Related papers: Can rodents conceive hyperbolic spaces?
About a decade ago grid cells were discovered in the medial entorhinal cortex of rat. Their peculiar firing patterns, which correlate with periodic locations in the environment, led to early hypothesis that grid cells may provide some form…
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…
The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show a triangular grid pattern, and once established might be based in part on path-integration mechanisms. Grid axes are tightly…
The grid firing patterns are thought to provide an efficient intrinsic metric capable of supporting universal spatial metric for mammalian spatial navigation in all environments. However, whether spatial representations of grid cells in the…
Grid cells in the entorhinal cortex fire when animals that are exploring a certain region of space occupy the vertices of a triangular grid that spans the environment. Different neurons feature triangular grids that differ in their…
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…
Grid cells in the entorhinal cortex are believed to establish their regular, spatially correlated firing patterns by path integration of the animal's motion. Mechanisms for path integration, e.g. in attractor network models, predict…
Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data across diverse modalities. Recent studies show that token distributions in foundation models exhibit scale-free properties, suggesting that hyperbolic…
Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…
Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…
Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…
The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…
Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…
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…
Encoding the distance between locations in space is essential for accurate navigation. Grid cells, a functional class of neurons in medial entorhinal cortex, are believed to support this computation. However, existing theories of how…
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…
Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
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 recorded in the parahippocampal formation of freely moving rodents provide a strikingly periodic representation of self-location whose underlying mechanism has been the subject of intense interest. Our previous work(1) showed…
Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability…