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The emergence of monotone quantifiers via iterated learning

This project explores the evolution of the universal of monotonicity in the semantics of quantifiers with the help of a computational model. It combines the iterated learning paradigm with neural networks as a model of learning. This repository contains everything that is needed to run the model as well as tools to analyse the results.

Getting Started

Running the model

The core function for running the model is iterate in The iterate function accepts the following parameters (See paper for more details on the meaning of each parameter):

  • num_trial: The index of the model run when running the model multiple times.
  • bottleneck: The number of observations used to train each neural network learner.
  • save_path: Where to save the model results.
  • n_generations: For how many generations of iterated learning to run.
  • n_agents: How many agents in each generation.
  • max_model_size: The number of elements in the restrictor set.
  • num_epochs: How many epochs to train the neural network learners for.
  • shuffle_input: Whether to shuffle the input of the neural networks.

Example of a run of the model:

python ../ --num_trial 1 --bottleneck 512 --save_path path/to/folder/ --n_generations 300 --n_agents 10 --max_model_size 10 --num_epochs 4 --shuffle_input True

iterate stores the results in an .npy file containing an array with shape (# generations, # objects in domain, # agents).

Analyzing the results

The core function for analyzing the results of a single model is summarize_trial in See function docstring for more details on the parameters.

Example of analysis:

data = np.load('path/to/results.npy')
# NB: parents and trial_info assumes that the files are named path/to/trial_info_dir/quantifiers.ext and path/to/trial_info_dir/parents.ext
parents = np.load('path/to/parents.npy').astype(int)
trial_info = trial_info_from_fname('path/to/results.npy')
table = summarize_trial(trial_info, data, parents)

When running the model repeatedly or with multiple values, it might become impractical to analyze each result file individually by hand. batch_convert_to_csv saves the summaries of each result file matching a file pattern.

Example of analysis of multiple files:

python --file_pattern pattern/to/results*.npy

Finally, when running the model multiple times for each of multiple combinations of parameter values, it is convenient to summarize the summaries of each combination of parameters that were obtained with summarize_trial or bath_convert_to_csv. summarize_summaries helps by grouping summary files by combinations of parameter values and printing summaries for each.

Example of analysis of multiple runs of multiple combinations of parameter values:

python --mode summarize --file_pattern pattern/matching/summaries*.csv

Plotting the results contains snippets of code needed to reproduce the plots shown in the CogSci paper. Other plotting functions can be found in


The original data plotted in the CogSci paper is available at


  • Shane Steinert-Threlkeld - Co-first author
  • Fausto Carcassi - Co-first author
  • Jakub Szymanik - Second author
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