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Research links neural networks, ODEs, and polynomial maps to primitive recursion

By PulseAugur Editorial · [2 sources] ·

A new paper explores the computational capabilities of recurrent neural networks, polynomial ordinary differential equations (ODEs), and discrete polynomial maps. The research establishes equivalent characterizations for primitive recursion across these frameworks, demonstrating how composition emerges from dynamics rather than explicit closure rules. This work offers dynamical characterizations of complexity classes by analyzing time bounds, polynomial degrees, and discretization resources. AI

IMPACT Provides a theoretical framework for understanding computation in dynamical systems, potentially influencing future AI architectures.

RANK_REASON Academic paper detailing theoretical computational equivalences.

Read on arXiv cs.LG →

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

Research links neural networks, ODEs, and polynomial maps to primitive recursion

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Academic paper detailing theoretical computational equivalences.
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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Olivier Bournez ·

    Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs

    arXiv:2604.24356v1 Announce Type: cross Abstract: What do recurrent neural networks, polynomial ODEs, and discrete polynomial maps each bring to computation, and what do they lack? All three operate over the continuum--real-valued states evolved by real-valued dynamics--even when…

  2. arXiv cs.LG TIER_1 English(EN) · Olivier Bournez ·

    Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs

    What do recurrent neural networks, polynomial ODEs, and discrete polynomial maps each bring to computation, and what do they lack? All three operate over the continuum--real-valued states evolved by real-valued dynamics--even when the target functions are discrete. We study them …

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