Shifting-based Optimizable Linear Relaxations for General Activation Functions
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Computer Science > Machine Learning
Title:Shifting-based Optimizable Linear Relaxations for General Activation Functions
Abstract:The use of neural networks (NNs) is rapidly increasing, including in safety- and security-critical domains. To provide formal guarantees about NN behavior, many verification methods rely on optimizable linear relaxations of activation functions. However, existing techniques depend on hand-crafted relaxations for each activation function. Extension to state-of-the-art activation functions therefore requires substantial manual effort. In contrast, our approach SLiR (Shifting-based Linear Relaxations) is broadly applicable, requiring only a Lipschitz constant or a set of critical points. SLiR parameterizes relaxations by their slope and computes the corresponding offset via a shifting procedure that ensures sound upper and lower bounds over the input domain, enabling efficient optimization while maintaining correctness. Our experiments show that SLiR produces tight relaxations across a wide range of practical activation functions and enables verification of up to 7.8x more properties compared to state-of-the-art methods.
| Comments: | 21 pages, under review |
| Subjects: | Machine Learning (cs.LG); Logic in Computer Science (cs.LO) |
| MSC classes: | 68Q60, 68T07, 65D15 |
| ACM classes: | D.2.4; I.2.6 |
| Cite as: | arXiv:2606.20292 [cs.LG] |
| (or arXiv:2606.20292v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.20292
arXiv-issued DOI via DataCite (pending registration)
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