Related papers: The Representation Theory of Neural Networks

Brain networks exhibit complications such as noise, neuron failures, and partial synaptic connectivity. These can make it difficult to model and analyze their behavior. This paper describes a way to address this difficulty, namely, breaking…

Evolution and its intelligence element present thrill and challenges in its exploration. Yet, how species have memory, retrieve them and maintain continuity are the fundamental questions. Most of the phenomenon can only be hypothesised by…

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…

In this study, we propose a neural network approach to capture the functional connectivities among anatomic brain regions. The suggested approach estimates a set of brain networks, each of which represents the connectivity patterns of a…

Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…

As NNs permeate various scientific and industrial domains, understanding the universality and reusability of their representations becomes crucial. At their core, these networks create intermediate neural representations, indicated as…

Neural network modeling is a key technology of science and research and a platform for deployment of algorithms to systems. In wireless communications, system modeling plays a pivotal role for interference cancellation with specifically…

Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…

The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

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…

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…

Analyzing and modeling the constitutive behavior of materials is a core area in materials sciences and a prerequisite for conducting numerical simulations in which the material behavior plays a central role. Constitutive models have been…

On the one hand, artificial neural networks have many successful applications in the field of machine learning and optimization. On the other hand, interferometers are integral parts of any field that deals with waves such as optics,…

In this paper, we explain the universal approximation capabilities of deep residual neural networks through geometric nonlinear control. Inspired by recent work establishing links between residual networks and control systems, we provide a…

Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…

Implicit neural representations have emerged as a powerful paradigm to represent signals such as images and sounds. This approach aims to utilize neural networks to parameterize the implicit function of the signal. However, when…

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…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

A neuron is a basic physiological and computational unit of the brain. While much is known about the physiological properties of a neuron, its computational role is poorly understood. Here we propose to view a neuron as a signal processing…