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Holographic property links neural networks and polynomial complexity

By PulseAugur Editorial · [2 sources] ·

Researchers have introduced a new concept called the "holographic property" to define bounded complexity in fuzzy Boolean functions. This property is shown to be equivalent to a function being uniformly close to a bounded-degree polynomial or the output of a neural network with specific constraints. The equivalence was demonstrated through mathematical proofs, utilizing variants of hypergraph regularity. AI

IMPACT Introduces a new theoretical framework for understanding neural network complexity and its relationship to mathematical structures.

RANK_REASON This cluster contains an academic paper detailing a new mathematical concept related to neural networks and complexity.

Read on arXiv cs.LG →

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

COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Balazs Szegedy ·

    Holographic functions and neural networks

    arXiv:2605.22666v1 Announce Type: cross Abstract: A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be re…

  2. arXiv cs.LG TIER_1 English(EN) · Balazs Szegedy ·

    Holographic functions and neural networks

    A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered, up to small error and with high probabili…

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