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New research proves W[1]-hardness for ICNN Lipschitz constant computation

By PulseAugur Editorial · [2 sources] ·

Researchers have established the parameterized complexity of computing $L_p$-Lipschitz constants for two-layer input-convex neural networks (ICNNs). This problem is equivalent to maximizing the $L_p$-norm over a zonotope. The study proves that for fixed rational $p$ between 1 and infinity, this maximization is W[1]-hard with respect to the dimension $d$. These findings resolve an open problem from COLT'25 and suggest that brute-force enumeration algorithms are nearly optimal under the Exponential Time Hypothesis. AI

IMPACT Establishes theoretical hardness limits for a specific class of neural network analysis, potentially guiding future research in efficient computation.

RANK_REASON The cluster contains an academic paper detailing theoretical computational complexity results for neural networks.

Read on arXiv cs.NE (Neural & Evolutionary) →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New research proves W[1]-hardness for ICNN Lipschitz constant computation

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Aritra Das, Vincent Froese, Moritz Grillo, Debayan Gupta, Christoph Hertrich, Tharrshann Jayan Logarajah, Georg Loho, Mihir More, Moritz Stargalla ·

    Parameterized Complexity of $L_p$-Lipschitz Constants for Input Convex Neural Networks and $L_p$-Norm Maximization over Zonotopes

    arXiv:2608.24865v1 Announce Type: cross Abstract: Lipschitz constants are a standard way to quantify the sensitivity of neural networks to small input perturbations, but computing them is difficult even for shallow ReLU networks. We study this problem for two-layer input-convex n…

  2. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Moritz Stargalla ·

    Parameterized Complexity of $L_p$-Lipschitz Constants for Input Convex Neural Networks and $L_p$-Norm Maximization over Zonotopes

    Lipschitz constants are a standard way to quantify the sensitivity of neural networks to small input perturbations, but computing them is difficult even for shallow ReLU networks. We study this problem for two-layer input-convex neural networks (ICNNs), a restricted architecture …

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