Decoding the representation of numerical values from brain activation patterns

Abstract

Human neuroimaging studies have increasingly converged on the possibility that the neural representation of specific numbers may be decodable from brain activity, particularly in parietal cortex. Multivariate machine learning techniques have recently demonstrated that the neural representation of individual concrete nouns can be decoded from fMRI patterns, and that some patterns are general over people. Here we use these techniques to investigate whether the neural codes for quantities of objects can be accurately decoded. The pictorial mode (nonsymbolic) depicted a set of objects pictorially (e.g., a picture of three tomatoes), whereas the digit-object mode depicted quantities as combination of a digit (e.g., 3) with a picture of a single object. The study demonstrated that quantities of objects were decodable from neural activation patterns, in parietal regions. These brain activation patterns corresponding to a given quantity were common across objects and across participants in the pictorial mode. Other important findings included better identification of individual numbers in the pictorial mode, partial commonality of neural patterns across the two modes, and hemispheric asymmetry with pictorially-depicted numbers represented bilaterally and numbers in the digit-object mode represented primarily in the left parietal regions. The findings demonstrate the ability to identify individual quantities of objects based on neural patterns, indicating the presence of stable neural representations of numbers. Additionally, they indicate a predominance of neural representation of pictorially depicted numbers over the digit-object mode.

Neural representations of magnitude for natural and rational numbers

“…Some studies have found that IPS activation was notation-independent (Eger et al, 2003;Naccache and Dehaene, 2001), whereas other studies suggest there may be both notationspecific and notation-independent areas (Bluthe et al, 2015;Cohen Kadosh et al, 2007;Darmla and Just, 2013). However, these studies all compared a single mathematical notation (whole numbers) versus natural language (number names).…”

“…Although neuroimaging methods, and functional magnetic resonance imaging (fMRI) in particular, have been employed to assess the neural substrates of numerical magnitude representation (e.g., Darmla and Just, 2013), numerical symbols representations (see Ansari, 2016) and algebra (e.g., Monti et al, 2012), there is no consensus regarding the interpretation of the behavioral differences observed between fractions and other number types. The present study applied neuroimaging methods to assess the relationships among the neural representations of magnitude for different symbolic formats.…”

Physics instruction induces changes in neural knowledge representation during successive stages of learning

“…To focus on the neural representations of the specific mechanical knowledge that was being learned, the voxel selection procedure applied was designed to optimize classification accuracy in machine learning of neurosemantic representations (Damarla and Just, 2013;Just et al, 2010;Mitchell et al, 2008). This method selects voxels whose activation profile (their set of activation levels over the four mechanical systems) remains consistent across the multiple presentations of the set of items (this description will be expanded below).…”

“…These voxels, referred to as stable voxels, are those that display a consistent tuning curve. This selection method has led to successful classification of the neural representation of a variety of concepts, such as concrete objects (Just et al, 2010), numerical quantities (Damarla and Just, 2013), and emotions (Kassam et al, 2013).…”

Symbolic Number Skills Predict Growth in Nonsymbolic Number Skills in Kindergarteners

“…The cost of mixing numerals and dots was also significantly higher than the cost of mixing numerals and number-words, suggesting the key distinction is not necessarily visual format but whether the stimuli point to symbolic (SNS) or nonsymbolic (AMS) representations. Recent neural evidence has also provided evidence consistent with this distinction (Bulthé et al, 2014(Bulthé et al, , 2015Damarla & Just, 2013, Damarla et al, 2016Lyons et al, 2015a). In other tasks that force one to translate between AMS stimuli and verbal symbols (number-words), one finds systematic biases Crollen et al, 2011).…”