Related papers: On the random satisfiable process
In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-$k$ random graphs}, and that are special in that their…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose clauses are chosen uniformly from among…
We give the first efficient algorithm to approximately count the number of solutions in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previous counting algorithm for the permissive version…
We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
The $k$-SAT problem for \L{}-clausal forms has been found to be NP-complete if $k\geq 3$. Similar to Boolean CNF formulas, \L{}-clausal forms are important from a theoretical and practical points of view for their expressive power,…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
It is well known that, as $n$ tends to infinity, the probability of satisfiability for a random 2-SAT formula on $n$ variables, where each clause occurs independently with probability $\alpha/2n$, exhibits a sharp threshold at $\alpha=1$.…
We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches)…
Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution. We build a rigorous foundational framework for pMCMC algorithms that situates these…
We introduce a class of random graph processes, which we call flip processes. Each such process is given by a rule which is a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labeled $k$-vertex graphs into itself ($k$…
Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is…
Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive…
This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…
The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…
Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low independence. A series of papers, beginning with work by Luby (1988), showed that in many cases…
Feedforward neural networks with random hidden nodes suffer from a problem with the generation of random weights and biases as these are difficult to set optimally to obtain a good projection space. Typically, random parameters are drawn…