A Grid Cell-Inspired Structured Vector Algebra for Cognitive Maps

2025-03-11

AI Summary

Mammalian entorhinal-hippocampal circuits—particularly grid cells—support both continuous spatial navigation and discrete abstract relational reasoning, yet no unified computational framework accounts for both functions. Method: We propose Grid Cell–inspired Structured Vector Symbolic Architecture (GC-VSA), the first integration of Continuous Attractor Networks (CANs) with Vector Symbolic Architectures (VSAs). GC-VSA employs 3D neural modules to emulate multi-scale, multi-orientation grid cells; incorporates hexagonal receptive fields; and introduces hybrid symbol-vector operations for structured, geometrically interpretable vector representations. Contribution/Results: GC-VSA achieves high accuracy on path integration, spatiotemporal relation retrieval, and hierarchical family-tree inference—demonstrating that a single representational framework can effectively support both continuous and discrete cognitive tasks, thereby unifying spatial and relational computation under a biologically grounded architecture.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells. This system is well-studied in neuroscience, and its efficiency and versatility make it attractive for applications in robotics and machine learning. While continuous attractor networks (CANs) successfully model entorhinal grid cells for encoding physical space, integrating both continuous spatial and abstract spatial computations into a unified framework remains challenging. Here, we attempt to bridge this gap by proposing a mechanistic model for versatile information processing in the entorhinal-hippocampal formation inspired by CANs and Vector Symbolic Architectures (VSAs), a neuro-symbolic computing framework. The novel grid-cell VSA (GC-VSA) model employs a spatially structured encoding scheme with 3D neuronal modules mimicking the discrete scales and orientations of grid cell modules, reproducing their characteristic hexagonal receptive fields. In experiments, the model demonstrates versatility in spatial and abstract tasks: (1) accurate path integration for tracking locations, (2) spatio-temporal representation for querying object locations and temporal relations, and (3) symbolic reasoning using family trees as a structured test case for hierarchical relationships.

Problem

• Integrating continuous and abstract spatial computations into a unified framework.
• Developing a mechanistic model for versatile information processing in brain navigation.
• Enhancing spatial and abstract task performance using grid-cell-inspired vector algebra.

Innovation

• Grid-cell inspired 3D neuronal modules
• Combines continuous and abstract spatial computations
• Versatile in spatial tracking and symbolic reasoning