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We consider a toy model that exhibits grokking, recently advanced by [Kumar et al, 2023], and take advantage of the simple setting to derive the dynamics of the train and test loss using Dynamical Mean Field Theory (DMFT). This gives a closed-form expression for the gap between train and test loss that characterizes grokking in this toy model, illustrating how two parameters of interest -- NTK alignment and network laziness -- control the size of this gap and how grokking emerges as a uniquely offline property during repeated training over the same dataset. This is the first quantitative characterization of grokking dynamics in a general setting that makes no assumptions about weight decay, weight norm, etc. 

Computational phenotyping has emerged as a powerful tool for characterizing individual variability across a variety of cognitive domains. An individual’s computational phenotype is defined as a set of mechanistically interpretable parameters obtained from fitting computational models to behavioural data. However, the interpretation of these parameters hinges critically on their psychometric properties, which are rarely studied. To identify the sources governing the temporal variability of the computational phenotype, we carried out a 12-week longitudinal study using a battery of seven tasks that measure aspects of human learning, memory, perception and decision making. To examine the influence of state effects, each week, participants provided reports tracking their mood, habits and daily activities. We developed a dynamic computational phenotyping framework, which allowed us to tease apart the time-varying effects of practice and internal states such as affective valence and arousal. Our results show that many phenotype dimensions covary with practice and affective factors, indicating that what appears to be unreliability may reflect previously unmeasured structure. These results support a fundamentally dynamic understanding of cognitive variability within an individual. 

Why, when, and how do stereotypes change? This paper develops a computational account based on the principles of structure learning: stereotypes are governed by probabilistic beliefs about the assignment of individuals to groups. Two aspects of this account are particularly important. First, groups are flexibly constructed based on the distribution of traits across individuals; groups are not fixed, nor are they assumed to map on to categories we have to provide to the model. This allows the model to explain the phenomena of group discovery and subtyping, whereby deviant individuals are segregated from a group, thus protecting the group’s stereotype. Second, groups are hierarchically structured, such that groups can be nested. This allows the model to explain the phenomenon of subgrouping, whereby a collection of deviant individuals is organized into a refinement of the superordinate group. The structure learning account also sheds light on several factors that determine stereotype change, including perceived group variability, individual typicality, cognitive load, and sample size. 

Social-structure learning is the process by which social groups are identified on the basis of experience. Building on models of structure learning in other domains, we formalize this problem within a Bayesian framework. According to this framework, the probabilistic assignment of individuals to groups is computed by combining information about individuals with prior beliefs about group structure. Experiments with adults and children provide support for this framework, ruling out alternative accounts based on dyadic similarity. More broadly, we highlight the implications of social-structure learning for intergroup cognition, stereotype updating, and coalition formation. 

Humans form social coalitions in every society, yet we know little about how we learn and represent social group boundaries. Here we derive predictions from a computational model of latent structure learning to move beyond explicit category labels and interpersonal, or dyadic similarity as the sole inputs to social group representations. Using a model-based analysis of functional neuroimaging data, we find that separate areas correlate with dyadic similarity and latent structure learning. Trial-by-trial estimates of 'allyship' based on dyadic similarity between participants and each agent recruited medial prefrontal cortex/pregenual anterior cingulate (pgACC). Latent social group structure-based allyship estimates, in contrast, recruited right anterior insula (rAI). Variability in the brain signal from rAI improved prediction of variability in ally-choice behavior, whereas variability from the pgACC did not. These results provide novel insights into the psychological and neural mechanisms by which people learn to distinguish 'us' from 'them'.