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

Abstract

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.

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

“…The best brain-like ANN model of mathematical operations should be determined in future studies using concepts such as the brain-score (Schrimpf et al 2020). Second, although the number of subjects was determined based on previous studies using encoding/decoding (Huth et al 2016;Nakai and Nishimoto 2020;Popham et al 2021;Horikawa et al 2020), the relatively small number of subjects involved may affect the current findings. Indeed, two subjects out of eight showed inconsistent patterns of prediction map similarity (Figure 2C, D).…”

“…Each condition consisted of 35 instances. Subjects also underwent another math problem-solving task in word format and a control sentence comprehension task; these tasks were analysed elsewhere (Nakai and Nishimoto 2022). Behavioural data were also analysed in this previous work.…”

“…We employed a previously described ME model (Nishimoto et al 2011;Nakai and Nishimoto 2020;Koide-Majima, Nakai, and Nishimoto 2020) available in a public repository (https://github.com/gallantlab/motion_energy_matlab). First, movie frames and pictures were spatially downsampled to 96 × 96 pixels.…”

“…Eight healthy college students (aged 20-23 years, three females, all with normal vision), denoted as ID01-ID08, participated in this study. This number is in the same range as previous encoding model studies (Huth et al 2016;Nakai and Nishimoto 2020;Popham et al 2021;Horikawa et al 2020). Subjects were all right-handed (laterality quotient, 80-100) as assessed using the Edinburgh inventory (Oldfield 1971).…”

“…Encoding models quantitatively predict brain activity based on a combination of features extracted from the presented stimuli. Researchers have adopted this approach to comprehensively examine visual (Kay, Naselaris, et al 2008;Nishimoto et al 2011;Naselaris et al 2009), auditory (Norman-Haignere, Kanwisher, and McDermott 2015; Nakai, Koide-Majima, and Nishimoto 2021), semantic (Huth et al 2012(Huth et al , 2016Popham et al 2021), emotional (Koide-Majima, Nakai, and Nishimoto 2020;Horikawa et al 2020) and many complex cognitive functions (Nakai and Nishimoto 2020). Encoding models also allow the comparison between sparse and latent features in the same brain data using feature-brain similarity (FBS) (Nakai, Koide-Majima, and Nishimoto 2021).…”