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Function Approximation research benchmarks – Page 4 · SOTA2 Research

Function Approximation

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

Feynman Function I.9.18 (val)

0Initial RMSE

1

Apr 20, 2026

Feynman Function I.6.2 (val)

0Initial RMSE

1

Apr 20, 2026

Lᵖ functions on [−1, 1]^d

3D ReLU Network

1Error

1

Mar 13, 2026

Analytic functions on [0, 1]^d, holomorphic in an ellipse

ReLU Network ([12])

2Approximation Error

1

Mar 13, 2026

Polynomial functions on [0, 1]

3D ReLU Network

2Error

1

Mar 13, 2026

C([a, b]^d) and L^p([a, b]^d)

—

—Primary metric

0

Jun 16, 2026

K^s_p function space (s in N, s >= 2) theoretical upper bound

—

—Primary metric

0

Jun 1, 2026

Analytic functions on polytope partition

—

—Primary metric

0

Feb 26, 2026

Continuous functions C(K) on polytope partition

—

—Primary metric

0

Feb 26, 2026

Infinitely smooth functions C^infinity([0, 1]^d) on cube partition

—

—Primary metric

0

Feb 26, 2026

Smooth functions C^s([0, 1]^d) on cube partition

—

—Primary metric

0

Feb 26, 2026

Continuous functions C([0, 1]^d) cube partition

—

—Primary metric

0

Feb 26, 2026

Function F1(xi) (test)

—

—Primary metric

0

Feb 26, 2026

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Feynman Function Bratley Sum KAN Paper Toy Functions Eq. (23)Sin

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