Sequential effects: Superstition or rational behavior?

TLDR

In many behavioral tasks, subjects exhibit a sequential effect—responding faster and more accurately when a stimulus reinforces a local pattern such as repetitions or alternations—even when the pattern is random and has no predictive value. The authors investigate whether sequential effects arise from the inadvertent use of adaptive mechanisms by applying a normative Bayesian framework. They model the behavior with a Bayes‑optimal algorithm that incorporates a prior over non‑stationarity and derive its approximation as a linear‑exponential filter linked to leaky‑integration dynamics. The study demonstrates that a prior belief in non‑stationarity generates the observed sequential effects in a Bayes‑optimal algorithm, which is well approximated by a linear‑exponential (leaky‑integration) filter that can be tuned via stochastic gradient descent on noisy binary inputs, showing that neurons can implement near‑optimal prediction and adaptive parameter learning without explicit probability representation.

Abstract

In a variety of behavioral tasks, subjects exhibit an automatic and apparently suboptimal sequential effect: they respond more rapidly and accurately to a stimulus if it reinforces a local pattern in stimulus history, such as a string of repetitions or alternations, compared to when it violates such a pattern. This is often the case even if the local trends arise by chance in the context of a randomized design, such that stimulus history has no real predictive power. In this work, we use a normative Bayesian framework to examine the hypothesis that such idiosyncrasies may reflect the inadvertent engagement of mechanisms critical for adapting to a changing environment. We show that prior belief in non-stationarity can induce experimentally observed sequential effects in an otherwise Bayes-optimal algorithm. The Bayesian algorithm is shown to be well approximated by linear-exponential filtering of past observations, a feature also apparent in the behavioral data. We derive an explicit relationship between the parameters and computations of the exact Bayesian algorithm and those of the approximate linear-exponential filter. Since the latter is equivalent to a leaky-integration process, a commonly used model of neuronal dynamics underlying perceptual decision-making and trial-to-trial dependencies, our model provides a principled account of why such dynamics are useful. We also show that parameter-tuning of the leaky-integration process is possible, using stochastic gradient descent based only on the noisy binary inputs. This is a proof of concept that not only can neurons implement near-optimal prediction based on standard neuronal dynamics, but that they can also learn to tune the processing parameters without explicitly representing probabilities.