Human and Computer Learning: An Experimental Study

Abstract

Simple memorizing tasks have been chosen such as a binary code on a 5 × 5 matrix. After the establishment of an appropriate protocol, the codified matrices were individually presented to 150 university students (conveniently preselected) who had to memorize them. Multiple presentations were offered seeking perfect performance verified through the correct reproduction of the code. We measured the individual percentage error as a function of the number of successive presentations, and then averaged over the examined population. The learning curve thus obtained decreases (almost monotonically) until becoming virtually zero when the number of presentations attains six. A computer simulation for a similar task is available which uses a two-level perceptron on which an algorithm was implemented allowing for some degree of globality or nonlocality (technically referred to as entropic nonextensivity within a current generalization of the usual, Boltzmann-Gibbs, statistical mechanics). The degree of nonextensivity is characterized by an index q, such that q = 1 recovers the usual, extensive, statistical mechanics, whereas q ≠ 1 implies some degree of nonextensivity. In other words, q – 1 is a (very sensitive) measure of globality (gestalt perception or learning). The computer curves fit well the human result for q . 1.02. It has been verified that even extremely small departures of q from unity lead to strong differences in the learning curve. Our main observation is that, for the very specific learning task on which we focus here, humans perform similarly to slightly nonextensive perceptrons. In addition to this experiment, some preliminary studies were done concerning the human learning of ambiguous images (based on figure-background perception). In spite of the complexity of drawing conclusions from such a comparison, some generic trends can be established. Moreover, the enormous and well-known difficulty for computationally defining semantic, hierarchic and strategic structures reveals clear-cut differences between human and machine learning.

A characterization of the scientific impact of Brazilian institutions

“…Nonextensive statistical mechanics has been applied successfully in physics (astrophysics, astronomy, cosmology, nonlinear dynamics) [19], biology [20], economics [21], human and computer sciences [22][23][24] and provide interesting insights into a variety of physical systems, and among others [25]). …”

Macroscopic thermodynamics of reaction times

“…Recently, some researchers have applied these ideas to explore issues related to human learning (Hadzibeganovic & Cannas, 2009;Tsallis, Tsallis, Magalhaes, & Tamarit, 2003). In a -preliminaryinvestigation of this issue, I did not observe evidence for Tsallis' entropic index q significantly deviating from one in these data.…”

I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status

“…Within this philosophy, we performed [186] an experiment of learning/memorization (of 5 × 5 and 7 × 7 square matrix having circles and crosses randomly distributed once for ever) with students of the University level; 150 students were interviewed, the first 30 in order to optimize the experimental protocol, and the other 120 to make the measurements of the time-evolution of the total amounts of errors when the original matrix was successively shown and hidden. The average results were then fitted with those obtained, for the same task, with a learning machine [187] having a perceptron architecture and an internal dynamics based on the Langevin equation [105] generalized by Stariolo to arbitrary q.…”