Hey HN, I’ve been building Versor, a PyTorch framework that swaps out standard matrix multiplications for Geometric Algebra (Clifford Rotors).
I started this because I was frustrated with how standard linear layers "smear" the data manifold. I wanted to see if using Rotors—which are intrinsically constrained to preserve distances and angles—could fix this.
So far, this approach has enabled:
- 100% accuracy on 13-hop reasoning (CLUTRR) with ~300K params. Rotor composition happens to be algebraically isomorphic to logical transitivity.
- Deterministic symbolic regression in ~23 seconds, skipping genetic algorithms entirely.
- A custom closed-form algebraic kernel for the exponential map to bypass slow matrix exponentials.
I'm currently using this core to build a Geometric Turing Machine for ARC-AGI. It's still a work in progress, but the core framework is solid.
I started this because I was frustrated with how standard linear layers "smear" the data manifold. I wanted to see if using Rotors—which are intrinsically constrained to preserve distances and angles—could fix this.
So far, this approach has enabled: - 100% accuracy on 13-hop reasoning (CLUTRR) with ~300K params. Rotor composition happens to be algebraically isomorphic to logical transitivity. - Deterministic symbolic regression in ~23 seconds, skipping genetic algorithms entirely. - A custom closed-form algebraic kernel for the exponential map to bypass slow matrix exponentials.
I'm currently using this core to build a Geometric Turing Machine for ARC-AGI. It's still a work in progress, but the core framework is solid.
Take a look and let me know what you think! (https://github.com/Concode0/Versor)