相关论文: Is Neuron Made from Mathematics?

To solve more complex things, computer systems becomes more and more complex. It becomes harder to be handled manually for various conditions and unknown new conditions in advance. This situation urgently requires the development of…

Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

In this work we study the problem of network morphism, an effective learning scheme to morph a well-trained neural network to a new one with the network function completely preserved. Different from existing work where basic morphing types…

This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to…

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…

We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites,…

The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and…

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer…

This paper describes a relatively simple way of allowing a brain model to self-organise its concept patterns through nested structures. Time is a key element and a simulator would be able to show how patterns may form and then fire in…

Artificial neural networks which are inspired from the learning mechanism of brain have achieved great successes in many problems, especially those with deep layers. In this paper, we propose a nucleus neural network (NNN) and corresponding…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Biological nervous systems exhibit astonishing complexity .Neuroscientists aim to capture this com- plexity by modeling and simulation of biological processes. Often very comple xm odels are nec- essary to depict the processes, which makes…

Graphic design is essential for visual communication with layouts being fundamental to composing attractive designs. Layout generation differs from pixel-level image synthesis and is unique in terms of the requirement of mutual relations…

Neural machine translation (NMT) models learn representations containing substantial linguistic information. However, it is not clear if such information is fully distributed or if some of it can be attributed to individual neurons. We…

The question of controllability of natural and man-made network systems has recently received considerable attention. In the context of the human brain, the study of controllability may not only shed light into the organization and function…

The superposition hypothesis states that single neurons may participate in representing multiple features in order for the neural network to represent more features than it has neurons. In neuroscience and AI, representational alignment…

This paper introduces repetition neurons, regarded as skill neurons responsible for the repetition problem in text generation tasks. These neurons are progressively activated more strongly as repetition continues, indicating that they…