Release v1.0.0: The Unbending Paradigm

[Concode0]

Versor 1.0.0 is officially released.

Over the past 5 weeks, the Versor framework has evolved from a theoretical proof-of-concept into a robust geometric computing engine. With this v1.0 milestone, the core architecture—spanning $Cl(p,q,r)$ kernels, signature-aware exponentials, and the Geometric Blade Network (GBN)—is now fully complete and mathematically grounded.

We replace standard matrix multiplications with pure Geometric Algebra (Rotor) operations to preserve the topological structure of data, achieving SOTA-level efficiency and performance.

What's Built

• Cl(p,q,r) kernel with null dimension support for Projective GA
• Signature-aware exp map — closed-form elliptic/hyperbolic/parabolic (no Taylor series)
• Hermitian metrics for positive-definite inner products in any signature
• Multi-Rotor GBN with K weighted rotors (geometric spectral decomposition)
• Rotor Gadget — parameter-efficient linear replacement (~63% param reduction)
• Automatic Metric Search via GeodesicFlow + bivector energy analysis
• CGA embedding Cl(n+1,1) for conformal geometric algebra
• Riemannian Adam optimizer — Adam momentum in the Lie algebra (bivector space)
• Geometric activations — GeometricGELU, GradeSwish, GeometricSquare
• Rotor-to-symbolic-formula translation — direct readout of trained weights as equations
• Iterative geometric unbending — 4-phase SR pipeline with blade rejection
• CliffordGraphConv for molecular graphs
• Bivector pruning for geometric sparsity
• GeometricTransformerBlock with entropy-gated attention

v1.0 Final Benchmarks

The cautious "alpha" performance has been shattered. Final metrics achieved on a single RTX Pro 4500:

• MD17 (Molecular Dynamics): Energy / Force MAE reached 0.476 / 0.077 (benzene) in ~40 mins, matching heavy E(3)-GNNs with pure $Cl(3,0,1)$ PGA. Error distributions perfectly peak at 0 (Gaussian).
• Symbolic Regression (SR): Median R² = 0.9525 on 15 First Principles equations using $Cl(4,0)$.
• LQA: 100% accuracy on Chain reasoning (up to length 13) on frozen embeddings via $Cl(4,1)$ CGA.
• DEAP (EEG): Mean RMSE 0.2576 (Cross-subject) / 0.2329 (Within-subject) using $Cl(3,1)$ Minkowski.

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Transition to Stabilization Phase

With the core foundation solidified, this project is entering a Stabilization Phase.

• For the Maintainer: I will be taking a scheduled break from aggressive feature development. My focus will strictly be on monitoring stability, reviewing critical bug fixes, and refining the theoretical documentation.
• For the Community: The ceiling has been broken, and the door is open. I invite researchers and developers to fork, experiment, and submit Pull Requests.

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(Archive) Previous v1.0-alpha Notes

The previously unmanageable number of tasks has been consolidated into four tasks, as shown below. Overall, the framework has been reorganized into general-purpose structures and task-specific layers. While significant tuning and logic improvements are required for each model structure at this stage, development of the core structure has been completed. Below is a brief summary of the performance and development history from the current testing phase, for your reference.

SR Tasks

For symbolic regression validation, we used 24 tasks proposed in the paper "SRBench 2.0" and currently support them. We focused on a structure that enables accurate equations to be derived from small amounts of data. At this stage, some logic may exhibit numerical instability, and rotor_translate may operate inefficiently or contain errors. Extensive parameter tuning is required, and some sections utilize non-geometric heuristics and methodologies. However, this can be considered a proposal for an IU-SR (Iterative Unbending for Symbolic Regression) architecture.

MD17 Task

This task is similar to the previous logic and guarantees basic operation, but requires improvement. Improvements and merges are planned for the next version 1.0, and a dynamic rotor system is planned to be introduced.

DEAP (EEG) Task

This model uses the newly added Neutralizer. While the model's performance has been verified, the simple decision logic in the details hinders performance. However, the RMSE values ​​are attached below.

The average RMSE is approximately 0.25, with some cases reporting values ​​as low as 0.14. (Based on LOSO, it takes about 5 minutes to train once and see the results - based on an RTX PRO 4050.)

LQA Task

We confirmed that the chain maintains 100 hops within 9 epochs, even when the number of hops increases to 13. (This is similar to a sanity check using geometric operations.)

The entailment and negation tasks yielded the following results.

Negation sentences are processed using geometric mirroring (Grade Involution), suppressing the deviation between Acc_Original (66.0%) and **Acc_Negated (65.3%) to within 0.7 percentage points. This indicates that the model geometrically perfectly preserves the logical operation "negation" regardless of the presence or absence of knowledge.

The HANS benchmark evaluation results observed an imbalance between Acc_Contradiction (10.9%) and **Acc_Entailment (79.7%). This indicates that the current model is biased toward the similarity signal of Grade-0 (scalar). This will be improved by introducing non-commutative inference logic utilizing Grade-2 (non-vector) components.

This is an alpha PR toward version 1.0. Thank you for your interest. Please open a PR or issue with any suggestions.