A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

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 vectors representing position and 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 be used to bind different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus. We provide model analysis of scaling, similarity preservation and convergence behavior as well as experiments demonstrating noise robustness, sub-integer resolution in representing position, and path integration. The model formalizes the computations in the cognitive map and makes testable experimental predictions.

Medial entorhinal cortex (MEC) supports a wide range of navigational and memory related behaviors.Well-known experimental results have revealed specialized cell types in MEC --- e.g.

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities.

How should the response profiles of these more "heterogeneous" cells be described, and how do they contribute to behavior? In this work, we took a computational approach to addressing these questions.

Episodic memory enables humans to recall past experiences by associating semantic elements such as objects, locations, and time into coherent event representations. While large pretrained models have shown remarkable progress in modeling semantic memory, the mechanisms for forming associative structures that support episodic memory remain underexplored. Inspired by hippocampal CA3 dynamics and its role in associative memory, we propose the Latent Structured Hopfield Network (LSHN), a biologically inspired framework that integrates continuous Hopfield attractor dynamics into an autoencoder architecture. LSHN mimics the cortical-hippocampal pathway: a semantic encoder extracts compact latent representations, a latent Hopfield network performs associative refinement through attractor convergence, and a decoder reconstructs perceptual input. Unlike traditional Hopfield networks, our model is trained end-to-end with gradient descent, achieving scalable and robust memory retrieval. Experiments on MNIST, CIFAR-10, and a simulated episodic memory task demonstrate superior performance in recalling corrupted inputs under occlusion and noise, outperforming existing associative memory models. Our work provides a computational perspective on how semantic elements can be dynamically bound into episodic memory traces through biologically grounded attractor mechanisms. Code: https://github.com/fudan-birlab/LSHN.

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 vectors representing position and 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 be used to bind different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus.