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Neural networks achieve super-fast convergence and represent complex functions with floating-point arithmetic

By PulseAugur Editorial · Summary by gemini-2.5-flash-lite from 2 sources

Two new arXiv papers explore theoretical aspects of neural network convergence and representation capabilities. The first paper demonstrates that neural network classifiers can achieve super-fast convergence rates under specific conditions, including a hard margin scenario, for various activation functions. The second paper investigates the representational power of floating-point networks, showing they can approximate both function values and gradients using automatic differentiation, even with practical activation functions and finite precision arithmetic. AI

Summary written by gemini-2.5-flash-lite from 2 sources. How we write summaries →

IMPACT These theoretical advancements could inform the design of more efficient and powerful neural network architectures in the future.

RANK_REASON Two academic papers published on arXiv presenting theoretical findings on neural network convergence and representation.

Read on arXiv cs.LG →

COVERAGE [2]

  1. arXiv cs.LG TIER_1 · Nathanael Tepakbong, Xiang Zhou, Ding-Xuan Zhou ·

    Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition

    arXiv:2505.08262v2 Announce Type: replace Abstract: We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent $q>0$, as well as its limit case $q=\infty$, which we refer to as the \…

  2. arXiv cs.LG TIER_1 · Sejun Park, Yeachan Park, Geonho Hwang ·

    Floating-Point Networks with Automatic Differentiation Can Represent Almost All Floating-Point Functions and Their Gradients

    arXiv:2605.01702v1 Announce Type: new Abstract: Theoretical studies show that for any differentiable function on a compact domain, there exists a neural network that approximates both the function values and gradients. However, such a result cannot be used in practice since it as…

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