[Paper Review] How to build a cognitive map: insights from models of the hippocampal formation

James C. R. Whittington, David McCaffary+2 more|arXiv (Cornell University)|Feb 3, 2022

Memory and Neural Mechanisms19 citations

TL;DR

This paper proposes that the hippocampal formation constructs cognitive maps through generalizable, abstract representations rooted in reinforcement learning, path integration, and sequence modeling. By unifying spatial and non-spatial cognition under a common computational framework, it explains how neural mechanisms for spatial mapping can support abstract reasoning, language, and mathematics through shared principles of factorization, manifold learning, and hierarchical abstraction.

ABSTRACT

Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviours for evolutionary viability. The concept of a cognitive map has emerged as one of the leading metaphors for these capacities, and unravelling the learning and neural representation of such a map has become a central focus of neuroscience. While experimentalists are providing a detailed picture of the neural substrate of cognitive maps in hippocampus and beyond, theorists have been busy building models to bridge the divide between neurons, computation, and behaviour. These models can account for a variety of known representations and neural phenomena, but often provide a differing understanding of not only the underlying principles of cognitive maps, but also the respective roles of hippocampus and cortex. In this Perspective, we bring many of these models into a common language, distil their underlying principles of constructing cognitive maps, provide novel (re)interpretations for neural phenomena, suggest how the principles can be extended to account for prefrontal cortex representations and, finally, speculate on the role of cognitive maps in higher cognitive capacities.

Motivation & Objective

• To unify diverse models of the hippocampal formation under a common computational framework for cognitive map construction.
• To explain how neural representations in the hippocampus and entorhinal cortex support not only spatial navigation but also abstract reasoning and task-level generalization.
• To provide normative explanations for neural phenomena such as grid and place cell firing in non-spatial domains.
• To extend principles of cognitive mapping to higher cognitive functions like language, logic, and mathematics.
• To bridge the gap between neural mechanisms, computation, and flexible behavior through a formal, generalizable theory of representation learning.

Proposed method

• Formalizing cognitive map construction as a problem of learning structured, low-dimensional manifolds from sensory and reward inputs.
• Applying reinforcement learning (RL) with value-based and policy-based learning to model how agents infer state representations and plan actions.
• Using path integration and vector-based navigation to simulate continuous spatial and abstract state transitions.
• Introducing factorization of state space into separable, interpretable dimensions (e.g., spatial, sensory, value-based) to enable generalization.
• Modeling sequence-based learning via recurrent and attention-based architectures (e.g., Transformers) to capture temporal and structural patterns in language and logic.
• Reinterpreting neural data (e.g., grid-like activity in fMRI, saccadic replay) as evidence of manifold-based representation in non-spatial domains.

Experimental results

Research questions

• RQ1 How can the same neural mechanisms that build spatial cognitive maps also support abstract reasoning in non-spatial domains?
• RQ2 What computational principles underlie the emergence of grid-like and place-like representations in abstract, non-spatial task spaces?
• RQ3 To what extent can reinforcement learning and path integration explain the formation of hierarchical, generalizable representations in the prefrontal cortex?
• RQ4 Can sequence-based models (e.g., RNNs, Transformers) account for cognitive functions like language and mathematical reasoning through shared mechanisms with spatial mapping?
• RQ5 How do neural representations in the hippocampal formation support systematic generalization across novel experiences and tasks?

Key findings

• Grid-like and place-like neural activity patterns, previously observed in spatial navigation, are also found in human and primate entorhinal and prefrontal cortices during abstract reasoning tasks involving value, sound frequency, or social hierarchies.
• fMRI studies show hexagonally symmetric activation patterns in the human entorhinal cortex and mPFC when navigating two-dimensional abstract spaces such as bird morphology or reward probability.
• Neural representations in the hippocampal formation can be understood as learning low-dimensional manifolds that support path integration and generalization across novel states.
• Reinforcement learning models with factorized state representations can explain the emergence of cognitive maps that enable rapid inference and planning from sparse observations.
• Sequence-based models such as Transformers and RNNs can account for complex cognitive tasks like language and mathematical reasoning by treating them as structured sequence problems with shared computational principles.
• Grid-like activity in the human and monkey entorhinal cortex during saccades on images suggests that visual perception may be processed through a dynamic, sequential sampling mechanism akin to spatial navigation.