相关论文: AlgebraNets
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
Developing strong AI signifies the arrival of technological singularity, contributing greatly to advancing human civilization and resolving social issues. Neural networks (NNs) and deep learning, which utilize NNs, are expected to lead to…
Artificial neural networks can acquire many aspects of human knowledge from data, making them promising as models of human learning. But what those networks can learn depends upon their inductive biases -- the factors other than the data…
Motivation: Real-world data often contain measurements with both continuous and discrete values. Despite the availability of many libraries, data sets with mixed data types require intensive pre-processing steps, and it remains a challenge…
While the deployment of neural networks, yielding impressive results, becomes more prevalent in various applications, their interpretability and understanding remain a critical challenge. Network inversion, a technique that aims to…
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…
With massive amounts of atomic simulation data available, there is a huge opportunity to develop fast and accurate machine learning models to approximate expensive physics-based calculations. The key quantity to estimate is atomic forces,…
Efficient algorithms for many problems in optimization and computational algebra often arise from casting them as systems of polynomial equations. Blum, Shub, and Smale formalized this as Hilbert's Nullstellensatz Problem $HN_R$: given…
Deep neural networks represent the gold standard for image classification. However, they usually need large amounts of data to reach superior performance. In this work, we focus on image classification problems with a few labeled examples…
Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…
Although traditionally binary visual representations are mainly designed to reduce computational and storage costs in the image retrieval research, this paper argues that binary visual representations can be applied to large scale…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
Training a neural network is synonymous with learning the values of the weights. By contrast, we demonstrate that randomly weighted neural networks contain subnetworks which achieve impressive performance without ever training the weight…
Over the year, people have been using deep learning to tackle inversion problems, and we see the framework has been applied to build relationship between recording wavefield and velocity (Yang et al., 2016). Here we will extend the work…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
MobileNet and Binary Neural Networks are two among the most widely used techniques to construct deep learning models for performing a variety of tasks on mobile and embedded platforms.In this paper, we present a simple yet efficient scheme…
Recurrent neural networks have been widely used in sequence learning tasks. In previous studies, the performance of the model has always been improved by either wider or deeper structures. However, the former becomes more prone to…