Introduction

Existing word embedding techniques rely on Euclidean geometry and symmetric relationships between words to derive vector representations. While these methods have shown significant success, they may not be sufficient for capturing the full complexity of linguistic structures, especially when considering higher-order relationships and non-commutative interactions.

TwistEmbed addresses these limitations by leveraging non-commutative geometry to model word embeddings. It can potentially improve the quality of word embeddings for various NLP tasks, such as text classification, sentiment analysis, and machine translation. Additionally, TwistEmbed opens up new avenues of research for exploring the geometric and algebraic properties of word embeddings and their application to natural language processing.

Features

• Construct a non-commutative algebra based on word embeddings and their relationships
• Define a Hilbert space representation for the word embeddings
• Implement a Dirac operator that captures the geometric information of the embeddings in the Hilbert space
• Utilize Connes' metric as a new distance metric derived from the non-commutative geometry
• Optimize embeddings based on the underlying geometric structure of the space

Requirements

• Python 3.6 or higher
• NumPy
• SciPy
• scikit-learn
• gensim (for loading pre-trained word embeddings)

Installation

To install TwistEmbed, simply clone the repository and install the required packages:

git clone https://github.com/yourusername/twistembed.git
cd twistembed
pip install -r requirements.txt

Usage

To use TwistEmbed, follow these steps:

1. Load pre-trained word embeddings using gensim (e.g., Word2Vec, GloVe, or FastText models).

from gensim.models import KeyedVectors

word_vectors = KeyedVectors.load_word2vec_format('path/to/word/embeddings', binary=True)

2. Import TwistEmbed and create an instance with the loaded word embeddings.

from twistembed import TwistEmbed

twist_embed = TwistEmbed(word_vectors)

3. Train the TwistEmbed model.

twist_embed.train()

4. Save the trained model for later use.

twist_embed.save('path/to/save/model')

5. Load a saved TwistEmbed model.

loaded_twist_embed = TwistEmbed.load('path/to/saved/model')

6. Use the trained TwistEmbed model for various NLP tasks (e.g., text classification, sentiment analysis, and machine translation).

vector_representation = twist_embed.get_vector('word')

Contributing

We welcome contributions to TwistEmbed! If you'd like to contribute, please fork the repository and submit a pull request with your changes. Be sure to include documentation and test cases for any new features or bug fixes.

License

TwistEmbed is released under the MIT License.