Samuel Debray

Project Description

Semantic Analysis of Mathematics

Associated Files

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A Concurrent NLP–fMRI Approach to the Brain's Mathematical Network

M2 CogMaster Internship, 2021–2022

Project Description

This project was started during my CogMaster internship under the supervision of Prof. Stanislas Dehaene in NeuroSpin's UNICOG lab.

The aim is to use NLP tools to explore the way mathematics are processed in the brain. This project follows an article entitled Origins of the Brain Networks for Advanced Mathematics in Expert Mathematicians published by Marie Amalric and Stanislas Dehaene in 2016 in PNAS.

This project was continued during my PhD, and led to the submission of an article (under review): Mapping and Modeling the Semantic Space of Math Concepts.

Semantic Analysis of Mathematics

The project consists in extracting a mathematical vocabulary from Wikipedia pages and representing it in two dimensions.

The vocabulary consists of 1,000 mathematical words selected manually from the most frequent words occurring in the mathematical articles of Wikipedia. The dataset was analysed using GloVe and 50-dimensional vectors were obtained for each word of the vocabulary.

Using spectral clustering with 100 clusters and tSNE, the GloVe vectors were clustered and projected in two dimensions, and boundaries were obtained by Voronoi tessellation.

Below is the map of mathematics we obtained (in French). The colours were assigned manually to reflect the mathematical tune of each cluster.

Another clustering was perfomed: hierarchical clustering with Ward's method. The dendrogram below presents this clustering (the number of leaves was set to 100 so as to match with the first clustering).

Associated Files

The thesis describes the project in great details. Here are also the slides of defense and a handout if you don't feel like reading the whole thesis (I wouldn't blame you!).

You can also read the paper which reports on this project: Mapping and Modeling the Semantic Space of Math Concepts.