Temporal regularities are everywhere in our everyday world: bird songs, traffic lights, weather changes, and even spoken language are examples of the wide range of temporal structures we are constantly exposed to. Detecting those temporal regularities allow us to formulate predictions about the future (e.g., that the traffic light will turn red) and adapt our behaviour accordingly (e.g., stop the car).
Although it is known that the human brain is sensitive to a very diverse repertoire of temporal structures; the precise algorithm we employ to detect temporal regularities remains unknown. In our recent Nature Human Behaviour article, we studied a very simple dichotomy between regularities allowing better than chance prediction, but with a different degree of certainty: deterministic rules (e.g., traffic lights) afford sure predictions, while statistical biases (e.g., weather changes) only allow uncertain predictions. The statistics-versus-rules debate has long divided cognitive scientists , and as a result, these types of regularity have been explored in mostly distinct lines of research, and we lack a unified account of how the human brain manages to identify them.
To assess how human participants detected these regularities, we combined fine-grained experimental psychology with detailed computational modelling. On the one hand, we presented human participants with very simple binary auditory sequence which could transition from random to regular (deterministic or statistical) such as ...ABBABAAAABAB|AABBAABBAABB... (where ‘|’ is the, hidden, change-point). In addition, we created a novel finger-tracking apparatus which allowed participants to report their beliefs about the probability of each hypothesis in a continuous, joint and online manner. On the other hand, we devised a normative learning model to which we input the same sequences that were presented to subjects and which also report its beliefs in all generative hypotheses.
Deterministic and statistical hypotheses are detected at different speed
We first simply looked at how participants detected the regularities we embedded in otherwise fully random sequences. By comparing the increase in reported probabilities for the statistical versus deterministic hypotheses, we observed that the confidence of participants in detecting a deterministic regularity built up much more rapidly than for statistical regularities. This feature was reproduced by our model and reflects the fact that the deterministic rule hypothesis considers only extreme probability values (essentially 0 versus 1), such that evidence for or against it accumulates rapidly. Strikingly, the detection dynamics seems to correspond to ‘aha-moment’  for deterministic rules while the detection of statistical biases would resemble a progressive evidence accumulation . Importantly, both learning dynamics have been previously reported in other experimental paradigms.
Deterministic and statistical hypotheses are constantly compared
Next, we asked whether participants compared statistical versus deterministic hypotheses constantly and gradually throughout the sequence or whether they alternated between them. To assess this, we included in our experimental design deterministic rules which also embed a statistical bias, such as AAAAABBBBB, which contains more repetitions than expected by chance. In these conditions, our model, which constantly compares both hypotheses, makes a key prediction: beliefs should first favour a statistical explanation, before exhibiting a ‘change-of-mind’ once enough observations have been received to conclude the regularity is in fact deterministic. As predicted by our model, in such cases, participants first favour the statistical bias hypothesis before changing to the deterministic hypothesis (again with a ballistic detection). The extent of this effect was predicted by the strength of the statistical bias characterizing the rules, with larger change-of-mind for strongly biased rules (quantified by Shannon entropy). This suggests that participants constantly evaluate and gradually compare both statistical and deterministic hypotheses against each other.
Deterministic and statistical hypotheses correspond to distinct hypothesis spaces
It is easy to see that deterministic regularities are a particular case of statistical biases in which the probability of events is 0 and 1. We thus asked whether participants were considering statistical and deterministic regularities indeed as pertaining to genuinely distinct hypothesis spaces, or instead to a continuum with rules as an extreme case. To do this, we compared our statistics versus rules two-system model against a variety of models of different flavours, but that all used statistical learning for both statistical biases and deterministic rules. We found that different aspects of human behaviour were best explained by the dual-system model, and rejected the all-statistical alternatives. We also compared alternative models resorting on non-normative arbitration between statistics and rules, which were also rejected.
Our study suggests that the human brain is equipped with, at least, two hypothesis spaces for temporal regularities: one for learning statistical trends, and the other for deterministic rules and patterns. The probability of both hypotheses is further expressed in the same currency which allows to constantly compare them and identify the hypothesis which best explains the observations.
This discovery has important implications for several other fields. On the one hand, because both statistical (e.g., the syllable ‘ry’ often follows the syllable ‘to’, as in ‘factory’) and deterministic (e.g., the -s mark for plural forms, as in ‘these factories’) regularities are embedded in language, this dual-system might also be recruited during language acquisition or production . On the other hand, dividing the space of possibilities into distinct hypothesis spaces is a promising avenue towards more general and less computationally expensive artificial learning agents .
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