Smooth Function

Smooth function approximation focuses on efficiently and accurately representing smooth functions using various computational methods, primarily aiming to overcome the challenges posed by high dimensionality and limited data. Current research emphasizes the use of neural networks, particularly shallow networks and those incorporating multiplicative operations, alongside derivative-free optimization techniques that rely solely on function comparisons. These advancements are crucial for diverse applications, including control systems, machine learning optimization, and scientific computing, where efficient and reliable function approximation is essential for model building and prediction.

Papers

March 18, 2022

Approximate Function Evaluation via Multi-Armed Bandits
Tavor Z. Baharav, Gary Cheng, Mert Pilanci, David Tse
Multi Armed Bandit Optimal Sampling Smooth Function Asymptotic Optimality Instance Conditioned Adaptation Directional Derivative

March 3, 2022

January 3, 2022

Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions
Kamil Doległo, Anna Paszyńska, Maciej Paszyński, Leszek Demkowicz
Deep Neural Network Physic Informed Neural Network Activation Function Theoretical Physic Higher Order B Spline Smooth Function

Smooth Function

Papers

Approximate Function Evaluation via Multi-Armed Bandits

Reconstruction of univariate functions from directional persistence diagrams

Polar Transformation Based Multiple Instance Learning Assisting Weakly Supervised Image Segmentation With Loose Bounding Box Annotations

Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions