Mykyta Lapin | Search arXiv

arXiv2026

Formation of structural attractors in neuromorphic systems

This paper examines the theory of Invariant Structural Learning (ISL), which proposes a non-optimization approach to concept formation. Learning is interpreted as convergence to structural attractors in a hypergraph space, rather than as the minimization of a global loss function. The paper presents the ISL model, including its mathematical formalization, computational verification, and a hypothetical neurobiological interpretation. The mathematical section introduces the formal apparatus of the structural reduction process and proves its finite convergence, the existence and uniqueness of class structural attractors, and the self-organization of attractor maps. The computational section demonstrates the feasibility of the proposed approach on classical image recognition tasks, utilizing the proposed learning mechanism without backpropagation and with extremely small training datasets. Finally, the neurobiological section formulates hypotheses regarding the possible implementation of structural attractors in dendritic trees, neural coding as a projection of internal attractor dynamics, and the development of neural architectures supporting the proposed learning concept. These hypotheses are discussed in the context of modern experimental data in the fields of dendritic computations, synaptic plasticity, and the structural organization of neural circuits. The proposed neurobiological mechanisms are presented as testable hypotheses rather than established biological facts. The results demonstrate the mathematical consistency and computational feasibility of the proposed model, while the neurobiological hypotheses outline potential directions for its experimental verification.

cs.AI↗

arXiv2025

Few-Shot Learning of a Graph-Based Neural Network Model Without Backpropagation

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. 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. 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.

cs.AI↗