Versor is a PyTorch framework designed to enhance deep learning through Geometric Algebra. By replacing standard matrix operations with geometric rotations, it preserves the topological structure of data. This innovative approach unlocks new possibilities in AI, enabling high-performance models like the Geometric Blade Network (GBN) that go beyond traditional linear algebra.
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.
RotorLayer, MultiRotorModel, and SemanticAutoEncoder, catering to different learning tasks in domains like molecular prediction, motion analysis, and semantic processing.Versor has demonstrated impressive results across various benchmarks:
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)))
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.
No comments yet.
Sign in to be the first to comment.