Related papers: On Path Integration of Grid Cells: Group Represent…
This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that…
The activity of the grid cell population in the medial entorhinal cortex (MEC) of the mammalian brain forms a vector representation of the self-position of the animal. Recurrent neural networks have been proposed to explain the properties…
This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding…
Grid cells enable the brain to model the physical space of the world and navigate effectively via path integration, updating self-position using information from self-movement. Recent proposals suggest that the brain might use similar…
Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and…
Work on deep learning-based models of grid cells suggests that grid cells generically and robustly arise from optimizing networks to path integrate, i.e., track one's spatial position by integrating self-velocity signals. In previous work,…
We present a minimalistic representation model for the head direction (HD) system, aiming to learn a high-dimensional representation of head direction that captures essential properties of HD cells. Our model is a representation of rotation…
Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have…
We develop a geometric representation for the ground state of the spin-1/2 quantum XXZ ferromagnetic chain in terms of suitably weighted random walks in a two-dimensional lattice. The path integral model so obtained admits a genuine…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…
Next-token predictors often appear to develop internal representations of the latent world and its rules. The probabilistic nature of these models suggests a deep connection between the structure of the world and the geometry of probability…
The grid cells (GCs) of the medial entorhinal cortex (MEC) and place cells (PCs) of the hippocampus are key elements of the brain network for the metric representation of space. Currently, any of the existing theoretical models can explain…
Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of…
High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…
In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an $xy$-monotone grid path connects the two endpoints without hitting an…
Grid cells, discovered more than a decade ago [5], are neurons in the brain of mammals that fire when the animal is located near certain specific points in its familiar terrain. Intriguingly, these points form, for a single cell, a…
Grid cells in the rodent entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space, and have been hypothesized to form the neural substrate for dead-reckoning. However, in previous models suggested…
We propose flexgrid2vec, a novel approach for image representation learning. Existing visual representation methods suffer from several issues, including the need for highly intensive computation, the risk of losing in-depth structural…
Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…