Artificial neural network modelling of the neural population code underlying mathematical operations

Area of Science:

• Cognitive Neuroscience
• Computational Neuroscience
• Neuroimaging

Background:

• Mathematical operations traditionally viewed as sparse, symbolic processes in neuroimaging.
• Artificial neural networks (ANNs) excel at extracting distributed representations.
• Prior studies compared ANN and biological neural networks (BNNs) in visual, auditory, and language domains, but not mathematics.

Purpose of the Study:

• To investigate if ANN-based distributed representations can explain brain activity patterns during symbolic mathematical operations.
• To explore shared neural representations between ANNs and biological neural networks (BNNs) in the domain of mathematics.
• To elucidate the neural code underlying mathematical thought.

Main Methods:

• Utilized fMRI data from participants solving mathematical problems with nine operator combinations.
• Constructed voxel-wise encoding/decoding models using sparse operator and latent ANN features.
• Employed representational similarity analysis and feature-brain similarity (FBS) analysis.

Main Results:

• Demonstrated shared representations between ANNs and BNNs, particularly in the intraparietal sulcus.
• Successfully reconstructed sparse mathematical operation representations from distributed ANN features using FBS analysis.
• Showed that features from deeper ANN layers improved reconstruction efficiency.
• Enabled decoding of novel operators from brain activity using latent ANN features.

Conclusions:

• ANN-based distributed representations offer a powerful framework for understanding the neural basis of mathematical cognition.
• The findings suggest a significant overlap in how ANNs and the brain process mathematical information.
• This research provides novel insights into the neural code supporting mathematical thought and computation.