Related papers: Learning from Survey Propagation: a Neural Network…

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully…

Finding biologically plausible alternatives to back-propagation of errors is a fundamentally important challenge in artificial neural network research. In this paper, we propose a learning algorithm called error-driven Local Representation…

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be…

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…

We investigate the complexity of training a two-layer ReLU neural network with weight decay regularization. Previous research has shown that the optimal solution of this problem can be found by solving a standard cone-constrained convex…

This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…

In this paper, we present a novel method for dynamically expanding Convolutional Neural Networks (CNNs) during training, aimed at meeting the increasing demand for efficient and sustainable deep learning models. Our approach, drawing from…

Graph Neural Networks (GNNs) have been recently leveraged to solve several logical reasoning tasks. Nevertheless, counting problems such as propositional model counting (#SAT) are still mostly approached with traditional solvers. Here we…

Let $\varPhi$ be a uniformly distributed random $k$-SAT formula with $n$ variables and $m$ clauses. For clauses/variables ratio $m/n \leq r_{k\text{-SAT}} \sim 2^k\ln2$ the formula $\varPhi$ is satisfiable with high probability. However, no…

Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While…

Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…

In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT. Then, we define a graph representation for…

We propose a novel method for training deep neural networks that are capable of interpolation, that is, driving the empirical loss to zero. At each iteration, our method constructs a stochastic approximation of the learning objective. The…

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a novel Distributed Approx-Newton algorithm that approximates the standard Newton optimization method. A main property of this…

We proposes a novel method that enables Graph Neural Networks (GNNs) to solve SAT problems by leveraging a technique developed for applying GNNs to Mixed Integer Linear Programming (MILP). Specifically, k-CNF formulae are mapped into MILP…

Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental…

Over-parameterization of deep neural networks (DNNs) has shown high prediction accuracy for many applications. Although effective, the large number of parameters hinders its popularity on resource-limited devices and has an outsize…

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…