O-Matrix Transformer: Lie-Algebraic Tangent Updates for Provably Safe O(1) Swarm Intelligence

Official implementation of the O-Matrix Transformer: Lie-Algebraic Tangent Updates for Provably Safe O(1) Swarm Intelligence. This repository contains the complete PyTorch code for the O-Matrix Transformer proposed in the paper. The model integrates a Transformer backbone with a Geometric MLP that directly parameterizes skew-symmetric Lie algebra generators (S ∈ 𝕊ₙ, K ∈ 𝕊ₘ) and banded scaling weights D. By enforcing non-zero entries within the k-banded support, it guarantees the Orthogonal Equivalence Transversality Property (OETP) by construction. Key features:- Provably singularity-free control (strictly positive OETP gap δ > 0)- True O(1) amortized latency per agent via local k-banded interactions- Soft Frobenius normalization to prevent norm explosion- Aggressive episodic reset training protocol (N=256 agents) The code reproduces all experiments reported in the paper and includes model checkpoints. Associated preprint: O-Matrix Transformer: Lie-Algebraic Tangent Updates for Provably Safe O(1) Swarm Intelligence (arXiv link will be added upon upload) This repository is intended to support reproducibility of the paper results.