Related papers: Renormalization-group-inspired neural networks for…
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained…
Image normalization, the correction for intra-volume inhomogeneities in magnetic resonance imaging (MRI) data has little significance for visual diagnosis, but is a crucial step before automated radiotherapy solutions. There are several…
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is…
Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic…
The paper presents Multi-layer Auto Resonance Networks (ARN), a new neural model, for image recognition. Neurons in ARN, called Nodes, latch on to an incoming pattern and resonate when the input is within its 'coverage.' Resonance allows…
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…
Graph Neural Networks (GNNs) have achieved remarkable success in graph-based learning by propagating information among neighbor nodes via predefined aggregation mechanisms. However, such fixed schemes often suffer from two key limitations.…
We improve the results by Siegelmann & Sontag (1995) by providing a novel and parsimonious constructive mapping between Turing Machines and Recurrent Artificial Neural Networks, based on recent developments of Nonlinear Dynamical Automata.…
We show that renormalization group (RG) theory applied to complex networks are useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world/fractal transition…
We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann…
The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a unidirectional bottom-up feed-forward fashion. However, practical experience and biological evidence tells us…
We attempt to de-mistify Artificial Neural Networks (ANNs) by considering special cases which are related to other statistical methods common in Astronomy and other fields. In particular we show how ANNs generalise Bayesian methods,…
We describe an Artificial Neural Network (ANN) approach to classification of galaxy images and spectra. ANNs can replicate the classification of galaxy images by a human expert to the same degree of agreement as that between two human…
The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…
Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift.…
Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…