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1. Neural Network Verification with Proof Production

   Isac, Omri; Barrett, Clark; Zhang, Min; Katz, Guy (October 2022, Proceedings of the 22nd International Conference on Formal Methods In Computer-Aided Design (FMCAD))

   Griggio, Alberto; Rungta, Neha (Ed.)

   Deep neural networks (DNNs) are increasingly being employed in safety-critical systems, and there is an urgent need to guarantee their correctness. Consequently, the verification community has devised multiple techniques and tools for verifying DNNs. When DNN verifiers discover an input that triggers an error, that is easy to confirm; but when they report that no error exists, there is no way to ensure that the verification tool itself is not flawed. As multiple errors have already been observed in DNN verification tools, this calls the applicability of DNN verification into question. In this work, we present a novel mechanism for enhancing Simplex-based DNN verifiers with proof production capabilities: the generation of an easy-to-check witness of unsatisfiability, which attests to the absence of errors. Our proof production is based on an efficient adaptation of the well-known Farkas' lemma, combined with mechanisms for handling piecewise-linear functions and numerical precision errors. As a proof of concept, we implemented our technique on top of the Marabou DNN verifier. Our evaluation on a safety-critical system for airborne collision avoidance shows that proof production succeeds in almost all cases and requires only minimal overhead. 

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2. Harnessing Neuron Stability to Improve DNN Verification

   https://doi.org/10.1145/3643765  

   Duong, Hai; Xu, Dong; Nguyen, Thanhvu; Dwyer, Matthew B (July 2024, Proceedings of the ACM on Software Engineering)

   Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interest in developing effective and scalable DNN verification techniques and tools. Recent developments in DNN verification have highlighted the potential of constraint-solving approaches that combine abstraction techniques with SAT solving. Abstraction approaches are effective at precisely encoding neuron behavior when it is linear, but they lead to overapproximation and combinatorial scaling when behavior is non-linear. SAT approaches in DNN verification have incorporated standard DPLL techniques, but have overlooked important optimizations found in modern SAT solvers that help them scale on industrial benchmarks. In this paper, we present VeriStable, a novel extension of the recently proposed DPLL-based constraint DNN verification approach. VeriStable leverages the insight that while neuron behavior may be non-linear across the entire DNN input space, at intermediate states computed during verification many neurons may be constrained to have linear behavior – these neurons are stable. Efficiently detecting stable neurons reduces combinatorial complexity without compromising the precision of abstractions. Moreover, the structure of clauses arising in DNN verification problems shares important characteristics with industrial SAT benchmarks. We adapt and incorporate multi-threading and restart optimizations targeting those characteristics to further optimize DPLL-based DNN verification. We evaluate the effectiveness of VeriStable across a range of challenging benchmarks including fully- connected feedforward networks (FNNs), convolutional neural networks (CNNs) and residual networks (ResNets) applied to the standard MNIST and CIFAR datasets. Preliminary results show that VeriStable is competitive and outperforms state-of-the-art DNN verification tools, including α-β-CROWN and MN-BaB, the first and second performers of the VNN-COMP, respectively. 

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3. Harnessing Neuron Stability to Improve DNN Verification

   Duong, Hai; Xu, Dong; Nguyen, Thanhvu; Dwyer, Matthew B (July 2024, Proceedings of the ACM on Software Engineering)

   Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interests in developing effective and scalable DNN verification techniques and tools. Recent developments in DNN verification have highlighted the potential of constraint-solving approaches that combine abstraction techniques with SAT solving. Abstraction approaches are effective at precisely encode neuron behavior when it is linear, but they lead to overapproximation and combinatorial scaling when behavior is non-linear. SAT approaches in DNN verification have incorporated standard DPLL techniques, but have overlooked important optimizations found in modern SAT solvers that help them scale on industrial benchmarks. In this paper, we present VeriStable, a novel extension of recently proposed DPLL-based constraint DNN verification approach. VeriStable leverages the insight that while neuron behavior may be non-linear across the entire DNN input space, at intermediate states computed during verification many neurons may be constrained to have linear behavior – these neurons are stable. Efficiently detecting stable neurons reduces combinatorial complexity without compromising the precision of abstractions. Moreover, the structure of clauses arising in DNN verification problems shares important characteristics with industrial SAT benchmarks. We adapt and incorporate multi-threading and restart optimizations targeting those characteristics to further optimize DPLL-based DNN verification. We evaluate the effectiveness of VeriStable across a range of challenging benchmarks including fully- connected feedforward networks (FNNs), convolutional neural networks (CNNs) and residual networks (ResNets) applied to the standard MNIST and CIFAR datasets. Preliminary results show that VeriStable is competitive and outperforms state-of-the-art DNN verification tools, including 𝛼-𝛽-CROWN and MN-BaB, the first and second performers of the VNN-COMP, respectively. 

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4. DNN Verification, Reachability, and the Exponential Function Problem

   Isac, Omri; Zohar, Yoni; Barrett, Clark; Katz, Guy (September 2023, Proceedings of the 34th International Conference on Concurrency Theory (CONCUR 2023))

   Pérez, Guillermo A.; Raskin, Jean-François (Ed.)

   Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: 1. The decidability of verifying DNNs with piecewise-smooth activation functions is equivalent to a well-known, open problem formulated by Tarski; and 2. The DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network’s activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools. 

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5. CIT4DNN: Generating Diverse and Rare Inputs for Neural Networks Using Latent Space Combinatorial Testing

   https://doi.org/10.1145/3597503.3639106  

   Dola, Swaroopa; McDaniel, Rory; Dwyer, Matthew B.; Soffa, Mary Lou (April 2024, ACM)

   Deep neural networks (DNN) are being used in a wide range of applications including safety-critical systems. Several DNN test gen- eration approaches have been proposed to generate fault-revealing test inputs. However, the existing test generation approaches do not systematically cover the input data distribution to test DNNs with diverse inputs, and none of the approaches investigate the re- lationship between rare inputs and faults. We propose cit4dnn, an automated black-box approach to generate DNN test sets that are feature-diverse and that comprise rare inputs. cit4dnn constructs diverse test sets by applying combinatorial interaction testing to the latent space of generative models and formulates constraints over the geometry of the latent space to generate rare and fault-revealing test inputs. Evaluation on a range of datasets and models shows that cit4dnn generated tests are more feature diverse than the state-of-the-art, and can target rare fault-revealing testing inputs more effectively than existing methods. 

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