Invariant structural learning: concept formation as hypergraph attractor dynamics
DOI:
https://doi.org/10.30837/2522-9818.2026.2.070Keywords:
invariant structural learning; structural attractor; concept formation; graph edit distance; few-shot recognition; explainable AI; MNIST; hypergraph reductionAbstract
Subject of study. The subject of study is the formation of object-class concepts in machine-learning systems as a process of structural and parametric reduction of hypergraph representations, rather than as the optimization of a loss function. Objective. To construct an alternative learning framework for artificial neural networks – without an error functional (back-propagation) – that realizes invariant structural learning, where a class concept is defined as a structural attractor (the fixed point of a monotone reduction operator on a partially ordered space of hypergraphs), and to validate this theory on the recognition of handwritten digits. Objectives. 1) Formalize the framework with axioms of segmentation stability, strict reductivity, positive-only training, and locality of attention; 2) prove convergence and uniqueness of the attractor; 3) establish order-invariance of learning; 4) decompose the attractor into structural and parametric levels; 5) evaluate the transfer on a complete-contour subset of MNIST. Methods. Hypergraphs are obtained by skeletonizing binary contours (Growing Neural Gas + Ramer–Douglas–Peucker); concept attractors form via graph reduction over critical-point anchors. Classification uses a graph-edit-distance comparator with property costs and a complexity-adjusted log prior. The training set consists of 76 hand-picked MNIST originals, augmented (rotation ±10°, shift ±10%) to 805 instances. Results. The transfer learns 13 concept-attractors with node counts ranging from 3 to 15. Of 8,707 admissible complete-contour MNIST images, 8,685 yielded valid skeletal graphs; on this valid set, the transfer achieves an accuracy of 85.80%, weighted precision of 89.31%, recall of 85.80%, and an F1-score of 86.66%. The error structure is interpretable per concept – every misclassification traces back to a named attractor and feature range. Conclusions. The reported performance, achieved without a loss function and using three to nine originals per concept-attractor, supports the claim that learning consists of constructing a structural attractor rather than minimizing an error functional. The framework offers a principled approach to interpretable few-shot classification and a constructive alternative to gradient-based learning.Downloads
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