arXiv subjects

Britt Anderson

Publications and source records attributed to Britt Anderson.

3 recordsLinked to original sources

arXiv2025

Explaining Human Choice Probabilities with Simple Vector Representations

We formalize human choice behavior in a probabilistic hide-and-seek task. In our geometric construction, vectors represent participant choice frequencies as well as probability matching and maximizing strategies. We measured choice behavior not just in the well-studied scenario of pursuing an objective (seeking), but also the rarely studied scenario of avoiding consequences (hiding). We used our geometric construction to define the avoidance counterpart of probability matching, probability antimatching, as a vector reflection across the uniform distribution. Decomposing the behavior of participants when they were seeking into matching and maximizing components, we could mathematically derive the analogous antimatching and minimizing strategies for hiding. Participants did change their choice frequencies between hiding and seeking conditions. In both cases, we found that a linear combination of just two vectors did an excellent job of fitting participant choice frequencies: matching + maximizing for seeking, antimatching + minimizing for hiding. We could account for diversity in participant strategy usage by varying the coefficients of the two relevant basis strategy vectors. We successfully applied this model in scenarios of up to 7 rooms. We conclude that an apparent diversity of human conduct in stochastic environments can, in some cases, be explained by varying the weighting of two principle strategies: whether to match/antimatch or maximize/minimize.

q-bio.NC↗

arXiv2025

Developing a Foundation of Vector Symbolic Architectures Using Category Theory

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.

cs.AI↗

arXiv2022

Plinko: Eliciting beliefs to build better models of statistical learning and mental model updating

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.

q-bio.NC↗