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

ICNNs 的 $L_p$-Lipschitz 常数的复杂性被证明为 W[1]-hard

作者 PulseAugur 编辑部 · [2 个来源] ·

研究人员研究了计算输入凸神经网络 (ICNNs) 的 $L_p$-Lipschitz 常数的参数化复杂性。该问题等价于在区域体上最大化 $L_p$-范数。虽然存在针对 $L_1$ 和 $L_ ext{inf}$ 范数的算法，但其他 $L_p$ 范数的复杂性仍然是一个悬而未决的问题。该研究证明，对于介于 1 和无穷大之间的固定有理数 $p$，在区域体上最大化 $L_p$-范数是关于维度的 W[1]-hard 问题，这意味着在指数时间假设下，穷举搜索几乎是最优的。这些发现解决了该领域的开放性问题，并对计算两层 ReLU ICNNs 的 Lipschitz 常数具有启示意义。 AI

影响 确立了分析某些神经网络特性的计算复杂性的理论极限，为未来的算法设计提供了信息。

排序理由 该集群包含一篇学术论文，详细介绍了特定类型神经网络的理论复杂性结果。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.NE (Neural & Evolutionary) 阅读 →

AI 生成摘要 · Google Gemini · 来自 2 个来源。 我们如何撰写摘要 →

ICNNs 的 $L_p$-Lipschitz 常数的复杂性被证明为 W[1]-hard

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该集群包含一篇学术论文，详细介绍了特定类型神经网络的理论复杂性结果。[lever_c_demoted from research: ic=1 ai=1.0]
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报道来源 [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 ·

    输入凸神经网络的 $L_p$-Lipschitz 常数的参数化复杂性与 $L_p$-范数在区域体上的最大化

    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 ·

    输入凸神经网络的 $L_p$-Lipschitz 常数的参数化复杂性及 $L_p$-范数在区域体上的最大化

    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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