Related papers: Grid Cells, Border Cells and Discrete Complex Anal…
The problem of optimising a network of discretely firing neurons is addressed. An objective function is introduced which measures the average number of bits that are needed for the network to encode its state. When this is minimised, it is…
We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as a promising platform for artificial neuron design. In this work, we introduce a modeling and analysis…
Convolutional neural networks (CNNs) handle the case where filters extend beyond the image boundary using several heuristics, such as zero, repeat or mean padding. These schemes are applied in an ad-hoc fashion and, being weakly related to…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
In recent years many methods have been developed to understand the internal workings of neural networks, often by describing the function of individual neurons in the model. However, these methods typically only focus on explaining the very…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…
A common approach to interpreting spiking activity is based on identifying the firing fields---regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at…
The grid cells (GCs) of the medial entorhinal cortex (MEC) and place cells (PCs) of the hippocampus are key elements of the brain network for the metric representation of space. Currently, any of the existing theoretical models can explain…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…
We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction.…
Deep neural networks and in particular, deep neural classifiers have become an integral part of many modern applications. Despite their practical success, we still have limited knowledge of how they work and the demand for such an…
A model of sensory information processing is presented. The model assumes that learning of internal (hidden) generative models, which can predict the future and evaluate the precision of that prediction, is of central importance for…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…
We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and…