Network Verification Research Articles

Intelligent system for analyzing battery charge consumption processes

The article develops an intelligent system of analysis and neural network forecasting of battery charge consumption for automated vehicles (AGVs). For this purpose, the types of AGV and the methods of effective forecasting of their battery charge consumption were analyzed. It is established that they are based on optimal robot control processes; application of technologies to increase capacity and extend service life. The data for the forecast was collected using the UAExpert OPC UA client, which allowed to convert the informative components of the data vector into a format suitable for further processing (csv). To eliminate outliers in the signals, a dispersion analysis of each parameter of AGV was carried out. Data for which the sigma value exceeded 1.5 were considered partialle lost and were replaced by a moving average of 12 points (the number of ANN inputs). For training, verification and testing of neural networks, parameters with high and medium positive correlation dependence were selected according to the Pearson correlation coefficient. Short-term and medium-term forecasting of battery charge consumption for AKTZ was carried out on the basis of ANN with deep learning, the model of which was tested in two modes: forecasting and prediction. The effectiveness of the developed system was investigated by testing it on the data obtained from Formica-1 AGV. The average absolute testing error was less than 1%. The highest value of the prediction error was less than 9 % when predicting such parameters as current position and X-coordinate, which are correlated with battery charge consumption for AGV. It has been established experimentally that the accuracy of the forecast of battery charge consumption for various types of AGV has been improved.

Leveraging Satisfiability Modulo Theory Solvers for Verification of Neural Networks in Predictive Maintenance Applications

Interest in machine learning and neural networks has increased significantly in recent years. However, their applications are limited in safety-critical domains due to the lack of formal guarantees on their reliability and behavior. This paper shows recent advances in satisfiability modulo theory solvers used in the context of the verification of neural networks with piece-wise linear and transcendental activation functions. An experimental analysis is conducted using neural networks trained on a real-world predictive maintenance dataset. This study contributes to the research on enhancing the safety and reliability of neural networks through formal verification, enabling their deployment in safety-critical domains.

A Semidefinite Relaxation Based Branch-and-Bound Method for Tight Neural Network Verification

We introduce a novel method based on semidefinite program (SDP) for the tight and efficient verification of neural networks. The proposed SDP relaxation advances the present state of the art in SDP-based neural network verification by adding a set of linear constraints based on eigenvectors. We extend this novel SDP relaxation by combining it with a branch-and-bound method that can provably close the relaxation gap up to zero. We show formally that the proposed approach leads to a provably tighter solution than the present state of the art. We report experimental results showing that the proposed method outperforms baselines in terms of verified accuracy while retaining an acceptable computational overhead.

Iteratively Enhanced Semidefinite Relaxations for Efficient Neural Network Verification

We propose an enhanced semidefinite program (SDP) relaxation to enable the tight and efficient verification of neural networks (NNs). The tightness improvement is achieved by introducing a nonlinear constraint to existing SDP relaxations previously proposed for NN verification. The efficiency of the proposal stems from the iterative nature of the proposed algorithm in that it solves the resulting non-convex SDP by recursively solving auxiliary convex layer-based SDP problems. We show formally that the solution generated by our algorithm is tighter than state-of-the-art SDP-based solutions for the problem. We also show that the solution sequence converges to the optimal solution of the non-convex enhanced SDP relaxation. The experimental results on standard benchmarks in the area show that our algorithm achieves the state-of-the-art performance whilst maintaining an acceptable computational cost.

Incremental Verification of Neural Networks

Complete verification of deep neural networks (DNNs) can exactly determine whether the DNN satisfies a desired trustworthy property (e.g., robustness, fairness) on an infinite set of inputs or not. Despite the tremendous progress to improve the scalability of complete verifiers over the years on individual DNNs, they are inherently inefficient when a deployed DNN is updated to improve its inference speed or accuracy. The inefficiency is because the expensive verifier needs to be run from scratch on the updated DNN. To improve efficiency, we propose a new, general framework for incremental and complete DNN verification based on the design of novel theory, data structure, and algorithms. Our contributions implemented in a tool named IVAN yield an overall geometric mean speedup of 2.4x for verifying challenging MNIST and CIFAR10 classifiers and a geometric mean speedup of 3.8x for the ACAS-XU classifiers over the state-of-the-art baselines.

Synthesizing Formal Network Specifications From Input-Output Examples

We propose, a tool that synthesizes network specifications in a declarative logic programming language from input-output examples. aims to accelerate the adoption of formal verification in networking practice, by reducing the effort and expertise required to specify network models or properties. aims to be i) highly expressive, capable of synthesizing network specifications with complex semantics; ii) scalable, by virtue of using a novel best-first search algorithm to efficiently explore an unbounded solution space, and iii) robust, avoiding the need for exhaustive input-output examples by actively generating new examples. Our experiments demonstrate that can synthesize a wide range of specifications used in network verification, analysis, and implementations. Furthermore, improves upon existing approaches in terms of expressiveness, robustness to examples, and the quality of synthesized programs.

Towards rigorous understanding of neural networks via semantics-preserving transformations

AbstractIn this paper, we present an algebraic approach to the precise and global verification and explanation of Rectifier Neural Networks, a subclass of Piece-wise Linear Neural Networks (PLNNs), i.e., networks that semantically represent piece-wise affine functions. Key to our approach is the symbolic execution of these networks that allows the construction of semantically equivalent Typed Affine Decision Structures (TADS). Due to their deterministic and sequential nature, TADS can, similarly to decision trees, be considered as white-box models and therefore as precise solutions to the model and outcome explanation problem. TADS are linear algebras, which allows one to elegantly compare Rectifier Networks for equivalence or similarity, both with precise diagnostic information in case of failure, and to characterize their classification potential by precisely characterizing the set of inputs that are specifically classified, or the set of inputs where two network-based classifiers differ. All phenomena are illustrated along a detailed discussion of a minimal, illustrative example: the continuous XOR function.

Theoretical analysis and experimental verification of fractional-order RC cobweb circuit network

Recent research has shown that ideal capacitors and inductors do not physically exist, and that the dynamics of real devices can be accurately described by fractional-order (FO) mathematical models. This paper investigates a class of 2×n order RC cobweb FO circuit network with central node. Based on the Kirchhoff’s laws, the impedance magnitude and phase between two points of the network are derived using difference equations and matrix transformations. Three impedance expressions are deduced, and their correctness is verified numerically and by simulations. The influence of various parameters of the electrical network, namely the resistance, capacitance, number of circuit units, frequency and fractional order, on the impedance is studied. Additionally, for the first time, physical experiments are presented to compare the effectiveness of FO and integer-order circuit networks for describing the impedance of actual physical circuits. These experiments confirm that FO circuit network models perform better than the integer-order ones for representing the characteristics of the impedance magnitude and phase.

Deep learning segmentation to analyze bubble dynamics and heat transfer during boiling at various pressures

Today, neural networks have increasingly gained the attention of researchers and become an effective instrument for a wide range of scientific applications, including issues related to the boiling. However, there are no universal tools in the literature that would allow detecting the life cycle of individual vapor bubbles and automatically measure a wide range of main boiling characteristics based on the high-speed visualization data. In this study, the U-net and Mask R-CNN convolutional neural networks were used to detect and segment bubbles obtained by visualization from the bottom side of a transparent heater during water boiling at various subatmospheric pressures. The key feature of the trained CNN architectures is the ability to detect bubbles located on a heated wall, while ignoring the bubbles that lift-off, and to determine the moment of their departure. The verification of various neural networks demonstrated that the Mask R-CNN architecture is more preferable to measure dynamic boiling characteristics. Through trained convolutional neural networks, a wide array of data on local boiling characteristics, including the nucleation site density, bubbles growth rate, life-time and departure diameters, waiting time between moments of bubbles departure and nucleation frequencies were automatically obtained for water boiling at various heat fluxes and pressures in the range of 42–103 kPa. Based on the parameters obtained, heat transfer simulation was carried out using various heat flux partitioning approaches and the ranges of their applicability were demonstrated.

Verification of Fuzzy Decision Trees

In recent years, there have been major strides in the safety verification of machine learning models such as neural networks and tree ensembles. However, fuzzy decision trees (FDT), also called soft or differentiable decision trees, are yet unstudied in the context of verification. They present unique verification challenges resulting from multiplications of input values; in the simplest case with a piecewise-linear splitting function, an FDT is piecewise-polynomial with degree up to the depth of the tree. We propose an abstraction-refinement algorithm for verification of properties of FDTs. We show that the problem is NP-Complete, like many other machine learning verification problems, and that our algorithm is complete in a finite precision setting. We benchmark on a selection of public data sets against an off-the-shelf SMT solver and a baseline variation of our algorithm that uses a refinement strategy from similar methods for neural network verification, finding the proposed method to be the fastest. Code for our algorithm along with our experiments and demos are available on GitHub at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/autonlab/fdt_verification</uri> .

The power of typed affine decision structures: a case study

AbstractTADS are a novel, concise white-box representation of neural networks. In this paper, we apply TADS to the problem of neural network verification, using them to generate either proofs or concise error characterizations for desirable neural network properties. In a case study, we consider the robustness of neural networks to adversarial attacks, i.e., small changes to an input that drastically change a neural networks perception, and show that TADS can be used to provide precise diagnostics on how and where robustness errors a occur. We achieve these results by introducing Precondition Projection, a technique that yields a TADS describing network behavior precisely on a given subset of its input space, and combining it with PCA, a traditional, well-understood dimensionality reduction technique. We show that PCA is easily compatible with TADS. All analyses can be implemented in a straightforward fashion using the rich algebraic properties of TADS, demonstrating the utility of the TADS framework for neural network explainability and verification. While TADS do not yet scale as efficiently as state-of-the-art neural network verifiers, we show that, using PCA-based simplifications, they can still scale to medium-sized problems and yield concise explanations for potential errors that can be used for other purposes such as debugging a network or generating new training samples.

In-situ integration and performance verification of large-scale PZT network for composite aerospace structure

Piezoelectric transducer (PZT) based structural health monitoring (SHM) technology has been proved to be effective in increasing safety and reliability of composite aircraft structures. However, the attachment of PZT network to the host structure is considered as a weak link when facing the long term durability requirement of aerospace SHM, which should be overcome for aerospace SHM. In this paper, a surface-mounted co-curing method is creatively proposed to realize in-situ integration of large-scale PZT network and composite structure. By jointly controlling curing temperature and pressure, the proposed method can realize integration of large-scale PZT network and structural surface with high reliability and performance consistency. Compared with the conventional integration methods, the proposed method does not affect the manufacturing process or reduce the mechanical property of structure, and can be easily implemented whenever the host structure is available. To evaluate the effectiveness of the proposed integration method, a large-scale PZT network with an overall dimension of 1100 mm × 600 mm is integrated with a carbon fiber composite panel of wing box. The integration caused influence on functional integrity is first assessed by performing electro-mechanical impedance based theoretical analysis and experimental investigation. Then guided wave signals of the integrated large-scale PZT network are also acquired and analyzed, which proves the good signal repeatability and consistency of the network. At last, the SHM performance of the network is verified by conducting impact damages on the composite panel and performing damage monitoring, experimental results show that accurate monitoring is realized.

Further results on observability verification of Boolean control networks

Further results on observability verification of Boolean control networks

Modelling the Level of the Enterprise’ Resource Security Using Artificial Neural Networks

Significant attention is paid to increasing the efficiency of using resources by business entities due to the growing dependence between economic growth and the number of consumed resources, problems with access to various types of resources on the market, as well as their exhaustion in the face of growing needs. At the same time, various digitization tools are widely used to solve these problems. This paper considers artificial neural networks as a tool for modelling and forecasting the level of resource security in the economic activity of an enterprise, which is divided into separate functional blocks (production, personnel, finance). To this end, a multi-layer perceptron model (MLP) was used by constructing and training a network on several possible architectures in order to select the one with the highest classification quality. In the process of training, testing and verification of MLP networks, 32 indicators were used as input data, characterizing the state and efficiency of using various types of enterprise resources, for 85 enterprises over the five years of their operation. The initial data were the values of the safety zone, which were set separately for each indicator, subsystem and enterprise using economic-mathematical modelling on the basis of determining the acceptable limits of indicator fluctuations. As a result, four MLP networks were selected (one network for each of the three functional subsystems, as well as one for the enterprise as a whole), which were characterized by the highest value of quality at each stage of calculations (training, testing, verification). The performed calculations proved that artificial neural networks can be a useful and convenient tool for determining the security level of an enterprise in various directions of its economic activity (types of consumed or involved resources), and therefore can be more widely used by business entities to increase the validity of management decisions.

Damage identification of seismic-isolated structure based on CAE network using vibration monitoring data

Seismic-isolated systems have been investigated and practiced globally to prevent the destruction of existing structures, and vibration-based structural health monitoring is important for maintaining the functionality of the isolation systems. Given the recent boom in computational science and machine learning algorithms, this paper deployed a structural health monitoring system for a rubber bearing-isolated gymnasium in an area with high seismic fortification intensity and introduced an unsupervised deep learning network named convolutional autoencoder (CAE) to identify damage from vibrations of the isolation layer. The CAE network is first trained by operational monitoring vibrations and tested by new data. The vibration assessment results indicate that the CAE network can accurately reconstruct daily data and effectively detect unexpected ground motion. Thereafter, to further test the network's damage identification and localization performance, an analytical finite element model of the gymnasium structure is established, and the undamaged and damaged datasets are generated for network verification and updating. The verification results demonstrate that the CAE network leads to reliable feature extraction power in global and local damage detection of the isolation layer. The proposed vibration assessment method is beneficial to building administrators in making accurate and timely decisions with the assistance of the score result provided by the CAE network.

Guarded Kleene Algebra with Tests: Automata Learning

Guarded Kleene Algebra with Tests (GKAT) is the fragment of Kleene Algebra with Tests (KAT) that arises by replacing the union and iteration operations of KAT with predicate-guarded variants. GKAT is more efficiently decidable than KAT and expressive enough to model simple imperative programs, making it attractive for applications to e.g. network verification. In this paper, we further explore GKAT's automata theory, and present GL*, an algorithm for learning the GKAT automaton representation of a black-box, by observing its behaviour. A complexity analysis shows that it is more efficient to learn a representation of a GKAT program with GL* than with Angluin's existing L* algorithm. We implement GL* and L* in OCaml and compare their performances on example programs.

Theoretical analysis of norm selection for robustness verification of neural networks

In the robustness verification of neural network, Lp-norm is generally used to measure the distance between two different data. However, different kinds of Lp-norm examine the specific differences between each dimension of the data. Some Lp-norm computational methods magnify specific differences between datasets. To verify the robustness of the network, the usual method is to calculate the different robustness radii of the L∞-norm. But which Lp norm performs best under a given network is rarely considered. To better reflect the nature of the network, this paper proposes a theoretical analysis of the robustness of the network that can be verified by choosing any norm type, and the relationship between the size of Lp-ball corresponding to different robust radii is proved. We conducted experiments on different classification networks and obtained a general norm selection method. As a result, a specific norm can be considered first for network robustness without computing all the different Lp-norm.

A Distributed Traffic Replay Framework for Network Emulation

Traffic replay can effectively improve the fidelity of network emulation and can support emerging network verification and network security evaluation. A distributed traffic replay framework for network emulation, named DTRF, is designed for large-scale and high-fidelity network traffic emulation on the cloud platform. A fast traffic replay strategy bypassing the kernel is proposed to improve the traffic replay performance in the single node by alleviating the problem of high overhead from the kernel protocol stack. To conveniently expand the emulation scale, an extendable method of workflow orchestration that can realize the flexible control and configuration of the execution process of emulation tasks is proposed. The experimental results show that, compared with that of the traditional method, the throughput of traffic replay is increased by 3.71 times on average, the number of concurrent streams is increased by 4.18 times on average, and the timestamp error of the replayed packets is reduced by 97.8% on average. The DTRF can expand the emulation scenario to a massive heterogeneous network.

Stability Verification for Heterogeneous Complex Networks via Iterative SOS Programming

This letter is to investigate the stability verification for heterogeneous polynomial complex networks through iterative sum-of-squares programming approach. With polynomial Lyapunov functions, a global asymptotic stability criterion is established for the heterogeneous complex networks under the directed topology. Based on the proposed criterion, the stability verification problem is then reduced to a sum-of-squares optimization problem for solving polynomial matrix inequalities. To process non-convex terms of the polynomial matrix inequalities, we present an iterative sum-of-squares programming approach to turn them into the convex polynomial matrix inequalities, yielding polynomial Lyapunov functions effectively to realize the stability verification. Finally, a numerical example is given to show the fully automatic verification of global asymptotic stability for the heterogeneous polynomial complex networks, which demonstrates the theoretical and algorithmic advantages of the proposed method.

Practical Verification of Railway Signalling Programs

SafeCap is a modern toolkit for modelling, simulation and formal verification of railway networks. This paper discusses the use of SafeCap for formal analysis and automated scalable safety verification of solid state interlocking (SSI) programs – a technology at the heart of many railway signalling solutions around the world. The main driving force behind SafeCap development was to make it easy for signalling engineers to use the technology and thus to ensure its smooth industrial deployment. The unique qualities and the novelty of SafeCap are in making the use of formal notations and proofs fully transparent for the engineers. In this paper we explain the formal foundations of the proposed method, its tool support, and its successful application by railway companies in developing industrial signalling projects.