Copyright (c) 2026 Eunkyum Kim nemonanconcode@gmail.com. All Rights Reserved.
Project Identity: A Specialized Research Extension of the Versor Framework Base Framework DOI: [10.5281/zenodo.18939519] License: Apache License 2.0
Research notebook exploring deterministic geometric beam search as an alternative to stochastic tree search (UCT/MCTS).
Built on the Versor geometric algebra framework for PyTorch.
Use Clifford algebra structure to replace probabilistic exploration with geometric exploration:
- Cl(3,0) state algebra: rotor-equivariant policy + grade-0 invariant value
- Bivector norm as exploration signal (Fisher Information connection, Prop 1)
- Cl(1,1) search algebra:
tanhfrom hyperbolic rotors as bounded exploration rate (Prop 2) - Null vectors as causal frontier boundary (Prop 3)
| Environment | GSS | UCB1 | Metric |
|---|---|---|---|
| 10-armed bandit | 38.6 | 114.8 | Cumulative regret |
| Chain MDP | ~7 steps | ~11 steps | Steps to goal |
| 5x5 Maze | 0.930 | 0.882 | Success rate |
GSS receives geometric embeddings encoding environment structure; UCB1 uses only visit counts and reward means. See Section 8 in the notebook for an honest discussion of this information asymmetry.
- Fully differentiable: all operations preserve
torch.autograd(unlike MCTS which breaks gradients at rollout/expansion/backup) - Grade-selective scaling: core ops (bivector exp, sandwich product) are O(n^2), not O(2^2n)
- GPU-native: standard PyTorch tensor ops throughout, no custom CUDA kernels
git clone --recurse-submodules https://github.com/Concode0/gss-research.git
cd gss-research
uv sync
uv run jupyter lab gss_research.ipynbProof-of-concept. Open problems: formal regret bound, convergence proof on Spin(3), adversarial/game testing, scale beyond toy environments. See the notebook discussion for details.
See src/ for more expanded research with GSS vs MCTS ( it need more analysis and bug fix may not fair in potential bugs.)
- Testing the possibility of effectively depicting Zero-Sum games through reflexive computation in adversarial game situations.
- A hypothesis management concept is needed to maintain better prune, directionality, and power than currently available.