Britt Anderson

Peter DiBerardino, Britt Anderson

When people pursue rewards in stochastic environments, they often match their choice frequencies to the observed target frequencies, even when this policy is demonstrably sub-optimal. We used a ``hide and seek'' task to evaluate this behavior under conditions where pursuit (seeking) could be toggled to avoidance (hiding), while leaving the probability distribution fixed, or varying complexity by changing the number of possible choices. We developed a model for participant choice built from choice frequency histograms treated as vectors. We posited the existence of a probability antimatching strategy for avoidance (hiding) rounds, and formalized this as a vector reflection of probability matching. We found that only two basis policies: matching/antimatching and maximizing/minimizing were sufficient to account for participant choices across a range of room numbers and opponent probability distributions. This schema requires only that people have the ability to remember the relative frequency of the different outcomes. With this knowledge simple operations can construct the maximizing and minimizing policies as well as matching and antimatching strategies. A mixture of these two policies captures human choice patterns in a stochastic environment.

Nolan P Shaw, P Michael Furlong, Britt Anderson et al.

Connectionist approaches to machine learning, \emph{i.e.} neural networks, are enjoying a considerable vogue right now. However, these methods require large volumes of data and produce models that are uninterpretable to humans. An alternative framework that is compatible with neural networks and gradient-based learning, but explicitly models compositionality, is Vector Symbolic Architectures (VSAs). VSAs are a family of algebras on high-dimensional vector representations. They arose in cognitive science from the need to unify neural processing and the kind of symbolic reasoning that humans perform. While machine learning methods have benefited from category-theoretical analyses, VSAs have not yet received similar treatment. In this paper, we present a first attempt at applying category theory to VSAs. Specifically, We generalise from vectors to co-presheaves, and describe VSA operations as the right Kan extensions of the external tensor product. This formalisation involves a proof that the right Kan extension in such cases can be expressed as simple, element-wise operations. We validate our formalisation with worked examples that connect to current VSA implementations, while suggesting new possible designs for VSAs.

Peter A. V. DiBerardino, Alexandre L. S. Filipowicz, James Danckert et al.

Prior beliefs are central to Bayesian accounts of cognition, but many of these accounts do not directly measure priors. More specifically, initial states of belief heavily influence how new information is assumed to be utilized when updating a particular model. Despite this, prior and posterior beliefs are either inferred from sequential participant actions or elicited through impoverished means. We had participants play a version of the game "Plinko", to first elicit individual participant priors in a theoretically agnostic manner. Subsequent learning and updating of participant beliefs was then directly measured. We show that participants hold a variety of priors that cluster around prototypical probability distributions that in turn influence learning. In follow-up experiments we show that participant priors are stable over time and that the ability to update beliefs is influenced by a simple environmental manipulation (i.e. a short break). This data reveals the importance of directly measuring participant beliefs rather than assuming or inferring them as has been widely done in the literature to date. The Plinko game provides a flexible and fecund means for examining statistical learning and mental model updating.