{"id":155,"date":"2025-11-13T13:17:48","date_gmt":"2025-11-13T05:17:48","guid":{"rendered":"https:\/\/www.tangent0712.top\/?p=155"},"modified":"2025-11-14T00:43:30","modified_gmt":"2025-11-13T16:43:30","slug":"01-introduction-of-machine%ef%bc%8fdeep-learning","status":"publish","type":"post","link":"https:\/\/www.tangent0712.top\/index.php\/2025\/11\/13\/01-introduction-of-machine%ef%bc%8fdeep-learning\/","title":{"rendered":"01 Introduction of Machine\uff0fDeep Learning"},"content":{"rendered":"\n<h3>Machine Learning \u2248 Looking for Function<\/h3>\n<ul>\n<li>Speech Recognition : <code>f(vocal.wav) = &quot;text&quot;<\/code><\/li>\n<li>Image Recognition : <code>f(animal.png) = &quot;animal&quot;<\/code><\/li>\n<li>Playing Go : <code>f(Current Situation) = &quot;Next Move&quot;<\/code><\/li>\n<\/ul>\n<h3>Different types of Functions<\/h3>\n<ul>\n<li>\n<p>Regression : The function outputs a scalar .<\/p>\n<ul>\n<li>Predict PM2.5 tomorrow<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Classification : Given options (classes) , the function outputs the correct one.<\/p>\n<ul>\n<li>Spam filtering<\/li>\n<li>Playing Go<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>Structured Learning<\/p>\n<ul>\n<li>create something with structure (image\/document)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Progress<\/h3>\n<ol>\n<li>\n<p>Function with Unknown Parameters<\/p>\n<p>For example , You want to predict the views on your YouTube .<\/p>\n<p>Model(A Function with Unknown Parameter) : $$y = b + wx_1$$<\/p>\n<\/li>\n<li>\n<p>Define Loss form Training Data<\/p>\n<p>Loss is a function of parameters : $$L(b,w)$$<\/p>\n<p>Loss indicates how good a set of value is .<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111123620-tfka0l5.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111123620-tfka0l5.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p>On this picture , red refers to large L ,blue refers to small L .<\/p>\n<\/li>\n<li>\n<p>Optimization<\/p>\n<p>$$ w^*,b^* = arg min L $$\nGradient Descent :<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111124003-e06fzz8.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111124003-e06fzz8.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p>$$w^1=w^0 &#8211;  \\eta \\left. \\frac{\\partial L}{\\partial w} \\right|_{w=w^0}  \\eta : learning rate (typerparameters)$$<\/p>\n<p>Attention : Global minima \u2260 Local minima , but it does not matter!<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111124504-l4jjyyz.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111124504-l4jjyyz.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<\/li>\n<\/ol>\n<h3>How to make Loss smaller?<\/h3>\n<p>To reduce the loss, one approach is to increase the dimensionality of the input data.<\/p>\n<p>We can use a new Function : $$y = b + \\sum_{j=1}^{7} w_j x_j$$.It receives the data from the previous seven days.<\/p>\n<p>Linear models have severe limitation : Model Bias.We need a more flexable model!<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125220-ttpkns6.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125220-ttpkns6.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p>All Piecewise Linear Curves can be fitted!<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125414-7jy3t2f.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125414-7jy3t2f.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p>How to represent the blue function(Hard Sigmoid)?<\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125559-0qbl7kb.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125559-0qbl7kb.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125715-accaubu.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125715-accaubu.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125748-iq1tfx5.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125748-iq1tfx5.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125820-vzusqm0.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125820-vzusqm0.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125851-57tr5f8.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125851-57tr5f8.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125916-44vmraf.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125916-44vmraf.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125944-39tdjv9.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111125944-39tdjv9.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130004-k7ujb0a.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130004-k7ujb0a.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130048-zz6te02.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130048-zz6te02.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130111-bmb9il7.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130111-bmb9il7.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p>Every time we renew the Parameters is called Update . <\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130247-lw0mjjc.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130247-lw0mjjc.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image\" \/><\/div><\/p>\n<p><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.tangent0712.top\/wp-content\/uploads\/2025\/11\/image-20251111130316-jsnsbui.png'><img class=\"lazyload lazyload-style-1\" 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