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State-Dependent Conformal Perception Bounds for Neuro-Symbolic Verification of Autonomous Systems

Thomas Waite, Yuang Geng, Trevor Turnquist, Ivan Ruchkin, Radoslav Ivanov

TL;DR

This work introduces state-dependent conformal bounds as a principled interface between neural perception and symbolic verification to enable high-confidence safety guarantees for autonomous systems. It leverages gradient-free optimization to partition the state space into regions and assigns region-specific perception bounds $\ eta(x)$, exploiting heteroskedasticity with respect to state to tighten reachable sets. The method combines two losses (EL, ETDL) to shape region partitions and applies scalar conformal prediction within each region, yielding per-region bounds that feed a high-confidence reachability analysis via Verisig. In a Mountain Car case study, state-dependent bounds produce significantly smaller reachable tubes than time-series CP baselines, demonstrating practical gains in verification conservatism and safety guarantees with controlled confidence $1-\\alpha$. The approach advances neuro-symbolic verification by marrying data-driven perception bounds with symbolic reachability under dynamical models, enabling tighter, probabilistic safety guarantees for complex autonomous systems.

Abstract

It remains a challenge to provide safety guarantees for autonomous systems with neural perception and control. A typical approach obtains symbolic bounds on perception error (e.g., using conformal prediction) and performs verification under these bounds. However, these bounds can lead to drastic conservatism in the resulting end-to-end safety guarantee. This paper proposes an approach to synthesize symbolic perception error bounds that serve as an optimal interface between perception performance and control verification. The key idea is to consider our error bounds to be heteroskedastic with respect to the system's state -- not time like in previous approaches. These bounds can be obtained with two gradient-free optimization algorithms. We demonstrate that our bounds lead to tighter safety guarantees than the state-of-the-art in a case study on a mountain car.

State-Dependent Conformal Perception Bounds for Neuro-Symbolic Verification of Autonomous Systems

TL;DR

This work introduces state-dependent conformal bounds as a principled interface between neural perception and symbolic verification to enable high-confidence safety guarantees for autonomous systems. It leverages gradient-free optimization to partition the state space into regions and assigns region-specific perception bounds , exploiting heteroskedasticity with respect to state to tighten reachable sets. The method combines two losses (EL, ETDL) to shape region partitions and applies scalar conformal prediction within each region, yielding per-region bounds that feed a high-confidence reachability analysis via Verisig. In a Mountain Car case study, state-dependent bounds produce significantly smaller reachable tubes than time-series CP baselines, demonstrating practical gains in verification conservatism and safety guarantees with controlled confidence . The approach advances neuro-symbolic verification by marrying data-driven perception bounds with symbolic reachability under dynamical models, enabling tighter, probabilistic safety guarantees for complex autonomous systems.

Abstract

It remains a challenge to provide safety guarantees for autonomous systems with neural perception and control. A typical approach obtains symbolic bounds on perception error (e.g., using conformal prediction) and performs verification under these bounds. However, these bounds can lead to drastic conservatism in the resulting end-to-end safety guarantee. This paper proposes an approach to synthesize symbolic perception error bounds that serve as an optimal interface between perception performance and control verification. The key idea is to consider our error bounds to be heteroskedastic with respect to the system's state -- not time like in previous approaches. These bounds can be obtained with two gradient-free optimization algorithms. We demonstrate that our bounds lead to tighter safety guarantees than the state-of-the-art in a case study on a mountain car.

Paper Structure

This paper contains 32 sections, 3 theorems, 15 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Background: reachability analysis.
  5. Background: scalar conformal prediction.
  6. Background: conformal prediction for time-series data.
  7. Novel setting: state-dependent conformal prediction.
  8. Approach
  9. Approach Overview
  10. Step 1: region-based perception noise bounds.
  11. Step 2: High-confidence reachability analysis.
  12. State-Dependent Conformal Prediction
  13. Solving the optimization problem.
  14. Reachable Tube Computation
  15. Case Study: Mountain Car
  16. ...and 17 more sections

Key Result

proposition 1

Consider the abstracted system in eq:abst_system_model with the state space partitioned into $M$ regions, $\mathcal{X} = \mathcal{S}_1 \cupdot \dots \cupdot \mathcal{S}_M$, and assume a high-confidence bound within each region: $\\$ Then the trajectory-wide bound holds: ${\mathbb{P}_{x_0\sim \mathcal{D}_0, v_k \sim \mathcal{V}_{k|k-1}}[\exists k = 0..T: \|y_k - g(x_k)\| > \eta(x_k)]} \le \alpha$.

Figures (4)

  • Figure 1: An overview of our approach to high-confidence reachability.
  • Figure 2: Perception errors and their respective bounds under our method and time-based baseline.
  • Figure 3: Reachable Sets for our state-based conformal perception bounds (GA+ETDL, $M=7$) vs. the time-based baseline bounds. Our reachable sets are tighter than the time-based method at all timesteps.
  • Figure 4: Images of the mountain car environment

Theorems & Definitions (5)

  • Remark
  • proposition 1
  • theorem 1
  • proposition 2: High-confidence region-based perception error bound
  • definition 1: Reachability-Informed Region Optimization