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Verification of Non-Linear Specifications for Neural Networks [article]

Chongli Qin, Krishnamurthy Dvijotham, Brendan O'Donoghue, Rudy Bunel, Robert Stanforth, Sven Gowal, Jonathan Uesato, Grzegorz Swirszcz, Pushmeet Kohli
2019 arXiv   pre-print
Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations  ...  In this paper, we extend verification algorithms to be able to certify richer properties of neural networks.  ...  ACKNOWLEDGEMENTS We thank Jost Tobias Springenberg and Jan Leike for careful proof-reading of this paper. REFERENCES Anish Athalye, Nicholas Carlini, and David Wagner.  ... 
arXiv:1902.09592v1 fatcat:ibx3uwef3nh2jnmf43fzvechpm

Neural class-specific regression for face verification

Guanqun Cao, Alexandros Iosifidis, Moncef Gabbouj
2018 IET Biometrics  
This allows us to derive linear, (reduced) kernel and neural network-based class-specific discriminant analysis methods using efficient batch and/or iterative training schemes, suited for large-scale learning  ...  We test the performance of these methods in two datasets describing medium- and large-scale face verification problems.  ...  Based on that, we propose a non-linear CSDA solution based on neural networks.  ... 
doi:10.1049/iet-bmt.2017.0081 fatcat:3nzxrecxibeqpj3vewuoukbt74

How Many Bits Does it Take to Quantize Your Neural Network? [chapter]

Mirco Giacobbe, Thomas A. Henzinger, Mathias Lechner
2020 Lecture Notes in Computer Science  
For this reason, we introduce a verification method for quantized neural networks which, using SMT solving over bit-vectors, accounts for their exact, bit-precise semantics.  ...  Quantization converts neural networks into low-bit fixedpoint computations which can be carried out by efficient integer-only hardware, and is standard practice for the deployment of neural networks on  ...  Acknowledgments An early version of this paper was put into the easychair repository as EasyChair Preprint no. 1000.  ... 
doi:10.1007/978-3-030-45237-7_5 fatcat:pcfd7jgqs5bendlhzjcan3qucm

Specification-Guided Safety Verification for Feedforward Neural Networks [article]

Weiming Xiang, Hoang-Dung Tran, Taylor T. Johnson
2018 arXiv   pre-print
This paper presents a specification-guided safety verification method for feedforward neural networks with general activation functions.  ...  In the framework of interval analysis, a computationally efficient formula which can quickly compute the output interval sets of a neural network is developed.  ...  There exist a number of results for verification of feedforward neural networks, especially for Rectifier Linear Unit (ReLU) neural networks, and a few results are devoted to neural networks with broad  ... 
arXiv:1812.06161v1 fatcat:aytofm3fxvfanetczdfx757jle

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

Christopher Lazarus, Mykel J. Kochenderfer
2022 arXiv   pre-print
We compare the runtime of our approach against state-of-the-art verification algorithms for full-precision neural networks.  ...  Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks.  ...  Binarized Neural Network Verification There are a few approaches designed specifically for verifying properties of BNNs.  ... 
arXiv:2203.07078v1 fatcat:p4i5sbcpwfd5fd55xgsrxpthbm

Code2Inv: A Deep Learning Framework for Program Verification [chapter]

Xujie Si, Aaditya Naik, Hanjun Dai, Mayur Naik, Le Song
2020 Lecture Notes in Computer Science  
We demonstrate the flexibility of Code2Inv by means of two small-scale yet expressive instances: a loop invariant synthesizer for C programs, and a Constrained Horn Clause (CHC) solver.  ...  We propose a general end-to-end deep learning framework Code2Inv, which takes a verification task and a proof checker as input, and automatically learns a valid proof for the verification task by interacting  ...  We thank the reviewers for insightful comments. We thank Elizabeth Dinella, Pardis Pashakhanloo, and Halley Young for feedback on improving the paper.  ... 
doi:10.1007/978-3-030-53291-8_9 fatcat:zwzve6xymvezrie4rdbv6uwj3u

Scalable Verification of Quantized Neural Networks (Technical Report) [article]

Thomas A. Henzinger, Mathias Lechner, Đorđe Žikelić
2022 arXiv   pre-print
In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable.  ...  Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle.  ...  There are many efficient methods for verification of neural networks (e.g.  ... 
arXiv:2012.08185v2 fatcat:wk6y2yzk3ncttaaeovqbu4fj74

Certified Monotonic Neural Networks [article]

Xingchao Liu, Xing Han, Na Zhang, Qiang Liu
2020 arXiv   pre-print
In this work, we propose to certify the monotonicity of the general piece-wise linear neural networks by solving a mixed integer linear programming problem.This provides a new general approach for learning  ...  Existing methods for learning monotonic neural networks either require specifically designed model structures to ensure monotonicity, which can be too restrictive/complicated, or enforce monotonicity by  ...  Learning Certified Monotonic Neural Networks We now introduce our simple procedure for learning monotonic neural networks with verification.  ... 
arXiv:2011.10219v1 fatcat:tlmeyymzxnbe3kq2ca6hskvei4

Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks [article]

Ruediger Ehlers
2017 arXiv   pre-print
We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function.  ...  We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the non-linear nodes in the network from partial node phase  ...  Acknowledgements This work was partially funded by the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative.  ... 
arXiv:1705.01320v3 fatcat:v4mwlbjt5be5xodspvvfhvkeuy

The Marabou Framework for Verification and Analysis of Deep Neural Networks [chapter]

Guy Katz, Derek A. Huang, Duligur Ibeling, Kyle Julian, Christopher Lazarus, Rachel Lim, Parth Shah, Shantanu Thakoor, Haoze Wu, Aleksandar Zeljić, David L. Dill, Mykel J. Kochenderfer (+1 others)
2019 Lecture Notes in Computer Science  
Deep neural networks are revolutionizing the way complex systems are designed. Consequently, there is a pressing need for tools and techniques for network analysis and certification.  ...  To help in addressing that need, we present Marabou, a framework for verifying deep neural networks.  ...  We thank Elazar Cohen, Justin Gottschlich, and Lindsey Kuper for their contributions to this project.  ... 
doi:10.1007/978-3-030-25540-4_26 fatcat:uxrh2xidszh37in5gdi2vazhqq

Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations [article]

Weiming Xiang, Hoang-Dung Tran, Taylor T. Johnson
2017 arXiv   pre-print
this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed.  ...  Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In  ...  In [12] , a specific kind of activation functions called Rectified Linear Unit (ReLU) is considered for verification of neural networks.  ... 
arXiv:1712.08163v1 fatcat:vshjgrbx3fcp7e5knqms7upkmy

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
It also covers an even more recent trend, namely the design of domain-specific languages for producing and training neural nets.  ...  But they can be vulnerable to attacks and the verification of their correctness is only just emerging as a scientific and engineering possibility.  ...  [11] proposed a two-player turn-based game framework for the verification of deep neural networks with provable guarantees, and to evaluate pointwise robustness of neural networks in safety-critical  ... 
arXiv:1901.11334v1 fatcat:fy7zq2r3uve5vcdwrfydxxqvyu

A Unified View of Piecewise Linear Neural Network Verification [article]

Rudy Bunel, Ilker Turkaslan, Philip H.S. Torr, Pushmeet Kohli, M. Pawan Kumar
2018 arXiv   pre-print
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models.  ...  These methods are however still far from scaling to realistic neural networks. To facilitate progress on this crucial area, we make two key contributions.  ...  Problem specification We now specify the problem of formal verification of neural networks.  ... 
arXiv:1711.00455v3 fatcat:xvudnrzkc5eulaj7zuifaxopau

Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks [chapter]

Rüdiger Ehlers
2017 Lecture Notes in Computer Science  
We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function.  ...  [KBD + 17] provide an alternative approach that allows to check the input/output behavior of a neural network with linear and so-called ReLU nodes against convex specifications.  ...  Acknowledgements This work was partially funded by the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative.  ... 
doi:10.1007/978-3-319-68167-2_19 fatcat:nduemt4ubbbr3p2xbcmciz5isi

An SMT-Based Approach for Verifying Binarized Neural Networks [article]

Guy Amir, Haoze Wu, Clark Barrett, Guy Katz
2021 arXiv   pre-print
One novelty of our technique is that it allows the verification of neural networks that include both binarized and non-binarized components.  ...  We propose an SMT-based technique for verifying Binarized Neural Networks - a popular kind of neural network, where some weights have been binarized in order to render the neural network more memory and  ...  One novelty of our technique is that it allows the verification of neural networks that include both binarized and non-binarized components.  ... 
arXiv:2011.02948v2 fatcat:iwlsns6mizb4zhrxux5ohredku
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