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

By PulseAugur Editorial · [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

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 →

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

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

COVERAGE [2]

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