# Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps

arXiv: https://arxiv.org/abs/2406.18808 · HTML: https://mlsanity.com/paper/2406.18808/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2024.

## Built on by (most cited first, 7 of 7)

- [Energy-Efficient Information Representation in MNIST Classification Using Biologically Inspired Learning](https://mlsanity.com/paper/2603.00588/) (2026)
- [Building spatial world models from sparse transitional episodic memories](https://mlsanity.com/paper/2505.13696/) (2025)
- [Geodesic Flow Matching for Denoising High-Dimensional Structured Representations](https://mlsanity.com/paper/2606.00248/) (2026)
- [Improved Cleanup and Decoding of Fractional Power Encodings](https://mlsanity.com/paper/2412.00488/) (2024)
- [A Grid Cell-Inspired Structured Vector Algebra for Cognitive Maps](https://mlsanity.com/paper/2503.08608/) (2025)
- [High-resolution spatial memory requires grid-cell-like neural codes](https://mlsanity.com/paper/2507.00598/) (2025)
- [Boosting Brain-inspired Path Integration Efficiency via Learning-based Replication of Continuous Attractor Neurodynamics](https://mlsanity.com/paper/2511.17687/) (2025)

## Abstract (arXiv)

We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in distributed representation. Spatial position is encoded in a residue number system, with individual residues represented by high-dimensional, complex-valued vectors. These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation. Self-consistency between the representations of the overall position and of the individual residues is enforced by a modular attractor network whose modules correspond to the grid cell modules in entorhinal cortex. The vector binding operation can also associate different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus. We show that the model achieves normative desiderata including superlinear scaling of patterns with dimension, robust error correction, and hexagonal, carry-free encoding of spatial position. These properties in turn enable robust path integration and association with sensory inputs. More generally, the model formalizes how compositional computations could occur in the hippocampal formation and leads to testable experimental predictions.