相关论文: Banach Space Representer Theorems for Neural Netwo…

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…

Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience.…

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…

We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We first prove that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set, where simple…

The large capacity of neural networks enables them to learn complex functions. To avoid overfitting, networks however require a lot of training data that can be expensive and time-consuming to collect. A common practical approach to…

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…

We study the natural function space for infinitely wide two-layer neural networks with ReLU activation (Barron space) and establish different representation formulae. In two cases, we describe the space explicitly up to isomorphism. Using a…

Neurons in the brain communicate with each other through discrete action spikes as opposed to continuous signal transmission in artificial neural networks. Therefore, the traditional techniques for optimization of parameters in neural…

Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…

A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network…

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also…

Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the…

In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source representation. Such cases typically occur in exponentially…

Network representation learning (NRL) methods aim to map each vertex into a low dimensional space by preserving the local and global structure of a given network, and in recent years they have received a significant attention thanks to…

Understanding neural representations will help open the black box of neural networks and advance our scientific understanding of modern AI systems. However, how complex, structured, and transferable representations emerge in modern neural…

Learning methods in Banach spaces are often formulated as regularization problems which minimize the sum of a data fidelity term in a Banach norm and a regularization term in another Banach norm. Due to the infinite dimensional nature of…

Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made…