Graph Neural Networks without Propagation

We propose a structural-graph approach to classifying contour images in a few-shot regime without using backpropagation. The core idea is to make structure the carrier of explanations: an image is encoded as an attributed graph (critical points and lines represented as nodes with geometric attributes), and generalization is achieved via the formation of concept attractors (class-level concept graphs). Purpose. To design and experimentally validate an architecture in which class concepts are formed from a handful of examples (5-6 per class) through structural and parametric reductions, providing transparent decisions and eliminating backpropagation. Objectives. (1) Define a vocabulary of node/edge types and an attribute set for contour graphs; (2) specify normalization and invariances; (3) develop structural and parametric reduction operators as monotonic structural simplifications; (4) describe a procedure for aggregating examples into stable concepts; (5) perform classification via graph edit distance (GED) with practical approximations; (6) compare with representative few-shot approaches. Methods. Contour vectorization is followed by constructing a bipartite graph (Point/Line as nodes) with normalized geometric attributes such as coordinates, length, angle, and direction; reductions include the elimination of unstable substructures or noise and the alignment of paths between critical points. Concepts are formed by iterative composition of samples, and classification is performed by selecting the best graph-to-concept match (using approximated GED). Results. On an MNIST subset with 5-6 base examples per class (single epoch), we obtain a consistent accuracy of around 82% with full traceability of decisions: misclassifications can be explained by explicit structural similarities. An indicative comparison with SVM, MLP, CNN, as well as metric and meta-learning baselines, is provided. Conclusions. The structural-graph scheme with concept attractors enables few-shot learning without backpropagation and offers built-in explanations through the explicit graph structure. Limitations concern the computational cost of GED and the quality of skeletonization; promising directions include classification-algorithm optimization, work with static scenes, and associative recognition.