Related papers: Learning Orientations: a Discrete Geometry Model
The brain constantly turns large flows of sensory information into selective representations of the environment. It, therefore, needs to learn to process those sensory inputs that are most relevant for behaviour. It is not well understood…
Computational models are an essential tool for understanding the origin and functions of the topographic organisation of the primate visual system. Yet, vision is most commonly modelled by convolutional neural networks that ignore…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
Biological neural networks exist in physical space where distance influences communication delays: a fundamental coupling between space and time absent in most artificial neural networks. While recent work has separately explored spatial…
The human brain represents objects in a way that is both invariant across instances and flexible enough to support different contexts and tasks. Yet it remains unknown how object representations are dynamically remapped as the same object…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences…
Can neural networks learn goal-directed behaviour using similar strategies to the brain, by combining the relationships between the current state of the organism and the consequences of future actions? Recent work has shown that recurrent…
The hippocampal-entorhinal complex plays a major role in the organization of memory and thought. The formation of and navigation in cognitive maps of arbitrary mental spaces via place and grid cells can serve as a representation of memories…
Spatial awareness in mammals is based on an internalized representation of the environment, encoded by large networks of spiking neurons. While such representations can last for a long time, the underlying neuronal network is transient:…
Tracking the positions of objects in local space is a core function of animal brains. We do not yet understand how it is done with limited neural resources. The challenges of spatial cognition are discussed under the criteria: (a) scaling…
Inspired by animal navigation strategies, we introduce a novel computational model to navigate and map a space rooted in biologically inspired principles. Animals exhibit extraordinary navigation prowess, harnessing memory, imagination, and…
Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…
Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity. Recent experiments established that these cells are functionally organized in discrete…
To navigate a space, the brain makes an internal representation of the environment using different cells such as place cells, grid cells, head direction cells, border cells, and speed cells. All these cells, along with sensory inputs,…
Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial…
Much of the genome is expressed in the vertebrate brain, with individual genes exhibiting different spatially-varying patterns of expression. These variations are not independent, with pairs of genes exhibiting complex patterns of…
Mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal…
Neurons in cortical areas often integrate signals from different origins. In the primary visual cortex (V1), neural responses are modulated by non-visual context such as the animal's position. However, the spatial profile of these position…
We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline…