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Sound Verification of Deployed Neural Networks

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
sound verificationbackdoor attacksdeploymentfloating point arithmetic
Abstract:

Verification methods aim at mathematically proving desirable properties of neural networks, such as robustness to adversarial perturbations. A verifier is sound if and only if it never claims that a neural network has the desired property when it does not. It was shown recently that none of the currently known verifiers that are claimed to be sound are guaranteed to be sound when considering the deployed version of the verified network. Due to this, all the known verifiers are vulnerable to certain backdoor attacks, where an adversarial network passes verification but, in reality, it exhibits adversarial behavior in specific deployment environments. So far, it has been suspected that sound verification is prohibitively expensive if we wish to verify all possible executions—including parallel and stochastic ones—in deployment. We are the first to propose an efficient error bounding technique that most known verifiers can apply to become practically sound. The technique enables both interval bound propagation and symbolic propagation methods to remain sound even if the deployment environment randomly selects a valid ordering and parenthesizing of the arithmetic operations to compute the network. We present a theoretical foundation for our approach and demonstrate empirically that our technique indeed discovers all known deployment-specific attacks, introducing only a limited performance overhead.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes an efficient error bounding technique enabling existing verifiers to achieve soundness under floating-point arithmetic in deployed neural networks. It resides in the 'Sound Deployment-Aware Verification' leaf, which contains only two papers total, indicating a relatively sparse research direction within the broader taxonomy of sound verification under floating-point constraints. This positioning suggests the work addresses a recognized but underexplored gap: ensuring verification guarantees hold across all possible execution orderings and environments in real deployment, not just idealized mathematical models.

The taxonomy reveals that neighboring leaves focus on interval-based and symbolic propagation methods, SMT-based verification with quantization, and software-level floating-point verification. These adjacent directions emphasize algorithmic soundness or specific verification paradigms, whereas the deployment-aware cluster explicitly targets the gap between verification-time assumptions and deployment-time realities. The scope note for this leaf highlights verification of 'all possible execution orderings and environments,' distinguishing it from theoretical soundness approaches that may not account for parallel or stochastic execution contexts encountered in practice.

Among thirty candidates examined, the contribution-level analysis shows mixed results. The efficient error bounding technique examined ten candidates with zero refutations, suggesting novelty in the specific method proposed. However, the theoretical foundation for deployment-sound verification examined ten candidates and found one refutable match, indicating some overlap with prior theoretical work in this limited search scope. The two sound verification algorithms with empirical validation examined ten candidates with no refutations, pointing to potential novelty in the algorithmic instantiation and experimental validation aspects.

Based on the top-thirty semantic matches examined, the work appears to occupy a sparsely populated research direction with some theoretical overlap but distinct methodological contributions. The analysis does not cover the full breadth of verification literature, and the single refutation among thirty candidates suggests the theoretical foundation builds on recognized prior work while the algorithmic and empirical components may offer more distinctive advances within the deployment-aware verification paradigm.

Taxonomy

Core-task Taxonomy Papers
30
3
Claimed Contributions
30
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: sound verification of neural networks under floating-point arithmetic. The field addresses the gap between idealized real-number semantics and the finite-precision arithmetic used in deployed systems. The taxonomy organizes research into several main branches: Floating-Point Error Analysis and Modeling examines how rounding errors propagate through network layers, with works like Backward Error Analysis[1] and Probabilistic Backward Error[2] developing formal frameworks for quantifying these deviations. Sound Verification Approaches and Tools focuses on building verifiers that account for floating-point semantics, including efforts such as Sound MILP Verification[19] and Software Level Verification[22] that ensure correctness at the implementation level. Robustness Analysis under Floating-Point Constraints investigates how finite precision affects adversarial robustness guarantees, exemplified by Randomized Smoothing Floating[3]. Certified Proof Production and Trust emphasizes generating machine-checkable certificates, as seen in Certified Proof Checker[7] and Imandra Proof Checker[25]. Quantization and Mixed-Precision Optimization explores reduced-precision representations, while Theoretical Foundations and Universal Approximation and Hardware Implementation branches address foundational questions and platform-specific concerns. A central tension runs through these branches: balancing soundness guarantees with practical scalability. Many studies tackle the challenge of taming rounding errors in verification workflows, with works like Rigorous Roundoff Error[5] and Taming Rounding Errors[26] proposing rigorous yet tractable error bounds. The original paper, Sound Verification Deployed[0], sits within the Sound Deployment-Aware Verification cluster, emphasizing verification that reflects real deployment conditions rather than idealized models. This positions it closely alongside No Soundness Real[11], which critiques verification approaches that ignore implementation-level discrepancies, and contrasts with more abstract robustness frameworks like Randomized Smoothing Floating[3]. The deployment-aware perspective highlights open questions about bridging the gap between verification at the algorithmic level and guarantees that hold on actual hardware, a theme echoed across certified proof production efforts and hardware-aware quantization studies.

Claimed Contributions

Efficient error bounding technique for sound verification

The authors introduce a novel bounding technique that enables verifiers to remain sound even when deployment environments randomly select valid orderings and parenthesizations of arithmetic operations. This technique allows both interval bound propagation and symbolic propagation methods to cover all possible expression trees in deployment.

10 retrieved papers
Theoretical foundation for deployment-sound verification

The paper provides formal proofs establishing that their bounding method correctly over-approximates the range of ReLU networks across all possible expression trees. This includes propositions and corollaries demonstrating soundness for both IBP and symbolic propagation approaches.

10 retrieved papers
Can Refute
Two sound verification algorithms with empirical validation

The authors implement two verification algorithms (FPSoundIBP and FPSoundSymbolic) that incorporate their bounding technique. They prove these algorithms are practically sound and demonstrate empirically that they correctly detect all known deployment-specific attacks with limited performance overhead.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Efficient error bounding technique for sound verification

The authors introduce a novel bounding technique that enables verifiers to remain sound even when deployment environments randomly select valid orderings and parenthesizations of arithmetic operations. This technique allows both interval bound propagation and symbolic propagation methods to cover all possible expression trees in deployment.

Contribution

Theoretical foundation for deployment-sound verification

The paper provides formal proofs establishing that their bounding method correctly over-approximates the range of ReLU networks across all possible expression trees. This includes propositions and corollaries demonstrating soundness for both IBP and symbolic propagation approaches.

Contribution

Two sound verification algorithms with empirical validation

The authors implement two verification algorithms (FPSoundIBP and FPSoundSymbolic) that incorporate their bounding technique. They prove these algorithms are practically sound and demonstrate empirically that they correctly detect all known deployment-specific attacks with limited performance overhead.

Table of Contents