On the use of formal methods to model and verify neuronal archetypes

Maria, Elisabetta De; Bahrami, Abdorrahim; L’Yvonnet, Thibaud; Felty, Amy P.; Gaffé, Daniel; Ressouche, Annie; Grammont, Franck

doi:10.1007/s11704-020-0029-6

Cited by 5 publications

(16 citation statements)

References 70 publications

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“…However, recently claims have been made that functional programming, too, can be valuable in this domain. There is a library [14] formalising small rational-valued neural networks in Coq. A more sizeable formalisation called MLCert [2] imports neural networks from Python, treats floating point numbers as bit vectors, and proves properties describing the generalisation bounds for the neural networks.…”

Section: Motivationmentioning

confidence: 99%

“…There are several options for defining neural networks in functional programming, ranging from defining neurons as record types [14] to treating them as functions with refinement types [12]. But we claim that two general considerations should be key to any NN formalisation choice.…”

Section: Motivationmentioning

confidence: 99%

“…The difference between the first and second approaches was discussed in [20] (in Agda, but with no neural network application in mind). The third method was taken in [14] using Coq (records were used there to encode individual neurons).…”

Section: Matrices In Neural Network Formalisationmentioning

confidence: 99%

“…When we formulate verification properties that genuinely require induction, formalisation of matrices as lists does result in more natural, and easily automatable proofs. For example, De Maria et al [14] formalise in Coq "neuronal archetypes" for biological neurons. Each archetype is a specialised kind of perceptron, in which additional functions are added to amplify or inhibit the perceptron's outputs.…”

Section: Matrices As Lists Of Listsmentioning

confidence: 99%

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Neural Networks in Imandra: Matrix Representation as a Verification Choice

Remi¹,

Passmore²,

Komendantskaya³

2022

Preprint

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The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks. Functional programming languages encourage diverse approaches to matrix definitions. This feature has already been successfully exploited in different applications. The question we ask is whether, and how, these ideas can be applied in neural network verification. A functional programming language Imandra combines the syntax of a functional programming language and the power of an automated theorem prover. Using these two key features of Imandra, we explore how different implementations of matrices can influence automation of neural network verification.

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Section: Motivationmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Matrices In Neural Network Formalisationmentioning

confidence: 99%

Section: Matrices As Lists Of Listsmentioning

confidence: 99%

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Neural Networks in Imandra: Matrix Representation as a Verification Choice

Remi¹,

Passmore²,

Komendantskaya³

2022

Preprint

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“…Scalability -modern networks can contain millions or even billions of nodes, whereas most ITPs will consume excessive amounts of memory when representing even very small networks. For example, recent formalisations in Coq [3,8] have have worked with networks of just 10 or 20 nodes. 3.…”

Section: Introductionmentioning

confidence: 99%

Vehicle: Interfacing Neural Network Verifiers with Interactive Theorem Provers

Daggitt¹,

Kokke²,

Atkey³

et al. 2022

Preprint

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Verification of neural networks is currently a hot topic in automated theorem proving. Progress has been rapid and there are now a wide range of tools available that can verify properties of networks with hundreds of thousands of nodes. In theory this opens the door to the verification of larger control systems that make use of neural network components. However, although work has managed to incorporate the results of these verifiers to prove larger properties of individual systems, there is currently no general methodology for bridging the gap between verifiers and interactive theorem provers (ITPs).In this paper we present Vehicle, our solution to this problem. Vehicle is equipped with an expressive domain specific language for stating neural network specifications which can be compiled to both verifiers and ITPs. It overcomes previous issues with maintainability and scalability in similar ITP formalisations by using a standard ONNX file as the single canonical representation of the network. We demonstrate its utility by using it to connect the neural network verifier Marabou to Agda and then formally verifying that a car steered by a neural network never leaves the road, even in the face of an unpredictable cross wind and imperfect sensors. The network has over 20,000 nodes, and therefore this proof represents an improvement of 3 orders of magnitude over prior proofs about neural network enhanced systems in ITPs.

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