Periodic Reporting for period 3 - COGTOM (Cognitive tomography of mental representations) Reporting period: 2020-05-01 to 2021-10-31 Summary of the context and overall objectives of the project Internal models are fundamental to our understanding of how the mind constructs percepts, makes decisions, controls movements, and interacts with others. Yet, we lack principled quantitative methods to systematically estimate internal models from observable behaviour. Current approaches for discovering the mental representations of internal models remain heuristic and piecemeal. The aim of the project is to develop a set of novel data analytical methods, using state-of-the-art statistical and machine learning techniques to infer humans’ internal models. This approach, cognitive tomography, takes a series of behavioural observations, each of which in itself may have very limited information content, and accumulates a detailed reconstruction of the internal model based on these observations. We also apply a set of stringent, quantifiable criteria which are systematically applied at each step of the work to rigorously assess the success of our approach. These methodological advances will allow us to track how the structured, task-general internal models that are so fundamental to humans’ superior cognitive abilities, change over time as a result of decay, interference, and learning. We apply cognitive tomography to a variety of experimental data sets, collected by our collaborators, in paradigms ranging from perceptual learning, through visual and motor structure learning, to social and concept learning. These analyses will allow us to conclusively and quantitatively test our central hypothesis that, rather than simply changing along a single "memory strength" dimension, internal models typically change via complex and consistent patterns of transformations along multiple dimensions simultaneously. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far First, we have examined the very bases of Bayesian ideal observer models, and their applicability to human behavioural data. It is crucial to clarify these foundations, as the project (and indeed, a vast amount of research in the field) rests on the assumption that Bayesian ideal observer models provide an accurate description of a variety of cognitive processes. Second, we have started in-depth analyses of eye movements that will be critical to increase the information bandwidth with which we can measure internal models from behaviour. Third, building on state-of-the-art "probabilistic simultaneous localisation and mapping" (SLAM) algorithms used in robotic navigation, we have also developed novel Bayesian internal models of navigation. Fourth, we have studied several implications of probabilistic internal models that can be used to develop more sensitive and powerful behavioural assays for their future measurement. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) We expect to discover the rules by which internal models in a structured cognitive domain (e.g. categorisation) transform longitudinally during learning and forgetting, and to be able to estimate infants' structured internal models based on their eye movements.