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New activation functions enable arbitrary accuracy in fixed-size neural networks

By PulseAugur Editorial · [3 sources] ·

Researchers have introduced new activation functions, the Elementary Universal Activation Function (EUAF) and Differentiable Universal Activation Functions (DUAF), designed to enable fixed-size neural networks to achieve arbitrary-accuracy Sobolev approximation. The study demonstrates that functions within $W^{s, ext{inf}}((a,b)^d)$ can be approximated with arbitrary accuracy in the $W^{s-1, ext{inf}}$-norm using networks with these novel activations. Explicit bounds for network width and depth are provided, and sigmoidal variants of DUAF are also explored. AI

IMPACT Introduces novel activation functions that could enhance the approximation capabilities of fixed-size neural networks.

RANK_REASON The cluster contains an academic paper detailing new theoretical contributions to neural network activation functions.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New activation functions enable arbitrary accuracy in fixed-size neural networks

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COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · Yahong Yang, Zecheng Zhang, Wei Zhu, Wenjing Liao, Hao Liu ·

    Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

    arXiv:2606.17419v1 Announce Type: new Abstract: We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms. In contrast to standard operator-learning settings with a single input function, our fram…

  2. arXiv cs.LG TIER_1 English(EN) · Baicheng Li, Haizhao Yang, Shijun Zhang ·

    Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

    arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitr…

  3. arXiv stat.ML TIER_1 English(EN) · Shijun Zhang ·

    Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

    In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm,…

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