cognitive modelers

Abstract: Concepts are commonly defined as abstract, compact representations of knowledge and treated as basic units of intelligent behavior. Yet, cognition, psychology, and AI lack a shared mathematical language for them. Modern systems represent concepts as vectors, distributions, symbols, graphs, and other structures, but these formalisms are typically treated as competing rather than as solutions to a common problem. We propose an operation-based view that evaluates mathematical frameworks by the conceptual operations they support, identifying thirteen operations (including similarity, composition, generalization, and grounding) that recur across cognition, psychology, and AI. We show that ten frameworks embody distinct commitments to concepts as self-contained content, relational structure, or evolving process, and that these commitments determine which operations each supports naturally. For example, vector-based models facilitate graded similarity and generalization but struggle with explicit composition, whereas symbolic models support composition but offer but generalize poorly. No single framework we examined naturally supports all operations without extension. We test this account empirically using categorization as a case study, operationalizing nine theories on the same items against human judgments. Despite addressing the same conceptual question, the theories produce different procedures and results, demonstrating that mathematical commitment shapes what a theory can explain. We call for hybrid formalisms that treat content, relation, and process as jointly primary.

Abstract: Probability is fundamental to theories of language comprehension, production, acquisition, and evolution, as well as to large language models. Existing theories estimate the probability of syntactic structures from language-specific data. Whether part of this probability structure can arise independently of language-specific experience remains unknown. Here I show that a universal prior over syntactic structures emerges from a cognitively motivated model of incremental language production, in which words are progressively integrated into syntactic structure through network growth. The resulting prior assigns probabilities to syntactic structures --represented as dependency trees-- without fitting parameters to linguistic data, and assigns higher probabilities to attested than to random trees in all 138 typologically diverse languages examined. These prior probabilities correlate positively with probabilities estimated from corpora in 33 of 34 languages. The results indicate that part of the probability structure of syntax can arise independently of language-specific statistical learning. Linguistic experience may therefore refine probabilities that are already structured by the process of language production, rather than create them from an initially uniform space. This identifies a possible cognitive origin for part of the probability distribution over syntactic structures, linking language production and statistical learning while providing a data-independent structural bias for probabilistic models of language.