Symbols, Dynamics, and Maps: A Neurosymbolic Approach to Spatial Cognition

Abstract

The discovery of various spatially sensitive neurons in the hippocampal formation, such as place, grid, and boundary cells, has provided valuable insights into the neural mechanisms underlying spatial representation and navigation. However, neural activity and connectivity data alone cannot fully reveal the brain’s algorithms. Bridging this gap requires computational models that not only explain the low-level activity of spatially sensitive cells but also link it to higher-level symbolic representations manipulable within a cognitive framework – models capable of binding spatial representations to discrete abstractions, while also supporting hierarchical and probabilistic structures that enable reasoning and decision-making.

The Semantic Pointer Architecture (SPA; Eliasmith, 2013), in combination with the Neural Engineering Framework (NEF; Eliasmith et al., 2003), provides a mathematical and computational framework to represent symbols and implement dynamical systems in spiking neural networks. Spatial Semantic Pointers (SSPs; Komer et al., 2019), an extension to the SPA, encode continuous variables, such as spatial locations, while supporting the binding of spatial information with other features – continuous or discrete – into compressed, multi-domain representations. This flexibility allows SSPs to model diverse cognitive processes, ranging from spatial memory to abstract reasoning, offering a unified theory for how continuous variables might be represented and manipulated in the brain.

In this thesis, we leverage these tools to model key components of spatial cognition, including path integration, cognitive map creation, and reinforcement learning. Our contributions include the development of SSP-PI, a SSP-based path integration model that combines velocity controlled oscillators with attractor dynamics to integrate continuous spatial variables. We also introduce SSP-SLAM, a biologically inspired spiking neural SLAM system capable of constructing semantic cognitive maps that bind and associate spatial and non spatial features. Furthermore, we propose spiking RL models that demonstrate how SSP embeddings can effectively represent successor features, reward distributions, and stochastic policies. Finally, we use the SPA and SSPs to construct state embeddings for deep RL networks, demonstrating their utility in tasks requiring mixed semantic-spatial representations.

Our findings underscore the potential of SSPs to act as a unifying framework for understanding spatial representation in the brain while advancing biologically inspired approaches to navigation and learning in artificial systems. This work bridges theoretical neuroscience and artificial intelligence, laying the groundwork for future explorations of shared principles across spatial and abstract cognition.