AntsNet: Unified Simulation of Ant Colony / Machine Learning Isomorphisms

Description

Implements the full suite of simulation, visualization, and analysis tools for exploring the mathematical isomorphisms between ant colony intelligence and three major paradigms of machine learning: random forests (Part I), boosting (Part II), and neural networks (Part III).

Part I — Random Forest Isomorphism

generate_regression_data

Synthetic regression data

simulate_ant_colony

Agent-based colony simulation

within_colony_correlation

Pairwise ant correlation

variance_decomposition_experiment

RF variance decomposition

colony_variance_experiment

Colony variance decomposition

isomorphism_test

Direct isomorphism comparison

optimal_decorrelation_experiment

Optimal theta sweep

sensitivity_analysis

Robustness across conditions

create_isomorphism_schematic

Figure 1: schematic

plot_variance_decomposition

Figure 2: variance

plot_correlation_decay

Figure 3: correlation decay

plot_optimal_decorrelation

Figure 4: optimal theta

plot_sensitivity_heatmap

Figure 5: sensitivity

Part II — Boosting Isomorphism

generate_classification_data

Synthetic classification data

adaboost

AdaBoost with decision stumps

predict_adaboost

Predict from AdaBoost ensemble

acar

Ant Colony Adaptive Recruitment

calculate_margins

Boosting margin computation

calculate_quorum_margin

Colony quorum margin

weak_learnability_experiment

Weak learnability test

convergence_experiment_boost

Convergence comparison

noise_experiment_boost

Noise robustness comparison

plot_weak_learnability

Figure 1: weak learnability

plot_weight_pheromone

Figure 2: weight/pheromone

plot_margin_quorum

Figure 3: margin/quorum

plot_convergence_boost

Figure 4: convergence

plot_noise_robustness_boost

Figure 5: noise

Part III — Neural Network Isomorphism

generate_synthetic_data

Synthetic data with complexity

gacl

Generational Ant Colony Learning

simple_neural_network

Single-layer neural network

plot_isomorphism

Figure 1: gradient isomorphism

plot_learning_curves

Figure 2: learning curves

plot_pheromone_weight

Figure 3: pheromone/weight

plot_learning_rate_sensitivity

Figure 4: LR sensitivity

plot_noise_robustness_nn

Figure 5: noise robustness

plot_convergence_complexity

Figure 6: complexity

plot_gradient_dynamics

Figure 7: gradient dynamics

plot_plasticity

Figure 8: plasticity/adaptation

Shiny Apps

launch_app

Interactive explorer (Part I or Part II)

Author(s)

Maintainer: Yuval Levental yhl3051@rit.edu

Authors:

• Gregory Babbitt gabsbi@rit.edu

• Ernest Fokoué epfeqa@rit.edu

See Also

Useful links:

• https://github.com/ylevental/IsomorphismSim_Full

• Report bugs at https://github.com/ylevental/IsomorphismSim_Full/issues

Ant Colony Adaptive Recruitment (ACAR)

Description

Simulates the adaptive recruitment dynamics of an ant colony, implementing Algorithm 3 (ACAR) from the Part II manuscript.

Usage

acar(
  site_qualities,
  n_ants = 50,
  n_waves = 100,
  rho = 0.1,
  gamma = 0.5,
  alpha = 1,
  beta = 1,
  noise_sd = 0.5,
  early_stop = TRUE
)

Arguments

Value

A list with:

pheromone_history

Matrix (waves x K) of pheromone concentrations.

fitness_history

Vector of colony fitness per wave.

decision_history

Integer vector of colony decisions per wave.

final_decision

Index of the chosen site.

AdaBoost with Decision Stumps

Description

Implements the AdaBoost algorithm using decision stumps as weak learners, following Freund & Schapire (1997).

Usage

adaboost(X, y, M = 100)

Arguments

Value

A list with components models (list of stumps), alpha (learner weights), and weight_history (M x n matrix of instance weights at each iteration).

Calculate Boosting Margins

Description

Computes the normalized margin of each training instance.

Usage

calculate_margins(result, X, y)

Arguments

Value

Numeric vector of margins.

Calculate Quorum Margin

Description

Computes the normalized pheromone margin between the best and second-best sites, analogous to boosting margins.

Usage

calculate_quorum_margin(result)

Arguments

Value

Numeric scalar: the quorum margin.

Experiment 2: Ant Colony Variance Decomposition

Description

Sweeps colony size and exploration probability, computing decision accuracy and the empirical variance/correlation of ant assessments.

Usage

colony_variance_experiment(
  n_ants_values = c(10, 20, 30, 50, 100),
  p_explore_values = seq(0, 1, by = 0.2),
  n_replicates = 50,
  n_sites = 5,
  site_qualities = c(10, 8, 6, 4, 2)
)

Arguments

Value

A data.frame with columns n_ants, p_explore, accuracy_mean, accuracy_sd, var_mean, cor_mean

Convergence Rate Experiment

Description

Compares convergence of AdaBoost and ACAR across iterations. For AdaBoost: test-set accuracy using first m iterations. For ACAR: P(correct final decision) using m waves, averaged across independent replicates.

Usage

convergence_experiment_boost(
  n_boost_reps = 30,
  n_acar_reps = 200,
  max_iters = 80,
  verbose = TRUE
)

Arguments

Value

A data.frame with columns iteration, accuracy, system, and rep.

Figure 1: Isomorphism Schematic

Description

Plots theoretical \rho = \rho_{max}(1-\theta) alongside empirical values from both random forest and ant colony experiments.

Usage

create_isomorphism_schematic(rf_results, colony_results)

Arguments

Value

A ggplot object

Find the Best Decision Stump

Description

Searches over all features and thresholds to find the stump that minimizes the weighted classification error.

Usage

find_best_stump(X, y, D)

Arguments

Value

A list describing the best stump: feature, threshold, and direction.

Generational Ant Colony Learning (GACL)

Description

Implements the full GACL algorithm with configurable parameters. Pheromone evolution across generations follows update equations isomorphic to stochastic gradient descent.

Usage

gacl(
  site_qualities,
  n_ants = 100,
  n_generations = 50,
  n_waves = 10,
  rho_wave = 0.3,
  rho_gen = 0.1,
  gamma = 0.5,
  alpha = 1,
  beta = 1,
  noise_sd = 0.2
)

Arguments

Value

A list with components:

pheromone_history

Matrix (generations x K) of pheromone levels.

fitness_history

Numeric vector of colony fitness per generation.

error_signal_history

Numeric vector of negative fitness (loss analog).

decision_history

Integer vector; best site per generation.

final_decision

Best site at the last generation.

Examples

result <- gacl(c(10, 7, 5, 4, 3), n_generations = 30)
plot(result$fitness_history, type = "l")

Generate All Manuscript Figures

Description

Runs all experiments and saves Figures 1–5 as PDFs in the specified output directory.

Usage

generate_all_figures(output_dir, verbose = TRUE)

Arguments

Value

Invisible NULL. Figures are saved as side effects.

Generate Synthetic Classification Data

Description

Creates a binary classification problem where the true boundary depends on the first three features: y = sign(x_1 + x_2 x_3 + 0.5 x_3^2), with optional label noise.

Usage

generate_classification_data(n = 500, p = 10, noise = 0.2)

Arguments

Value

A list with X (n x p matrix), y (label vector), and true_labels.

Generate Synthetic Regression Data

Description

Creates data with a known sparse signal (first 5 features active) and controllable signal-to-noise ratio. Used to benchmark both random forest and ant colony simulation experiments.

Usage

generate_regression_data(n = 1000, p = 50, signal_strength = 1, noise_sd = 1)

Arguments

Value

A list with components:

X

A data.frame of features (n rows, p columns)

y

Numeric response vector

f_true

True function values (without noise)

Examples

d <- generate_regression_data(n = 200, p = 20, signal_strength = 2, noise_sd = 1)
plot(d$f_true, d$y, xlab = "True signal", ylab = "Observed response")

Generate Synthetic Classification Data

Description

Creates a binary classification dataset with a non-linear decision boundary whose complexity can be varied.

Usage

generate_synthetic_data(n = 1000, p = 5, noise = 0.1, complexity = 2)

Arguments

Value

A list with components X (matrix), y (labels with noise), and true_labels.

Examples

d <- generate_synthetic_data(n = 500, p = 5, complexity = 2)
table(d$y)

Experiment 3: Direct Isomorphism Test

Description

Runs random forest and ant colony under matched \theta values (m_try/p = p_explore) and compares the resulting pairwise correlation and ensemble variance.

Usage

isomorphism_test(n_replicates = 50, p_vals = c(0.1, 0.3, 0.5, 0.7, 0.9))

Arguments

Value

A data.frame with theta, system, correlation, cor_sd, ensemble_var, var_sd

Launch an Interactive Shiny App

Description

Opens an interactive Shiny application for exploring the ant colony / machine learning isomorphisms.

Usage

launch_app(part = c("part1", "part2"), ...)

Arguments

Value

No return value, called for side effects (launches a Shiny app).

Examples

if (interactive()) launch_app("part1")
if (interactive()) launch_app("part2")

Noise Robustness Experiment

Description

Compares how AdaBoost and ACAR degrade under increasing noise. Both systems are measured as P(correct) across independent replicates. Parameters are calibrated so both show visible, parallel degradation.

Usage

noise_experiment_boost(
  noise_levels = seq(0, 0.45, by = 0.05),
  n_replicates = 50,
  verbose = TRUE
)

Arguments

Value

A data.frame with columns noise, accuracy, and system.

Experiment 4: Optimal Decorrelation

Description

Sweeps ensemble size and \theta to find the performance-optimal decorrelation parameter. Uses MSE for random forests and 1-accuracy for ant colonies so both metrics point downward.

Usage

optimal_decorrelation_experiment(
  ensemble_sizes = c(10, 30, 100),
  theta_values = seq(0.1, 0.9, by = 0.1),
  n_replicates = 30
)

Arguments

Value

A data.frame with M, theta, system, performance, se

Supplementary: Colony Accuracy vs Size

Description

Supplementary: Colony Accuracy vs Size

Usage

plot_colony_accuracy(colony_results)

Arguments

Value

A ggplot object

Plot Figure 4: Convergence Rates

Description

Plot Figure 4: Convergence Rates

Usage

plot_convergence_boost(results)

Arguments

Value

A ggplot object.

Plot Convergence Across Complexity (Figure 6)

Description

Three-panel plot showing convergence for linear, quadratic, and complex decision boundaries.

Usage

plot_convergence_complexity(n_replicates = 15, n_generations = 50)

Arguments

Value

Invisibly, NULL.

Figure 3: Correlation Decay Comparison

Description

Figure 3: Correlation Decay Comparison

Usage

plot_correlation_decay(iso_results)

Arguments

Value

A ggplot object

Plot Gradient Dynamics (Figure 7)

Description

Two-panel plot comparing the error signal and gradient magnitude in both systems.

Usage

plot_gradient_dynamics(site_qualities = c(10, 7, 5, 4, 3), n_generations = 50)

Arguments

Value

Invisibly, a list with both results.

Plot the Gradient Descent Isomorphism (Figure 1)

Description

Runs one GACL and one neural-network simulation and overlays their normalised error/loss trajectories.

Usage

plot_isomorphism(site_qualities = c(10, 7, 5, 4, 3), n_generations = 50, ...)

Arguments

Value

Invisibly, a list with the GACL and NN results.

Plot Learning Curves with Replicates (Figure 2)

Description

Runs multiple GACL and neural-network replicates, plots individual traces, mean curves, and SE ribbons.

Usage

plot_learning_curves(
  site_qualities = c(10, 7, 5, 4, 3),
  n_replicates = 20,
  n_generations = 50,
  ...
)

Arguments

Value

Invisibly, a list with gacl_mat and nn_mat.

Plot Learning Rate Sensitivity (Figure 4)

Description

Sweeps the evaporation rate / learning rate and plots final normalised performance for both systems with error bars.

Usage

plot_learning_rate_sensitivity(
  site_qualities = c(10, 7, 5, 4, 3),
  learning_rates = c(0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5),
  n_replicates = 15,
  n_generations = 30
)

Arguments

Value

Invisibly, a data frame of summary statistics.

Plot Figure 3: Margin vs Quorum

Description

Plot Figure 3: Margin vs Quorum

Usage

plot_margin_quorum(boost_result, X, y, acar_result)

Arguments

Value

A combined patchwork plot.

Plot Figure 5: Noise Robustness

Description

Plot Figure 5: Noise Robustness

Usage

plot_noise_robustness_boost(results)

Arguments

Value

A ggplot object.

Plot Noise Robustness (Figure 5)

Description

Sweeps noise levels and compares degradation in both systems.

Usage

plot_noise_robustness_nn(
  site_qualities = c(10, 7, 5, 4, 3),
  noise_levels = seq(0, 0.5, by = 0.05),
  n_replicates = 15
)

Arguments

Value

Invisibly, a summary data frame.

Figure 4: Optimal Decorrelation

Description

Figure 4: Optimal Decorrelation

Usage

plot_optimal_decorrelation(optimal_results)

Arguments

Value

A ggplot object

Plot Pheromone vs Weight Evolution (Figure 3)

Description

Two-panel plot comparing the evolution of pheromone concentrations across sites with the evolution of representative neural-network weights across epochs.

Usage

plot_pheromone_weight(site_qualities = c(10, 7, 5, 4, 3), n_generations = 50)

Arguments

Value

Invisibly, the GACL result.

Plot Plasticity and Adaptation (Figure 8)

Description

Simulates an environmental shift at the midpoint and compares the recovery dynamics of both systems.

Usage

plot_plasticity(n_replicates = 15)

Arguments

Value

Invisibly, NULL.

Figure 5: Sensitivity Heat-map

Description

Figure 5: Sensitivity Heat-map

Usage

plot_sensitivity_heatmap(sensitivity_results)

Arguments

Value

A ggplot object

Figure 2: Variance Decomposition

Description

Side-by-side panels showing (A) correlation vs m_try/p and (B) theoretical vs empirical ensemble variance.

Usage

plot_variance_decomposition(rf_results)

Arguments

Value

A combined ggplot (via ggpubr::ggarrange)

Plot Figure 1: Weak Learnability Theorem

Description

Plot Figure 1: Weak Learnability Theorem

Usage

plot_weak_learnability(results)

Arguments

Value

A ggplot object.

Plot Figure 2: Weight vs Pheromone Evolution

Description

Plot Figure 2: Weight vs Pheromone Evolution

Usage

plot_weight_pheromone(boost_result, acar_result, site_qualities)

Arguments

Value

A combined patchwork plot.

Predict with an AdaBoost Ensemble

Description

Predict with an AdaBoost Ensemble

Usage

predict_adaboost(result, X, up_to = NULL)

Arguments

Value

Numeric prediction vector in {-1, +1}.

Predict with a Decision Stump

Description

Predict with a Decision Stump

Usage

predict_stump(stump, X)

Arguments

Value

Numeric prediction vector in {-1, +1}.

Experiment 5: Sensitivity Analysis

Description

Tests whether the isomorphism holds under varying signal strengths, noise levels, and \theta values.

Usage

sensitivity_analysis(
  signal_strengths = c(0.5, 1, 2, 5),
  noise_levels = c(0.5, 1, 2, 4),
  n_replicates = 20
)

Arguments

Value

A data.frame with signal, noise, theta, system, correlation, cor_sd

Boosting and Adaptive Recruitment Simulation

Description

Runs AdaBoost and ant colony adaptive recruitment in parallel.

Usage

sim_boost_recruitment(n_iterations = 100, n_ants = 50,
                      n_sites = 10, evaporation_rate = 0.1,
                      noise_level = 0.15, n_rep = 100)

Arguments

Value

An S3 object of class "boost_recruitment" with elements $boost and $colony (numeric learning curves), and print() and plot() methods.

Colony Convergence Simulation

Description

Tracks the colony's probability estimates over time, demonstrating convergence to the best site via Thompson sampling and recruitment.

Usage

sim_colony_convergence(n_ants = 50, n_sites = 5,
                       site_qualities = c(0.9, 0.7, 0.5, 0.3, 0.1),
                       n_steps = 200, p_explore = 0.3)

Arguments

Value

An S3 object of class "colony_convergence" with print() and plot() methods.

Decorrelation Parameter Sweep

Description

Sweeps the decorrelation parameter theta for both random forests and ant colonies and returns empirical pairwise correlations.

Usage

sim_decorrelation(theta_range = seq(0, 1, by = 0.05),
                  n_sites = 20, n_ants = 50, n_trees = 50,
                  n_features = 20, n_rep = 200)

Arguments

Value

An S3 object of class "decorrelation" with print() and plot() methods.

Gradient Descent and Generational Colony Learning

Description

Simulates generational pheromone evolution alongside neural network training via SGD.

Usage

sim_gradient_colony(n_generations = 50, n_ants = 30,
                    n_trails = 10, evaporation_rate = 0.05,
                    learning_rate = 0.05,
                    hidden_units = c(16, 8),
                    task = "classification", n_rep = 50)

Arguments

Value

An S3 object of class "gradient_colony" with elements $colony and $neural_net (numeric vectors of normalized performance), and print(), summary(), and plot() methods.

Margin Analysis

Description

Computes margin distributions for boosting and ant colony quorum decisions.

Usage

sim_margin_analysis(n_iterations = 200, n_ants = 100,
                    noise_level = 0.2)

Arguments

Value

An S3 object of class "margin_analysis" with print() and plot() methods.

Plasticity and Environmental Adaptation

Description

Demonstrates neural plasticity / colony adaptation correspondence, with optional environmental shift.

Usage

sim_plasticity(n_generations = 300, n_trails = 20,
               ltp_rate = 0.1, ltd_rate = 0.05,
               prune_threshold = 0.01, genesis_rate = 0.02,
               env_shift_at = NULL)

Arguments

Value

An S3 object of class "plasticity_sim" with print() and plot() methods.

Variance Decomposition Simulation

Description

Simulates both an ant colony and a random forest across a range of ensemble sizes and correlation levels, validating the variance decomposition formula.

Usage

sim_variance_decomp(N_range = c(5, 10, 25, 50, 100),
                    rho_range = seq(0, 1, by = 0.2),
                    sigma2 = 1, n_rep = 500)

Arguments

Value

An S3 object of class "variance_decomp" with print(), summary(), and plot() methods.

Simple Neural Network with Stochastic Gradient Descent

Description

Implements a single-hidden-layer perceptron trained with mini-batch SGD and binary cross-entropy loss. Under the isomorphism, weight updates correspond to pheromone updates in gacl().

Usage

simple_neural_network(
  X,
  y,
  n_epochs = 50,
  batch_size = 32,
  learning_rate = 0.1,
  n_hidden = 10,
  validation_split = 0.2
)

Arguments

Value

A list with components:

train_loss

Numeric vector of training loss per epoch.

val_loss

Numeric vector of validation loss per epoch.

val_acc

Numeric vector of validation accuracy per epoch.

gradient_norm

Numeric vector of gradient L2 norm per epoch.

final_weights

List of weight matrices (W1, b1, W2, b2).

Examples

d <- generate_synthetic_data(n = 300, p = 5)
nn <- simple_neural_network(d$X[1:240, ], d$y[1:240], n_epochs = 30)
plot(nn$val_acc, type = "l")

Simulate an Ant Colony Decision Process

Description

Agent-based simulation of Temnothorax-style nest-site selection. Each ant probabilistically explores or follows pheromone trails, makes noisy observations of site quality, and contributes to recruitment. The colony reaches a decision when recruitment exceeds a quorum threshold.

Usage

simulate_ant_colony(
  n_ants = 50,
  n_sites = 5,
  site_qualities = c(10, 8, 6, 4, 2),
  p_explore = 0.3,
  n_steps = 100,
  noise_sd = 2,
  quorum_threshold = 20,
  alpha = 0.1,
  beta = 0.05,
  gamma = 0.2
)

Arguments

Value

A list with components:

history

List of per-step snapshots (pheromone, recruitment, preferences)

final_preferences

Colony-average quality estimates per site

final_recruitment

Final recruitment levels per site

decision

Index of chosen site

ant_states

Matrix of visit counts (n_ants x n_sites)

ant_preferences

Matrix of estimated qualities (n_ants x n_sites)

Examples

sim <- simulate_ant_colony(n_ants = 30, p_explore = 0.4)
cat("Colony chose site", sim$decision, "\n")

Test Isomorphism Between Two Learning Curves

Description

Compares two numeric vectors (e.g. colony fitness and NN loss) using a Kolmogorov-Smirnov test, correlation analysis, or dynamic time warping.

Usage

test_isomorphism(ant_result, ml_result,
                 method = c("ks", "correlation", "dtw"))

Arguments

Value

An S3 object of class "iso_test" with print() and summary() methods.

Track AdaBoost Weight Evolution

Description

Convenience wrapper that returns only the weight history.

Usage

track_weights(X, y, M = 50)

Arguments

Value

An M x n matrix of instance weights.

Experiment 1: Random Forest Variance Decomposition

Description

Validates that \mathrm{Var}[\hat{f}_{\mathrm{rf}}] = \rho\sigma^2 + (1-\rho)\sigma^2/M holds empirically and that \rho varies with m_try/p.

Usage

variance_decomposition_experiment(
  n_train = 500,
  n_test = 1000,
  p = 50,
  m_try_values = c(1, 2, 5, 10, 20, 50),
  n_trees = 500,
  n_replicates = 100,
  signal_strength = 2,
  noise_sd = 1
)

Arguments

Value

A data.frame with columns m_try, rep, rho, sigma2, ensemble_var, pred_error, theoretical_var

Weak Learnability Experiment

Description

Tests whether gamma-weak ant colonies converge to correct decisions with sufficient recruitment waves, as predicted by Theorem 4. Parameters are calibrated so that small gamma is genuinely hard (slow convergence) while large gamma converges quickly.

Usage

weak_learnability_experiment(
  gamma_values = c(0.05, 0.1, 0.2, 0.3),
  wave_counts = c(3, 5, 8, 12, 18, 25, 40, 60, 90, 130, 200, 300),
  n_replicates = 200,
  verbose = TRUE
)

Arguments

Value

A data.frame with columns gamma, waves, rep, and accuracy.

Compute Within-Colony Ant Correlation

Description

Measures the mean pairwise correlation between ants' preference vectors over all candidate sites within a single colony. This is the correct analogue of tree-tree correlation in a random forest: each ant's preference vector over K sites corresponds to a tree's prediction vector over test points.

Usage

within_colony_correlation(ant_preferences)

Arguments

Value

Mean pairwise correlation (scalar), or NA if fewer than 2 ants have visited at least 2 sites.

Examples

sim <- simulate_ant_colony(n_ants = 30, p_explore = 0.3)
within_colony_correlation(sim$ant_preferences)