Neural network verification complexity analyzed in new arXiv paper

A new paper published on arXiv explores the parameterized computational complexity of neural network verification. Researchers have proven that for neural networks with $\ell$ layers and ReLU activations, determining properties like positivity and surjectivity is W[$\ell-1$]-hard when parameterized by input dimension $d$. This finding resolves an open problem and has implications for problems in computational geometry, control theory, and robotics, such as zonotope non-containment. The research also shows that approximating Lipschitz constants and other properties in these networks are NP-hard and W[$\ell-1$]-hard with respect to $d$, and NP- and W[$t$]-hard with respect to $\ell$ for constant $d$. AI

IMPACT Establishes theoretical limits on the tractability of verifying properties of ReLU neural networks, impacting future algorithm design.

RANK_REASON The cluster contains a research paper detailing theoretical computational complexity results for neural network verification. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Exponential Time Hypothesis
• Froese et al.
• Moritz Stargalla
• W[1]
• W[$\ell-1$]
• W[$t$]

• paper
• other

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