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

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.

Can Vision-Language Models See Squares? Text-Recognition Mediates Spatial Reasoning Across Three Model Families

We present a simple experiment that exposes a fundamental limitation in vision-language models (VLMs): the inability to accurately localize filled cells in binary grids when those cells lack textual identity. We generate fifteen 15x15 grids with varying density (10.7%-41.8% filled cells) and render each as two image types -- text symbols (. and #) and filled squares without gridlines -- then ask three frontier VLMs (Claude Opus, ChatGPT 5.2, and Gemini 3 Thinking) to transcribe them. In the text-symbol condition, Claude and ChatGPT achieve approximately 91% cell accuracy and 84% F1, while Gemini achieves 84% accuracy and 63% F1. In the filled-squares condition, all three models collapse to 60-73% accuracy and 29-39% F1. Critically, all conditions pass through the same visual encoder -- the text symbols are images, not tokenized text. The text-vs-squares F1 gap ranges from 34 to 54 points across models, demonstrating that VLMs behave as if they possess a high-fidelity text-recognition pathway for spatial reasoning that dramatically outperforms their native visual pathway. Each model exhibits a distinct failure mode in the squares condition -- systematic under-counting (Claude), massive over-counting (ChatGPT), and template hallucination (Gemini) -- but all share the same underlying deficit: severely degraded spatial localization for non-textual visual elements.