Related papers: Learning Orientations: a Discrete Geometry Model
The mammalian hippocampus plays a principal role in producing a cognitive map of space---an internalized representation of the animal's environment. The neuronal mechanisms producing this map depend primarily on the temporal structure of…
The acoustic cues used by humans and other animals to localise sounds are subtle, and change during and after development. This means that we need to constantly relearn or recalibrate the auditory spatial map throughout our lifetimes. This…
The brain transforms visual inputs into high-dimensional cortical representations that support diverse cognitive and behavioral goals. Characterizing how this information is organized and routed across the human brain is essential for…
Inspired by research in psychology, we introduce a behavioral approach for visual navigation using topological maps. Our goal is to enable a robot to navigate from one location to another, relying only on its visual input and the…
A neural network system in an animal brain contains many modules and generates adaptive behavior by integrating the outputs from the modules. The mathematical modeling of such large systems to elucidate the mechanism of rapidly finding…
How do humans and other animals learn new tasks? A wave of brain recording studies has investigated how neural representations change during task learning, with a focus on how tasks can be acquired and coded in ways that minimise mutual…
Topological data analyses are rapidly turning into key tools for quantifying large volumes of neurobiological data, e.g., for organizing the spiking outputs of large neuronal ensembles and thus gaining insights into the information produced…
The mammalian brain is a metabolically expensive device, and evolutionary pressures have presumably driven it to make productive use of its resources. For sensory areas, this concept has been expressed more formally as an optimality…
In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, having Cognitome theory of brain function in mind. In our…
We propose a novel machine learning strategy for studying neuroanatomical shape variation. Our model works with volumetric binary segmentation images, and requires no pre-processing such as the extraction of surface points or a mesh. The…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Animal navigation research posits that organisms build and maintain internal spatial representations, or maps, of their environment. We ask if machines -- specifically, artificial intelligence (AI) navigation agents -- also build implicit…
Finding a code to unravel the population of neural responses that leads to a distinct animal behavior has been a long-standing question in the field of neuroscience. With the recent advances in machine learning, it is shown that the…
For decades, neuroscientists and computer scientists have pursued a shared ambition: to understand intelligence and build it. Modern artificial neural networks now rival humans in language, perception, and reasoning, yet it is still largely…
Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid…
Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their…
A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we…
In cognitive science and AI, a longstanding question is whether machines learn representations that align with those of the human mind. While current models show promise, it remains an open question whether this alignment is superficial or…
Whether it be in a man-made machine or a biological system, form and function are often directly related. In the latter, however, this particular relationship is often unclear due to the intricate nature of biology. Here we developed a…