Shifting-based Optimizable Linear Relaxations for General Activation Functions

• URL: http://arxiv.org/abs/2606.20292v1
• Date: Thu, 18 Jun 2026 14:32:05 GMT
• Title: Shifting-based Optimizable Linear Relaxations for General Activation Functions
• Abstract summary: We develop a new verification method for neural networks (NNs) in safety- and security-critical domains.<n>Our approach SLiR (Shifting-based Linear Relaxations) requires only a Lipschitz constant or a set of critical points.<n>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.
• Score: 0.2449909275410287
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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