Abstract
Divisive normalization has long been used to account for computations in various neural processes and behaviours. The model proposes that inputs into a neural system are divisively normalized by the system’s total activity. More recently, dynamical versions of divisive normalization have been shown to account for how neural activity evolves over time in value-based decision making. Despite its ubiquity, divisive normalization has not been studied in decisions that require evidence to be integrated over time. Such decisions are important when the information is not all available at once. A key feature of such decisions is how evidence is weighted over time, known as the integration kernel. Here, we provide a formal expression for the integration kernel in divisive normalization, and show that divisive normalization quantitatively accounts for 133 human participants’ perceptual decision making behaviour, performing as well as the state-of-the-art Drift Diffusion Model, the predominant model for perceptual evidence accumulation.
Highlights
Divisive normalization has long been used to account for computations in various neural processes and behaviours
We found that only after introducing both bound and sensory adaptation (i.e., Brunton model) can Drift Diffusion Model (DDM) account for the behavioral data as well as divisive normalization can, both in formal model comparison using log likelihood, Akaike information criterion (AIC), and Bayesian information criterion (BIC) (Table 1), and in integration kernel and choice curve (Supplementary Note 4, Supplementary Fig. 8, and Supplementary Table 1; distribution of fitted parameters plotted in Supplementary Fig. 11)
We propose dynamic divisive normalization as a model for perceptual evidence accumulation
Summary
In an interrogation paradigm such as ours, a decision is made by comparing the accumulator activity with the bias when the stimulus ends, e.g., in our task, if the accumulator activity is larger than the bias, the model chooses left This form of DDM: da 1⁄4 CðtÞdt þ σdW ð10Þ with only drift (input, i.e., clicks C) and diffusion (noise added by Wiener process W), and without any bound, would predict that every piece of evidence over time is integrated with equal weight—i.e., a flat integration kernel. We show that the LCA with the addition of just a bound does not account for the bump shaped integration kernel either (Supplementary Note 6, Supplementary Fig. 10, and Supplementary Table 1), suggesting that decreasing the number of parameters worsens the model performance This result that divisive normalization can account for behavior as well as DDM can further support divisive normalization as a model for evidence accumulation
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