arXiv:2609.06826cs.AIcs.LG2026-09

提出神经形态系统中结构吸引子的形成机制,无需反向传播即可学习。

Formation of structural attractors in neuromorphic systems

  • 用超图空间中的结构吸引子替代优化损失函数来实现学习
  • 在极小数据集上完成经典图像识别任务,无需反向传播
  • 提出可验证的神经生物学假说,连接理论与真实脑结构

本文研究了不变结构学习(ISL)理论,提出一种非优化型概念形成方法。学习被解释为在超图空间中收敛至结构吸引子,而非最小化全局损失函数。论文构建了ISL模型,包含数学形式化、计算验证及假设性神经生物学解释。数学部分引入结构简化过程的形式工具,证明其有限收敛性、类结构吸引子的存在唯一性以及吸引子映射的自组织特性。计算部分展示了该方法在经典图像识别任务中的可行性,仅需极小训练数据集且不依赖反向传播。神经生物学部分提出结构吸引子可能在树突树中实现,神经编码作为内部吸引子动态的投影,以及支持该学习概念的神经架构演化。这些假说结合现代树突计算、突触可塑性和神经回路结构实验数据进行讨论。所提机制为可检验的假说,非既定生物事实。结果表明模型具有数学一致性与计算可行性,神经生物学假说指明了未来实验验证方向。

原文摘要 · Abstract (English)

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.

神经形态结构学习吸引子无反向传播

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