Decorrelation, Diversity, and Emergent Intelligence: The Isomorphism Between Social Insect Colonies and Ensemble Machine Learning

Ernest Fokoué; Gregory Babbitt; Yuval Levental

stat.MLMar 20, 2026

Decorrelation, Diversity, and Emergent Intelligence: The Isomorphism Between Social Insect Colonies and Ensemble Machine Learning

Authors: Ernest Fokoué, Gregory Babbitt, Yuval Levental

Organizations: School of Mathematics and Statistics, Rochester Institute of Technology · Gosnell School of Life Sciences, Rochester Institute of Technology · Center for Imaging Science, Rochester Institute of Technology

Abstract

Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation -- through stochastic response to local cues and positive feedback -- map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that both systems implement identical variance reduction strategies through decorrelation of identical units. We derive explicit mappings between ant recruitment rates and tree weightings, pheromone trail reinforcement and out-of-bag error estimation, and quorum sensing and prediction averaging. This isomorphism suggests that collective intelligence, whether biological or artificial, emerges from a universal principle: \textbf{randomized identical agents + diversity-enforcing mechanisms $\rightarrow$ emergent optimality}.

Figures & tables

Figure 1: Empirical validation of the random forest variance decomposition. (A) Average pairwise tree correlation

\rho

increases with the feature subsampling ratio

m_{\text{try}}/p

, confirming that random feature selection is the primary decorrelation mechanism. Error bars show

\pm 2

standard deviations across replicates; the dashed red line is the linear fit. (B) Theoretical variance from the decomposition

\rho\sigma^{2}+(1-\rho)\sigma^{2}/M

plotted against the empirical ensemble variance, demonstrating near-perfect agreement (points fall on the

y=x

line).

Ant Colony	Random Forest	Mathematical Mapping
Individual ant $a_{i}$	Decision tree $T_{b}$	Identical base units
Thompson sampling randomness	Bootstrap sampling + random feature selection	Diversity-generating mechanisms
Recruitment rate $R_{j}(t)$	Tree prediction weight	Aggregation weights
Pheromone trail reinforcement	Out-of-bag error estimation	Feedback without central coordination
Quorum sensing threshold	Majority vote threshold	Decision rules
Site quality $Q_{j}$	True function $f(\mathbf{x})$	Latent target

Table 1: Correspondence between ant colony and random forest

Figure 2: Direct isomorphism validation: pairwise correlation

\rho

as a function of the decorrelation parameter

\theta

for both random forests (

\theta=1-m_{\text{try}}/p

, within-forest tree correlation) and ant colonies (

\theta=p_{\text{explore}}

, within-colony ant correlation over 20 sites with 50 time steps). Both systems exhibit a clear decreasing relationship: correlation is high when units rely on shared information (low

\theta

) and low when units explore independently (high

\theta

). Shaded bands show 95% confidence intervals across Monte Carlo replicates.

Figure 3: The isomorphism between ant colonies and random forests, demonstrated empirically. The theoretical curve

\rho=\rho_{\max}(1-\theta)

(solid black) is overlaid with empirical measurements from random forest experiments (green,

\theta=1-m_{\text{try}}/p

) and ant colony simulations (brown,

\theta=p_{\text{explore}}

, measured as within-colony correlation over 20 sites with 50 time steps). Both systems exhibit the predicted decay: correlation decreases with the decorrelation parameter

\theta

, confirming that the mapping between systems preserves the variance–correlation structure.

Figure 4: Optimal decorrelation: performance (error, lower is better) as a function of

\theta

for different ensemble sizes

M

. Left: Random forest mean squared error vs.

m_{\text{try}}/p

, showing a U-shaped curve where intermediate

\theta

is optimal—too little subsampling leaves trees correlated, while too much forces trees onto weak features. Right: Ant colony decision error (

1-\text{accuracy}

) vs.

p_{\text{explore}}

on a 20-site task with quality gap 4. Error decreases monotonically with

\theta

: unlike random forests, high exploration does not actively hurt ants because random site visits provide unbiased (if noisy) information, whereas random feature subsets can force trees onto irrelevant variables. In both systems, larger ensembles achieve lower error, confirming the variance reduction principle. Error bars show

\pm 1.96\times\text{SE}

Figure 5: Sensitivity analysis: pairwise tree correlation $\rho$ across different signal strengths and noise levels for three values of $\theta$ . The isomorphism’s core prediction—that $\rho$ is governed by $\theta$ regardless of problem difficulty—is robust: within each $\theta$ panel, correlation remains relatively stable across conditions, confirming that the decorrelation mechanism operates independently of the signal-to-noise regime.

Figure 6: Task complexity sweep: within-colony ant correlation vs. exploration probability for varying numbers of sites and quality gaps. With more sites and smaller quality differences, the correlation decay with

p_{\text{explore}}

becomes clearly visible, demonstrating the isomorphism’s decorrelation mechanism in the colony.

Figure 7: Time horizon sweep: within-colony ant correlation vs.

p_{\text{explore}}

at 20 sites with quality gap 2, for different numbers of simulation steps. Shorter time horizons force ants to rely on pheromone trails, creating higher correlation at low

p_{\text{explore}}

and a steeper decay curve.

Figure 8: Emergence function

E(t)

and alignment over time for different exploration probabilities. (A)

E(t)

measures the transition from disordered to ordered recruitment (Knar, 2025). Lower

p_{\text{explore}}

produces faster convergence. (B) Fraction of ants whose best-estimated site matches the true optimum. All colonies converge, but exploitation-heavy colonies (

p_{\text{explore}}=0.1

) converge faster at the cost of higher inter-ant correlation.

Figure 9: Regime search: $\Delta\rho$ (range of within-colony correlation across $p_{\text{explore}}$ values) for different combinations of task complexity (number of sites) and time pressure (simulation steps). Larger $\Delta\rho$ indicates a stronger isomorphism signal. The optimal regime ( $K=50$ , $T=50$ ) produces $\Delta\rho=0.412$ with a slope of $-0.500$ .

Figure 10: Ant colony correlation decay at the best-identified regime (

K=50

sites,

T=50

steps). The empirical values (brown points) follow the theoretical curve

\rho=\rho_{\max}(1-\theta)

(black line), directly validating the isomorphism mapping.

Panel of Figure 11 — Figure 11: The isomorphism between ant colony decision-making and random forest learning. The $\Phi$ mappings connect the corresponding components.

Panel of Figure 12 — Figure 12: The isomorphism between ant colony decision-making and random forest learning. Each side follows a three‑stage process: (1) diversity generation, (2) aggregation, (3) output. The red double arrows show the mapping between corresponding components.

Feature	Ant Colony Adjustment	Random Forest Analogue
Diversity	Increase $p_{\text{explore}}$ (random search)	Decrease $m_{\text{try}}$
Weighting	Adjust recruitment rate scaling $\alpha$	Use weighted voting / OOB error
Convergence	Increase time to reach Quorum	Increase number of trees ( $M$ )
Stability	Pheromone evaporation rate $\rho$	Regularization / Pruning depth

Table 2: Isomorphic Mapping of Decorrelation and Convergence Parameters

Metric	Random Forest	ACDF	aACDF
Accuracy	$0.842\pm 0.031$	$0.839\pm 0.034$	$0.831\pm 0.029$
AUC	$0.891\pm 0.027$	$0.888\pm 0.030$	$0.879\pm 0.026$
F1 Score	$0.835\pm 0.035$	$0.832\pm 0.037$	$0.824\pm 0.032$
Tree Size (nodes)	$127.4\pm 42.3$	$131.2\pm 38.7$	$89.6\pm 31.2$

Table 3: Performance comparison of Random Forest, ACDF, and aACDF across 20 UCI datasets. Values are mean

\pm

standard deviation.

Panel of Figure 13 — Figure 13: Scatter plot of RF vs ACDF accuracies across 20 UCI datasets. Points closely follow the diagonal, demonstrating statistical equivalence.

Dataset	Random Forest	ACDF	aACDF
H-bond (Type I)	$0.873\pm 0.021$	$0.868\pm 0.024$	$0.861\pm 0.022$
H-bond (Type II)	$0.891\pm 0.019$	$0.887\pm 0.022$	$0.879\pm 0.020$
H-bond (Mixed)	$0.856\pm 0.025$	$0.852\pm 0.027$	$0.844\pm 0.024$

Table 4: H-bond detection accuracy on protein structure datasets.

Shared Decision-Making

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Mar 25, 2026J/K move · Enter open · S save

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

Ernest Fokoué, Gregory Babbitt, Yuval Levental

School of Mathematics and Statistics, Rochester Institute of Technology · Gosnell School of Life Sciences, Rochester Institute of Technology · Center for Imaging Science, Rochester Institute of Technology

Ensemble Learning Emergent Behavior in Multi-Agent Systems Statistical Learning Theory

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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.

Abstract

Shared Decision-Making

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