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Lagrangian Decomposition for Neural Network Verification
[article]
2020
arXiv
pre-print
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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]
2022
arXiv
pre-print
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2021 pre-print arXiv:2106.09117v1 fatcat:yzrgrbtffjhi3pgkg3iw65xida
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]
2020
arXiv
pre-print
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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]
2021
arXiv
pre-print
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2021 pre-print arXiv:2102.09479v1 fatcat:lcmjtahrird3nkeaqxe4zzocbm
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]
2021
arXiv
pre-print
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, 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
2021
IEEE Access
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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
2021
Sensors
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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
2020
Journal of Vibroengineering
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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]
2021
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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
2021
Journal of Mathematics
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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
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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
2021
Sustainability
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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]
2021
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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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