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A Mixed Integer Programming Approach for Verifying Properties of Binarized Neural Networks [article]

Christopher Lazarus, Mykel J. Kochenderfer
2022 arXiv   pre-print
This paper proposes a simple mixed integer programming formulation for BNN verification that leverages network structure.  ...  Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks.  ...  Our proposed approach encodes BNN as mixed integer linear programs and is able to verify properties of binarized neural networks and partially binarized neural networks.  ... 
arXiv:2203.07078v1 fatcat:p4i5sbcpwfd5fd55xgsrxpthbm

Deep Binary Reinforcement Learning for Scalable Verification [article]

Christopher Lazarus, Mykel J. Kochenderfer
2022 arXiv   pre-print
We provide an approach to train RL policies that are more easily verifiable. We use binarized neural networks (BNNs), a type of network with mostly binary parameters.  ...  Recently, neural network verification has emerged as a way to certify safety properties of networks.  ...  ACKNOWLEDGMENT The NASA University Leadership initiative (grant #80NSSC20M0163) provided funds to assist the authors with their research, but this article solely reflects the opinions and conclusions of  ... 
arXiv:2203.05704v1 fatcat:a4cyawb24jfa3fu6hlwzsn6fiu

Portfolio solver for verifying Binarized Neural Networks

Gergely Kovásznai, Krisztián Gajdár, Nina Narodytska
2021 Annales Mathematicae et Informaticae  
Verifying of properties of neural networks such as adversarial robustness and network equivalence sheds light on the trustiness of such systems.  ...  We focus on an important family of deep neural networks, the Binarized Neural Networks (BNNs) that are useful in resourceconstrained environments, like embedded devices.  ...  There exist approaches that formulate the verification of neural networks to Satisfiability Modulo Theories (SMT) [13, 19, 23] , while others do the same to Mixed-Integer Programming (MIP) [11, 15, 36  ... 
doi:10.33039/ami.2021.03.007 fatcat:pvigltjexzgftkdscfi6zojrjm

Verifying Properties of Binarized Deep Neural Networks [article]

Nina Narodytska, Shiva Prasad Kasiviswanathan, Leonid Ryzhyk, Mooly Sagiv, Toby Walsh
2018 arXiv   pre-print
In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean  ...  For this property, our experimental results demonstrate that our approach scales to medium-size deep neural networks used in image classification tasks.  ...  Mixed Integer Linear Program Encoding We start with a Mixed Integer Linear Programming (MILP) encoding of BLK and O blocks.  ... 
arXiv:1709.06662v2 fatcat:dirxvig4kzbo7fhjy4vhkiadsi

Algorithms for Verifying Deep Neural Networks

Changliu Liu, Tomer Arnon, Christopher Lazarus, Christopher Strong, Clark Barrett, Mykel J. Kochenderfer
2020 Foundations and Trends® in Optimization  
resource allocation, and other areas Information for Librarians  ...  practical problems • applications of optimization in machine learning, statistics, and data analysis, signal and image processing, computational economics and finance, engineering design, scheduling and  ...  This article surveys a class of methods that are capable of formally verifying properties of deep neural networks over the full input space.  ... 
doi:10.1561/2400000035 fatcat:udnpbqyaqbeatcjrbkohospau4

Automated Verification of Neural Networks: Advances, Challenges and Perspectives [article]

Francesco Leofante, Nina Narodytska, Luca Pulina, Armando Tacchella
2018 arXiv   pre-print
In this work, we propose a primer of such techniques and a comprehensive categorization of existing approaches for the automated verification of neural networks.  ...  Neural networks are one of the most investigated and widely used techniques in Machine Learning.  ...  MIP Mixed Integer Linear Programming (MIP) solves linear problems over a set of integer and real valued variables.  ... 
arXiv:1805.09938v1 fatcat:34zozzdndfg7xmrv7o53fsqpwq

Digital Biologically Plausible Implementation of Binarized Neural Networks with Differential Hafnium Oxide Resistive Memory Arrays [article]

Tifenn Hirtzlin, Marc Bocquet, Bogdan Penkovsky, Jacques-Olivier Klein, Etienne Nowak, Elisa Vianello, Jean-Michel Portal, Damien Querlioz
2019 arXiv   pre-print
In parallel, the recently proposed concept of Binarized Neural Network, where multiplications are replaced by exclusive NOR (XNOR) logic gates, offers a way to implement artificial intelligence using very  ...  operations of the neural network directly within the sense amplifiers.  ...  Binarized Neural Networks require minimal arithmetic: no multiplication, and only integer addition with a low bit width.  ... 
arXiv:1908.04066v2 fatcat:uxdfotmafrbdtkpcsj4k5j2qaa

A Review of Formal Methods applied to Machine Learning [article]

Caterina Urban, Antoine Miné
2021 arXiv   pre-print
The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques.  ...  We then provide a comprehensive and detailed review of the formal methods developed so far for machine learning, highlighting their strengths and limitations.  ...  [142] proposed RefineZono, a combination of abstract interpretation and (mixed integer) linear programming for proving local robustness to adversarial perturbations [148] of neural networks with piecewise-linear  ... 
arXiv:2104.02466v2 fatcat:6ghs5huoynbc5h7lndajmsoxyu

Verification of Binarized Neural Networks via Inter-Neuron Factoring [article]

Chih-Hong Cheng, Georg Nührenberg, Chung-Hao Huang, Harald Ruess
2018 arXiv   pre-print
We study the problem of formal verification of Binarized Neural Networks (BNN), which have recently been proposed as a energy-efficient alternative to traditional learning networks.  ...  The overall framework allows applying verification techniques to moderately-sized BNNs for embedded devices with thousands of neurons and inputs.  ...  In our own previous work on neural network verification we establish maximum resilience bounds for FPA-NNs based on reductions to mixed-integer linear programming (MILP) problems [8] .  ... 
arXiv:1710.03107v2 fatcat:nb24wwoqlbethldozlaeekr4ee

Strong mixed-integer programming formulations for trained neural networks [article]

Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma
2019 arXiv   pre-print
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network.  ...  , 2) decreases the solve time of a state-of-the-art MIP solver by a factor of 7 on smaller instances, and 3) nearly matches the dual bounds of a state-of-the-art MIP solver on harder instances, after just  ...  The authors gratefully acknowledge Yeesian Ng and Ondřej Sýkora for many discussions on the topic of this paper, and for their work on the development of the tf.opt package used in the computational experiments  ... 
arXiv:1811.08359v2 fatcat:s3ecgsxvujapxgcfxc4sqq4bfa

Formal methods and software engineering for DL. Security, safety and productivity for DL systems development [article]

Gaetan J.D.R. Hains and Arvid Jakobsson and Youry Khmelevsky
2019 arXiv   pre-print
As machine-learning that relies on training instead of algorithm programming, they offer a high degree of productivity.  ...  It also covers an even more recent trend, namely the design of domain-specific languages for producing and training neural nets.  ...  ACKNOWLEDGMENT Arvid Jakobsson is supported by a CIFRE industrial PhD contract between Huawei Technologies France and LIFO, Université d'Orléans, funded in part by A.N.R.T.  ... 
arXiv:1901.11334v1 fatcat:fy7zq2r3uve5vcdwrfydxxqvyu

Extremely Low Bit Neural Network: Squeeze the Last Bit Out with ADMM [article]

Cong Leng, Hao Li, Shenghuo Zhu, Rong Jin
2017 arXiv   pre-print
Extensive experiments on image recognition and object detection verify that the proposed algorithm is more effective than state-of-the-art approaches when coming to extremely low bit neural network.  ...  In this paper, we focus on compressing and accelerating deep models with network weights represented by very small numbers of bits, referred to as extremely low bit neural network.  ...  For example, the weights in a ternary neural network are restricted to be −1, 0 or +1. Training such network can be mathematically formulated as mixed integer programs: min W f (W ) s.t.  ... 
arXiv:1707.09870v2 fatcat:lg7lnntm5vgwfeg5z4ez4kwx3a

Counting the Number of Solutions to Constraints [article]

Jian Zhang, Cunjing Ge, Feifei Ma
2020 arXiv   pre-print
We describe some techniques and tools for solving the counting problems, as well as some applications (e.g., applications to automated reasoning, program analysis, formal verification and information security  ...  The constraints may take various forms, including, formulas in the propositional logic, linear inequalities over the reals or integers, Boolean combination of linear constraints.  ...  The property P can be defined over the union of inputs and outputs of neural networks in N . [3] proposed an approach which encodes a binarized neural network into a propositional logical formula.  ... 
arXiv:2012.14366v1 fatcat:fzhrfpfkanbvth6kwzrwpxioa4

Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI [article]

Zhishen Huang, Saiprasad Ravishankar
2022 arXiv   pre-print
In this work, we propose a data-driven sampler using a convolutional neural network, MNet, to provide object-specific sampling patterns adaptive to each scanned object.  ...  We propose an accompanying alternating-type training framework with a mask-backward procedure that efficiently generates training labels for the sampler network and jointly trains an image reconstruction  ...  We thank all reviewers for their constructive comments on our initial draft.  ... 
arXiv:2111.09212v2 fatcat:ikmkfv2hfrcathmkhryqymvjh4

Verifying Quantized Neural Networks using SMT-Based Model Checking [article]

Luiz Sena, Xidan Song, Erickson Alves, Iury Bessa, Edoardo Manino, Lucas Cordeiro, Eddie de Lima Filho
2021 arXiv   pre-print
Artificial Neural Networks (ANNs) are being deployed for an increasing number of safety-critical applications, including autonomous cars and medical diagnosis.  ...  Furthermore, for small- to medium-sized ANN, our approach completes most of its verification runs in minutes.  ...  In particular, Baranowski et al. presented a practical SMT-based approach for verifying neural networks' properties considering fixed-point arithmetic.  ... 
arXiv:2106.05997v2 fatcat:7rzp3pbvgzg3nke4coejvfct6y
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