From 97ee7402a8c87e56e2a038ac4af4a3c85aac3670 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 19 Oct 2018 06:30:26 +0200 Subject: [PATCH] additional typos --- doc/pub/NeuralNet/html/._NeuralNet-bs099.html | 16 +++++++-------- doc/pub/NeuralNet/html/._NeuralNet-bs102.html | 3 +-- doc/pub/NeuralNet/html/NeuralNet-reveal.html | 19 +++++++++--------- .../NeuralNet/html/NeuralNet-solarized.html | 19 +++++++++--------- doc/pub/NeuralNet/html/NeuralNet.html | 19 +++++++++--------- doc/pub/NeuralNet/ipynb/NeuralNet.ipynb | 19 +++++++++--------- .../ipynb/ipynb-NeuralNet-src.tar.gz | Bin 88051 -> 88051 bytes doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf | Bin 664860 -> 664815 bytes doc/src/NeuralNet/NeuralNet.do.txt | 19 +++++++++--------- 9 files changed, 54 insertions(+), 60 deletions(-) diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs099.html b/doc/pub/NeuralNet/html/._NeuralNet-bs099.html index 3d60f368d..6674d6455 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs099.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs099.html @@ -370,24 +370,24 @@ The idea of the gradient descent algorithm is to update parameters in direction where the cost function decreases goes to a minimum.

-In general, the update of some parameters \( \vec \omega \) given a cost -function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \), +In general, the update of some parameters \( \hat{\omega} \) given a cost +function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \), goes as follows: $$ -\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega), +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), $$

-for a number of iterations or until $ \big|\big| \vec -\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some +for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) +is smaller than some given tolerance.

The value of \( \lambda \) decides how large steps the algorithm must take -in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The -notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to -the elements in \( \vec \omega \). +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to +the elements in \( \hat{\omega} \).

diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs102.html b/doc/pub/NeuralNet/html/._NeuralNet-bs102.html index 68b801209..9a6b42535 100644 --- a/doc/pub/NeuralNet/html/._NeuralNet-bs102.html +++ b/doc/pub/NeuralNet/html/._NeuralNet-bs102.html @@ -372,8 +372,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri The \( i \)-th neuron at layer \( l \) recieves the result \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in -\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec -w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are +\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias \( b_i^{(l), \ \mathrm{hidden} } \): diff --git a/doc/pub/NeuralNet/html/NeuralNet-reveal.html b/doc/pub/NeuralNet/html/NeuralNet-reveal.html index da0e17bf7..26dec382d 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-reveal.html +++ b/doc/pub/NeuralNet/html/NeuralNet-reveal.html @@ -4238,26 +4238,26 @@ The idea of the gradient descent algorithm is to update parameters in direction where the cost function decreases goes to a minimum.

-In general, the update of some parameters \( \vec \omega \) given a cost -function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \), +In general, the update of some parameters \( \hat{\omega} \) given a cost +function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \), goes as follows:

 
$$ -\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega), +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), $$

 

-for a number of iterations or until $ \big|\big| \vec -\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some +for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) +is smaller than some given tolerance.

The value of \( \lambda \) decides how large steps the algorithm must take -in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The -notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to -the elements in \( \vec \omega \). +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to +the elements in \( \hat{\omega} \). @@ -4353,8 +4353,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri The \( i \)-th neuron at layer \( l \) recieves the result \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in -\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec -w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are +\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias \( b_i^{(l), \ \mathrm{hidden} } \): diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html index bfbe755ff..419531dea 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html +++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html @@ -4090,24 +4090,24 @@ The idea of the gradient descent algorithm is to update parameters in direction where the cost function decreases goes to a minimum.

-In general, the update of some parameters \( \vec \omega \) given a cost -function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \), +In general, the update of some parameters \( \hat{\omega} \) given a cost +function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \), goes as follows: $$ -\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega), +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), $$

-for a number of iterations or until $ \big|\big| \vec -\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some +for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) +is smaller than some given tolerance.

The value of \( \lambda \) decides how large steps the algorithm must take -in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The -notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to -the elements in \( \vec \omega \). +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to +the elements in \( \hat{\omega} \).











@@ -4200,8 +4200,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri The \( i \)-th neuron at layer \( l \) recieves the result \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in -\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec -w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are +\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias \( b_i^{(l), \ \mathrm{hidden} } \): diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html index e4b6df910..ff0d73330 100644 --- a/doc/pub/NeuralNet/html/NeuralNet.html +++ b/doc/pub/NeuralNet/html/NeuralNet.html @@ -4095,24 +4095,24 @@ The idea of the gradient descent algorithm is to update parameters in direction where the cost function decreases goes to a minimum.

-In general, the update of some parameters \( \vec \omega \) given a cost -function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \), +In general, the update of some parameters \( \hat{\omega} \) given a cost +function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \), goes as follows: $$ -\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega), +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), $$

-for a number of iterations or until $ \big|\big| \vec -\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some +for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \) +is smaller than some given tolerance.

The value of \( \lambda \) decides how large steps the algorithm must take -in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The -notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to -the elements in \( \vec \omega \). +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to +the elements in \( \hat{\omega} \).











@@ -4205,8 +4205,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri The \( i \)-th neuron at layer \( l \) recieves the result \( \hat{x}_j^{(l-1),\mathrm{hidden} } \) from the \( j \)-th neuron at layer \( l-1 \). The \( i \)-th neuron at layer \( l \) weights all of the elements in -\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( \vec -w_{i,j}^{(l), \ \mathrm{hidden} } \) with as many weigths as there are +\( \hat{x}_j^{(l-1),\mathrm{hidden} } \) with a weight vector \( w_{i,j}^{(l), \ \mathrm{hidden}} \) with as many weigths as there are elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias \( b_i^{(l), \ \mathrm{hidden} } \): diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb index 07dc89694..dad165cbf 100644 --- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb +++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb @@ -4545,8 +4545,8 @@ "The idea of the gradient descent algorithm is to update parameters in\n", "direction where the cost function decreases goes to a minimum.\n", "\n", - "In general, the update of some parameters $\\vec \\omega$ given a cost\n", - "function defined by some weights $\\vec \\omega$, $c(x, \\vec \\omega)$,\n", + "In general, the update of some parameters $\\hat{\\omega}$ given a cost\n", + "function defined by some weights $\\hat{\\omega}$, $c(x, \\hat{\\omega})$,\n", "goes as follows:" ] }, @@ -4555,7 +4555,7 @@ "metadata": {}, "source": [ "$$\n", - "\\vec \\omega_{\\mathrm{new} } = \\vec \\omega - \\lambda \\nabla_{\\vec \\omega} c(x, \\vec \\omega),\n", + "\\hat{\\omega}_{\\mathrm{new} } = \\hat{\\omega} - \\lambda \\nabla_{\\hat{\\omega}} c(x, \\hat{\\omega}),\n", "$$" ] }, @@ -4563,14 +4563,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "for a number of iterations or until $ \\big|\\big| \\vec\n", - "\\omega_{\\mathrm{new} } - \\vec \\omega \\big|\\big|$ is smaller than some\n", + "for a number of iterations or until $\\big|\\big| \\hat{\\omega}_{\\mathrm{new} } - \\hat{\\omega} \\big|\\big|$ \n", + "is smaller than some\n", "given tolerance.\n", "\n", "The value of $\\lambda$ decides how large steps the algorithm must take\n", - "in the direction of $ \\nabla_{\\vec \\omega} c(x, \\vec \\omega)$. The\n", - "notatation $\\nabla_{\\vec \\omega}$ denotes the gradient with respect to\n", - "the elements in $\\vec \\omega$.\n", + "in the direction of $ \\nabla_{\\hat{\\omega}} c(x, \\hat{\\omega})$. The\n", + "notatation $\\nabla_{\\hat{\\omega}}$ denotes the gradient with respect to\n", + "the elements in $\\hat{\\omega}$.\n", "\n", "\n", "## More on GD and cost function\n", @@ -4671,8 +4671,7 @@ "The $i$-th neuron at layer $l$ recieves the result\n", "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ from the $j$-th neuron at layer\n", "$l-1$. The $i$-th neuron at layer $l$ weights all of the elements in\n", - "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ with a weight vector $\\vec\n", - "w_{i,j}^{(l), \\ \\mathrm{hidden} }$ with as many weigths as there are\n", + "$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \\ \\mathrm{hidden}}$ with as many weigths as there are\n", "elements in$\\hat{x}_j^{(l-1),\\mathrm{hidden} }$, and adds a bias\n", "$b_i^{(l), \\ \\mathrm{hidden} }$:" ] diff --git a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz index 67b12625b2de244be7b042aa6abdd06bd5cd1667..3f80b06c93f81314bdbce3191f64022a5a19f327 100644 GIT binary patch delta 20 ccmeyop7ry3RyO%=4u*}fjci-l7~h5i09PpooB#j- delta 20 bcmeyop7ry3RyO%=4hF`EMz*bNjBmpMP|*hG diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf index 95ce8247487b5f10bbd324755a5e0aa3adadf8d7..1ae904c28e92788dc74642eedca395e870062a41 100644 GIT binary patch delta 47370 zcmV(_qfXmiDvMD1b^ z3Fd(W2{KspEt53Vw%RSUEp_y0_vF{7$Rce~rpI>2gKRFANRh?jS6>yY=pLIlE~!s26wQ!>)WbWyH>H;6gZp+y@>lU z%X&S(YEfp=FB5&wp2z}am;YnZGYJhZGEw7Qz$tjxnvH?`BdXe0gHb)kbnlT zGENhE%I3MGBvUk+(~RVth1tAlI!oq$?K7zT9-rXK(5Pv+q6#?fVI4X zId{!)9mvXcxd9t)tFF9TwZ&3nhx*-F)ow2Fej18+$mQ4HtUW@Uzr-HbqHo9+yW{Hu zBP7R+@O_-(@|5BNbhSaQ6B{N;fqw&Hx~Z~l@4A1rS6Ndp`6hbIL(()9BlDei8vpQy z++~`#_!cq8RyS;}f>8Z@$!^G$*r0~S*xGCa&YMpAF%1IQ)weUJF)TlRWHh1_KErpN z!eo@BOhj{*5v3GP_yitamGz9%7@US@GJaon3)f+!&@9SfIhGm)NuE?>UnoOBBVaO8KbRAh-tXEA7XZ^+s>u_A( zV0(C;&0+A;WDdGxeD3RkRgL}2sx5b+G@2;Rb4Ic(Ma8#|Wov|Srzp4i9Opu_enw-P zi0F=Gxq#s`F1oVAo)zfEvVYh$QB@un_}El+wb2_KHUu4>BnFaDs zdLfp^tFkUzQ#o)Ak5LV}eFT_AS;xF)V|zxJARG9|jt&aYjc_?x`=54#8cmodkpJ$o z#@~gh;daCYBRrW%T~#j{fU-tK3)IqL3~xThOta!k!bM#!v3WmZd4K%%z>rz0BA!A{ zn_5d+1OW7{Sr5*G85pJy!H`nI_POxe_MH+bcLQz$B2tnlwe!$`7J_g}-2fd*0zx=Z znRH`be-4=x3_wqAMNPKi!vR}SBSmOnyPhI92(;n8vfKyGTOW96)@v|nqv79nKZSIL zKqeG~Bo4aM3#|a3Qh$nbR(YRkgS(ycw1xO`LC(A;p z+m8Ux&G;U%BxE}CwjaY}K#nAe?#8r%{Q*#tdi!$<=c7@8Qz{N{QrPK&6Q;lGx3M2&N-VwYC-(p@^GsB1H<3SAr32Z2Xc?;qpKU)>Ll8wi|*p zgwfEK@Pq?<(j*5jg9R@Q4^tnr9F!9u^T-T7CU_c+#*I8JnSc3YGPw$Hq1zPeH4-O*bGxW*H=a)Lwm%PpM;etR(bqm&X5WCMqF$7k zJB0WQtfKJTCt)HL@ykrYLAxGovv~-`I4g-kswgP+CGDftF$@@k43kTL8e~V1|8;s* z9zSCIM-|pZyDG82>&xd3dwZv_%lqKe*kF(G!a?T}VGwRWuK-hs; zl};#G)_+ZpiIYq3;YF87u%&U8r0nIVerwAP^M7Eoo!JDV2+MMl7hx1}bq!we7|AwM ztLlLDvILU&^oq$b374hdXHbQCW$9lVQ;b15YJ3%*pWfrM(06V6#TE{ke_eJMsOUjN z&?Pg}!J{%OkDH;z3Tpus-3|6_ZK%=jkA-f$=zm~jdrW}`eWtRj{_T2o=(6vwv{4fc zgO1751mZpSwF^an@s@ZB5dd-@Z_N;72v&UewBns7X^B?AZ3e=Zt+YZGm?iA?Ry;;uw~GkXWY@GDk? 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minimum. -In general, the update of some parameters $\vec \omega$ given a cost -function defined by some weights $\vec \omega$, $c(x, \vec \omega)$, +In general, the update of some parameters $\hat{\omega}$ given a cost +function defined by some weights $\hat{\omega}$, $c(x, \hat{\omega})$, goes as follows: !bt \[ -\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega), +\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}), \] !et -for a number of iterations or until $ \big|\big| \vec -\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some +for a number of iterations or until $\big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big|$ +is smaller than some given tolerance. The value of $\lambda$ decides how large steps the algorithm must take -in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The -notatation $\nabla_{\vec \omega}$ denotes the gradient with respect to -the elements in $\vec \omega$. +in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The +notatation $\nabla_{\hat{\omega}}$ denotes the gradient with respect to +the elements in $\hat{\omega}$. !split @@ -3536,8 +3536,7 @@ The feedforward step is similar to as for the neural netowork, but now consideri The $i$-th neuron at layer $l$ recieves the result $\hat{x}_j^{(l-1),\mathrm{hidden} }$ from the $j$-th neuron at layer $l-1$. The $i$-th neuron at layer $l$ weights all of the elements in -$\hat{x}_j^{(l-1),\mathrm{hidden} }$ with a weight vector $\vec -w_{i,j}^{(l), \ \mathrm{hidden} }$ with as many weigths as there are +$\hat{x}_j^{(l-1),\mathrm{hidden} }$ with a weight vector $w_{i,j}^{(l), \ \mathrm{hidden}}$ with as many weigths as there are elements in$\hat{x}_j^{(l-1),\mathrm{hidden} }$, and adds a bias $b_i^{(l), \ \mathrm{hidden} }$: