Rate-Coding Bundle Memory: A Unified Model of Memory and Control for Symbolic Computation in the Brain

A central tenet of human cognition is systematicity, the principle that understanding one concept is inherently tied to understanding close variations of that concept. Do reasoning models robustly exhibit such systematicity? If so, we would expect consistent performance on structurally equivalent variants of the same task. Here, we extend established rule induction tasks from cognitive science to assess the systematicity of thought in current reasoning models. Each task family has compositional structure that we use to create structurally equivalent task variations through task isomorphisms such as recombination and substitution. We find that despite being able to correctly solve a task, models often fail on structurally equivalent variants of the same task. These findings suggest that many model behaviors lack systematicity, rendering it difficult to robustly establish the cognitive abilities of reasoning models beyond the particular contexts they were evaluated in.

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.

This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing. Whereas traditional neural networks rely on continuous weights and matrix multiplication, this framework works with sparse binary data. It represents information as discrete sets, directly modeling biological neural population codes. I demonstrate that associative memory emerges naturally from network topologies featuring a combinatorially expanded hidden layer. Learning is driven by topological plasticity rather than scalar weight adjustments. This architecture unifies auto-associative and hetero-associative learning under a single core algorithm: information retrieval via subset pattern matching and exact nearest-neighbor search. Operating with constant-time complexity, these mechanisms bridge perceptual data (sparse distributed representations) and symbols (sparse holographic representations) without continuous bottlenecks. Mapping this framework to neuroanatomy, I propose that both the cerebellum and the neocortex implement variants of this algorithm, making subset pattern matching the fundamental engine of cognition. Because it relies on discrete logic rather than matrix arithmetic, this algorithm translates directly into in-memory hardware. This opens a new route toward synthetic intelligence with human-level energy efficiency.