Related papers: Can rodents conceive hyperbolic spaces?
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
Behavioral flexibility is learning from previous experiences and planning appropriate actions in a changing or novel environment. Successful behavioral adaptation depends on internal models the brain builds to represent the relational…
Grid cells play a principal role in enabling mammalian cognitive representations of ambient environments. The key property of these cells -- the regular arrangement of their firing fields -- is commonly viewed as means for establishing…
Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values…
Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…
To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step…
Representing and reasoning about physical space is fundamental to animal survival, and the mammalian lineage expresses a wealth of specialized neural representations that encode space. Grid cells, whose discovery earned a Nobel prize, are a…
Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces. We simulated place cell populations that encoded either Euclidean- or graph-based positions of a rat navigating to goal nodes in a maze…
Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…
Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation…
Grid cells in the medial entorhinal cortex and place cells in the hippocampus together support spatial navigation. The two regions are reciprocally connected, and there is a chicken-and-egg problem for how both arise and reinforce each…
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
Research on network mechanisms and coding properties of grid cells assume that the firing rate of a grid cell in each of its fields is the same. Furthermore, proposed network models predict spatial regularities in the firing of inhibitory…
Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and…
Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…
Negatively curved, or hyperbolic, regions of space in an FRW universe are a realistic possibility. These regions might occur in voids where there is no dark matter with only dark energy present. Hyperbolic space is strange and various…
The hippocampus encodes space through a striking gradient of place field sizes along its dorsal-ventral axis, yet the principles generating this continuous gradient from discrete grid cell inputs remain debated. We propose a unified…
Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the…