Related papers: Improved Bounds on Neural Complexity for Represent…

Combinatorial complexes have unified set-based (e.g., graphs, hypergraphs) and part-whole (e.g., simplicial, cellular complexes) structures into a common topological framework. Existing topological neural networks and Weisfeiler-Lehman…

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether…

Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…

The rapidly decreasing computation and memory cost has recently driven the success of many applications in the field of deep learning. Practical applications of deep learning in resource-limited hardware, such as embedded devices and smart…

We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network…

Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and…

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…

Strong intelligent machines powered by deep neural networks are increasingly deployed as black boxes to make decisions in risk-sensitive domains, such as finance and medical. To reduce potential risk and build trust with users, it is…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to…

Convolutional neural networks (CNNs) are able to attain better visual recognition performance than fully connected neural networks despite having much fewer parameters due to their parameter sharing principle. Modern architectures usually…

The success of convolutional neural networks (CNNs) in various applications is accompanied by a significant increase in computation and parameter storage costs. Recent efforts to reduce these overheads involve pruning and compressing the…

In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the…

Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in…

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…

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

It is well known that Convolutional Neural Networks (CNNs) have significant redundancy in their filter weights. Various methods have been proposed in the literature to compress trained CNNs. These include techniques like pruning weights,…

Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…

Deep convolutional neural networks provide a powerful feature learning capability for image classification. The deep image features can be utilized to deal with many image understanding tasks like image classification and object…