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Complexity of L_p-Lipschitz constants for ICNNs proven W[1]-hard

By PulseAugur Editorial · [2 sources] ·

Researchers have investigated the parameterized complexity of calculating $L_p$-Lipschitz constants for input-convex neural networks (ICNNs). This problem is equivalent to maximizing the $L_p$-norm over a zonotope. While algorithms exist for $L_1$ and $L_ ext{inf}$ norms, the complexity for other $L_p$ norms remained an open question. The study proves that for fixed rational $p$ between 1 and infinity, maximizing the $L_p$-norm over a zonotope is W[1]-hard with respect to the dimension, implying that brute-force enumeration is nearly optimal under the Exponential Time Hypothesis. These findings resolve open problems in the field and have implications for computing Lipschitz constants of two-layer ReLU ICNNs. AI

IMPACT Establishes theoretical limits on the computational complexity of analyzing certain neural network properties, informing future algorithm design.

RANK_REASON The cluster contains an academic paper detailing theoretical complexity results for a specific type of neural network. [lever_c_demoted from research: ic=1 ai=1.0]

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

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

Complexity of L_p-Lipschitz constants for ICNNs proven W[1]-hard

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The cluster contains an academic paper detailing theoretical complexity results for a specific type of neural network. [lever_c_demoted from research: ic=1 ai=1.0]
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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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