Presented by Ivan Ruchkin at the 3rd TACPS workshop https://www.tacps.org/ Paper link: https://arxiv.org/abs/2502.21308

1. State-Dependent Conformal Perception Bounds
for Neuro-Symbolic Verification
Thomas Waite1
, Yuang Geng2
, Trevor Turnquist2
, Ivan Ruchkin2
*, Radoslav Ivanov1
*
1
Rensselaer Polytechnic Institute
2
University of Florida
* Co-last authors: equal contribution in supervision
July 21, 2025 — Zagreb, Croatia — co-located with CAV’25
3rd TACPS workshop
Supported by the NSF CPS Grants CCF-2403615 and CCF-2403616

2. • TEA Lab’s mission: make autonomous CPS safer and more trustworthy through
rigorous engineering methods with strong guarantees
• Across many domains: autonomous driving, mobile robots, UAVs/UUVs
• Research areas: formal methods, AI/ML, CPS, robotics
• Theory → techniques/algorithms/tools → simulations+physical deployment
TEA Lab: Trustworthy Engineered Autonomy
tea.ece.ufl.edu
2
Research platform:
small-scale racing cars
ivan.ece.ufl.edu
iruchkin@ece.ufl.edu

3. • 2006–2011: Undergrad @ Moscow State University
• Moscow, Russia — applied math & computer science
• Industry and government roles
• AFRL VFRP, NASA JPL, CMU SEI, Google Summer of Code, …
• 2011–2018: PhD @ Carnegie Mellon University
• Pittsburgh, PA — software engineering & formal methods
Ivan Ruchkin: Brief Bio
3
• 2018–2022: Postdoc @ University of Pennsylvania
• Philadelphia, PA — guarantees for learning-enabled systems
• 2022–present: Assistant professor @ University of Florida
• Gainesville, FL — trustworthy methods for autonomy

4. Motivation: Safety for Neural CPS
• Modern cyber-physical systems use advanced neural perception & control,
but lack safety guarantees
• Existing approaches attempt to bridge neural perception & verification, but
suffer from excessive conservatism and confidence decay over time
4

5. Perception-driven Systems
Major Question:
How do we provide tight,
high-confidence safety guarantees for
perception-driven systems?
5
Original Blurred
[ T. Waite, Y. Geng, T. Turnquist, I. Ruchkin, R. Ivanov, “State-Dependent Conformal
Perception Bounds for Neuro-Symbolic Verification of Autonomous Systems”, NeuS 2025 ]

6. High-Confidence Reachability Problem
6

7. Related Work
• Vanilla conformal prediction (CP) leads to overly conservative guarantees
without considering closed-loop dynamics
[ V. Vovk, “Algorithmic Learning in a Random World”, 2005 ]
• Time-based CP exploits the dependency of error on time — but not state
[ M. Cleaveland, I. Lee, G. Pappas, L. Lindemann, “Conformal prediction regions for time series using
linear complementarity programming”, AAAI 2024 ]
• Other works combine CP with reachability verification — but in a different
and/or handcrafted pattern
[ Y. Geng, J. Baldauf, S. Dutta, C. Huang, I. Ruchkin, “Bridging Dimensions: Confident Reachability for
High-Dimensional Controllers”, FM 2024 ]
• Our insights: (a) perception error can also be heteroskedastic in state, and
(b) the knowledge of system dynamics can reduce conservatism
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8. Background: Scalar Conformal Prediction
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Given:
• Calibration dataset
• Desired confidence
Provides:
➔ Upper bound for the next sample:
Details: [ Lars Lindemann’s & Jyo Deshmukh’s tutorial
“Formal Verification and Control with Conformal Prediction” ]

9. State-Dependent Conformal Prediction Problem
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10. Approach Overview
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NEURAL NEURO-SYMBOLIC
SYMBOLIC

11. Step 2: High-Confidence Reachability
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12. Approach Overview
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13. Step 1: Searching for State Regions
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Solution recipe:
1. Define a loss function over perception error bounds
2. Synthesize boundaries of state regions
3. Obtain an upper error bound for each with confidence
Solve with gradient-free optimization:
Simulated Annealing (SA) or
Genetic Algorithm (GA)
Experience Loss (EL):
Experience Time-Decay Loss (EL):

14. 14
(a) Original (b) Low-Contrast (c) High-Contrast (d) Blur
Case Study: Mountain Car

15. Our Error Bounds Are Tighter
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• Perception error is heteroskedastic over both space and time
• Trade-off between low- and high-error regions

16. Our Reachsets Are Tighter
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• Our method (GA+ETDL) for 7 regions vs. the time-based method

17. Our Method is Slower But Less Conservative
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18. Limitations
1. Inflexible confidence: same for all regions
2. Partitioning along only one state dimension
3. Unclear what partitioning is truly the best for reachability verification
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19. Summary
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[ T. Waite, Y. Geng, T. Turnquist, I. Ruchkin, R. Ivanov, “State-Dependent Conformal
Perception Bounds for Neuro-Symbolic Verification of Autonomous Systems”, NeuS 2025 ]
1. Optimized conformal bounds
over state regions
2. High-confidence verification of perception-driven systems
3. Evaluation on a mountain car with visual distribution shift
NEURAL NEURO-SYMBOLIC
SYMBOLIC