Related papers: The Complexity of Integer Bound Propagation
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…
The Bin Packing Problem is one of the most important problems in discrete optimization, as it captures the requirements of many real-world problems. Because of its importance, it has been approached with the main theoretical and practical…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
In various scenarios motivated by real life, such as medical data analysis, autonomous driving, and adversarial training, we are interested in robust deep networks. A network is robust when a relatively small perturbation of the input…
With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…
The past decade has witnessed substantial developments in string solving. Motivated by the complexity of string solving strategies adopted in existing string solvers, we investigate a simple and generic method for solving string…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We describe the use of array expressions as constraints, which represents a consequent generalisation of the "element" constraint. Constraint propagation for array constraints is studied theoretically, and for a set of domain reduction…
This paper presents a novel selective constraint propagation method for constrained image segmentation. In the literature, many pairwise constraint propagation methods have been developed to exploit pairwise constraints for cluster…
Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…
Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms.…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The…
Artificial neural network pruning is a method in which artificial neural network sizes can be reduced while attempting to preserve the predicting capabilities of the network. This is done to make the model smaller or faster during inference…