279 lines
17 KiB
HTML
279 lines
17 KiB
HTML
<!--
|
|
HTML file automatically generated from DocOnce source
|
|
(https://github.com/doconce/doconce/)
|
|
doconce format html week40.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week40-bs --no_mako
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
|
<meta name="description" content="Week 40: Neural networks">
|
|
<title>Week 40: Neural networks</title>
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<!-- doconce format html week40.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week40-bs --no_mako -->
|
|
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
|
<!-- not necessary
|
|
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
|
-->
|
|
<style type="text/css">
|
|
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
|
.dropdown-menu {
|
|
height: auto;
|
|
max-height: 400px;
|
|
overflow-x: hidden;
|
|
}
|
|
/* Adds an invisible element before each target to offset for the navigation
|
|
bar */
|
|
.anchor::before {
|
|
content:"";
|
|
display:block;
|
|
height:50px; /* fixed header height for style bootstrap */
|
|
margin:-50px 0 0; /* negative fixed header height */
|
|
}
|
|
</style>
|
|
</head>
|
|
|
|
<!-- tocinfo
|
|
{'highest level': 2,
|
|
'sections': [('Plan for week 40', 2, None, 'plan-for-week-40'),
|
|
('Overview video on Stochastic Gradient Descent',
|
|
2,
|
|
None,
|
|
'overview-video-on-stochastic-gradient-descent'),
|
|
('Practical tips', 2, None, 'practical-tips'),
|
|
('Automatic differentiation',
|
|
2,
|
|
None,
|
|
'automatic-differentiation'),
|
|
('Videos on Neural Networks',
|
|
2,
|
|
None,
|
|
'videos-on-neural-networks'),
|
|
('Neural networks', 2, None, 'neural-networks'),
|
|
('Artificial neurons', 2, None, 'artificial-neurons'),
|
|
('Neural network types', 2, None, 'neural-network-types'),
|
|
('Feed-forward neural networks',
|
|
2,
|
|
None,
|
|
'feed-forward-neural-networks'),
|
|
('Convolutional Neural Network',
|
|
2,
|
|
None,
|
|
'convolutional-neural-network'),
|
|
('Recurrent neural networks',
|
|
2,
|
|
None,
|
|
'recurrent-neural-networks'),
|
|
('Other types of networks', 2, None, 'other-types-of-networks'),
|
|
('Multilayer perceptrons', 2, None, 'multilayer-perceptrons'),
|
|
('Why multilayer perceptrons?',
|
|
2,
|
|
None,
|
|
'why-multilayer-perceptrons'),
|
|
('Illustration of a single perceptropn model and a '
|
|
'multi-perceptron model',
|
|
2,
|
|
None,
|
|
'illustration-of-a-single-perceptropn-model-and-a-multi-perceptron-model'),
|
|
('Examples of XOR, OR and AND gates',
|
|
2,
|
|
None,
|
|
'examples-of-xor-or-and-and-gates'),
|
|
('Does Logistic Regression do a better Job?',
|
|
2,
|
|
None,
|
|
'does-logistic-regression-do-a-better-job'),
|
|
('Adding Neural Networks', 2, None, 'adding-neural-networks'),
|
|
('Mathematical model', 2, None, 'mathematical-model'),
|
|
('Mathematical model', 2, None, 'mathematical-model'),
|
|
('Mathematical model', 2, None, 'mathematical-model'),
|
|
('Mathematical model', 2, None, 'mathematical-model'),
|
|
('Mathematical model', 2, None, 'mathematical-model'),
|
|
('Matrix-vector notation', 3, None, 'matrix-vector-notation'),
|
|
('Matrix-vector notation and activation',
|
|
3,
|
|
None,
|
|
'matrix-vector-notation-and-activation'),
|
|
('Activation functions', 3, None, 'activation-functions'),
|
|
('Activation functions, Logistic and Hyperbolic ones',
|
|
3,
|
|
None,
|
|
'activation-functions-logistic-and-hyperbolic-ones'),
|
|
('Relevance', 3, None, 'relevance'),
|
|
('The multilayer perceptron (MLP)',
|
|
2,
|
|
None,
|
|
'the-multilayer-perceptron-mlp'),
|
|
('From one to many layers, the universal approximation theorem',
|
|
2,
|
|
None,
|
|
'from-one-to-many-layers-the-universal-approximation-theorem'),
|
|
('Deriving the back propagation code for a multilayer perceptron '
|
|
'model',
|
|
2,
|
|
None,
|
|
'deriving-the-back-propagation-code-for-a-multilayer-perceptron-model'),
|
|
('Definitions', 2, None, 'definitions'),
|
|
('Derivatives and the chain rule',
|
|
2,
|
|
None,
|
|
'derivatives-and-the-chain-rule'),
|
|
('Derivative of the cost function',
|
|
2,
|
|
None,
|
|
'derivative-of-the-cost-function'),
|
|
('Bringing it together, first back propagation equation',
|
|
2,
|
|
None,
|
|
'bringing-it-together-first-back-propagation-equation'),
|
|
('Derivatives in terms of $z_j^L$',
|
|
2,
|
|
None,
|
|
'derivatives-in-terms-of-z-j-l'),
|
|
('Bringing it together', 2, None, 'bringing-it-together'),
|
|
('Final back propagating equation',
|
|
2,
|
|
None,
|
|
'final-back-propagating-equation'),
|
|
('Setting up the Back propagation algorithm',
|
|
2,
|
|
None,
|
|
'setting-up-the-back-propagation-algorithm'),
|
|
('Setting up the Back propagation algorithm',
|
|
2,
|
|
None,
|
|
'setting-up-the-back-propagation-algorithm')]}
|
|
end of tocinfo -->
|
|
|
|
<body>
|
|
|
|
|
|
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
TeX: {
|
|
equationNumbers: { autoNumber: "none" },
|
|
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
|
</script>
|
|
|
|
|
|
<!-- Bootstrap navigation bar -->
|
|
<div class="navbar navbar-default navbar-fixed-top">
|
|
<div class="navbar-header">
|
|
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
</button>
|
|
<a class="navbar-brand" href="week40-bs.html">Week 40: Neural networks</a>
|
|
</div>
|
|
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
|
<ul class="nav navbar-nav navbar-right">
|
|
<li class="dropdown">
|
|
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
|
<ul class="dropdown-menu">
|
|
<!-- navigation toc: --> <li><a href="._week40-bs001.html#plan-for-week-40" style="font-size: 80%;"><b>Plan for week 40</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs002.html#overview-video-on-stochastic-gradient-descent" style="font-size: 80%;"><b>Overview video on Stochastic Gradient Descent</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="#practical-tips" style="font-size: 80%;"><b>Practical tips</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs004.html#automatic-differentiation" style="font-size: 80%;"><b>Automatic differentiation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs005.html#videos-on-neural-networks" style="font-size: 80%;"><b>Videos on Neural Networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs006.html#neural-networks" style="font-size: 80%;"><b>Neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs007.html#artificial-neurons" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs008.html#neural-network-types" style="font-size: 80%;"><b>Neural network types</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs009.html#feed-forward-neural-networks" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs010.html#convolutional-neural-network" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs011.html#recurrent-neural-networks" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs012.html#other-types-of-networks" style="font-size: 80%;"><b>Other types of networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs013.html#multilayer-perceptrons" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs014.html#why-multilayer-perceptrons" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs015.html#illustration-of-a-single-perceptropn-model-and-a-multi-perceptron-model" style="font-size: 80%;"><b>Illustration of a single perceptropn model and a multi-perceptron model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs016.html#examples-of-xor-or-and-and-gates" style="font-size: 80%;"><b>Examples of XOR, OR and AND gates</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs017.html#does-logistic-regression-do-a-better-job" style="font-size: 80%;"><b>Does Logistic Regression do a better Job?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs018.html#adding-neural-networks" style="font-size: 80%;"><b>Adding Neural Networks</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs023.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs023.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs023.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs023.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs023.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs024.html#matrix-vector-notation" style="font-size: 80%;"> Matrix-vector notation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs025.html#matrix-vector-notation-and-activation" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs026.html#activation-functions" style="font-size: 80%;"> Activation functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs027.html#activation-functions-logistic-and-hyperbolic-ones" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs028.html#relevance" style="font-size: 80%;"> Relevance</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs029.html#the-multilayer-perceptron-mlp" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs030.html#from-one-to-many-layers-the-universal-approximation-theorem" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs031.html#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs032.html#definitions" style="font-size: 80%;"><b>Definitions</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs033.html#derivatives-and-the-chain-rule" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs034.html#derivative-of-the-cost-function" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs035.html#bringing-it-together-first-back-propagation-equation" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs036.html#derivatives-in-terms-of-z-j-l" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs037.html#bringing-it-together" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs038.html#final-back-propagating-equation" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs040.html#setting-up-the-back-propagation-algorithm" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week40-bs040.html#setting-up-the-back-propagation-algorithm" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
|
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div> <!-- end of navigation bar -->
|
|
<div class="container">
|
|
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
|
<a name="part0003"></a>
|
|
<!-- !split -->
|
|
<h2 id="practical-tips" class="anchor">Practical tips </h2>
|
|
|
|
<ul>
|
|
<li> <b>Randomize the data when making mini-batches</b>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</li>
|
|
<li> <b>Transform your inputs</b>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</li>
|
|
<li> <b>Monitor the out-of-sample performance.</b> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</li>
|
|
<li> <b>Adaptive optimization methods don't always have good generalization.</b> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</li>
|
|
</ul>
|
|
<p>Geron's text, see chapter 11, has several interesting discussions.</p>
|
|
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li><a href="._week40-bs002.html">«</a></li>
|
|
<li><a href="._week40-bs000.html">1</a></li>
|
|
<li><a href="._week40-bs001.html">2</a></li>
|
|
<li><a href="._week40-bs002.html">3</a></li>
|
|
<li class="active"><a href="._week40-bs003.html">4</a></li>
|
|
<li><a href="._week40-bs004.html">5</a></li>
|
|
<li><a href="._week40-bs005.html">6</a></li>
|
|
<li><a href="._week40-bs006.html">7</a></li>
|
|
<li><a href="._week40-bs007.html">8</a></li>
|
|
<li><a href="._week40-bs008.html">9</a></li>
|
|
<li><a href="._week40-bs009.html">10</a></li>
|
|
<li><a href="._week40-bs010.html">11</a></li>
|
|
<li><a href="._week40-bs011.html">12</a></li>
|
|
<li><a href="._week40-bs012.html">13</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._week40-bs040.html">41</a></li>
|
|
<li><a href="._week40-bs004.html">»</a></li>
|
|
</ul>
|
|
<!-- ------------------- end of main content --------------- -->
|
|
</div> <!-- end container -->
|
|
<!-- include javascript, jQuery *first* -->
|
|
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
|
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
|
<!-- Bootstrap footer
|
|
<footer>
|
|
<a href="https://..."><img width="250" align=right src="https://..."></a>
|
|
</footer>
|
|
-->
|
|
<center style="font-size:80%">
|
|
<!-- copyright only on the titlepage -->
|
|
</center>
|
|
</body>
|
|
</html>
|
|
|