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

• URL: http://arxiv.org/abs/2604.00038v1
• Date: Wed, 25 Mar 2026 03:04:21 GMT
• Title: Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part II-On the Strength of Weak Learnability and the Boosting Paradigm
• Abstract summary: In Part I of this series, we established a rigorous mathematical isomorphism between ant colony decision-making and random forest learning.<n>Here we turn to the complementary mechanism: bias reduction through adaptive weighting.<n>We prove that these processes are mathematically isomorphic, establishing that the fundamental theorem of weak learnability has a direct analog in colony decision-making.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part III -- Gradient Descent, Neural Plasticity, and the Emergence of Deep Intelligence [0.0]
  We prove that the fundamental learning algorithm underlying deep neural networks is mathematically isomorphic to the generational learning dynamics of ant colonies.<n>We show that neural plasticity mechanisms have direct analogs in colony-level adaptation.<n>This final isomorphism reveals that all three major paradigms of machine learning -- parallel ensembles, sequential ensembles, and gradient-based deep learning -- have direct analogs in the collective intelligence of social insects.
  arXiv  Detail & Related papers  (2026-04-03T00:59:49Z)
• Decorrelation, Diversity, and Emergent Intelligence: The Isomorphism Between Social Insect Colonies and Ensemble Machine Learning [0.0]
  Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively.<n>We develop a rigorous framework demonstrating that ant colony decision-making and random forest learning are emergent under a common formalism of textbfstochastic ensemble intelligence.
  arXiv  Detail & Related papers  (2026-03-20T03:14:57Z)
• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• A Theoretical Analysis of Mamba's Training Dynamics: Filtering Relevant Features for Generalization in State Space Models [36.99162631444728]
  We present a first-step analysis of generalization and learning dynamics for a simplified but representative Mamba block.<n>Our study adopts a structured data model with tokens that include both class-relevant and class-irrelevant patterns under token-level noise.<n>We prove that the model achieves guaranteed generalization by establishing non-asymptotic sample complexity and convergence rate bounds.
  arXiv  Detail & Related papers  (2026-02-13T00:44:26Z)
• Preconditioning Benefits of Spectral Orthogonalization in Muon [50.62925024212989]
  We study the effectiveness of a simplified variant of Muon in two case studies: matrix factorization and in-context learning of linear transformers.<n>Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior.
  arXiv  Detail & Related papers  (2026-01-20T00:08:31Z)
• Provable Benefit of Curriculum in Transformer Tree-Reasoning Post-Training [76.12556589212666]
  We show that curriculum post-training avoids the exponential complexity bottleneck.<n>Under outcome-only reward signals, reinforcement learning finetuning achieves high accuracy with sample complexity.<n>We establish guarantees for test-time scaling, where curriculum-aware querying reduces both reward oracle calls and sampling cost from exponential to order.
  arXiv  Detail & Related papers  (2025-11-10T18:29:54Z)
• Ultracoarse Equilibria and Ordinal-Folding Dynamics in Operator-Algebraic Models of Infinite Multi-Agent Games [0.0]
  We develop an operator algebraic framework for infinite games with a continuum of agents.<n>We prove that regret based learning dynamics governed by a noncommutative continuity equation converge to a unique quantal response equilibrium.<n>We introduce the ordinal folding index, a computable ordinal valued metric that measures the self referential depth of the dynamics.
  arXiv  Detail & Related papers  (2025-07-25T22:20:42Z)
• Nested replicator dynamics, nested logit choice, and similarity-based learning [56.98352103321524]
  We consider a model of learning and evolution in games with action sets endowed with a partition-based similarity structure. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar. Because of this implicit bias toward similar strategies, the resulting dynamics do not satisfy any of the standard monotonicity rationalitys for imitative game dynamics.
  arXiv  Detail & Related papers  (2024-07-25T07:09:53Z)
• Two Tales of Single-Phase Contrastive Hebbian Learning [9.84489449520821]
  We show that it is possible for a fully local learning algorithm named dual propagation'' to bridge the performance gap to backpropagation.<n>The algorithm has the drawback that its numerical stability relies on symmetric nudging, which may be restrictive in biological and analog implementations.
  arXiv  Detail & Related papers  (2024-02-13T16:21:18Z)
• Harnessing Heterogeneity: Learning from Decomposed Feedback in Bayesian Modeling [68.69431580852535]
  We introduce a novel GP regression to incorporate the subgroup feedback. Our modified regression has provably lower variance -- and thus a more accurate posterior -- compared to previous approaches. We execute our algorithm on two disparate social problems.
  arXiv  Detail & Related papers  (2021-07-07T03:57:22Z)
• LieTransformer: Equivariant self-attention for Lie Groups [49.9625160479096]
  Group equivariant neural networks are used as building blocks of group invariant neural networks. We extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups.
  arXiv  Detail & Related papers  (2020-12-20T11:02:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.