Related papers: Permutation Binary Neural Networks: Analysis of Pe…
Recently, the deep neural network (derived from the artificial neural network) has attracted many researchers' attention by its outstanding performance. However, since this network requires high-performance GPUs and large storage, it is…
In this paper, we present a novel neural network for MIMO symbol detection. It is motivated by several important considerations in wireless communication systems; permutation equivariance and a variable number of users. The neural detector…
Artificial spiking neural networks have found applications in areas where the temporal nature of activation offers an advantage, such as time series prediction and signal processing. To improve their efficiency, spiking architectures often…
This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the…
Recurrent networks of binary neurons are a foundational concept in artificial intelligence. While these networks are traditionally assumed to be fully connected, complex dynamics can emerge when the graph structure is varied. One graph…
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in terms of a permutationally-invariant part described by the…
Deep learning has become a powerful and popular tool for a variety of machine learning tasks. However, it is challenging to understand the mechanism of deep learning from a theoretical perspective. In this work, we propose a random active…
Binary representation is desirable for its memory efficiency, computation speed and robustness. In this paper, we propose adjustable bounded rectifiers to learn binary representations for deep neural networks. While hard constraining…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
A large number of current machine learning methods rely upon deep neural networks. Yet, viewing neural networks as nonlinear dynamical systems, it becomes quickly apparent that mathematically rigorously establishing certain patterns…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of…
In computer vision and machine learning, a crucial challenge is to lower the computation and memory demands for neural network inference. A commonplace solution to address this challenge is through the use of binarization. By binarizing the…
Recent research has shown that one can train a neural network with binary weights and activations at train time by augmenting the weights with a high-precision continuous latent variable that accumulates small changes from stochastic…
Deep neural networks are a family of computational models that are naturally suited to the analysis of hierarchical data such as, for instance, sequential data with the use of recurrent neural networks. In the other hand, ordinal regression…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the…