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ReLU networks can represent max function with fewer layers

By PulseAugur Editorial · [2 sources] ·

Researchers have demonstrated that the maximum of n real numbers can be precisely represented by a ReLU network with two hidden layers for any n up to 10. This is achieved by translating the problem into exact rational linear algebra, solving for necessary cancellations computationally. The study also shows that for n > 10, the maximum can be represented with fewer hidden layers than previously thought, improving upon prior bounds. AI

IMPACT This research advances the theoretical understanding of ReLU networks, potentially influencing the design and efficiency of future neural network architectures.

RANK_REASON The cluster contains a research paper published on arXiv detailing theoretical advancements in neural network representations.

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

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

ReLU networks can represent max function with fewer layers

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Kilian Rue{\ss}, Gennadiy Averkov, Florestan Brunck, Moritz Grillo, Christoph Hertrich, Georg Loho, Jack Stade, Moritz Stargalla, Matthew Sun, Martin Winter ·

    Shallower ReLU Network Representations via Exact Linear Algebra

    arXiv:2607.21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$. The constructions are obtained by reducing the problem to exact rational linear algebra: after a sy…

  2. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Martin Winter ·

    Shallower ReLU Network Representations via Exact Linear Algebra

    We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$. The constructions are obtained by reducing the problem to exact rational linear algebra: after a symmetry reduction, the necessary cancellations ar…

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