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Narrow Neural Networks Achieve Turing Completeness at Width 4

By PulseAugur Editorial · [1 sources] ·

Researchers have demonstrated that iterated narrow neural networks with a width of 4 can achieve Turing completeness. This means these networks, when iterated, can simulate any deterministic Turing machine. The study also shows that the complexity of verifying these networks spans the entire computational hierarchy, from NP-complete to undecidable, depending on the iteration bound. Furthermore, extending the width to 6 with common smooth activation functions like tanh or sigmoid also results in NP-complete verification problems. AI

IMPACT Establishes theoretical limits and capabilities of narrow neural networks, impacting understanding of their computational power.

RANK_REASON Academic paper detailing theoretical properties of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]

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

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Narrow Neural Networks Achieve Turing Completeness at Width 4

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Academic paper detailing theoretical properties of neural networks. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Adrian Wurm ·

    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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