SEEXC: a model of response time in skill acquisition

Heathcote, Andrew; Brown, Scott · 2002 · NOVA (University of Newcastle Australia)

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Summary

This paper introduces SEEXC (Self-Exciting EXpert Competition), a neural network model designed to explain choice response time (RT) and skill acquisition. The research is motivated by a debate regarding the "Law of Practice," which describes how mean RT decreases with the number of practice trials ($N$). While previous models, such as Page’s (2000) extension of Usher and McClelland’s leaky competitive integrator, predicted a power-law relationship, empirical data better fits an exponential function. The authors argue that Page’s model, which assumes practice increases input strength, fails to match this data unless input increases at an implausibly fast rate. SEEXC proposes an alternative mechanism: practice modulates the recurrent self-connection weights (self-excitation) of neural units, thereby offsetting information leakage. The study analyzes deterministic, mathematically tractable versions of the SEEXC model for one-unit (simple RT) and two-unit (two-choice RT) systems. The model dynamics are defined by differential equations where activation changes based on input, leakage, competition, and self-excitation. Self-excitation ($\epsilon$) increases with practice according to a standard neural network learning law, bounded by the leakage parameter ($k$). The authors derive analytic solutions for the one-unit system and use sum-and-difference transformations to analyze the two-unit system. They also employ numerical simulations to examine response times and the Relative Learning Rate (RLR)—the rate of RT decrease relative to remaining improvement potential—across various parameter settings. The results demonstrate that SEEXC successfully reproduces practice curves consistent with empirical exponential data. Analytically, the one-unit model yields an RLR that is bounded and decreases slightly with practice, approaching a constant value asymptotically, which aligns with the APEX function fit to human data. In contrast, the authors prove that input-learning models only match this data if input increases faster than the square of $N$, which is theoretically implausible. Numerical simulations of the two-unit system confirm that its practice curves exhibit similar RLR properties to the one-unit system, approaching the learning rate constant $\lambda$ as $N$ increases. The model also explains how practice transitions the system from convergent to divergent dynamics, ensuring responses even with small input differences. The significance of this work lies in providing a mechanistic explanation for the exponential nature of skill acquisition within a neural network framework. By attributing practice effects to changes in self-excitation rather than input strength, SEEXC resolves the discrepancy between previous theoretical predictions and empirical observations. The findings suggest that expertise reduces information leakage, allowing for more efficient integration of evidence. This model offers a constrained framework for designing more complex stochastic simulations and implies that local modulation of self-excitation is a plausible biological mechanism for learning, distinct from global threshold adjustments often used in other models.

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• automaticity skill acquisition