Learning a Vector-Symbolic Model for Socio-Cultural Tasks

How can we better represent the impact of sociocultural structures on decision making in computational cognitive models? Modeling this impact requires traversing multiple levels of semantic representation, however it is not immediately clear to a modeler which levels of representation are most salient to a given situation. Though large language models and cognitively grounded corpus models can represent broad semantic associations through co-occurences, the role of self representations in memory should be accounted for to determine how cultural associations shape decision making. We propose a declarative memory system to be used in the ACT-R cognitive architecture that represents semantic associations at multiple levels via a vector-symbolic autoencoder. We use a simple HRR operation to encode episodic memories differently from semantic memory vectors extracted from text to produce a final chunk activation for a memory request. We use ACT-R cognitive models of a racially contextualized implicit association test (IAT) to test this new declarative memory system.

Toward a Functional Geometric Algebra for Natural Language Semantics

Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable empirical success, yet they face persistent structural limitations in compositional semantics, type sensitivity, and interpretability. I argue in this paper that geometric algebra (GA) -- specifically, Clifford algebras -- provides a mathematically superior foundation for semantic representation, and that a Functional Geometric Algebra (FGA) framework extends GA toward a typed, compositional semantics capable of supporting inference, transformation, and interpretability while retaining full compatibility with distributional learning and modern neural architectures. I develop the formal foundations, identify three core capabilities that GA provides and linear algebra does not, present a detailed worked example illustrating operator-level semantic contrasts, and show how GA-based operations already implicit in current transformer architectures can be made explicit and extended. The central claim is not merely increased dimensionality but increased structural organization: GA expands an $n$-dimensional embedding space into a $2^n$ multivector algebra where base semantic concepts and their higher-order interactions are represented within a single, principled algebraic framework.