Related papers: On Conformal Isometry of Grid Cells: Learning Dist…
Space is represented in the mammalian brain by the activity of hippocampal place cells as well as in their spike-timing correlations. Here we propose a theory how this temporal code is transformed to spatial firing rate patterns via…
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
In this paper we explain the strikingly regular activity of the 'grid' cells in rodent dorsal medial entorhinal cortex (dMEC) and the spatially localized activity of the hippocampal place cells in CA3 and CA1 by assuming that the…
Finding interesting symmetrical topological structures in high-dimensional systems is an important problem in statistical machine learning. Limited amount of available high-dimensional data and its sensitivity to noise pose computational…
The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet one class of models describing the formation of grid unit selectivity is…
Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…
A common approach for modeling the environment of an autonomous vehicle are dynamic occupancy grid maps, in which the surrounding is divided into cells, each containing the occupancy and velocity state of its location. Despite the advantage…
Place cells in the rat hippocampus play a key role in creating the animal's internal representation of the world. During active navigation, these cells spike only in discrete locations, together encoding a map of the environment.…
Grid cells are believed to play an important role in both spatial and non-spatial cognition tasks. A recent study observed the emergence of grid cells in an LSTM for path integration. The connection between biological and artificial neural…
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…
Place cells in the hippocampus are active when an animal visits a certain location (referred to as a place field) within an environment. Grid cells in the medial entorhinal cortex (MEC) respond at multiple locations, with firing fields that…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
The human brain possesses the extraordinary capability to contextualize the information it receives from our environment. The entorhinal-hippocampal plays a critical role in this function, as it is deeply engaged in memory processing and…
We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric…
While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…
Growing demands in the semiconductor industry result in the need for enhanced performance of lithographic equipment. However, position tracking accuracy of high precision mechatronics is often limited by the presence of disturbance sources,…
Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…
Grid cells in medial entorhinal cortex are believed to play a key role in path integration. However, the relation between path integration and the grid-like arrangement of their firing field remains unclear. We provide theoretical evidence…