arXiv:2604.00038stat.MLcs.LG2026-04被引 2

蚂蚁觅食与增强学习共享同一数学原理,揭示群体智能的统一机制。

Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part II-On the Strength of Weak Learnability and the Boosting Paradigm

  • 将自适应加权机制映射为蚂蚁通过信息素动态强化路径。
  • 模拟显示自适应招募的蚁群可实现与提升算法相当的偏差降低效果。
  • 打通生物与计算群体智能的理论桥梁,适合机器学习与复杂系统研究者。

在本系列第一部分中,我们建立了蚁群决策与随机森林学习之间的严格数学同构关系,证明通过去相关实现方差降低是生物与计算群体共同遵循的普适原则。本文转向互补机制:通过自适应加权实现偏差降低。正如提升算法依次关注困难样本,蚁群通过信息素介导的招募动态放大成功觅食路径。我们证明这些过程在数学上同构,确立弱可学习性基本定理在蚁群决策中的直接对应。我们建立AdaBoost的自适应重加权与蚁群招募动态之间的形式映射,表明提升算法的边界理论对应于群体决策的稳定性,并通过全面模拟验证了实施自适应招募的蚁群能获得与提升算法相当的偏差减少收益。这完成了群体智能的统一理论,揭示方差降低(第一部分)与偏差降低(第二部分)均为支配生物与计算系统集体智能的同一数学原理的体现。

原文摘要 · Abstract (English)

In Part I of this series, we established a rigorous mathematical isomorphism between ant colony decision-making and random forest learning, demonstrating that variance reduction through decorrelation is a universal principle shared by biological and computational ensembles. Here we turn to the complementary mechanism: bias reduction through adaptive weighting. Just as boosting algorithms sequentially focus on difficult instances, ant colonies dynamically amplify successful foraging paths through pheromone-mediated recruitment. We prove that these processes are mathematically isomorphic, establishing that the fundamental theorem of weak learnability has a direct analog in colony decision-making. We develop a formal mapping between AdaBoost's adaptive reweighting and ant recruitment dynamics, show that the margin theory of boosting corresponds to the stability of quorum decisions, and demonstrate through comprehensive simulation that ant colonies implementing adaptive recruitment achieve the same bias-reduction benefits as boosting algorithms. This completes a unified theory of ensemble intelligence, revealing that both variance reduction (Part I) and bias reduction (Part II) are manifestations of the same underlying mathematical principles governing collective intelligence in biological and computational systems.

群体智能增强学习蚁群算法机器学习

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