Neuronal codes for arithmetic rule processing in the human brain

2022

Preprint

Mathematical thoughts can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modeling of mathematical problem solving has yet to be attempted. In the present study, eight subjects were subjected to 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra-and cross-format encoding modeling significantly predicted brain activity in the bilateral intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the bilateral IPS. These findings support the idea that our mathematical thoughts are represented in the brain in a format-invariant manner.

Section: Discussionsupporting

confidence: 93%

Quantitative modeling demonstrates format-invariant representations of mathematical problems in the brain

2022

Preprint

“…In particular, certain double-operator problems were closely located based on the shared single-operator, for example, the AddDiv and SubDiv problems and the AddMul and SubMul problems were paired. Our results for operator-specific representations are consistent with previous reports of double dissociation between different operators (Dehaene & Cohen, 1997) and operator-selective neurons (Kutter et al, 2022), which would contribute to the formatinvariant predictability of cortical activations.…”

Section: Discussionsupporting

confidence: 92%

Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

2023

Eur J of Neuroscience

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel‐wise encoding models. Both intra‐ and cross‐format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format‐invariant manner.

“…In contrast to previous studies on operator decoding (Pinheiro-Chagas, Piazza, and Dehaene 2019; Kutter et al 2022;Knops et al 2009;Haynes et al 2007), we successfully decoded novel operators (Figure 5). Such generalisation was achieved by using latent ANN features.…”

Section: Discussioncontrasting

confidence: 87%

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

2022

Preprint

Mathematical operations have long been regarded as a sparse, symbolic process in neuroimaging studies. In contrast, advances in artificial neural networks (ANN) have enabled extracting distributed representations of mathematical operations. Recent neuroimaging studies have compared distributed representations of the visual, auditory and language domains in ANNs and biological neural networks (BNNs). However, such a relationship has not yet been examined in mathematics. Here we used the fMRI data of a series of mathematical problems with nine different combinations of operators to construct voxel-wise encoding models using both sparse operator and latent ANN features. Representational similarity analysis demonstrated shared representations between ANN and BNN, an effect particularly evident in the intraparietal sulcus. Feature-brain similarity analysis served to reconstruct a sparse representation of mathematical operations based on distributed ANN features. Such reconstruction was more efficient when using features from deeper ANN layers. Moreover, latent ANN features allowed the decoding of novel operators not used during model training from brain activity. The current study provides novel insights into the neural code underlying mathematical thought.