Related papers: To which extend is the "neural code" a metric ?
We investigate the synchronization features of a network of spiking neurons under a distance-dependent coupling following a power-law model. The interplay between topology and coupling strength leads to the existence of different…
Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
The practical applications based on recurrent spiking neurons are limited due to their non-trivial learning algorithms. The temporal nature of spiking neurons is more favorable for hardware implementation where signals can be represented in…
In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…
Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However,…
Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…
We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theory", W.C. Huffman, J.-L. Kim, and P. Sole' Eds., CRC Press. The chapter gives an introduction to the mathematical theory of rank-metric codes. Treated topics include:…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
Spiking Neural Networks (SNNs), models inspired by neural mechanisms in the brain, allow for energy-efficient implementation on neuromorphic hardware. However, SNNs trained with current direct training approaches are constrained to a…
Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been…
Decision trees are a widely used method for classification, both by themselves and as the building blocks of multiple different ensemble learning methods. The Max-Cut decision tree involves novel modifications to a standard, baseline model…
Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed L_p Victor-Purpura metric is used to cluster…
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained…
This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons…
The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…
Whether, when, and how causal interactions between neurons can be meaningfully studied from observations of neural activity alone are vital questions in neural data analysis. Here we aim to better outline the concept of functional…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…