A theory of memory for binary sequences: Evidence for a mental compression algorithm in humans

Abstract

Working memory capacity can be improved by recoding the memorized information in a condensed form. Here, we tested the theory that human adults encode binary sequences of stimuli in memory using an abstract internal language and a recursive compression algorithm. The theory predicts that the psychological complexity of a given sequence should be proportional to the length of its shortest description in the proposed language, which can capture any nested pattern of repetitions and alternations using a limited number of instructions. Five experiments examine the capacity of the theory to predict human adults’ memory for a variety of auditory and visual sequences. We probed memory using a sequence violation paradigm in which participants attempted to detect occasional violations in an otherwise fixed sequence. Both subjective complexity ratings and objective violation detection performance were well predicted by our theoretical measure of complexity, which simply reflects a weighted sum of the number of elementary instructions and digits in the shortest formula that captures the sequence in our language. While a simpler transition probability model, when tested as a single predictor in the statistical analyses, accounted for significant variance in the data, the goodness-of-fit with the data significantly improved when the language-based complexity measure was included in the statistical model, while the variance explained by the transition probability model largely decreased. Model comparison also showed that shortest description length in a recursive language provides a better fit than six alternative previously proposed models of sequence encoding. The data support the hypothesis that, beyond the extraction of statistical knowledge, human sequence coding relies on an internal compression using language-like nested structures.

Author summary

Sequence processing, the ability to memorize and retrieve temporally ordered series of elements, is central to many human activities, especially language and music. Although statistical learning (the learning of the transitions between items) is a powerful way to detect and exploit regularities in sequences, humans also detect more abstract regularities that capture the multi-scale repetitions that occur, for instance, in many musical melodies. Here we test the hypothesis that humans memorize sequences using an additional and possibly uniquely human capacity to represent sequences as a nested hierarchy of smaller chunks embedded into bigger chunks, using language-like recursive structures. For simplicity, we apply this idea to the simplest possible music-like sequences, i.e. binary sequences made of two notes A and B. We first make our assumption more precise by proposing a recursive compression algorithm for such sequences, akin to a “language of thought” with a very small number of simple primitive operations (e.g. “for” loops). We then test whether our theory can predict the fluctuations in the human memory for various binary sequences Using a violation detection task, across many experiments with auditory and visual sequences of different lengths, we find that sequence complexity, defined as the shortest description length in the proposed formal language, correlates well with performance, even when statistical learning is taken into account, and performs better than other measures of sequence complexity proposed in the past. Our results therefore suggest that human individuals spontaneously use a recursive internal compression mechanism to process sequences.