Beyond linear regression: mapping models in cognitive neuroscience should align with research goals

Abstract

Advances in cognitive neuroscience are often accompanied by an increased complexity in the methods we use to uncover new aspects of brain function. Recently, many studies have started to use large feature sets to predict and interpret brain activity patterns. Of crucial importance in this paradigm is the mapping model, which defines the space of possible relationships between the features and neural data. Until recently, most encoding and decoding studies have used linear mapping models. However, some researchers have argued that the space of linear mappings is overly constrained and advocated for the use of more flexible nonlinear mapping models. Here, we discuss the choice of a mapping model in the context of three overarching goals: predictive accuracy, interpretability, and biological plausibility. We show that, contrary to popular intuition, these goals do not map cleanly onto the linear/nonlinear divide. Moreover, we argue that, instead of categorically treating the mapping models as linear or nonlinear, we should instead aim to estimate the complexity of these models. We show that, in most cases, complexity provides a more accurate reflection of restrictions imposed by various research goals and outline several complexity metrics that can be used to effectively evaluate mapping models.

Linear Modeling of Neurophysiological Responses to Speech and Other Continuous Stimuli: Methodological Considerations for Applied Research

“…Additionally, non-linear models generally outperform linear models in predicting neural data (but see Lalor et al, 2008 ; Crosse, 2011 ). However, they can be more difficult to interpret than linear models, and can be harder to compare across feature sets ( Ivanova et al, 2021 ). Furthermore, it is not yet clear how much benefit non-linear models provide for modeling non-invasive population recordings (for discussion see Crosse et al, 2016a ).…”

Many but not all deep neural network audio models capture brain responses and exhibit correspondence between model stages and brain regions

“…The conclusions here are also limited by the two metrics of model-brain similarity that we used. The regression-based metric of explained variance is based on the assumption that representational similarity can be meaningfully assessed using a linear mapping between responses to natural stimuli 38, 64, 65 . This assumption is common in systems neuroscience, but could obscure aspects of a model representation that deviate markedly from those of the brain, because the linear mapping picks out only the model features that are predictive of brain responses.…”

Linear Modeling of Neurophysiological Responses to Naturalistic Stimuli: Methodological Considerations for Applied Research

“…But it is of course not the only method of neural data analysis. The relative utility of linear models versus nonlinear models (which assume a nonlinear relationship between stimulus properties and the neural response) is an active area of debate (Ivanova et al, 2020). Furthermore, deep neural networks have shown promise for generating artificial neural responses that mimic the processing stages of sensory systems in the brain (Yamins and DiCarlo, 2016;Richards et al, 2019).…”