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.
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem.
In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT 2 C 2 ) satisfying the following requirements: 1) to be simple enough so that the complexity of any given finite binary sequence can be computed, 2) to be based on tangible operations of human reasoning (printing, repeating,. . . ), 3) to be sufficiently powerful to generate all possible sequences but not too powerful as to identify regularities which would be invisible to humans. We first formalize LT 2 C 2 , giving its syntax and semantics and defining an adequate notion of program size. Our setting leads to a Kolmogorov complexity function relative to LT 2 C 2 which is computable in polynomial time, and it also induces a prediction algorithm in the spirit of Solomonoff's inductive inference theory. We then prove the efficacy of this language by investigating regularities in strings produced by participants attempting to generate random strings. Participants had a profound understanding of randomness and hence avoided typical misconceptions such as exaggerating the number of alternations. We reasoned that remaining regularities would express the algorithmic nature of human thoughts, revealed in the form of specific patterns. Kolmogorov complexity relative to LT 2 C 2 passed three expected tests examined here: 1) human sequences were less complex than control PRNG sequences, 2) human sequences were not stationary, showing decreasing values of complexity resulting from fatigue, 3) each individual showed traces of algorithmic stability since fitting of partial sequences was more effective to predict subsequent sequences than average fits. This work extends on previous efforts to combine notions of Kolmogorov complexity theory and algorithmic information theory to psychology, by explicitly proposing a language which may describe the patterns of human thoughts. *
Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most of these studies is to reveal the underlying language structuring these representations and providing a general substrate for thought. However, describing a model of thought that is fixed once trained is against the extensive literature that shows how experience shapes concept learning. Here, we ask about the plasticity of these symbolic descriptive languages. We perform a concept learning experiment that demonstrates that humans can change very rapidly the repertoire of symbols they use to identify concepts, by compiling expressions that are frequently used into new symbols of the language. The pattern of concept learning times is accurately described by a Bayesian agent that rationally updates the probability of compiling a new expression according to how useful it has been to compress concepts so far. By portraying the language of thought as a flexible system of rules, we also highlight the difficulties to pin it down empirically.
Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we show how the set of productions of a LoT grammar can be effectively selected from a broad repertoire of possible productions by an inferential process starting from experimental data. We then test this method in the language of geometry, a specific LoT model (Amalric et al., 2017). Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence's probability and its complexity consistent with the theoretical relationship for universal languages described by Levin's Coding Theorem.
When people seek to understand concepts from an incomplete set of examples and counterexamples, there is usually an exponentially large number of classification rules that can correctly classify the observed data, depending on which features of the examples are used to construct these rules. A mechanistic approximation of human concept-learning should help to explain how humans prefer some rules over others when there are many that can be used to correctly classify the observed data. Here, we exploit the tools of propositional logic to develop an experimental framework that controls the minimal rules that are simultaneously consistent with the presented examples. For example, our framework allows us to present participants with concepts consistent with a disjunction and also with a conjunction, depending on which features are used to build the rule. Similarly, it allows us to present concepts that are simultaneously consistent with two or more rules of different complexity and using different features. Importantly, our framework fully controls which minimal rules compete to explain the examples and is able to recover the features used by the participant to build the classification rule, without relying on supplementary attention-tracking mechanisms (e.g. eye-tracking). We exploit our framework in an experiment with a sequence of such competitive trials, illustrating the emergence of various transfer effects that bias participants’ prior attention to specific sets of features during learning.
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