前馈神经网络-反向传播(Back Propagation)公式推导走读
构造:输入神经元个数等于输入向量维度,输出神经元个数等于输出向量维度。(x1=(1,2,3),则需要三个输入神经元
![](https://images2015.cnblogs.com/blog/751250/201704/751250-20170415160345064-1506295789.png)
一 前向后传播
隐层:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAa4AAABRCAYAAACKRkLiAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABwvSURBVHhe7Z3Llx3Vdcb991iMQV4rMECQAAO1bMALsACB8FrolUxMt5xJ6BYZJBES2DFgI4FjBxIL1krsBMkDAyE2YMBZEB6eBElkFklmkAd+jG7qd25/1/vuPnWr6t6q7lu396BW9606dR77fGd/e++zq+pzv/vdZ4M4QgaBgcBAYCAw0BcMfK4vHY1+xqIKDAQGAgOBATAQxBUeZ3jcgYHAQGCgVxgI4grA9gqwYXGHxR0YCAwEcQVxBXEFBgIDgYFeYSCIKwDbK8CGtR3WdmAgMBDEFcQVxBUYCAwEBnqFgSCuAGyvABvWdljbgYHAQBBXEFcQV2AgMBAY6BUGgrgCsL0CbFjbYW0HBgIDQVxBXEFcgYHAQGCgVxgI4grA9gqwYW2HtR0YCAwEcQVxBXEFBgIDgYFeYSCIKwDbK8CGtR3WdmAgMBDEFcQVxBUYCAwEBnqFgSCuAGyngH38O38z+MbT3ys9vnnq+522H9Z5WOeBgcXDQBBXEFdnxPHjV14bfHHfHw9ef+ud1AYkdtV1ewZXPr2cfnN+5813ddZ+KKzFU1gxpzGn8VmTIK1OSWNl7fiIpADbweW1wZ57j4y1ec+ho532IRRdKLrAwOJhIDyuIK/OiOORk0+N1Y13dezEk2PnfJlQMounZGJOY07bxkAQVxDXGJEQxrv38NcH733wYWNC+/cPPyq9h2uECc+9/C+N620L9Bc++WSsbfqyvPpXW9aftsYV9QQxbDcMBHE54jp/8WIvFdnHFy7U6vfRQlFDTBxnfnh2wz2E904/d6ZWXX6xHFpZHfzs529n733m+RfG9re2YqExZj+/a4UHyLEV/Yk2g3ACA9NhIIjLENfZn7yalCtJBH0C1Orxv079PvPDlyr7zRjZV6K8J5lnnn9xcPfBlcFvf/t/pfUgm8e+/d102P/5fWhlbXDj7V8dXPzPcc8GWXKNRI2u5VrVvy/d9ydjfbj8q8tFgsidpYTbdX+j/ukUV8hte8stiMsQF4obJbaV4axpFuTB5dXBDbc9kCWMXH0iLktQKPAv3HJXpQInhAjh+ePcy6+m+08/90KWnLh27MQTnRNXrm+cg9SRUa5/nOPaJMKeZl7inu2tXGP+u5v/IK5ttseFcsbbwrOyC2tW5Q0xvPCjjaFH2nj/o1+mNkmP36rFDGkqLd/3AdIe7r+9umX92yq5RLvdKdeQbXeyDeLaZsSF94GSJrRnFxYhtLVHv9Wq4oaw3nj7F4Ojx06kNl/8p3ODN9/5t1bbaEM5QOYQ+fLDkajRhjyjju4Udsh2KNtaxHXhk4tpP4OD/1noVz69MncKaNKk/qx42PXx4g0OHH5vh7HwdgdChZPGdf7ihVRGcqA9rHX+sq/Deet10M7jT/9ebip/pvBMHivKnq5oj7opm/ZtioP27RjJ1PNt5rwJ9Tn1Z/0hYCuDS1cuJWJh/ysnQ2RCX7nXywc8cOi+s0WmnuqBqJCrsKO3aHS9+JATcrfyTXIs+mL7avsBkUe4MBRu19iM+tvBWCVxoTCvuemOwQ+KUBB7P7uKvYBdt+4fHHhotTXiggh/85v/bXQ0AcDy6vHBnn1HBpAXBw/BSnFDDoyHsaG4VkqsbkJh7NOgfAk5sU+El8Jf6qDOn7751mDHdUvJc3moaBNlSFlkxb20sfuew0mWtM89X3TJAhoXSndncc9qURdlTxX7MJZc2GuibeovS8yAQGiXflAHyRH8przdz6HfuWQNES3eCHVxv5/3nbfcOQo70ifq2eHqbzJXs5ZFtjzozDw/VMzlDUWyCPOPPJEle5i5vSzml76XEdus/Yr721FYIceQY6XHdbJQeCxm+0yPFjjXykBEiKguwBSmQTk2Ocikq9OGQmNSSHqeCELmfsJDIjGUeu5NDnhR3iNhv4Zz3I9MThfp3owF4uL8u+9/MOqf+gBB4t2o35KvvDadR8FSB4Rix7hUEN2u2/andugnYxqNx82H2rTJCCIWnzlIGU9mahc5KVvxhtsfGHvzheqzYUdIY6uIC1lYYpUMIDBkhiFA37y8GavKlqXz18FalAmlGhjYHAyUelwoRZTZ3oPLY8pTyrZsgRMyw6ptMoEolaZH3frVXyxuFBb94xwhL9rEw+Lv2Z+8ksbrs86UbedTuUXg/FXoUMrP7xXRds4rgkBQpHibGg+eAmVRtn6MKo+XpQw92vLGBePBe/TzULa/BfFQh+2H2sZb4f/3ClKAlCHVkVe4Tnj02fYfgm4zQw9CgqjxOifNO3K2CRiao5fWQ6DM+0vFPOfqCOLaHIVTd91GuZiPSRgoJS4UJ8qM0IutQMqzTDGhYHZcu9SIuLoEqYiAsXBAQLk3PKCgc6EieSOe0PC0fHkUI8rdKnLGdmDdC7HeVvIACoInXGhlSdnk3bk3TFCGvkN02usSQUFSVoZS2D7ZQATlPTmdn0Q2a0VWnifILPEWIckc6c4yxzI+rmloENEP5iPnYfn+BHGFopwFo3Hv5uInS1w2rGITAnS+7CFVkgBQgk2Jq6m31dSahwT2rns3KF/vESg5gTc/5Lwcv/8jwvD1DBX50pjnUkZQetjZEuIw1Mge0dIGjwXlyzWUt8afCwfSf57rKvPwOO8V+SSPi/rKxgvx5tLq6zwI3WSh4yUTgixLHsnVpT57w6Cs3SCuzVU8TeY/ysbceAyUEldSkkVShiWJ3+8PDfe3yBhThcqqI1TThLgIT+0s2rnqut2Njof+7C8qvTpCRAp10U8UNnsgfg9GXpWe47GKN/ewLmQOAdhEDu1vQZBWyJKZDbFxfegNDL0nwpa0qTpyhgGeL23a/STr9SF/9Vt9tnuT1H1VQYh6Ozv7dsoQFIlaj9COgTmirySc6LyezTr51LNuH+5wLQ+nC2XEeBTCJtTtQ5uSc4QKQxF2gb+oc/NwVUpcSpSwk2FTqdnzsBvhKHEUQ1PikkXf1OuqAolIwGeRsSfk9+1Q9JAn96D4bIhN5GAJfGXt0Q0ejSx2n7QiUvTeAtl4e9ZfgUSqNuVog6xN78VAuGTHQTryloZEtCd5IsgCQhNxad/L9lnkRDnOX/+l+zd4bmX7liIBOzZlM1oi5Zwlt6o5avs6HrDCmcrCtKFuzikpx7cdWYWbp3Tanveob/vNXekelxTuxxfOJwXHgr/+1vuTYkBB4clo05sQoTbFpyGuLoBHn6+5+Y6RJ4PXwN4T+0F+jwtCUFq7svXUJ5Q25Kc0eN65p/0yG0YtS1o5sB628/tb9I3MSIhoqUiRFyER1rShSdpnb2vp3sNjz1CJuCAOpcarz8r2E5ExP4xbHhveliUceWOTQnzMPf2gn4wFmSGXQ0ePJXxwfu+B5S1LJ9d8Q+T0D5nSv1N/eyb1D6zSv7L9Lsi+LFW+C3xGndtP2cactzfnE5/jgrxY7F8pDiULEPLinEJfhKgOF8qLNyRwoCRRkPy/1Q8pKz1aY4Bs/UO8gAlFj1KGtHKJG1xH0eN9kdgACfj9LZQ+7Xhw0qZ/SwVl8ATwrPBa/eMDSckW13bffSjVWUYonKff7Gl5WeM9yWtW+5TnHOTry1e9OYJ5xpvCUwMPyCTJtyCKpeIZuQe/9nBWdpu5WDW+BwuZ0jcO5AiJgdcyPEJsVePfzHFEW+0puJDlYsqy8gHkqkQI7W3p7QgKrfE795bwrQBS1Ria9EmPCSza64H0EtoqWeWuV93TRL6zlp2mf5rTeIZrMZXcrJiK++cPF5XE1XTSeDsEHlfT++axPB4n33Cyb1NQCNWnlM9j/5v0Ke2vFXtETTL3mtQ/z2XxSP2+4jz3N/o2f4o05mRz56RV4uLddIShCLkdWjm2ZfsdbYHI7mUpcYO3ayyatyV58RC2/15VW7Kc13rqfs5lXvsf/dpchRnyng95t0pcizapJDFAwljj7JNM+sLvooydJIXcntyijM+OA2OE+W37ubNFlFWMaT4UdsxDg7fDh7C2F2iXV4dJKIs+76efO1OQVv4bYos+9hjf9lrTizbf4XFts+9xLRqAYzyhgAMD2w8DQVxBXAvvWYVi236KLeZ8sec8iCuIK4grMBAYCAz0CgNBXAHYXgE2LOnFtqRjfmN+62AgiCuIK4grMBAYCAz0CgNBXAHYXgG2jjUWZcJqDwwsNgaCuIK4NhDX2okn07sIY/Ev9uKP+Y35bRsDL/zo3KY8YhLE5Yhrnt671zaoqI9nl3jTP++SzL2bb/XRJwYQVxdtR52hKAMDi42By7+6lF7YwGevupzrIC5DXLxN/MYvf3Xw9//4UqdCb3tCf1D094bb9meJyLfFWzEoy+us/HsJh2++3198+uNSr8bftjyjvsVWrjG/3c4v0Rq+1H7+4sXO9EgQlyEufVMLIugTuPkGlT6gWKff+gq0Jaj0qfvbHyg+txJvkvAy7HIB1pmvPpeJkPP0JPHxhQu90kMWp8trxwccXWE3iMuFCnPf4+pK+G3VCwHVBfnwg4t3pQ9B2rAoXuY1N905dq6t/vW9HkIf2+EVWG3Pk75zxkdc26570etLX3C/dndv1+NPi+8B7iiiOnX1UtP5DOLaZskZEDPe2Vqxl2XBApGtFO8obAqg7VA+iGs6ryGIazq5sab6TlwpglNsO7Cn3oWO2DbEhVdCMgJHbg8Hi7pOWINyHHXqIMSkNq98enk0gbRTpz0mn7LU8fpb72wAAH2gniqrRnVQDiD5/S0sYqyjSSHSd9//oHQPzXputNFVaI2xIgvJUvLtqj0tuFmJi34jP7+AfSIQ83Thk09aX+i0I9mpD8isDMdtKZo2iKtsneRkZ9dYW2OwekN1aj11uRc8K3FN0g1edv/6xs9Ha6otuVEPX0fn6wtt1qm65oK4EGTTo4kweAP4jcX+DYkJHHzu3oYE8TaOFZl0O4sQWtknPQDrHxaJG3gllKG+w0cfSZ86oS9M0Mmnnh2RAh4N58jeoz2+c4VS4ntlqoP2jpbEgVmwtEEdtEc7tP/+R79M7aF4qJdruUQLylCWdg8ur476zG9Iyi66oVu/VBoOWyn6yHjoj/fU6INkAGnRF8bVZnYmCgk50DYHIU1Cm5IN7VWRdxO8+LJ7DyxPFSq0/UZ2YMHWbfEGvpAdczxLX/29YIA5ApvggP9PFcYLsls9/q3BF275SmeGxizEBT61fob4fmUkF7BPvxkT48Xgooxw2Jb80BFaY9TN/+AOOa48/JdpPbTVVs6o+fwfTBcqlG4Ab8jFZg8LZ/oqggzZox1EW9BN6Jo2dcHcEJcAypeGc8c9xfnc4RVoGYCkTLVHwe8E+kKo3PPYd76bFjLCFVH4ugAw91i3l4kHFFgV515+NaWQJyupIADOW++F7D3OUYe1vDWx3nJT3Z5EdxWuNzKif5AJlhIgpW5fVn2mnMbz0no//P6WFv6lK/+1YSGSrEHdjI37WLyqD1kyXlLoOYei3rPvSOtgJZnEyu3z1+1O5IjcMAIYP3PYlRKZlriQG7LVvqLmjn6eXf9SuPrNWMjEanOhKzVZpI5njaxIwuEaCpjf4KgL2c1CXOBWHiEysesdTCYyK2RIv1HG4AGia0tJIp89Bda1JugLbaoNZMjvrvbEGce0xEUf6ZdISgSf9N26oavoksrU9YxY40R/6ni30itdGJVz43GxqPzB5OXOc64uQDVRIi4U/d3rE0sdS4WiVUgOIEoJayEDYAht1233jy1ukQBkxverAIr2j8jys4pAE3j6+RfGzkN6LEq7ec0k7ywILvcp+bsPraTy7xYLlQ9b0gaKL+dxMUbvWQFSSzTqowg0t4m+dO/hpOSGJLUnEabuk7WGLHQOZVKW5IHizj079kwhl7LvYuEN2jbpiwwG2sQAgdj8QmIu8IibKuSc5y/iyl2bVL8wM8KKmX8MHebChqflRXpsMzY8ZXt+6L0fS4bM0WOPZkOMMjrUx9H+5vpzeuDWy465kAF5bp0Y6sgwJxvwBI5//ev/yUZUyupljsEd15FJMgRNtivZamDRGloYoKwnXyeyw2C05/FCwdQjJ58qlR3Ytm3K+JTxeqAgfW884+EQuWH9tyE7iEu6zsu3THboN+bU6gatOeqAoPz6RJ65ZzfBGAaB2hLmmA9FfiZhQ2TfRWLTXBBXnYUxbRkBf2hp7k+AzcWmWcSU8daBiMFPLL99CrrKWkVOv7XQbN3avGQD0yokylKvf5ZMoEPZjYU5C6vw6pvuGFuYAoxfyLn9LVlhVZZ+jiBFvFaeLBItHDtnKEQftmCRo3xzYbSy+ZanUvasXTJMCmVJvTuuXapNXNxX5vWj+PA0c9frfC1a2NJenLxXsjvt3DNv3nBCDsgJ2aksypjxiawhLhRMlRU8msMSQkLx/viV15LMUEy0ybxVrT3Id5Lsyq7VeewEgrAGWPJei1CxjxqA7ZzXDYl4HIA3KV70QZ3wLPMyKUvuG09/b8BhZVeHvF57/c1S2SH/Mtn5ZzBzcwT54xkKN8OI0J5ErLa8IgO+DkjOyw58IP8qTHB9WxBXl3tckAzCBgjJ3T88vmGoUA6LwU8ISjiFU8wXgUeKx6WPS5FbS7CMoOT9WEJUP7w1SZ8EOksw3oJW36UovXIf9m9pA3HzJg3v+Vk5lI0XjyKXVu8VCApbnm/O49JeRp3FMPRUqtNsaacJcdF2mXePx0U4LXe9qs/DOR1XtBA98+AVCMrRGz2MAyK2xMU5fstLxRK2v8v6lMOnLcs82D7xf919nJxs8LTo+2ef/fdUsmMdMdfWAFPo3xuSinrY8UAceEUWB56QtQ80ifSFf29k2raQlfVOmA+/p1k2L2Wyw+NChtPgThES+yyViMRn+u09uLxBJ2CwMHd+DcmjrMI919GZae+8wGud8k3KbLnHJU+izLIoO1/H0mWBnynenSXFz2tIsJwBlQ2LKWYuRW9dWykNS0ZaUHaRyxJUiEOToIXGwrITs3biiTGPDSIbktPSKEziFyH9tvVIib/34YfJ2pYVOQwpjgNGClQhRspqsTLuSR6XSNN6UlKW3kM4WCSfeK9VXq73uDS+KuLSXEmBXH3zuIeZywadhrjKFs60e1zUJwNFe6qcE/F4ggdrPkyI7FRe15C9DQ8yj2WK0soO403zr7Fa2aGsrIdFKI16mygUb/Awpmmf40Lh+f1Lhd2tx4Fcdt99aKyfyIT1mcOBzdykTNn+juQ9ItD1EFxOdrSnejVfOSOtrixpe9o9LtpQpEn7gJzLGY8YUbvvGZcd44B0OTxxYahyHu+S9xJOGo/0Sp1s7bpyUbktJ65Jlm6ZBVxnj0uK2lqqtIUCwX22grJvkkDpPvi1h0fXU6jBhGm4TyE3a7lokxNCsnWLFP0bKfBW5MZjZSu5A+XC/pRXACk27V6jgoUnjweQSBEqjGnr0GLCAkU2JHpoYULUkywjkW9O+eKtWZLeWygq2y6KEMuXtqYhLska+cmKtPt/2g/xCl/jbbogcuVnIS5ZudbQUt+sgYSS9m8aQEHgVXvi8n1EgSBbn0rPXHNeKeV+Dxd55vZSVT/elt1fbCpL5mQW4hJJWTnlMuXAvsUh/cQz0OMSOc8bb/Xrj5xIpJXztoY6YSnVoTVs8Z+bL+SPQsc4rlLqVbKclbj0FiAvO8Zk1wrry0dmMI6RiScu7S9jNHEdbEzyKoeRnPH2qsZd9/pcEFfdzjYpJy/hxJPPjDwuJVpYK4Q6CR3K6oKovELR4qdO7RP4jfXR/pHbPwAEPjwnz0reE1mT2v8AcBCS9fAoB6HZvS3VATikvLXXpH0gZYtBqrtuvX+Ufcj4rEKSRenDVJK3QpjyMPlN+MYrQi+7lPW3nswxLXHhPSIPxq7FqDq11+Pnk37Pi8fFvGL4aK4xujA2rCfBOBinfR6N8YrsJhEX97JHk1OUYBrZacOe/xViSxmHRZtl1vCzf/di6mfVvtmkNTkrcXlvFZxCpshOWOXc0r5hApH6grzkOZbhgIgD2XGQjE8M0tpizUhONkEEwiey4p8fVMadElxmld0sHtdoL/gf/jnJ5T/On09vzJEu45wMF0tk9F2eoicuDFAbDqWszTL2WMAQw0Buorfrll1Y4kIAWGzX33pfIiUOrL/cpmZ63VHhzWBZ597VxyLhfsCK8iRNlvJ2wpnk3KYloc5cKIIQ241ffiCFOPwmLmREwgWEynWUXu4hW86zkBmXT8sly+rq5L2tpGQJ7qc8Xh4KyVrnCsFNeis89RPjR0nQHjJDlpxjfIQbvOVmE2GmJS7aoL/puaNCZvQDb1Vt5khrnoiLvqAYkftSMQ4OMIYBBIaQZQ4DzJX1iH14WwucJI2yjEzmI833fcPnjzBYrv6jOxImaLMslIVCB7ezKF76NytxUcdwbRap7kV/WH+QWYqagLtifTAWi315ArTNUeWt6tETLwvaYK6IfjBfHLTJb/REVRo8Zf0eZl2lLNnNQlzUwRjQSUPZHUl9Zg0l3BVy0zn1C52ApyrZibiEQ0LH4E3lKTspzIoM/BZJExlMKrvQxGU9Bh9K8kLRZJUJS9eHG+sbM3MEtiYTM6lNrtUNiZaNLVd/WZvpwewi5brKgvZ9Un25PihOrr8oXx649umxepC4SvZ2PqtkMy8el8eglVNd2SEz7WFZBYsikQJF6eS8Lj/fVTjHE0Ehqd91Ewxyc9cGcWld5caRw4Ddn6HvVnZcw0jcd+RPR4YbJF22P9hEdpCUNSAg/ln3B2clLsmubM36OfOy0xiQI9f8XjTelsWKrW8YaegmMYN2tgVxNSETWxaQrx5/YszyVNy9TirvtO1uxX3pAdjCOutiI5XxKJkj9+qqKuKaRh5tEhde36zexzRj0D1SrrYOvFlCNVzj+POT32707FCuP5AWSl11vvH2L8Ys7GnGsNXrxO91ooQJdymRSR5XDpd1x6vkGAwJ3UMkxHondeuy5bp6z1/dvmg/UeWFOX4j10mPYBC9mbR/WrcPZeWCuIpJKBMOLjVWE1Yt1hdWBPsJPnNw1kmYl/sJLZAV2HZ/UA48QIss+SvLFGsNRclzUsgVC68qBFPVNylftUf9VqFU3T9v15GRHQuyU0q3Hu/Q31mUL+NWxq2td1blu5XyZN7BFeMBB2BL2Ybs4eGhcr3Os2pV42BeUOw854TMfDi+6v55u85atLIDcxyc/+ap76e/Ze/VxAjeectdtb4POO24g7gmEJcSJdI+VXGwWUtIrcuXa047kW3dx2uAttpKbmssi1yPDTNWhf+ayMHX2+TePpXFY+Bo86XG1KV6+ySLpn2tkhk6pOuvqAdxTSAuJpSFTPgs9x6/phPeh/JYpG14Pn0Ya/Rx+s9uhOxCdjkMEN7s4oW9vq0grgriigUaCzQwEBgIDMwXBoK4grha39OKRT5fizzmI+Zj0TAQxBXEFcQVGAgMBAZ6hYEgrgBsrwC7aJZjjCe8ocBAcwwEcQVxBXEFBgIDgYFeYSCIKwDbK8CGddrcOg2ZhcwWDQNBXEFcQVyBgcBAYKBXGAjiCsD2CrCLZjnGeMIbCgw0x0AQVxBXEFdgIDAQGOgVBoK4ArC9AmxYp82t05BZyGzRMBDEFcQVxBUYCAwEBnqFgSCuAGyvALtolmOMJ7yhwEBzDARxBXEFcQUGAgOBgV5hIIgrANsrwIZ12tw6DZmFzBYNA/8PMOirYQ8Kc4UAAAAASUVORK5CYII=)
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输出层:![](data:image/png;base64,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)
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一般化
,向量表示 ![](data:image/png;base64,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)
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二 反向传播
1计算梯度delta:均方误差,利用了sigmoid函数导数的有趣性。
输出层梯度:
--> eg. ![](data:image/png;base64,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)
隐层梯度:
--> eg. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASMAAAApCAYAAAB+zE//AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAzTSURBVHhe7Z3Pk11FFcf5ewz7hIXZJLGEBTNaQBVY+YFgFckkutGZ4IpkdKMmQa0SUBDQUn5W+TMJlhAwKga0SiTgRhJYCuhKKWB17U/PfIem0923773vzrtOzuJVZt7r2336nO/5nh/db3LNhx++19jLdGAYMAzMGwPXzFsAW9+cwDBgGAADRkaWGVpmbBiYBAaMjAyIkwCiZUeWHRkZGRkZGRkGJoEBIyMD4iSAaJmRZUZGRkZGRkaGgUlgwMjIgDgJIFpmZJmRkZGRkZGRYWASGDAyMiBOAoiWGVlmZGRkZGRkZBiYBAaMjAyIkwCiZUaWGRkZGRkZGRkGJoEBIyMD4iSAaJmRZUadyOiDD/7b8DLgvNc8+YszzZlnn79qdHH2uRf8nrvY/oc/fap54/LlTs90mX/oWMNzNwLsq69a7FST0akHHmm2f/rW5rrrb2sOraxeVY4Yg/6Jn59uFvcfuaqIGSDuWzrasPcaEnjcjVs59s2qsTXzzXrMsRPfaz6x88bmU7d84arHc41uH/zJk82OG27z/r/v8N0NgabmOcbUYqeKjP766sVmeR1YDzkhdjiBcMZaYbbSOCL97pvvyEZ8FP/7P720JcnqnX+97W3/ysXXirZn/7tvuqNh/BRtf+bZcw3BFVvhZNfuXGwOLR+bpKxT0B/2PrR83OvrjMuQwcB29+pSJdVgp4qMHnIGC6McE08VaGMbD6Pc64Acr3P+xQvN0spxH2kB97ZPLjTvv/+fLQdw9r7fRcacngHo7pvv7FzSjW23cP5vf//R5rjLjPQeWH733++MYivmHWvuzdIZwSX0/7ff/Wcv/xd2ciRWRUYwIw7WFhE3SznzWgejbHN6SPVBeI/P/3Hpki9ntioZAUR0cPa5dL+MMm779bd2ipqbbU/sdN0Nn2suvfnmKAQU7gcHPHX/w6OvM6YOwTY2R29D1mnDThUZ+Wjn0u7PHPhiL0YcsoEpPbty/Fut5Zfq461KRtiDkgZdpGxD+b6c+WwqtsRGlBnguUup0Ud+yCiVSfeZa57PYNc9LusfWhGBHaqL1F6qyIgHH/vZr312RONvnkrpurbv4Vx4efCpjgi5bf9TJCMA9Aeng1k5Hs61x5Vi8XyKfE8UTt3+9trrVRk2Wcvlt94aDWsnXbYCnukddcVUl/FDyYispKYiGVtfj6/7/5I7vOqy/3hsDjuMayUj6t17XY29sP+wb1yRrr3iADVEoM16lmYbTkPz/a4v39Osnrzfs/Lp357rLL8cjVOikvxTIiNsx553uawWp1vYd9ifglBGDnF0+mOpcvX8ehkL+ad0hB14kWXTOA7HINvBr6w1kVUWMG7WWIGYV0/c53UhPI95/WAIGfEsOkEPcRDce2hlQ1/YeYcrOyk9Z60v5gM7u5wfcZoOgWPnvuvksNNKRhiOVJaUHCdDOQgzqzRcDS0aovELh8m9ahQBaXjFOcfR+L1uTt5rI5TU/NTLPNtWN4uMGDvvBvaisx0viJQ9ET237VzwRDIkS1IPMdYF9mT+1NzonM+VYWJb6VnzKUtBXhHFEDljO+K0KTwTbGsw1WdMXzICtypnfA/S6VXr45fYUCfcvA+5MmaWfTB0jwxgiDXpB4Jr/KiPLngmh51WMkIJnIxoYYGZ91Mg4ZSCcqBWUOYD0NmXm4soqxcRrMbBteG4r8HvJYO9+vrfs/Xs/xsZ4diePCN78F5IBLGtsGHbHRJswDzxnaMSGd24b8kDGhvy7PGT923ghNPamOi5YElGIJyRyX3NZXkErad+eTaLMS7YsYd4X8xDNoFjxSQY6gPCevixp/06/Dv0JKwvGR10vRX8Qxl52Gfhsi36Qm/hXsIgg9zoi7LqOz/4UVZff3zpz1nMYyN6a+oToUPWiEt08HLgyFf9Om36EnZC2bWHbJkm5wsBtybMggdzTEb0AlBQFzKqJa2u42iSrZ3+XfyYEQB3CPB4Xpp0OUdF4TX765MZAbpUdlh6D33n9LIWOReu2KtIOjzWDueQDVPOHI5jj+gibszyXC7rUlnI2vHJLI4WPweOdPcHgKMLAR2iWg3ILMwYKFVS8qfwjGOwbmhzrmdIVmQoXWMIdYKsKXvhuGAu9Rlr5WxIYOQzZSPh7Xd0iH3DXhI25zIizygDFEYgiZS+GId8KcxvBI2gR4zd8ZFrg+yX3xW8IG9IqeSvOewUMyPuFcR9ATFj6oKYH+/u1sybjOSIMHqYRUm5uVvBAJjImSOjsTOjYoaYyB5LEUgAjveqDCR3LE9/gv23kZGiW0xGpcwIsAnMYUDgPUqyWO/IKgdMkQ9OFIOe/eIcKfmXVo55PKtklTy8Jz2B3ZggaskIx0/ZcPmebzS8Up+VAor2hq/FclNqorMwISBbEuEocGoOsh8CQHwShp7YewrzasmEpbjspwvPZKHMG2KR30v7ymGnSEYIGN+yVJkWNx/ZFAJ0JaNSzyiXFZSiCRsCUCpFQmOph6RML2zg8jOGZB/zIqOu2V9pvIAUp8JrwF7woGTPIYhUYteQkTKsdJmW70eleh1kAKlTLWRV/4P+CWOIvOwb54pL8GfO/c7dfXohS6a+5RCUfWH/Qqd/3BFjHZU1yFZLRjl79C3TRJb44N6llQ3ixWbISBkXrgmpKFNCZghLn0vHYaKADrF5DvOpbFXJiEpsnkWWUA5+L5X5Sgo6lWlsjnsFsUPTUQ8ZFhJSJOpKRq09o0w/qeSIqrHjtJRmH4pCGZyyhaUKn2HkEhnJAdtOEvqUabMkIuZSBgTgwrmJpjQ6eQ9nVtTDDrJhDRnlskSic+5SKGvqufA4XcEjbCJjo7vWT9YkP/JiP5zs6OqJjxEpeDy6frcpJ/9BVwrGgYagygXNEM/gRuuwVlsPpM12Q8hIWUR4kpbSF/IvBN+V1B4km54JSz1VNznMY4+4dD4d2Zf5UmRUyqxLFUZrz0hsy4ZJjeOsKOzodyWjNkP2+VypZBhNlBXpRAKZ5YiwuCJGiYyYFyIunbww5qO6eq0k0Ht99tL3GWWwylyQQc4MCeNgNJQ1v8iY32vICH0qwwpl3LipeyF99JvKjIjAvqEd9CZ4L071sRPNWAiV8aFjEThFKDn5aeQjs47xPZ5dsI1PVsmwIDut09bMb7PREDIS5hZv/+h7oGQl7D/0O96DKCSLen8iUmUw2osqGcbnMI/fQ0Y6jVaQDYnRXylw9lB/S2VbiYxy2CmWaXxI+rrrps974+y55c4rHJFFRVY+hZtAzwi5MQZfZsUBiRhEYhRFyst7MmSYESC/DJM7Tia68koBUPcnADwNPl4Ykxe9qDbQzvpzjL6hgwNH/KkaoOU+Cmk82SFrAlARswDX1jNinvBUSrLzPKVQibDBFHbw/anDR30WR4BDb+Bs0ckaX5rEdirLcABIiUY1P/OZ/pRLm/ysxZ0ryI4MMV6HTFJlGXMjD44vZ+tjoyFkxHoESnQKhpCbazVrX7lZwzJN69RFXJWsrK9DA+YKK5k2zIMRMOT15e4ZptbRCTSYYU04oIQfsMMJfcrHWi898hAbSB2pkw6GvR2lt7nTmj7GHPIMZBNummgYRlyiayg/mR9Mz3spADIeZ86RlbKgeWRDKT0hB5lAKC+/h5f8UjZED6nTF61RIhwcpO0eCvJAgHEzGWcJ39N6ZDvxwQglFOQB1kIbYj/kz/V62vCMQ4W6hJCGZEdDyQhZkJmgH+sr1mHOV1SmQbAx5tGXMJ/DEH5U8zUQ9bNKDWzILResWsmoCxlARnGfosvz8x4Lo5calv7PILhSLUyJ5y3zrNcPG7ipuXGAuG94Zak228t3RGbKp3AdyCh1ixz7le7VlPSlhm44BlIekhmRtW32H+FTw1pys4fcdwlF5H1xBF5070tEl5urDTszISOY9+unHvApLfcMSpfS+m567OcA8Gdv/5JP//k593UJUv2hJyxj76XP/OxXNkQPORuSpbR98ZMeTtjT6CNP+Ayyke08/atnfLC7O5GtMOa7D/7Y2w/5+bnrurrPxKndiy//xeNAjfGuc81zPLog2/nN8+f9HnKNeD5DX8J8H5mxC+uAl1yACDPcEnZmQkbhJnIlTJ+NbvYzteUVZUjqaHKz5R1rvZwNyQhr/sIlGSTj2r4600V+9Ycomdq+VzcUg7rFPSQj6rK3McaiI3TVVqnUYj4no0o/dFY6eazBzszJaAzFTm1OlE4Dt+bS2tRk7ysPeyUrqj3qZjyEVNNr6CuTPdftb1jPS1+12DEyGvC/g7RF6HkZf4x140uSNWuM+RcUa9a3MdMgq1rsGBkNICMD+zTAbnbYGnYwMjIy6tzoNeffGs4/NTsaGRkZGRkZBiaBASMjA+IkgDi1KG3ybH72Z2RkZGRkZBiYBAb+Bw4xim03yudAAAAAAElFTkSuQmCC)
2更新权重:![](data:image/png;base64,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)
eg输出层:![](data:image/png;base64,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)
eg隐层:![](data:image/png;base64,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)
备注 反向传播的公式推导
0目标函数:![]()
![](data:image/png;base64,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)
1梯度下降法优化目标函数![]()
, 怎么计算出误差对于每个权重的偏导数呢?
2netj是第j个神经元的加权输入作为传导,链式求导法则 :
,。
区分输出层和隐藏层两种情况:
3.1 输出层: 借用yj作为传导,netj和Ed都是与yj有关的函数,链式求导法则:![]()
![](data:image/png;base64,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)
第一项:![](data:image/png;base64,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)
第二项:![]()
![](data:image/png;base64,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)
带入![](data:image/png;base64,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)
,所以输出层梯度:![]()
![](data:image/png;base64,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)
3.2隐层:借用节点的所有直接下游节点的集合Downstream(j),链式法则:aj
带入求得梯度![]()
备注:
激活函数: sigmoid函数是一个非线性函数,导数有趣,可用自身表示。
参考:网络博客