480 lines
31 KiB
HTML
480 lines
31 KiB
HTML
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<title>Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</title>
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'sections': [('Plans for week 45', 2, None, 'plans-for-week-45'),
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('Material for the lab sessions, additional ways to present '
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'classification results and other practicalities',
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2,
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('Setting it up', 2, None, 'setting-it-up'),
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('Strong correlations', 2, None, 'strong-correlations'),
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('Layers of a CNN', 2, None, 'layers-of-a-cnn'),
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('Systematic reduction', 2, None, 'systematic-reduction'),
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('Prerequisites: Collect and pre-process data',
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2,
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None,
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'prerequisites-collect-and-pre-process-data'),
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('Importing Keras and Tensorflow',
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2,
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None,
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'importing-keras-and-tensorflow'),
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('Running with Keras', 2, None, 'running-with-keras'),
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('Final part', 2, None, 'final-part'),
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('Final visualization', 2, None, 'final-visualization'),
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('The CIFAR01 data set', 2, None, 'the-cifar01-data-set'),
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('Verifying the data set', 2, None, 'verifying-the-data-set'),
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('Set up the model', 2, None, 'set-up-the-model'),
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('Add Dense layers on top', 2, None, 'add-dense-layers-on-top'),
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('Compile and train the model',
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2,
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None,
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'compile-and-train-the-model'),
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('Finally, evaluate the model',
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2,
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('Building our own CNN code',
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('Cost functions', 3, None, 'cost-functions'),
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('Usage of cost functions', 3, None, 'usage-of-cost-functions'),
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('Activation functions', 3, None, 'activation-functions'),
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('Usage of activation functions',
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('Convolution', 3, None, 'convolution'),
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('Layers', 3, None, 'layers'),
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('Convolution2DLayer: convolution in a hidden layer',
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'convolution2dlayer-convolution-in-a-hidden-layer'),
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('Backpropagation in the convolutional layer',
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3,
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'backpropagation-in-the-convolutional-layer'),
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('Demonstration', 3, None, 'demonstration'),
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('Pooling Layer', 3, None, 'pooling-layer'),
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('Flattening Layer', 3, None, 'flattening-layer'),
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('Fully Connected Layers', 3, None, 'fully-connected-layers'),
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('Optimized Convolution2DLayer',
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3,
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'optimized-convolution2dlayer'),
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('The Convolutional Neural Network (CNN)',
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3,
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None,
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'the-convolutional-neural-network-cnn'),
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('Usage of CNN code', 3, None, 'usage-of-cnn-code'),
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('Additional Remarks', 3, None, 'additional-remarks'),
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('Remarks on the speed', 3, None, 'remarks-on-the-speed'),
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('Convolution using separable kernels',
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3,
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None,
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'convolution-using-separable-kernels'),
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('Convolution in the Fourier domain',
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3,
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'convolution-in-the-fourier-domain'),
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('From FFNNs and CNNs to recurrent neural networks (RNNs)',
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2,
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'from-ffnns-and-cnns-to-recurrent-neural-networks-rnns'),
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('Feedback connections', 2, None, 'feedback-connections'),
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('Vanishing gradients', 2, None, 'vanishing-gradients'),
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('Recurrent neural networks (RNNs): Overarching view',
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2,
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None,
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'recurrent-neural-networks-rnns-overarching-view'),
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('Sequential data only?', 2, None, 'sequential-data-only'),
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('Differential equations', 2, None, 'differential-equations'),
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('A simple example', 2, None, 'a-simple-example'),
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('RNNs', 2, None, 'rnns'),
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('What kinds of behaviour can RNNs exhibit?',
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2,
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None,
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'what-kinds-of-behaviour-can-rnns-exhibit'),
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('Basic layout, "Figures from Sebastian Rashcka et al, Machine '
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'learning with Sickit-Learn and '
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'PyTorch":"https://sebastianraschka.com/blog/2022/ml-pytorch-book.html"',
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2,
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None,
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'basic-layout-figures-from-sebastian-rashcka-et-al-machine-learning-with-sickit-learn-and-pytorch-https-sebastianraschka-com-blog-2022-ml-pytorch-book-html'),
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('Solving differential equations with RNNs',
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2,
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None,
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'solving-differential-equations-with-rnns'),
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('Two first-order differential equations',
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2,
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None,
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'two-first-order-differential-equations'),
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('Velocity only', 2, None, 'velocity-only'),
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('Linking with RNNs', 2, None, 'linking-with-rnns'),
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('Minor rewrite', 2, None, 'minor-rewrite'),
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('RNNs in more detail', 2, None, 'rnns-in-more-detail'),
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('RNNs in more detail, part 2',
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2,
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None,
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'rnns-in-more-detail-part-2'),
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('RNNs in more detail, part 3',
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2,
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None,
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'rnns-in-more-detail-part-3'),
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('RNNs in more detail, part 4',
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2,
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None,
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'rnns-in-more-detail-part-4'),
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('RNNs in more detail, part 5',
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2,
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None,
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'rnns-in-more-detail-part-5'),
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('RNNs in more detail, part 6',
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2,
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||
None,
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'rnns-in-more-detail-part-6'),
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('RNNs in more detail, part 7',
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2,
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||
None,
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||
'rnns-in-more-detail-part-7'),
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('Backpropagation through time',
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2,
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||
None,
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'backpropagation-through-time'),
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('The backward pass is linear',
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2,
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||
None,
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'the-backward-pass-is-linear'),
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('The problem of exploding or vanishing gradients',
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2,
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||
None,
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'the-problem-of-exploding-or-vanishing-gradients'),
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('Mathematical setup', 2, None, 'mathematical-setup'),
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('Back propagation in time through figures, part 1',
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2,
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||
None,
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||
'back-propagation-in-time-through-figures-part-1'),
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||
('Back propagation in time, part 2',
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||
2,
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||
None,
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||
'back-propagation-in-time-part-2'),
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||
('Back propagation in time, part 3',
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||
2,
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||
None,
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||
'back-propagation-in-time-part-3'),
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||
('Back propagation in time, part 4',
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||
2,
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||
None,
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||
'back-propagation-in-time-part-4'),
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||
('Back propagation in time in equations',
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||
2,
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||
None,
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||
'back-propagation-in-time-in-equations'),
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||
('Chain rule again', 2, None, 'chain-rule-again'),
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||
('Gradients of loss functions',
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||
2,
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||
None,
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||
'gradients-of-loss-functions'),
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||
('Summary of RNNs', 2, None, 'summary-of-rnns'),
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||
('Summary of a typical RNN',
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||
2,
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||
None,
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||
'summary-of-a-typical-rnn'),
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||
('Four effective ways to learn an RNN and preparing for next '
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'week',
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||
2,
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||
None,
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||
'four-effective-ways-to-learn-an-rnn-and-preparing-for-next-week'),
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||
('Gating mechanism: Long Short Term Memory (LSTM)',
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||
2,
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||
None,
|
||
'gating-mechanism-long-short-term-memory-lstm'),
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||
('Implementing a memory cell in a neural network',
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||
2,
|
||
None,
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||
'implementing-a-memory-cell-in-a-neural-network'),
|
||
('LSTM details', 2, None, 'lstm-details'),
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||
('Basic layout', 2, None, 'basic-layout'),
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||
('More LSTM details', 2, None, 'more-lstm-details'),
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||
('The forget gate', 2, None, 'the-forget-gate'),
|
||
('Input gate', 2, None, 'input-gate'),
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||
('Forget and input', 2, None, 'forget-and-input'),
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('Output gate', 2, None, 'output-gate')]}
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<a class="navbar-brand" href="week45-bs.html">Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week45-bs001.html#plans-for-week-45" style="font-size: 80%;"><b>Plans for week 45</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs002.html#material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities" style="font-size: 80%;"><b>Material for the lab sessions, additional ways to present classification results and other practicalities</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs003.html#material-for-lecture-monday-november-4" style="font-size: 80%;"><b>Material for Lecture Monday November 4</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs004.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;"><b>Convolutional Neural Networks (recognizing images)</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs005.html#what-is-the-difference" style="font-size: 80%;"><b>What is the Difference</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs006.html#neural-networks-vs-cnns" style="font-size: 80%;"><b>Neural Networks vs CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs007.html#why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc" style="font-size: 80%;"><b>Why CNNS for images, sound files, medical images from CT scans etc?</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs008.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;"><b>Regular NNs don’t scale well to full images</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs009.html#3d-volumes-of-neurons" style="font-size: 80%;"><b>3D volumes of neurons</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs010.html#layers-used-to-build-cnns" style="font-size: 80%;"><b>Layers used to build CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs011.html#cnns-in-brief" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs012.html#a-deep-cnn-model-from-raschka-et-al-https-github-com-rasbt-machine-learning-book" style="font-size: 80%;"><b>A deep CNN model ("From Raschka et al":"https://github.com/rasbt/machine-learning-book")</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs013.html#key-idea" style="font-size: 80%;"><b>Key Idea</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs014.html#building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;"><b>Building convolutional neural networks in Tensorflow and Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs015.html#setting-it-up" style="font-size: 80%;"><b>Setting it up</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs016.html#the-mnist-dataset-again" style="font-size: 80%;"><b>The MNIST dataset again</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs017.html#strong-correlations" style="font-size: 80%;"><b>Strong correlations</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs018.html#layers-of-a-cnn" style="font-size: 80%;"><b>Layers of a CNN</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs019.html#systematic-reduction" style="font-size: 80%;"><b>Systematic reduction</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs020.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;"><b>Prerequisites: Collect and pre-process data</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs021.html#importing-keras-and-tensorflow" style="font-size: 80%;"><b>Importing Keras and Tensorflow</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs022.html#running-with-keras" style="font-size: 80%;"><b>Running with Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs023.html#final-part" style="font-size: 80%;"><b>Final part</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs024.html#final-visualization" style="font-size: 80%;"><b>Final visualization</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs025.html#the-cifar01-data-set" style="font-size: 80%;"><b>The CIFAR01 data set</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs026.html#verifying-the-data-set" style="font-size: 80%;"><b>Verifying the data set</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs027.html#set-up-the-model" style="font-size: 80%;"><b>Set up the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs028.html#add-dense-layers-on-top" style="font-size: 80%;"><b>Add Dense layers on top</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs029.html#compile-and-train-the-model" style="font-size: 80%;"><b>Compile and train the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs030.html#finally-evaluate-the-model" style="font-size: 80%;"><b>Finally, evaluate the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#building-our-own-cnn-code" style="font-size: 80%;"><b>Building our own CNN code</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#list-of-contents" style="font-size: 80%;"> List of contents:</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#schedulers" style="font-size: 80%;"> Schedulers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-schedulers" style="font-size: 80%;"> Usage of schedulers</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#cost-functions" style="font-size: 80%;"> Cost functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-cost-functions" style="font-size: 80%;"> Usage of cost functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#activation-functions" style="font-size: 80%;"> Activation functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-activation-functions" style="font-size: 80%;"> Usage of activation functions</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution" style="font-size: 80%;"> Convolution</a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs031.html#layers" style="font-size: 80%;"> Layers</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution2dlayer-convolution-in-a-hidden-layer" style="font-size: 80%;"> Convolution2DLayer: convolution in a hidden layer</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#backpropagation-in-the-convolutional-layer" style="font-size: 80%;"> Backpropagation in the convolutional layer</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#demonstration" style="font-size: 80%;"> Demonstration</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#pooling-layer" style="font-size: 80%;"> Pooling Layer</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#flattening-layer" style="font-size: 80%;"> Flattening Layer</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#fully-connected-layers" style="font-size: 80%;"> Fully Connected Layers</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#optimized-convolution2dlayer" style="font-size: 80%;"> Optimized Convolution2DLayer</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#the-convolutional-neural-network-cnn" style="font-size: 80%;"> The Convolutional Neural Network (CNN)</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#usage-of-cnn-code" style="font-size: 80%;"> Usage of CNN code</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#remarks-on-the-speed" style="font-size: 80%;"> Remarks on the speed</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution-using-separable-kernels" style="font-size: 80%;"> Convolution using separable kernels</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs031.html#convolution-in-the-fourier-domain" style="font-size: 80%;"> Convolution in the Fourier domain</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs032.html#from-ffnns-and-cnns-to-recurrent-neural-networks-rnns" style="font-size: 80%;"><b>From FFNNs and CNNs to recurrent neural networks (RNNs)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs033.html#feedback-connections" style="font-size: 80%;"><b>Feedback connections</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs034.html#vanishing-gradients" style="font-size: 80%;"><b>Vanishing gradients</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs035.html#recurrent-neural-networks-rnns-overarching-view" style="font-size: 80%;"><b>Recurrent neural networks (RNNs): Overarching view</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs036.html#sequential-data-only" style="font-size: 80%;"><b>Sequential data only?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs037.html#differential-equations" style="font-size: 80%;"><b>Differential equations</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs038.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs039.html#rnns" style="font-size: 80%;"><b>RNNs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs040.html#what-kinds-of-behaviour-can-rnns-exhibit" style="font-size: 80%;"><b>What kinds of behaviour can RNNs exhibit?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs041.html#basic-layout-figures-from-sebastian-rashcka-et-al-machine-learning-with-sickit-learn-and-pytorch-https-sebastianraschka-com-blog-2022-ml-pytorch-book-html" style="font-size: 80%;"><b>Basic layout, "Figures from Sebastian Rashcka et al, Machine learning with Sickit-Learn and PyTorch":"https://sebastianraschka.com/blog/2022/ml-pytorch-book.html"</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs042.html#solving-differential-equations-with-rnns" style="font-size: 80%;"><b>Solving differential equations with RNNs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs043.html#two-first-order-differential-equations" style="font-size: 80%;"><b>Two first-order differential equations</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs045.html#linking-with-rnns" style="font-size: 80%;"><b>Linking with RNNs</b></a></li>
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||
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<!-- navigation toc: --> <li><a href="._week45-bs047.html#rnns-in-more-detail" style="font-size: 80%;"><b>RNNs in more detail</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs048.html#rnns-in-more-detail-part-2" style="font-size: 80%;"><b>RNNs in more detail, part 2</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs049.html#rnns-in-more-detail-part-3" style="font-size: 80%;"><b>RNNs in more detail, part 3</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs050.html#rnns-in-more-detail-part-4" style="font-size: 80%;"><b>RNNs in more detail, part 4</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._week45-bs051.html#rnns-in-more-detail-part-5" style="font-size: 80%;"><b>RNNs in more detail, part 5</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs052.html#rnns-in-more-detail-part-6" style="font-size: 80%;"><b>RNNs in more detail, part 6</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs053.html#rnns-in-more-detail-part-7" style="font-size: 80%;"><b>RNNs in more detail, part 7</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs054.html#backpropagation-through-time" style="font-size: 80%;"><b>Backpropagation through time</b></a></li>
|
||
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|
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<!-- navigation toc: --> <li><a href="._week45-bs056.html#the-problem-of-exploding-or-vanishing-gradients" style="font-size: 80%;"><b>The problem of exploding or vanishing gradients</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs057.html#mathematical-setup" style="font-size: 80%;"><b>Mathematical setup</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs058.html#back-propagation-in-time-through-figures-part-1" style="font-size: 80%;"><b>Back propagation in time through figures, part 1</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs059.html#back-propagation-in-time-part-2" style="font-size: 80%;"><b>Back propagation in time, part 2</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs060.html#back-propagation-in-time-part-3" style="font-size: 80%;"><b>Back propagation in time, part 3</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs061.html#back-propagation-in-time-part-4" style="font-size: 80%;"><b>Back propagation in time, part 4</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs062.html#back-propagation-in-time-in-equations" style="font-size: 80%;"><b>Back propagation in time in equations</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs063.html#chain-rule-again" style="font-size: 80%;"><b>Chain rule again</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs064.html#gradients-of-loss-functions" style="font-size: 80%;"><b>Gradients of loss functions</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs065.html#summary-of-rnns" style="font-size: 80%;"><b>Summary of RNNs</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs066.html#summary-of-a-typical-rnn" style="font-size: 80%;"><b>Summary of a typical RNN</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs067.html#four-effective-ways-to-learn-an-rnn-and-preparing-for-next-week" style="font-size: 80%;"><b>Four effective ways to learn an RNN and preparing for next week</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs068.html#gating-mechanism-long-short-term-memory-lstm" style="font-size: 80%;"><b>Gating mechanism: Long Short Term Memory (LSTM)</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs069.html#implementing-a-memory-cell-in-a-neural-network" style="font-size: 80%;"><b>Implementing a memory cell in a neural network</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs070.html#lstm-details" style="font-size: 80%;"><b>LSTM details</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs071.html#basic-layout" style="font-size: 80%;"><b>Basic layout</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs072.html#more-lstm-details" style="font-size: 80%;"><b>More LSTM details</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._week45-bs073.html#the-forget-gate" style="font-size: 80%;"><b>The forget gate</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs074.html#input-gate" style="font-size: 80%;"><b>Input gate</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs075.html#forget-and-input" style="font-size: 80%;"><b>Forget and input</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._week45-bs076.html#output-gate" style="font-size: 80%;"><b>Output gate</b></a></li>
|
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|
||
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<a name="part0000"></a>
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<h1>Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</h1>
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<!-- author(s): Morten Hjorth-Jensen -->
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<b>Morten Hjorth-Jensen</b>
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<b>Department of Physics, University of Oslo</b>
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<br>
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<h4>November 4-8</h4>
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<br>
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