发表机构
Augusta University; National Technical University "Kharkiv Polytechnic Institute"（奥古斯塔大学; 哈尔科夫国立技术大学“哈尔科夫理工学院”）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出不变结构学习（ISL）理论，将学习视为超图空间中向结构吸引子的收敛，通过数学证明、无反向传播的图像识别验证及神经生物学假设，展示了该非优化概念形成方法的可行性与验证方向。
AI 中文摘要
本文探讨了不变结构学习（ISL）理论，该理论提出了一种非优化的概念形成方法。学习被解释为超图空间中向结构吸引子的收敛，而非全局损失函数的最小化。本文介绍了ISL模型，包括其数学形式化、计算验证以及假设性的神经生物学解释。数学部分引入了结构约简过程的形式化工具，并证明了其有限收敛性、类别结构吸引子的存在性与唯一性，以及吸引子图的自组织性。计算部分在经典图像识别任务上展示了所提出方法的可行性，该方法利用所提出的学习机制，无需反向传播且训练数据集极小。最后，神经生物学部分就结构吸引子在树突树中的可能实现、神经编码作为内部吸引子动力学的投影，以及支持所提出学习概念的神经架构的发展提出了假设。这些假设在树突计算、突触可塑性和神经回路结构组织等领域的现代实验数据背景下进行了讨论。所提出的神经生物学机制被呈现为可检验的假设，而非已确立的生物学事实。结果表明了所提出模型的数学一致性和计算可行性，而神经生物学假设则勾勒了其实验验证的潜在方向。
英文摘要
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.
Comments131 pages, 4 figures, 5 tables
