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Lagrangian Decomposition for Neural Network Verification [article]

Rudy Bunel, Alessandro De Palma, Alban Desmaison, Krishnamurthy Dvijotham, Pushmeet Kohli, Philip H.S. Torr, M. Pawan Kumar
2020 arXiv   pre-print
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take.  ...  This results in an overall speed-up when employing the bounds for formal verification. Code for our algorithms is available at https://github.com/oval-group/decomposition-plnn-bounds.  ...  RB wishes to thank Leonard Berrada for helpful discussions on the convex hull of sigmoid activation functions.  ... 
arXiv:2002.10410v3 fatcat:3h56za34nvcr7iz656r46epwti

DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting [article]

Shaoru Chen, Eric Wong, J. Zico Kolter, Mahyar Fazlyab
2022 arXiv   pre-print
However, even for reasonably-sized neural networks, these relaxations are not tractable, and so must be replaced by even weaker relaxations in practice.  ...  Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex  ...  Neural network verification refers to the problem of verifying whether the output of a neural network satisfies certain properties for a bounded set of input perturbations.  ... 
arXiv:2106.09117v2 fatcat:wmuclkb6yzdkzf24pz7s7wbrpe

Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming [article]

Sumanth Dathathri, Krishnamurthy Dvijotham, Alexey Kurakin, Aditi Raghunathan, Jonathan Uesato, Rudy Bunel, Shreya Shankar, Jacob Steinhardt, Ian Goodfellow, Percy Liang, Pushmeet Kohli
2020 arXiv   pre-print
This precludes applications that involve verification-agnostic networks, i.e., networks not specially trained for verification.  ...  Convex relaxations have emerged as a promising approach for verifying desirable properties of neural networks like robustness to adversarial perturbations.  ...  Acknowledgements We are grateful to Yair Carmon, Ollie Hinder, M Pawan Kumar, Christian Tjandraatmadja, Vincent Tjeng, and Rahul Trivedi for helpful discussions and suggestions.  ... 
arXiv:2010.11645v2 fatcat:2z2gfv5kivd4bgq7zsd4nhwwaa

Make Sure You're Unsure: A Framework for Verifying Probabilistic Specifications [article]

Leonard Berrada, Sumanth Dathathri, Krishnamurthy Dvijotham, Robert Stanforth, Rudy Bunel, Jonathan Uesato, Sven Gowal, M. Pawan Kumar
2021 arXiv   pre-print
In this direction, we first introduce a general formulation of probabilistic specifications for neural networks, which captures both probabilistic networks (e.g., Bayesian neural networks, MC-Dropout networks  ...  Despite the promise of formal verification in ensuring the reliability of neural networks, progress in the direction of probabilistic specifications has been limited.  ...  Introduction Neural network (NN) verification algorithms seek to prove input-output specifications, i.e., specifications requiring that the output of the network satisfies certain constraints for all inputs  ... 
arXiv:2102.09479v2 fatcat:becbh7ou7nevtebcrrhz2id65q

Machine-Learning Non-Conservative Dynamics for New-Physics Detection [article]

Ziming Liu, Bohan Wang, Qi Meng, Wei Chen, Max Tegmark, Tie-Yan Liu
2021 arXiv   pre-print
, which are represented by a Lagrangian Neural Network (LNN) and a universal approximator network (UAN), respectively, trained to minimize the force recovery error plus a constant λ times the magnitude  ...  This paper presents a method for data-driven "new physics" discovery.  ...  Lagrangian neural networks To guarantee energy conservation, inductive biases have recently been embedded into neural networks, including Lagrangian Neural Network [9] , Hamiltonian Neural Network [10  ... 
arXiv:2106.00026v2 fatcat:hrpvibaulzex7mcy7f6oxeehau

An improved bearing fault diagnosis scheme based on Hierarchical fuzzy entropy and Alexnet network

Xiaoyu Shi, Gen Qiu, Chun Yin, Xuegang Huang, Kai Chen, Yuhua Cheng, Shouming Zhong
2021 IEEE Access  
For the neural network for fault diagnosis, the Alexnet network is used in this paper.  ...  For the neural network for fault diagnosis, the Alexnet network is used in this article.  ... 
doi:10.1109/access.2021.3073708 fatcat:rzns2gw6ifc4fgkvb6e2qgz6pq

Intelligent Fault Diagnosis and Forecast of Time-Varying Bearing Based on Deep Learning VMD-DenseNet

Shih-Lin Lin
2021 Sensors  
Coupled with the lightweight network, DenseNet, for image classification and prediction.  ...  This research proposes variational mode decomposition (VMD)-DenseNet to diagnose faults in bearings.  ...  Acknowledgments: The author thanks the University of Ottawa for allowing us to access the data of the time-varying bearing experimental device from their website.  ... 
doi:10.3390/s21227467 pmid:34833542 pmcid:PMC8619351 fatcat:zqx3bswewnbsxmpddivcp737vy

A novel wind turbine gearbox fault diagnosis method based on ASO-VMD and NRF

Wenyi Liu, Mengchen Shan
2020 Journal of Vibroengineering  
Aiming at reducing the number of parameters that need to be adjusted and training time, this paper proposes a variational mode decomposition (VMD) based on atomic search optimization (ASO) and neural random  ...  After ASO-VMD decomposition, signals will be used as the input of NRF. We evaluate our method on simulation gearbox model which is established by Solidworks and Adams.  ...  The literature [34] pointed out that the decision tree can be seen as a two-layer neural network model. For each layer of the neural network, its activation function is shown in Eq.  ... 
doi:10.21595/jve.2020.21316 fatcat:pk4n5uqbnzgiva5vfhooaw5geq

Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification [article]

Shiqi Wang, Huan Zhang, Kaidi Xu, Xue Lin, Suman Jana, Cho-Jui Hsieh, J. Zico Kolter
2021 arXiv   pre-print
Bound propagation based incomplete neural network verifiers such as CROWN are very efficient and can significantly accelerate branch-and-bound (BaB) based complete verification of neural networks.  ...  By terminating BaB early, our method can also be used for efficient incomplete verification.  ...  and LP based verifiers using a learned Graph Neural Network (GNN) to guide the ReLU splits; (5) BDD+ BaBSR [6] , a verification framework based on Lagrangian decomposition on GPUs (BDD+) with BaBSR branching  ... 
arXiv:2103.06624v2 fatcat:ier7kpgjnbgpreabp26ik43eda

A Dual Approach to Scalable Verification of Deep Networks [article]

Krishnamurthy Dvijotham, Robert Stanforth, Sven Gowal, Timothy Mann, Pushmeet Kohli
2018 arXiv   pre-print
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and  ...  outputs (robustness to bounded norm adversarial perturbations, for example).  ...  CONCLUSIONS We have presented a novel framework for verification of neural networks.  ... 
arXiv:1803.06567v2 fatcat:jxiioie3crfuvchtcki5lcqv7e

Multistep Wind Speed Forecasting Based on a Hybrid Model of VMD and Nonlinear Autoregressive Neural Network

Yuqiao Zheng, Bo Dong, Yuhan Liu, Xiaolei Tong, Lei Wang, Heng Liu
2021 Journal of Mathematics  
The methodology used the variational mode decomposition (VMD) to extract wind characteristics, and then, the characteristics were put in the nonlinear autoregressive neural network (Narnet) and long short-term  ...  memory network (LSTM) for prediction; the forecast results of VMD-Narnet and VMD-LSTM are compared with the actual wind speed.  ...  decomposition and neural network considering the time correlation of wind is considerable according to these studies.  ... 
doi:10.1155/2021/6644668 fatcat:6xefjxqp7zf6bcojd7kszx4bva

Table of Contents

2021 IEEE Transactions on Industrial Informatics  
Wang 4714 Finite-Time and Predefined-Time Convergence Design for Zeroing Neural Network: Theorem, Method, and Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ...  Shen 4788 Tracking Protocol for Network of Double-Integrator Systems With Heterogeneous Time Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1109/tii.2021.3064472 fatcat:kohytcjronbqxgepuqvhgjbb5q

Bus Load Forecasting Method of Power System Based on VMD and Bi-LSTM

Jiajie Tang, Jie Zhao, Hongliang Zou, Gaoyuan Ma, Jun Wu, Xu Jiang, Huaixun Zhang
2021 Sustainability  
A bus load forecasting method based on variational modal decomposition (VMD) and bidirectional long short-term memory (Bi-LSTM) network was proposed in this article.  ...  The effective prediction of bus load can provide an important basis for power system dispatching and planning and energy consumption to promote environmental sustainable development.  ...  verification.  ... 
doi:10.3390/su131910526 fatcat:ycche6dhlbg4lasrxfsimuslj4

Neural Network Branch-and-Bound for Neural Network Verification [article]

Florian Jaeckle and Jingyue Lu and M. Pawan Kumar
2021 arXiv   pre-print
Specifically, we learn two graph neural networks (GNN) that both directly treat the network we want to verify as a graph input and perform forward-backward passes through the GNN layers.  ...  Our combined framework achieves a 50\% reduction in both the number of branches and the time required for verification on various convolutional networks when compared to several state-of-the-art verification  ...  Improved branch and bound for neural network verification via lagrangian decomposition. arXiv preprint arXiv:2104.06718, 2021.  ... 
arXiv:2107.12855v1 fatcat:3hktdiw2vbfndbyec4c7yohvsm

GoTube: Scalable Stochastic Verification of Continuous-Depth Models [article]

Sophie Gruenbacher, Mathias Lechner, Ramin Hasani, Daniela Rus, Thomas A. Henzinger, Scott Smolka, Radu Grosu
2021 arXiv   pre-print
Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent  ...  GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models.  ...  A more scalable approach for rectified linear unit (ReLU) networks (Nair and Hinton 2010) was recently proposed based on Lagrangian decomposition; this approach significantly improves the speed and tightness  ... 
arXiv:2107.08467v2 fatcat:lird25izyjc6rb6qk3zaqw753y
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