相关论文: Is Neuron Made from Mathematics?

This paper considers neural representation through the lens of active inference, a normative framework for understanding brain function. It delves into how living organisms employ generative models to minimize the discrepancy between…

We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of ion channels are compared to those of ions and that only few ions may be simultaneously in any single channel.…

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…

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…

We study a mathematical model of biological neuronal networks composed by any finite number $N \geq 2$ of non necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental. We undertake a systematic study of the role that symmetry plays. In particular, we…

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness…

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…

We can define a neural network that can learn to recognize objects in less than 100 lines of code. However, after training, it is characterized by millions of weights that contain the knowledge about many object types across visual scenes.…

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that…

In the brain, the structure of a network of neurons defines how these neurons implement the computations that underlie the mind and the behavior of animals and humans. Provided that we can describe the network of neurons as a graph, we can…

This paper highlights the possibility of creating quantum neural networks that are trained by Grover's Search Algorithm. The purpose of this work is to propose the concept of combining the training process of a neural network, which is…

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g. adversarial noise leading to erroneous decisions. We…

Neuromorphic computing takes inspiration from the brain to create energy efficient hardware for information processing, capable of highly sophisticated tasks. In this article, we make the case that building this new hardware necessitates…

We describe the operation of a neuronal device which embodies the computational principles of the `paper-and-pencil' machine envisioned by Alan Turing. The network is based on principles of cortical organization. We develop a plausible…

Artificial neural networks (ANNs), inspired by the interconnection of real neurons, have achieved unprecedented success in various fields such as computer vision and natural language processing. Recently, a novel mathematical ANN model,…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…