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We develop a mathematical approach to formally proving that certain neural computations and representations exist based on patterns observed in an organism's behaviour. To illustrate, we provide a simple set of conditions under which an ant's ability to determine how far it is from its nest would logically imply neural structures isomorphic to the natural numbers ℕ. We generalise these results to arbitrary behaviours and representations and show what mathematical characterisation of neural computation and representation is simplest while being maximally predictive of behaviour. We develop this framework in detail using a path integration example, where an organism's ability to search for its nest in the correct location implies representational structures isomorphic to two‐dimensional coordinates under addition. We also study a system for processing anbn strings common in comparative work. Our approach provides an objective way to determine what theory of a physical system is best, addressing a fundamental challenge in neuroscientific inference. These results motivate considering which neurobiological structures have the requisite formal structure and are otherwise physically plausible given relevant physical considerations such as generalisability, information density, thermodynamic stability and energetic cost. [ABSTRACT FROM AUTHOR]

The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take finite data and go far beyond what they directly observe or perceive. To illustrate, this paper then outlines a model which acquires a counting procedure using observations of sets and words, extending the proposal of Piantadosi et al. (2012). This new version of the model responds to several critiques of the original work and outlines an approach which is likely appropriate for acquiring further aspects of mathematics. [ABSTRACT FROM AUTHOR]

The capacity to generate recursive sequences is a marker of rich, algorithmic cognition, and perhaps unique to humans. Yet, the precise processes driving recursive sequence generation remain mysterious. We investigated three potential cognitive mechanisms underlying recursive pattern processing: hierarchical reasoning, ordinal reasoning, and associative chaining. We developed a Bayesian mixture model to quantify the extent to which these three cognitive mechanisms contribute to adult humans' performance in a sequence generation task. We further tested whether recursive rule discovery depends upon relational information, either perceptual or semantic. We found that the presence of relational information facilitates hierarchical reasoning and drives the generation of recursive sequences across novel depths of center embedding. In the absence of relational information, the use of ordinal reasoning predominates. Our results suggest that hierarchical reasoning is an important cognitive mechanism underlying recursive pattern processing and can be deployed across embedding depths and relational domains. [ABSTRACT FROM AUTHOR]

Hierarchical cognitive mechanisms underlie sophisticated behaviors, including language, music, mathematics, tool‐use, and theory of mind. The origins of hierarchical logical reasoning have long been, and continue to be, an important puzzle for cognitive science. Prior approaches to hierarchical logical reasoning have often failed to distinguish between observable hierarchical behavior and unobservable hierarchical cognitive mechanisms. Furthermore, past research has been largely methodologically restricted to passive recognition tasks as compared to active generation tasks that are stronger tests of hierarchical rules. We argue that it is necessary to implement learning studies in humans, non‐human species, and machines that are analyzed with formal models comparing the contribution of different cognitive mechanisms implicated in the generation of hierarchical behavior. These studies are critical to advance theories in the domains of recursion, rule‐learning, symbolic reasoning, and the potentially uniquely human cognitive origins of hierarchical logical reasoning. [ABSTRACT FROM AUTHOR]

Standard models in quantitative linguistics assume that word usage follows a fixed frequency distribution, often Zipf's law or a close relative. This view, however, does not capture the near daily variations in topics of conversation, nor the short‐term dynamics of language change. In order to understand the dynamics of human language use, we present a corpus of daily word frequency variation scraped from online news sources every 20 min for more than 2 years. We construct a simple time‐varying model with a latent state, which is observed via word frequency counts. We use Bayesian techniques to infer the parameters of this model for 20,000 words, allowing us to convert complex word‐frequency trajectories into low‐dimensional parameters in word usage. By analyzing the inferred parameters of this model, we quantify the relative mobility and drift of words on a day‐to‐day basis, while accounting for sampling error. We quantify this variation and show evidence against "rich‐get‐richer" models of word use, which have been previously hypothesized to explain statistical patterns in language. [ABSTRACT FROM AUTHOR]

Zipf famously stated that, if natural language lexicons are structured for efficient communication, the words that are used the most frequently should require the least effort. This observation explains the famous finding that the most frequent words in a language tend to be short. A related prediction is that, even within words of the same length, the most frequent word forms should be the ones that are easiest to produce and understand. Using orthographics as a proxy for phonetics, we test this hypothesis using corpora of 96 languages from Wikipedia. We find that, across a variety of languages and language families and controlling for length, the most frequent forms in a language tend to be more orthographically well‐formed and have more orthographic neighbors than less frequent forms. We interpret this result as evidence that lexicons are structured by language usage pressures to facilitate efficient communication. [ABSTRACT FROM AUTHOR]

Complex systems are often built from a relatively small set of basic features or operations that can be combined in myriad ways. We investigated the developmental origins of this compositional architecture in 9‐month‐old infants, extending recent work that demonstrated rudimentary compositional abilities in preschoolers. Infants viewed two separate object‐occlusion events that depicted a single‐feature‐change operation. They were then tested with a combined operation to determine whether they expected the outcome of the two feature changes, even though this combination was unfamiliar. In contrast to preschoolers, infants did not appear to predictively compose these simple feature‐change operations. A second experiment demonstrated the ability of infants to track two operations when not combined. The failure to compose basic operations is consistent with limitations on object tracking and early numerical cognition (Feigenson & Yamaguchi, Infancy, 2009, 14, 244). We suggest that these results can be unified via a general principle: Infants have difficulty with multiple updates to a representation of an unobservable. [ABSTRACT FROM AUTHOR]

Abstract: Objectives: We assessed associations between child stunting, recovery, and faltering with schooling and human capital skills in a native Amazonian society of horticulturalists‐foragers (Tsimane'). Methods: We used cross‐sectional data (2008) from 1262 children aged 6 to 16 years in 53 villages to assess contemporaneous associations between three height categories: stunted (height‐for‐age Z score, HAZ<–2), moderately stunted (–2 ≤ HAZ≤–1), and nonstunted (HAZ>–1), and three categories of human capital: completed grades of schooling, test‐based academic skills (math, reading, writing), and local plant knowledge. We used annual longitudinal data (2002–2010) from all children (n = 853) in 13 villages to estimate the association between changes in height categories between the first and last years of measure and schooling and academic skills. Results: Stunting was associated with 0.4 fewer completed grades of schooling (∼24% less) and with 13–15% lower probability of showing any writing or math skills. Moderate stunting was associated with ∼20% lower scores in local plant knowledge and 9% lower probability of showing writing skills, but was not associated with schooling or math and writing skills. Compared with nonstunted children, children who became stunted had 18–21% and 15–21% lower probabilities of showing math and writing skills, and stunted children had 0.4 fewer completed grades of schooling. Stunted children who recovered showed human capital outcomes that were indistinguishable from nonstunted children. Conclusions: The results confirm adverse associations between child stunting and human capital skills. Predictors of growth recovery and faltering can affect human capital outcomes, even in a remote, economically self‐sufficient society. [ABSTRACT FROM AUTHOR]

Although the mapping between form and meaning is often regarded as arbitrary, there are in fact well-known constraints on words which are the result of functional pressures associated with language use and its acquisition. In particular, languages have been shown to encode meaning distinctions in their sound properties, which may be important for language learning. Here, we investigate the relationship between semantic distance and phonological distance in the large-scale structure of the lexicon. We show evidence in 100 languages from a diverse array of language families that more semantically similar word pairs are also more phonologically similar. This suggests that there is an important statistical trend for lexicons to have semantically similar words be phonologically similar as well, possibly for functional reasons associated with language learning. [ABSTRACT FROM AUTHOR]

Infants must learn about many cognitive domains (e.g., language, music) from auditory statistics, yet capacity limits on their cognitive resources restrict the quantity that they can encode. Previous research has established that infants can attend to only a subset of available acoustic input. Yet few previous studies have directly examined infant auditory attention, and none have directly tested theorized mechanisms of attentional selection based on stimulus complexity. This work utilizes model-based behavioral methods that were recently developed to examine visual attention in infants (e.g., Kidd, Piantadosi, & Aslin, 2012). The present results demonstrate that 7- to 8-month-old infants selectively attend to nonsocial auditory stimuli that are intermediately predictable/complex with respect to their current implicit beliefs and expectations. These findings provide evidence of a broad principle of infant attention across modalities and suggest that sound-to-sound transitional statistics heavily influence the allocation of auditory attention in human infants. [ABSTRACT FROM AUTHOR]

We show that children in the Tsimane', a farming-foraging group in the Bolivian rain-forest, learn number words along a similar developmental trajectory to children from industrialized countries. Tsimane' children successively acquire the first three or four number words before fully learning how counting works. However, their learning is substantially delayed relative to children from the United States, Russia, and Japan. The presence of a similar developmental trajectory likely indicates that the incremental stages of numerical knowledge - but not their timing - reflect a fundamental property of number concept acquisition which is relatively independent of language, culture, age, and early education. [ABSTRACT FROM AUTHOR]

Studies of infant looking times over the past 50 years have provided profound insights about cognitive development, but their dependent measures and analytic techniques are quite limited. In the context of infants' attention to discrete sequential events, we show how a Bayesian data analysis approach can be combined with a rational cognitive model to create a rich data analysis framework for infant looking times. We formalize (i) a statistical learning model, (ii) a parametric linking between the learning model's beliefs and infants' looking behavior, and (iii) a data analysis approach and model that infers parameters of the cognitive model and linking function for groups and individuals. Using this approach, we show that recent findings from Kidd, Piantadosi and Aslin () of a U-shaped relationship between look-away probability and stimulus complexity even holds within infants and is not due to averaging subjects with different types of behavior. Our results indicate that individual infants prefer stimuli of intermediate complexity, reserving attention for events that are moderately predictable given their probabilistic expectations about the world. [ABSTRACT FROM AUTHOR]

Absolute linguistic universals are often justified by cross-linguistic analysis: If all observed languages exhibit a property, the property is taken to be a likely universal, perhaps specified in the cognitive or linguistic systems of language learners and users. In many cases, these patterns are then taken to motivate linguistic theory. Here, we show that cross-linguistic analysis will very rarely be able to statistically justify absolute, inviolable patterns in language. We formalize two statistical methods-frequentist and Bayesian-and show that in both it is possible to find strict linguistic universals, but that the numbers of independent languages necessary to do so is generally unachievable. This suggests that methods other than typological statistics are necessary to establish absolute properties of human language, and thus that many of the purported universals in linguistics have not received sufficient empirical justification. [ABSTRACT FROM AUTHOR]