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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 valuebased 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.

Integrating evidence over time is crucial for e ective decision making. For simple perceptual decisions, a large body of work suggests that humans and animals are capable of integrating evidence over time fairly well, but that their performance is far from optimal. This suboptimality is thought to arise from a number of di erent sources including (1) noise in sensory and motor systems, (2) unequal weighting of evidence over time, (3) order e ects from previous trials and (4) irrational side biases for one choice over another. In this work we investigated whether and how these di erent sources of suboptimality are related to pupil dilation, a putative correlate of norepinephrine tone. In particular, we measured pupil response in humans making a series of decisions based on rapidly-presented auditory information in an evidence accumulation task. We found that people exhibited all four types of suboptimality, but that only noise and the uneven weighting of evidence over time, the 'integration kernel', were related to the change in pupil response during the stimulus. Moreover, these two di erent suboptimalities were related to di erent aspects of the pupil signal, with the individual di erences in pupil response associated with individual di erences in integration kernel, while trial-by-trial fluctuations in pupil response were associated with trial-by-trial fluctuations in noise. These results suggest that di erent sources of suboptimality in human perceptual decision making are related to distinct pupil-linked processes possibly related to tonic and phasic norepinephrine activity.

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SummaryDivisive 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 total activity of the system. 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 we do not have all the information 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 can quantitatively account for the perceptual decision making behaviour of 133 human participants, performing as well as the state-of-the-art Drift Diffusion Model, the predominant model for perceptual evidence accumulation.