LawKAN: Group-Law Layers for Composition -- When Imposing a Known Law Pays Off
LawKAN: Group-Law Layers for Composition -- When Imposing a Known Law Pays Off
This research introduces LawKAN, a neural layer design that embeds known non-commutative group laws to learn local increments and correction terms for hardware deviations. The method achieves high accuracy on fixed-angle SU(2) composition with significantly fewer parameters than baselines and demonstrates transferability across multiple robot arm vendors.
The authors propose LawKAN, a neural architecture layer that incorporates exact non-commutative group laws to learn only local increments and unknown deviations, achieving high accuracy on fixed-angle SU(2) composition with 54 parameters while transferring performance gains across three robot arm vendors.
Source: arXiv Robotics — research abstracts · Read original article ↗
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What the source reports
Publisher-reported claims, with original evidence. These results have not been independently verified by RoboSignal.
Reported numbers
error reduction
27
View original evidence
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3parameter count
54
View original evidence
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3parameter count
306
View original evidence
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3error range
1.12–1.14
View original evidence
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3accuracy gap
0.05
View original evidence
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3
- paper: not_reported
What remains unknown
Not established in the collected evidence: Environment, Control, Data origin.
Reported performance applies to the described task. It does not establish general autonomy or deployment readiness.
Source excerpts and review record
Automatically extracted; no manual editorial approval recorded.
crements, and a zero-initialized correction psi learns unknown deviations of the law. A pre-training criterion predicts exact representability. On fixed-angle SU(2) composition, a 54-parameter dense edge is the most accurate dense model, at 27x fewer parameters than the strongest fixed-matrix baseline, and lies 0.05 deg above the Bayes floor. On real robot arms, an isolated 306-parameter psi reaches 1.12-1.14 mm vers
Open source S3
Source：arXiv Robotics — research abstracts · arxiv.org