Related papers: Bound Propagation
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
In this paper, we present BERN-NN as an efficient tool to perform bound propagation of Neural Networks (NNs). Bound propagation is a critical step in wide range of NN model checkers and reachability analysis tools. Given a bounded input…
Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
This work initiates the study of memory-query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non-edges inside clusters plus…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
This paper aims at studying the sample complexity of graph convolutional networks (GCNs), by providing tight upper bounds of Rademacher complexity for GCN models with a single hidden layer. Under regularity conditions, theses derived…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded…
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…