神经网络普遍逼近定理的可视化证明（Matlab代码实现）

       目录

1 概述

2 运行结果

3 参考文献

‍4 Matlab代码

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1 概述

本代码探索了普遍逼近定理，该定理指出，单层“人工神经元”可以用来逼近任何函数，具有任意小的逼近误差。这个项目通过视觉辅助工具提供了定理的直观证明。该项目允许用户改变不同的网络参数，以近似任意函数f（x）。​

2 运行结果

主函数部分代码：

function [varargout] = requiredToolboxes(mfiles, levels)​if nargin < 1    mfiles = 'imshow.m';endif nargin < 2    levels = 3;end​% Get the first level of files[files builtins classes] = depfun(mfiles,'-toponly','-quiet');% Initial list of all required filesreqFiles = union(files, classes);for i = 2:levels    [files builtins classes] = depfun(files,'-toponly','-quiet');    % Update the list of all required files    reqFiles = union(reqFiles,union(files, classes));end​% Parse the list of required files to determine what toolboxes they are fromreqToolboxFolders = {};for i = 1:length(reqFiles)    remain = reqFiles{i};​    toolbox = '';    while true        [str, remain] = strtok(remain, filesep);        if isempty(str),            break;        end        if strcmpi(str,'toolbox')            toolbox = strtok(remain, filesep);            break;        end    end    if ~isempty(toolbox)        reqToolboxFolders = union(reqToolboxFolders,toolbox);    endend​baseMATLABFolders = {'matlab','shared','local'};reqAddonToolboxes = setdiff(reqToolboxFolders,baseMATLABFolders);​if nargout == 0    if ~isempty(reqAddonToolboxes)        disp('Required toolboxes:')        cellfun(@disp,reqAddonToolboxes)    else        disp('Only base MATLAB is required')    endelse    if nargout >= 1        varargout{1} = reqAddonToolboxes;    end    if nargout >= 2        varargout{2} = reqFiles;    endend

3 参考文献

[1]南东. RBF和MLP神经网络逼近能力的几个结果[D].大连理工大学,2007.

部分理论引用网络文献，若有侵权联系博主删除。