Shifting-based Optimizable Linear Relaxations for General Activation Functions

2026-06-18 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Cybersecurity & Data Privacy · Depth: Expert, quick

Summary

SLiR (Shifting-based Linear Relaxations) is a novel approach designed to generate optimizable linear relaxations for general neural network activation functions. Unlike existing techniques that require hand-crafted relaxations for each function, SLiR is broadly applicable, needing only a Lipschitz constant or a set of critical points. It parameterizes relaxations by their slope and computes the corresponding offset via a shifting procedure, ensuring sound upper and lower bounds over the input domain. This method enables efficient optimization while maintaining correctness. Experiments demonstrate that SLiR produces tight relaxations across a wide range of practical activation functions and facilitates the verification of up to 7.8x more properties compared to current state-of-the-art methods.

Key takeaway

For AI Security Engineers or Machine Learning Engineers focused on formal guarantees for neural networks, SLiR provides a significant advancement. Your teams can leverage this method to generate tight, optimizable linear relaxations for a broad spectrum of activation functions, potentially verifying up to 7.8x more properties. Consider integrating SLiR to reduce manual effort in developing relaxations and enhance the robustness of your NN verification processes, especially in safety-critical applications.

Key insights

SLiR offers a general, optimizable method for creating linear relaxations for diverse neural network activation functions.

Principles

• Relaxations can be parameterized by slope.
• Shifting procedures ensure sound upper and lower bounds.

Method

SLiR parameterizes relaxations by slope and computes the offset via a shifting procedure, requiring a Lipschitz constant or critical points to ensure sound bounds.

In practice

• Generate linear relaxations for new activation functions.
• Improve neural network verification coverage.

Topics

• Neural Network Verification
• Activation Functions
• Linear Relaxations
• Formal Guarantees
• SLiR

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Security Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.