Related papers: Improved Branch and Bound for Neural Network Verif…

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same…

The problem of planar registration consists in finding the transformation that better aligns two point sets. In our setting, the search domain is the set of planar rigid transformations and the objective function is the sum of the distances…

As a new programming paradigm, deep neural networks (DNNs) have been increasingly deployed in practice, but the lack of robustness hinders their applications in safety-critical domains. While there are techniques for verifying DNNs with…

Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enforcement compete during optimization. We present a…

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…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of…

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform…

Neural networks have emerged as essential components in safety-critical applications -- these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is…

The ability of Deep Neural Networks to approximate highly complex functions is key to their success. This benefit, however, comes at the expense of a large model size, which challenges its deployment in resource-constrained environments.…

While binary neural networks (BNNs) offer significant benefits in terms of speed, memory and energy, they encounter substantial accuracy degradation in challenging tasks compared to their real-valued counterparts. Due to the binarization of…

This study investigates the application of Bayesian Optimization (BO) for the hyperparameter tuning of neural networks, specifically targeting the enhancement of Convolutional Neural Networks (CNN) for image classification tasks. Bayesian…

While Branch and Bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective Branch and Bound methods are only rarely applied compared to the predominant objective space…

As neural networks make their way into safety-critical systems, where misbehavior can lead to catastrophes, there is a growing interest in certifying the equivalence of two structurally similar neural networks. For example, compression…

Spatial Branch and Bound (B&B) algorithms are widely used for solving nonconvex problems to global optimality, yet they remain computationally expensive. Though some works have been carried out to speed up B&B via CPU parallelization, GPU…

The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization…

Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at…

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…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…