Related papers: On a general framework for network representabilit…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

The constant increase in the complexity of data networks motivates the search for strategies that make it possible to reduce current monitoring times. This paper shows the way in which multilayer network representation and the application…

Brains learn to represent information from a large set of stimuli, typically by weak supervision. Unsupervised learning is therefore a natural approach for exploring the design of biological neural networks and their computations.…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

This paper analyzes representations of continuous piecewise linear functions with infinite width, finite cost shallow neural networks using the rectified linear unit (ReLU) as an activation function. Through its integral representation, a…

We propose a novel explanation method that explains the decisions of a deep neural network by investigating how the intermediate representations at each layer of the deep network were refined during the training process. This way we can a)…

We propose a new directed graphical representation of utility functions, called UCP-networks, that combines aspects of two existing graphical models: generalized additive models and CP-networks. The network decomposes a utility function…

Researchers commonly believe that neural networks model a high-dimensional space but cannot give a clear definition of this space. What is this space? What is its dimension? And does it has finite dimensions? In this paper, we develop a…

Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…

While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional functions with the same accuracy as shallow networks but with…

Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural networks. In a quadratic neuron, the inner product of a vector…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between…

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…

We prove and extend a conjecture of Kempe, Kleinberg, and Tardos (KKT) on the spread of influence in social networks. A social network can be represented by a directed graph where the nodes are individuals and the edges indicate a form of…

Neural networks (NNs) whose subnetworks implement reusable functions are expected to offer numerous advantages, including compositionality through efficient recombination of functional building blocks, interpretability, preventing…

In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Networks are representations of complex underlying social processes. However, the same given network may be more suitable to model one behavior of individuals than another. In many cases, aggregate population models may be more effective…

Neural networks trained on standard image classification data sets are shown to be less resistant to data set bias. It is necessary to comprehend the behavior objective function that might correspond to superior performance for data with…