Versor

Versor is an advanced PyTorch framework designed to elevate deep learning through the application of Geometric Algebra. By replacing traditional matrix multiplications with rotor operations, it preserves the topological structure of data, enabling models to achieve superior performance in a range of tasks. The framework is built on the foundations of the Geometric Blade Network (GBN), introducing innovative model architectures that leverage geometric rotations via Clifford Algebra.

Key Features

• Geometric Algebra: Versor utilizes geometric algebra operations, providing a means to perform interpretable transformations on data.
• Metric-Agnostic Kernel: Supports various algebraic structures, allowing seamless transitions between different domains such as 3D geometry, spacetime, and high-dimensional manifolds.
• Inherently Explainable AI: Every learnable parameter in Versor is a Bivector, which has a geometric interpretation, fostering a landscape of transparency and interpretability.
• Automatic Metric Search: The framework intelligently identifies the optimal metric signature based on the underlying data topology.
• Diverse Model Architectures: Includes components for creating a variety of neural network models, such as RotorLayer, MultiRotorModel, and SemanticAutoEncoder, catering to different learning tasks in domains like molecular prediction, motion analysis, and semantic processing.

Performance Benchmarks

Versor has demonstrated impressive results across various benchmarks:

• QM9 (Molecular Property Prediction): Validation MAE of 7.64 meV with real-time inference on CPU.
• Motion Alignment: Achieved ~100% accuracy in high-dimensional motion data alignment.
• Semantic Disentanglement: Demonstrated perfect grade purity and robust noise tolerance in semantic tasks.

Usage Example

Here is how to incorporate Versor's capabilities in a model:

import torch
from core.algebra import CliffordAlgebra
from layers.rotor import RotorLayer
from layers.linear import CliffordLinear
from functional.activation import GeometricGELU

# Create a 3D Euclidean Clifford Algebra
algebra = CliffordAlgebra(p=3, q=0)

# Build a model with geometric layers
rotor = RotorLayer(algebra, channels=4)
linear = CliffordLinear(algebra, in_channels=4, out_channels=8)
activation = GeometricGELU(algebra, channels=8)

# Input: [Batch, Channels, 2^n] multivectors
x = torch.randn(32, 4, algebra.dim)
out = activation(linear(rotor(x)))

Documentation

Versor is accompanied by comprehensive documentation, including resources on its philosophical background, tutorials for implementation, and deep dives into the mathematics behind its operations.

For those interested in exploring the intersection of deep learning and geometric algebra, Versor offers a powerful ecosystem for driving innovation beyond conventional linear models.