Related papers: Is Neuron Made from Mathematics?

Cue integration, the combination of different sources of information to reduce uncertainty, is a fundamental computational principle of brain function. Starting from a normative model we show that the dynamics of multi-compartment neurons…

We introduce network with sub-networks, a neural network which its weight layers could be detached into sub-neural networks during inference. To develop weights and biases which could be inserted in both base and sub-neural networks,…

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product…

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved,…

Understanding the function of individual units in a neural network is an important building block for mechanistic interpretability. This is often done by generating a simple text explanation of the behavior of individual neurons or units.…

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting…

Computational modeling plays an increasingly important role in neuroscience, highlighting the philosophical question of how computational models explain. In the context of neural network models for neuroscience, concerns have been raised…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

Neural networks and particularly Deep learning have been comparatively little studied from the theoretical point of view. Conversely, Mathematical Morphology is a discipline with solid theoretical foundations. We combine these domains to…

Since the 1980s, and particularly with the Hopfield model, recurrent neural networks or RNN became a topic of great interest. The first works of neural networks consisted of simple systems of a few neurons that were commonly simulated…

Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…

Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way. For networks, previously proposed systems are developed. Perceptron networks in disjunctive…

Traditional neural networks assume vectorial inputs as the network is arranged as layers of single line of computing units called neurons. This special structure requires the non-vectorial inputs such as matrices to be converted into…

This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics we investigate the two main bifurcations from a stable…

A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous…

Artificial Intelligence has historically relied on planning, heuristics, and handcrafted approaches designed by experts. All the while claiming to pursue the creation of Intelligence. This approach fails to acknowledge that intelligence…

A quantized physical framework, called the five-anchor model, is developed for a general understanding of the working mechanism of ion channels. According to the hypotheses of this model, the following two basic physical principles are…

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…