Parameter Division Approach for Unsupervised Transformation Categorization

A new method for unsupervised categorization of transformations between pairs of inputs is proposed, using parameter division within a single transformation. This approach builds on prior Galois-theoretic work that decomposed groups via normal subgroups, but eliminates auxiliary assumptions like motion and isometry restrictions. The new method covers both commutative and non-commutative cases without relying on such constraints, addressing limitations of classical disentanglement which favors independent factors and fails when factors are coupled. The study is theoretical, with no empirical results reported in the abstract.