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The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…

Data Structures and Algorithms · Computer Science 2025-04-25 Lars Gottesbüren , Nikolai Maas , Dominik Rosch , Peter Sanders , Daniel Seemaier

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…

Machine Learning · Computer Science 2024-06-17 Matthias König , Xiyue Zhang , Holger H. Hoos , Marta Kwiatkowska , Jan N. van Rijn

Resilience and robustness are important properties in the reliability and attack-tolerance analysis of networks. In recent decades, various qualitative and heuristic-based quantitative approaches have made significant contributions in…

Optimization and Control · Mathematics 2022-12-15 Milad Dehghani Filabadi

Spiking neural networks encode information in spike timing and offer a pathway toward energy efficient artificial intelligence. However, a key challenge in spiking neural networks is realizing nonlinear and expressive computation in…

Neural and Evolutionary Computing · Computer Science 2026-04-06 Steven Louis , Hannah Bradley , Artem Litvinenko , Cody Trevillian , Darrin Hanna , Vasyl Tyberkevych

Most real world applications require dealing with stochasticity like sensor noise or predictive uncertainty, where formal specifications of desired behavior are inherently probabilistic. Despite the promise of formal verification in…

Behavior-Interaction-Priority (BIP) is a layered embedded system design and verification framework that provides separation of functionality, synchronization, and priority concerns to simplify system design and to establish correctness by…

Software Engineering · Computer Science 2014-09-30 Mohamad Jaber , Mohamad Noureddine , Fadi A. Zaraket

The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…

Machine Learning · Computer Science 2021-02-26 Yuuki Takai , Akiyoshi Sannai , Matthieu Cordonnier

While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-evaluation gap be addressed? While specific techniques…

Machine Learning · Computer Science 2022-06-03 Nathan Tsoi , Kate Candon , Deyuan Li , Yofti Milkessa , Marynel Vázquez

Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but…

Machine Learning · Computer Science 2020-01-13 Hadi Salman , Greg Yang , Huan Zhang , Cho-Jui Hsieh , Pengchuan Zhang

State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…

Machine Learning · Computer Science 2022-05-03 Claudio Ferrari , Mark Niklas Muller , Nikola Jovanovic , Martin Vechev

This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black-box; this has…

Systems and Control · Electrical Eng. & Systems 2020-07-31 Andreas Venzke , Spyros Chatzivasileiadis

Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…

Machine Learning · Computer Science 2021-10-12 Yuyang Zhang , Dik Hin Leung , Min Guo , Yijia Xiao , Haoyue Liu , Yunfei Li , Jiyuan Zhang , Guan Wang , Zhen Chen

In this paper, we explore model-based approach to training robust and interpretable binarized regression models for multiclass classification tasks using Mixed-Integer Programming (MIP). Our MIP model balances the optimization of prediction…

Machine Learning · Computer Science 2022-03-22 Sanjana Tule , Nhi Ha Lan Le , Buser Say

The choice of activation function plays a critical role in neural networks, yet most architectures still rely on fixed, uniform activation functions across all neurons. We introduce SmartMixed, a two-phase training strategy that allows…

Machine Learning · Computer Science 2025-11-03 Amin Omidvar

We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…

Machine Learning · Statistics 2014-06-10 Guido Montúfar , Razvan Pascanu , Kyunghyun Cho , Yoshua Bengio

A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…

Optimization and Control · Mathematics 2021-04-20 Suresh Bolusani , Stefano Coniglio , Ted. K. Ralphs , Sahar Tahernejad

Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying…

Machine Learning · Computer Science 2023-12-29 Pei Huang , Haoze Wu , Yuting Yang , Ieva Daukantas , Min Wu , Yedi Zhang , Clark Barrett

We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…

Optimization and Control · Mathematics 2023-11-09 Jasper van Doornmalen , Leon Eifler , Ambros Gleixner , Christopher Hojny

Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…

Optimization and Control · Mathematics 2026-03-03 Hongpei Li , Hui Yuan , Han Zhang , Jianghao Lin , Dongdong Ge , Mengdi Wang , Yinyu Ye