A Multi-Layer Regression based Predicable Function Fitting Network

TL;DR

This paper introduces a multi-layer regression network that effectively handles complex stationary and non-stationary functions, improving generalization and fitting accuracy for mathematical and real-world data.

Contribution

It proposes a novel function fitting network with stationary transform, feature encoding, and regression layers to address existing challenges in handling complex functions.

Findings

High-quality fitting results on mathematical functions

Effective generalization to real-world functions

Outperforms traditional methods in handling non-stationary data

Abstract

Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve Function, are presented in these years. However, there are two main problems in these approaches: 1) hard to handle the complex functions of stationary and non-stationary, periodic and non-periodic, high order and low order; 2) hard to generalize the fitting functions from training data to test data. In this paper, a multiple regression based function fitting network that solves the two main problems is introduced as a predicable function fitting technique. This technique constructs the network includes three main parts: 1) the stationary transform layer, 2) the feature encoding layers, and 3) the fine tuning regression layer. The stationary transform layer recognizes the order of input function data, and transforms non-stationary function to stationary function. The feature encoding layers encode the raw input sequential data to a novel linear regression feature that can capture both the structural and the temporal characters of the sequential data. The fine tuning regression layer then fits the features to the target ahead values. The fitting network with the linear regression feature layers and a non-linear regression layer come up with high quality fitting results and generalizable predictions. The experiments of both mathematic function examples and the real word function examples verifies the efficiency of the proposed technique.