Related papers: Circuit Model Reduction with Scaled Relative Graph…
The fundamentals of Fourier Transform are presented, with analytical solutions derived for Continuous Fourier Transform (CFT) of truncated signals, to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFT were…
We characterise the computational power of recurrent graph neural networks (GNNs) in terms of arithmetic circuits over the real numbers. Our networks are not restricted to aggregate-combine GNNs or other particular types. Generalising…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
Given a static reference string $R$ and a source string $S$, a relative compression of $S$ with respect to $R$ is an encoding of $S$ as a sequence of references to substrings of $R$. Relative compression schemes are a classic model of…
The shrinking rank method is a variation of slice sampling that is efficient at sampling from multivariate distributions with highly correlated parameters. It requires that the gradient of the log-density be computable. At each individual…
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
Graphs are a fundamental abstraction in computer science and discrete mathematics, where information is encoded in their combinatorial structure. Graph-reduction techniques aim at simplifying graphs while preserving selected structural…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function.…
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…
We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…
The classical continued fraction is generalized for studying the rational approximation problem on multi-formal Laurent series in this paper, the construction is called m-continued fraction. It is proved that the approximants of an…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…
We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
Link prediction on graphs is a fundamental problem. Subgraph representation learning approaches (SGRLs), by transforming link prediction to graph classification on the subgraphs around the links, have achieved state-of-the-art performance…