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We propose a multigrid extension of convolutional neural networks (CNNs). Rather than manipulating representations living on a single spatial grid, our network layers operate across scale space, on a pyramid of grids. They consume multigrid…

A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from…

Learning and memory may rely on the ability of neuronal circuits to reorganize by dendritic spine remodeling. We have looked for geometrical parameters of cortical circuits, which maximize information storage capacity associated with this…

In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a…

Recent advances in neuroscience together with nanoscale electronic device technology have resulted in huge interests in realizing brain-like computing hardwares using emerging nanoscale memory devices as synaptic elements. Although there…

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

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…

Why do we forget? Why do we remember things that never happened? The conventional answer points to biological hardware. We propose a different one: geometry. Here we show that high-dimensional embedding spaces, subjected to noise,…

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading…

We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly…

Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative…

We represent the sequence of fMRI (Functional Magnetic Resonance Imaging) brain volumes recorded during a cognitive stimulus by a graph which consists of a set of local meshes. The corresponding cognitive process, encoded in the brain, is…

Many deep neural network architectures loosely based on brain networks have recently been shown to replicate neural firing patterns observed in the brain. One of the most exciting and promising novel architectures, the Transformer neural…

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph…

Human brain anatomy and function display a combination of modular and hierarchical organization, suggesting the importance of both cohesive structures and variable resolutions in the facilitation of healthy cognitive processes. However,…

This thesis presents a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for…

Robotic and animal mapping systems share many of the same objectives and challenges, but differ in one key aspect: where much of the research in robotic mapping has focused on solving the data association problem, the grid cell neurons…