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New research explores neural network approximation for complex functional operators · 3 sources tracked

By PulseAugur Editorial · [5 sources] ·

Researchers are exploring advanced neural network architectures for approximating complex functions. One paper details how deep ReLU networks can approximate smooth functionals on infinite-dimensional Hilbert spaces, establishing error bounds based on coordinate decay and sensitivity. Another study introduces fractal interpolation functions using shallow neural network operators to preserve function smoothness, validated with Python experiments. A third paper investigates neural operators for nonlinear functionals on reproducing kernel Hilbert spaces, using point evaluations instead of integration for simpler architectures and deriving approximation rates and learning guarantees. AI

IMPACT These theoretical advancements could lead to more efficient and accurate AI models for complex data analysis and function approximation.

RANK_REASON The cluster contains three academic papers published on arXiv detailing theoretical advancements in neural network approximation techniques.

Read on Hugging Face Daily Papers →

AI-generated summary · Google Gemini · from 5 sources. How we write summaries →

New research explores neural network approximation for complex functional operators · 3 sources tracked

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The cluster contains three academic papers published on arXiv detailing theoretical advancements in neural network approximation techniques.
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COVERAGE [5]

  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks

    Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights. We extend these results from uniform approximation to approximation in Sobolev norm. Specifically, we analyze how well Sobolev functions in $…

  2. arXiv cs.LG TIER_1 English(EN) · Shuhao Jiao ·

    ReLU Neural Network Approximation to Smooth Functional Operator: Dimensional Decay and Error Analysis

    arXiv:2609.15355v1 Announce Type: cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural networks. Writing the functional input as $X(t)=\sum_{d\geq1}\xi_d\nu_d(t)$, we quantify…

  3. arXiv cs.LG TIER_1 English(EN) · Aaqib Ayoub Bhat, Asif Khan, M. Mursaleen ·

    Neural Network Operator-Based Fractal Approximation: Smoothness Preservation and Convergence Analysis

    arXiv:2505.06229v2 Announce Type: replace Abstract: This paper introduces the construction of fractal interpolation functions (FIFs), whose graphs are the attractors of an iterated function system (IFS). Integrating concepts from approximation theory, $\alpha$-fractal functions a…

  4. arXiv cs.LG TIER_1 English(EN) · Tian-Yi Zhou, Namjoon Suh, Guang Cheng, Xiaoming Huo ·

    Neural Operators for Nonlinear Functionals on RKHS

    arXiv:2403.12187v2 Announce Type: replace-cross Abstract: Motivated by the abundance of functional data, such as time series and images, we study the approximation and statistical learning of nonlinear functionals defined on reproducing kernel Hilbert spaces (RKHSs) using neural …

  5. arXiv stat.ML TIER_1 English(EN) · Xianjun Li, Yunfei Yang ·

    Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks

    arXiv:2609.19937v1 Announce Type: new Abstract: Recent studies have shown that smooth functions can be well approximated by ReLU neural networks with path norm constraint on the weights. We extend these results from uniform approximation to approximation in Sobolev norm. Specific…

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