Abstract
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.
Abstract (translated)
我们提出了一种结构图方法，用于在少量样本的情况下对轮廓图像进行分类，并且不使用反向传播。核心思想是使结构成为解释的载体：一个图像被编码为带有几何属性（关键点和线段作为具有几何属性的节点）的有向图，并通过形成概念吸引子（类级别的概念图）来实现泛化。 目的：设计并实验验证一种架构，其中类别概念可以从少量示例（每类5-6个样本）中通过结构和参数上的简化建立起来，提供透明决策并消除反向传播。 方法： 1. 轮廓矢量化后构建一个二分图（点/线作为节点），使用归一化的几何属性如坐标、长度、角度和方向。 2. 简化包括去除不稳定的子结构或噪声以及关键点之间的路径对齐。 3. 通过样本的迭代组合形成概念，分类是通过对最佳图到概念匹配的选择来实现（使用近似GED）。 结果： 在具有5-6个基础示例的MNIST子集上（单轮），我们获得了大约82%的一致准确率，并且可以完全追踪决策过程：误分可通过明确的结构相似性进行解释。还提供了一个与SVM、MLP、CNN以及度量和元学习基线的指示性比较。 采用概念吸引子的结构图方案能够实现无反向传播的少量样本学习，并通过显式的图形结构提供内置的解释。限制包括GED计算成本较高和骨架化质量；有前景的方向包括分类算法优化，静态场景的工作以及关联识别。
URL
https://arxiv.org/abs/2512.18412
