On the Verification of Neural ODEs with Stochastic Guarantees

Gruenbacher, Sophie; Hasani, Ramin; Lechner, Mathias; Cyranka, Jacek; Smolka, Scott A.; Grosu, Radu

doi:10.1609/aaai.v35i13.17372

Cited by 13 publications

(4 citation statements)

References 49 publications

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“…Moreover, we speculate that inferring causality from ODE-based networks might be more straightforward than a closed-form solution 24 . It would also be beneficial to assess whether verifying a continuous neural flow 35 is more tractable by using an ODE representation of the system or its closed form.…”

Section: What Are the Limitations Of Cfcs?mentioning

confidence: 99%

Closed-form continuous-time neural networks

et al. 2022

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Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making tasks. These models are typically represented by continuous differential equations. However, their expressive power when they are deployed on computers is bottlenecked by numerical differential equation solvers. This limitation has notably slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show that it is possible to closely approximate the interaction between neurons and synapses—the building blocks of natural and artificial neural networks—constructed by liquid time-constant networks efficiently in closed form. To this end, we compute a tightly bounded approximation of the solution of an integral appearing in liquid time-constant dynamics that has had no known closed-form solution so far. This closed-form solution impacts the design of continuous-time and continuous-depth neural models. For instance, since time appears explicitly in closed form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared with differential equation-based counterparts. More importantly, in contrast to ordinary differential equation-based continuous networks, closed-form networks can scale remarkably well compared with other deep learning instances. Lastly, as these models are derived from liquid networks, they show good performance in time-series modelling compared with advanced recurrent neural network models.

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Section: What Are the Limitations Of Cfcs?mentioning

confidence: 99%

Closed-form continuous-time neural networks

et al. 2022

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“…Similar to RNNs, neural ODEs are also deep learning models with "memory", which makes them suitable to learn time-series data, but are also applicable to other tasks such as continuous normalizing flows (CNF) and image classification [11,61]. However, existing work is limited to a stochastic reachability approach [27,28], reachability approaches using star and zonotope reachability methods for a general class of neural ODEs (GNODE) with continuous and discrete time layers [52], and GAINS [89], which leverages ODE-solver information to discretize the models using a computation graph that represent all possible trajectories from a given input to accelerate their bound propagation method. However, one of the main challenges is to find a framework that is able to verify several of these models successfully.…”

Section: Related Workmentioning

confidence: 99%

NNV 2.0: The Neural Network Verification Tool

Lopez

Choi

Tran

et al. 2023

Lecture Notes in Computer Science

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This manuscript presents the updated version of the Neural Network Verification (NNV) tool. NNV is a formal verification software tool for deep learning models and cyber-physical systems with neural network components. NNV was first introduced as a verification framework for feedforward and convolutional neural networks, as well as for neural network control systems. Since then, numerous works have made significant improvements in the verification of new deep learning models, as well as tackling some of the scalability issues that may arise when verifying complex models. In this new version of NNV, we introduce verification support for multiple deep learning models, including neural ordinary differential equations, semantic segmentation networks and recurrent neural networks, as well as a collection of reachability methods that aim to reduce the computation cost of reachability analysis of complex neural networks. We have also added direct support for standard input verification formats in the community such as VNNLIB (verification properties), and ONNX (neural networks) formats. We present a collection of experiments in which NNV verifies safety and robustness properties of feedforward, convolutional, semantic segmentation and recurrent neural networks, as well as neural ordinary differential equations and neural network control systems. Furthermore, we demonstrate the capabilities of NNV against a commercially available product in a collection of benchmarks from control systems, semantic segmentation, image classification, and time-series data.

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“…Neural networks have been shown to generalize well to unseen test data on a large range of tasks, despite achieving zero loss on training data (Zhang et al, 2017(Zhang et al, , 2021. But this performance is useless if neural networks cannot be used in practice due to safety and security issues (Gruenbacher et al, 2022;Grunbacher et al, 2021;Lechner et al, 2020Xiao et al, 2021Xiao et al, , 2022. A fundamental question in the security of neural networks is how much information is leaked via this training procedure, that is, can adversaries with access to trained models, or predictions from a model, infer what data was used to train the model?…”

Section: Introductionmentioning

confidence: 99%

Dataset Distillation Fixes Dataset Reconstruction Attacks

Noel¹,

Hasani²,

Lechner³

et al. 2023

Preprint

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Modern deep learning requires large volumes of data, which could contain sensitive or private information which cannot be leaked. Recent work has shown for homogeneous neural networks a large portion of this training data could be reconstructed with only access to the trained network parameters. While the attack was shown to work empirically, there exists little formal understanding of its effectiveness regime, and ways to defend against it. In this work, we first build a stronger version of the dataset reconstruction attack and show how it can provably recover their entire training set in the infinite width regime. We then empirically study the characteristics of this attack on two-layer networks and reveal that its success heavily depends on deviations from the frozen infinite-width Neural Tangent Kernel limit. More importantly, we formally show for the first time that dataset reconstruction attacks are a variation of dataset distillation. This key theoretical result on the unification of dataset reconstruction and distillation not only sheds more light on the characteristics of the attack but enables us to design defense mechanisms against them via distillation algorithms.

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On the Verification of Neural ODEs with Stochastic Guarantees

Cited by 13 publications

References 49 publications

Closed-form continuous-time neural networks

Closed-form continuous-time neural networks

NNV 2.0: The Neural Network Verification Tool

Dataset Distillation Fixes Dataset Reconstruction Attacks

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