mlsanityData to 7 Oct 2026

GoTube: Scalable Stochastic Verification of Continuous-Depth Models

arXiv 2107.08467 ↗First posted 18 Jul 2021cs.LG cs.AI cs.NEcited by 12

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Abstract (arXiv)

We introduce a new stochastic verification algorithm that formally quantifies the behavioral robustness of any time-continuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness. GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. 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 in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments. GoTube is stable and sets the state-of-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 37 of its 90 references that are in the map. First posted on arXiv 18 Jul 2021.

Builds on

37 of 90 references.

References · 37

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25 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 4; 2023: 4; 2024: 0; 2025: 0; 2026: 1.

12 papers.

  1. 2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 24
  2. 2022Reachability Analysis of a General Class of Neural Ordinary Differential Equationscited by 13
  3. 2021A Simple and Efficient Sampling-based Algorithm for General Reachability Analysiscited by 12
  4. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 11
  5. 2023Neural Abstractionscited by 11
  6. 2022Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Drivingcited by 10
  7. 2022On the Forward Invariance of Neural ODEscited by 10
  8. 2022Safety Verification for Neural Networks Based on Set-boundary Analysiscited by 5
  9. 2023Verifying Safety of Neural Networks from Topological Perspectivescited by 1
  10. 2026TNODEV: Toolbox for Neural ODE Verificationcited by 1
  11. 2023On the Trade-off Between Efficiency and Precision of Neural Abstractioncited by 0
  12. 2023Robustness Analysis of Continuous-Depth Models with Lagrangian Techniquescited by 0