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[2410.06816] Expressiveness of Multi-Neuron Convex Relaxations in Neural Network Certification
Summary
This paper explores the limitations and potential of multi-neuron convex relaxations in neural network certification, revealing a universal convex barrier and proposing methods for achieving completeness.
Why It Matters
Understanding the expressiveness of multi-neuron convex relaxations is crucial for advancing neural network certification methods, which ensure the robustness of AI systems. This research highlights inherent limitations and offers new avenues for improving certification techniques, directly impacting AI safety and reliability.
Key Takeaways
- Multi-neuron relaxations do not overcome the convex barrier in neural network certification.
- A universal convex barrier exists, extending limitations observed in single-neuron relaxations.
- Completeness can be achieved through augmenting networks with additional ReLU neurons or partitioning input domains.
- The findings suggest new directions for certified robustness in AI systems.
- Training and verification methods can be tailored to leverage multi-neuron relaxations.
Computer Science > Machine Learning arXiv:2410.06816 (cs) [Submitted on 9 Oct 2024 (v1), last revised 20 Feb 2026 (this version, v4)] Title:Expressiveness of Multi-Neuron Convex Relaxations in Neural Network Certification Authors:Yuhao Mao, Yani Zhang, Martin Vechev View a PDF of the paper titled Expressiveness of Multi-Neuron Convex Relaxations in Neural Network Certification, by Yuhao Mao and 2 other authors View PDF HTML (experimental) Abstract:Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU networks, a limitation known as the *single-neuron convex barrier*. While multi-neuron relaxations have been heuristically applied to address this issue, two central questions arise: (i) whether they overcome the convex barrier, and if not, (ii) whether they offer theoretical capabilities beyond those of single-neuron relaxations. In this work, we present the first rigorous analysis of the expressiveness of multi-neuron relaxations. Perhaps surprisingly, we show that they are inherently incomplete, even when allocated sufficient resources to capture finitely many neurons and layers optimally. This result extends the single-neuron barrier to a *universal convex barrier* for neural network certification. On the positive side, we show that completeness can be achieved by either (i) augmenting the network...