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Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verification [article]

Shaojie Xu, Joel Vaughan, Jie Chen, Aijun Zhang, Agus Sudjianto
2022 arXiv   pre-print
Our polytope traversing algorithm can be adapted to verify a wide range of network properties related to robustness and interpretability, providing an unified approach to examine the network behavior.  ...  As the traversing algorithm explicitly visits all local polytopes, it returns a clear and full picture of the network behavior within the traversed region.  ...  CONCLUSION We explored the unique topological structure that ReLU NNs create in the input space; identified the adjacency among the partitioned local polytopes; developed a traversing algorithm based on  ... 
arXiv:2111.08922v2 fatcat:ahqwu2zedrgihfmukvvwkazdpi

Algorithms for Verifying Deep Neural Networks [article]

Changliu Liu, Tomer Arnon, Christopher Lazarus, Clark Barrett, Mykel J. Kochenderfer
2020 arXiv   pre-print
Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties.  ...  Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control.  ...  The authors would like to thank many of the authors of the referenced papers for their help in clarifying their algorithms and reviewing early drafts of this survey: Weiming Xiang, Taylor Johnson, Hoang-Dung  ... 
arXiv:1903.06758v2 fatcat:25pqxtxpfzfz7phnnsx53q3j5y

SoK: Certified Robustness for Deep Neural Networks [article]

Linyi Li, Tao Xie, Bo Li
2022 arXiv   pre-print
Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on a wide range of tasks.  ...  for DNNs, and 4) provide an open-sourced unified platform to evaluate over 20 representative certifiably robust approaches for a wide range of DNNs.  ...  ACKNOWLEGMENT We would like to thank Xiangyu Qi (from Princeton University) for conducting the benchmark evaluation of probabilistic verification approaches for smoothed DNNs.  ... 
arXiv:2009.04131v6 fatcat:crruzud4wrexlngaubhz2ceqku

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 review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems.  ...  Acknowledgements This work is partially supported by Airbus and the European Research Council under Consolidator Grant Agreement 681393 -MOPSA.  ... 
arXiv:2104.02466v2 fatcat:6ghs5huoynbc5h7lndajmsoxyu

Neural Network Approximation [article]

Ronald DeVore, Boris Hanin, Guergana Petrova
2020 arXiv   pre-print
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems.  ...  So the stability of numerical approximation using NNs is a large part of the analysis put forward. The survey, for the most part, is concerned with NNs using the popular ReLU activation function.  ...  Acknowledgment: All three authors were supported by a MURI grant N00014-20-1-2787, administered through the Office of Naval Research.  ... 
arXiv:2012.14501v1 fatcat:4vn5h2g6qzd4jkznc6pfdkcthu

Neural network approximation

Ronald DeVore, Boris Hanin, Guergana Petrova
2021 Acta Numerica  
Neural networks (NNs) are the method of choice for building learning algorithms.  ...  So the stability of numerical approximation using NNs is a large part of the analysis put forward.The survey, for the most part, is concerned with NNs using the popular ReLU activation function.  ...  Acknowledgement All three authors were supported by MURI grant N00014-20-1-2787, administered through the US Office of Naval Research.  ... 
doi:10.1017/s0962492921000052 fatcat:isl6y4skajhitgcx32hgf3e7em

Shared Certificates for Neural Network Verification [article]

Christian Sprecher, Marc Fischer, Dimitar I. Dimitrov, Gagandeep Singh, Martin Vechev
2021 arXiv   pre-print
Existing neural network verifiers compute a proof that each input is handled correctly under a given perturbation by propagating a convex set of reachable values at each layer.  ...  In this work we introduce a new method for reducing this verification cost based on the key insight that convex sets obtained at intermediate layers can overlap across different inputs and perturbations  ...  A Unified View of Piecewise Linear Neural Network Verification.  ... 
arXiv:2109.00542v2 fatcat:mpaw2yt45zcclcstnkrkwkmv7y

Formal Verification of Industrial Software and Neural Networks

Marko Kleine Büning, Carsten Sinz
2022
Acknowledgments I want to thank Carsten Sinz for the opportunity to pursue a PhD in his research group and for his advice and guidance throughout my time as a PhD student.  ...  I also want to thank Bernhard Beckert for his review of my dissertation and for our collaborations. Acknowledgments  ...  Part III Verification of Neural Networks 103 Chapter 10 Equivalence Verification of Neural Networks The third part of this thesis presents the contribution C2 and therefore a framework for the verification  ... 
doi:10.5445/ir/1000146737 fatcat:ooebupngwjcenil4azzhe2yubu

Network Structures, Concurrency, and Interpretability: Lessons from the Development of an AI Enabled Graph Database System

Hal James Cooper
2019
a workflow more typical of a graph database than a graph computing system; massive concurrent access allowing for arbitrarily asynchronous execution of queries and analytics across the entire system.  ...  The need for such a system has been independently recognized in the isolated fields of graph databases, graph computing, and computational graph deep learning systems, such as TensorFlow.  ...  Hence, we need to unify the size of input samples for the generator to learn.  ... 
doi:10.7916/d8-hfry-nr98 fatcat:fejno2bh25hdxmvedioxpylism

Enforcing and Discovering Structure in Machine Learning [article]

Francesco Locatello
2021 arXiv   pre-print
In this dissertation, we consider two different research areas that concern structuring a learning algorithm's solution: when the structure is known and when it has to be discovered.  ...  The world is structured in countless ways.  ...  The posterior distribution is approximated by a variational distribution Q(z|x), again parameterized using a deep neural network (i.e., an encoder network q φ (z|x)).  ... 
arXiv:2111.13693v1 fatcat:2urmfjeh6nhvjeiv3qoiy5hrum

MMEDIA 2017 The Ninth International Conferences on Advances in Multimedia MMEDIA 2017 Committee MMEDIA Steering Committee MMEDIA 2017 Technical Program Committee

Marco Martalò, Shohei Yokoyama, Jean-Claude Moissinac, Telecom Paristech, France Thalmann, Alexander Loui, Jean-Claude Moissinac, Telecom Paristech, France Thalmann, Trista Chen, Trista Consulting, Alexander Usa (+38 others)
The Ninth International Conferences on Advances in Multimedia (MMEDIA 2017), held between   unpublished
We also gratefully thank the members of the MMEDIA 2017 organizing committee for their help in handling the logistics and for their work that made this professional meeting a success.  ...  We hope that MMEDIA 2017 was a successful international forum for the exchange of ideas and results between academia and industry and to promote further progress in the field of multimedia.  ...  ACKNOWLEDGMENT The authors gratefully acknowledge the support of the Austrian Research Promotion Agency, the Forschungsförderungsgesellschaft (FFG) for the research project AEDA (K-Projekt "Advanced Engineering  ... 
fatcat:b64rri5ymbctxnl7uklbozddii

COGNITIVE 2017 Committee COGNITIVE Steering Committee COGNITIVE 2017 Technical Program Committee

Olga Chernavskaya, Paul Smart, Tiago Primo, Jose Alfredo, F Costa, Om Rishi, Olga Chernavskaya, Po-Hsun Cheng, Jose Alfredo, F Costa, Om Rishi, Olga Chernavskaya (+38 others)
2017 unpublished
We also gratefully thank the members of the COGNITIVE 2017 organizing committee for their help in handling the logistics and for their work that made this professional meeting a success.  ...  We hope that COGNITIVE 2017 was a successful international forum for the exchange of ideas and results between academia and industry and to promote further progress in the area of cognitive technologies  ...  ACKNOWLEDGMENT This work was partially supported by the Russian Foundation for Humanities, grant 15-06-10894_a, grant 16-06-00133_a, and RFBR, grant 16-06-00501_a. Government. The U.S. and U.K.  ... 
fatcat:ybtgrbqmhjaqteagryegaz3x5y

Text-image synergy for multimodal retrieval and annotation [article]

Sreyasi Nag Chowdhury, Universität Des Saarlandes
2021
Y OLO [128] unifies learning with global context into a single neural network for the entire image. It exploits a word tree derived from the WordNet whose leaf nodes appear in ImageNet.  ...  Here we provide a brief overview of the basic concepts of deep neural networks -networks of nodes and edges that facilitate Deep Learning.  ... 
doi:10.22028/d291-34509 fatcat:yt6hqzkwwrgklanctuc4ijbhwm