A Geometric Algebra NN Framework (100% on 13-hop reasoning)

Name: A Geometric Algebra NN Framework (100% on 13-hop reasoning)
Availability: InStock
Author: concode0

by concode0·Mar 23, 2026·3 points·1 comment

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AI Analysis

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Geometric Algebra rotors replace matrix multiplications for 100% accuracy on 13-hop reasoning.

Strengths

•Novel architecture with verifiable benchmarks across molecular dynamics, EEG, and logical reasoning domains.
•Custom closed-form algebraic kernel bypasses slow matrix exponentials entirely.
•Proper academic documentation with DOI, MkDocs, and multi-task benchmark table.

Weaknesses

•Research-stage with Geometric Turing Machine still marked as work in progress.
•Narrow audience—only matters if you're already exploring beyond standard deep learning.

Post Description

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.

Take a look and let me know what you think! (https://github.com/Concode0/Versor)