Presented by Thomas Waite in 2nd International Conference on Neuro-symbolic Systems (NeuS) on May 29, 2025 in Philadelphia, PA.

1. State-Dependent Conformal Perception Bounds for
Neuro-Symbolic Verification of Autonomous Systems
Thomas Waite1, Yuang Geng2, Trevor Turnquist2, Ivan Ruchkin2*, Radoslav Ivanov1*
1RPI, 2UF, *Co-last authors: Equal contribution in supervision
NeuS 2025

2. Setting & Motivation
Key Question:
How do we provide tight, high-confidence safety
guarantees for perception-driven autonomous
systems?

3. High-Confidence Reachability
Abstracted System (2):
𝑥𝑘+1 = 𝑓 𝑥𝑘, 𝑢𝑘 ; 𝑦𝑘 = 𝑔 𝑥𝑘 + 𝑣𝑘; 𝑢𝑘 = ℎ 𝑦𝑘 .
Problem 1: (High-Confidence Reachability)
Given:
• Abstract system in (2).
• Trajectory Dataset D with perception errors.
Compute:
• Reachable set sets 𝒳0, … , 𝒳𝑇 such
that ℙ ∀𝑘 = 0 … 𝑇: 𝑥𝑘 ∈ 𝒳𝑘 ≥ 1 − 𝛼.
𝒙𝒌+𝟏 = 𝒇 𝒙𝒌, 𝒖𝒌 𝒖𝒌 = 𝒉 𝒚𝒌
𝒚𝒌 = 𝒏𝒏 𝒛𝒌 ≔ 𝒈 𝒙𝒌 +𝒗𝒌

4. State-Dependent Conformal Prediction

5. State-Dependent Conformal Prediction