approximation theory

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papersTODAY 04:00 UTC

Neural Network Operator Approach to Fractal Approximation Preserves Smoothness

A new arXiv paper studies fractal interpolation functions built from iterated function systems and combines them with neural network operators. The authors construct alpha-fractal functions and analyze how smoothness is retained alongside convergence guarantees. The work sits at the intersection of approximation theory and neural operator methods.

fractal/approximation-theory/neural-operators/convergence

papersSEP 11 04:00 UTC

Lower Bounds Derived for Shallow ReLU^k Network Approximation on the Sphere

A new arXiv paper proves two distinct lower bounds on how well shallow ReLU^k neural networks can approximate functions defined on the unit sphere. For any fixed choice of inner network parameters, the best L2 approximation error is bounded from below, with a second result addressing a related configuration-dependent setting. The work characterizes fundamental limits of shallow architectures with higher-order ReLU activations rather than proposing a new method.

theory/neural-networks/approximation/relu