English(EN) Iterated Narrow Networks: Turing Completeness at Width 4 on Convex Input Spaces and the Complexity of Verification

窄神经网络在宽度为4时即可达到图灵完备性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-11-02 09:41

研究人员证明了宽度为4的迭代窄神经网络可以达到图灵完备性。这意味着这些网络在迭代后可以模拟任何确定性图灵机。研究还表明，这些网络的验证复杂度跨越了整个计算层级，从NP完全到不可判定，具体取决于迭代次数的上限。此外，使用tanh或sigmoid等常见平滑激活函数将宽度扩展到6，也会导致NP完全的验证问题。 AI

影响确立了窄神经网络的理论极限和能力，影响了对其计算能力的理解。

排序理由关于神经网络理论特性的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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

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arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Adrian Wurm · 2026-11-02 09:41

Iterated Narrow Networks: Turing Completeness at Width 4 on Convex Input Spaces and the Complexity of Verification

We study the iterates of a fixed ReLU network $N$ of width 4, that is, the discrete-time system $x_{k+1} = N(x_k)$ on $[0,1]^4$. Equivalently, $x_k$ is the output of a weight-tied network made of $k$ copies of $N$, or of a recurrent network with no external input, started at $x_0…

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Iterated Narrow Networks: Turing Completeness at Width 4 on Convex Input Spaces and the Complexity of Verification

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