Bridging Efficiency and Safety: Formal Verification of Neural Networks with Early Exits

Ensuring the safety and efficiency of AI systems is a central goal of modern research. Formal verification provides guarantees of neural network robustness, while early exits improve inference efficiency by enabling intermediate predictions. Yet verifying networks with early exits introduces new challenges due to their conditional execution paths. In this work, we define a robustness property tailored to early exit architectures and show how off-the-shelf solvers can be used to assess it. We present a baseline algorithm, enhanced with an early stopping strategy and heuristic optimizations that maintain soundness and completeness. Experiments on multiple benchmarks validate our framework's effectiveness and demonstrate the performance gains of the improved algorithm. Alongside the natural inference acceleration provided by early exits, we show that they also enhance verifiability, enabling more queries to be solved in less time compared to standard networks. Together with a robustness analysis, we show how these metrics can help users navigate the inherent trade-off between accuracy and efficiency.

Abstraction-Based Proof Production in Formal Verification of Neural Networks

Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN verification results. However, current proofproducing verifiers do not support abstraction-based reasoning, creating a gap between scalability and provable guarantees. We address this gap by introducing a novel framework for proof-producing abstraction-based DNN verification. Our approach modularly separates the verification task into two components: (i) proving the correctness of an abstract network, and (ii) proving the soundness of the abstraction with respect to the original DNN. The former can be handled by existing proof-producing verifiers, whereas we propose the first method for generating formal proofs for the latter. This preliminary work aims to enable scalable and trustworthy verification by supporting common abstraction techniques within a formal proof framework.

Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations

Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that it is possible to obtain explanations with formal guarantees by identifying subsets of input features that are sufficient to determine that predictions remain unchanged using neural network verification techniques. Despite the appeal of these explanations, their computation faces significant scalability challenges. In this work, we address this gap by proposing a novel abstraction-refinement technique for efficiently computing provably sufficient explanations of neural network predictions. Our method abstracts the original large neural network by constructing a substantially reduced network, where a sufficient explanation of the reduced network is also provably sufficient for the original network, hence significantly speeding up the verification process. If the explanation is in sufficient on the reduced network, we iteratively refine the network size by gradually increasing it until convergence. Our experiments demonstrate that our approach enhances the efficiency of obtaining provably sufficient explanations for neural network predictions while additionally providing a fine-grained interpretation of the network's predictions across different abstraction levels.

Tighter Abstract Queries in Neural Network Verification

Neural networks have become critical components of reactive systems in various domains within computer science. Despite their excellent performance, using neural networks entails numerous risks that stem from our lack of ability to understand and reason about their behavior. Due to these risks, various formal methods have been proposed for verifying neural networks; but unfortunately, these typically struggle with scalability barriers. Recent attempts have demonstrated that abstraction-refinement approaches could play a significant role in mitigating these limitations; but these approaches can often produce networks that are so abstract, that they become unsuitable for verification. To deal with this issue, we present CEGARETTE, a novel verification mechanism where both the system and the property are abstracted and refined simultaneously. We observe that this approach allows us to produce abstract networks which are both small and sufficiently accurate, allowing for quick verification times while avoiding a large number of refinement steps. For evaluation purposes, we implemented CEGARETTE as an extension to the recently proposed CEGAR-NN framework. Our results are very promising, and demonstrate a significant improvement in performance over multiple benchmarks.

Neural Network Verification using Residual Reasoning

With the increasing integration of neural networks as components in mission-critical systems, there is an increasing need to ensure that they satisfy various safety and liveness requirements. In recent years, numerous sound and complete verification methods have been proposed towards that end, but these typically suffer from severe scalability limitations. Recent work has proposed enhancing such verification techniques with abstraction-refinement capabilities, which have been shown to boost scalability: instead of verifying a large and complex network, the verifier constructs and then verifies a much smaller network, whose correctness implies the correctness of the original network. A shortcoming of such a scheme is that if verifying the smaller network fails, the verifier needs to perform a refinement step that increases the size of the network being verified, and then start verifying the new network from scratch -- effectively ``wasting'' its earlier work on verifying the smaller network. In this paper, we present an enhancement to abstraction-based verification of neural networks, by using \emph{residual reasoning}: the process of utilizing information acquired when verifying an abstract network, in order to expedite the verification of a refined network. In essence, the method allows the verifier to store information about parts of the search space in which the refined network is guaranteed to behave correctly, and allows it to focus on areas where bugs might be discovered. We implemented our approach as an extension to the Marabou verifier, and obtained promising results.

An Abstraction-Based Framework for Neural Network Verification

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several approaches have recently been proposed to formally verify them. However, network size is often a bottleneck for such approaches and it can be difficult to apply them to large networks. In this paper, we propose a framework that can enhance neural network verification techniques by using over-approximation to reduce the size of the network - thus making it more amenable to verification. We perform the approximation such that if the property holds for the smaller (abstract) network, it holds for the original as well. The over-approximation may be too coarse, in which case the underlying verification tool might return a spurious counterexample. Under such conditions, we perform counterexample-guided refinement to adjust the approximation, and then repeat the process. Our approach is orthogonal to, and can be integrated with, many existing verification techniques. For evaluation purposes, we integrate it with the recently proposed Marabou framework, and observe a significant improvement in Marabou's performance. Our experiments demonstrate the great potential of our approach for verifying larger neural networks.