mhjensen
375 lines
12 KiB
HTML
375 lines
12 KiB
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<section>
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<!-- ------------------- main content ---------------------- -->
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<center><h1 style="text-align: center;">Data Analysis and Machine Learning: Recurrent neural networks</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<p> <br>
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p> <br>
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<center><h4>Dec 17, 2019</h4></center> <!-- date -->
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<br>
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<p>
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</section>
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<section>
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<h2 id="___sec0">Recurrent neural networks: Overarching view </h2>
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<p>
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Till now our focus has been, including convolutional neural networks
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as well, on feedforward neural networks. The output or the activations
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flow only in one direction, from the input layer to the output layer.
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<p>
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A recurrent neural network (RNN) looks very much like a feedforward
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neural network, except that it also has connections pointing
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backward.
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<p>
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RNNs are used to analyze time series data such as stock prices, and
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tell you when to buy or sell. In autonomous driving systems, they can
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anticipate car trajectories and help avoid accidents. More generally,
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they can work on sequences of arbitrary lengths, rather than on
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fixed-sized inputs like all the nets we have discussed so far. For
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example, they can take sentences, documents, or audio samples as
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input, making them extremely useful for natural language processing
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systems such as automatic translation and speech-to-text.
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<p>
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<b>The text here is under development</b>. Planned finished mid Jan 2020.
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</section>
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<section>
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<h2 id="___sec1">Set up of an RNN </h2>
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<p>
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The figure here displays a simple example of an RNN, with inputs \( x_t \)
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at a given time \( t \) and outputs \( y_t \). Introducing time as a variable
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offers an intutitive way of understanding these networks. In addition
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to the inputs \( x_t \), the layer at a time \( t \) receives also as input
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the output from the previous layer \( t-1 \), that is \( y_{t1} \).
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<p>
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This means also that we need to have weights that link both the inputs
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\( x_t \) to the outputs \( y_t \) as well as weights that link the output
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from the previous time \( y_{t-1} \) and \( y_t \). The figure here shows an
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example of a simple RNN.
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</section>
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<section>
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<h2 id="___sec2">Solving differential equations and eigenvalue problems with RNNs </h2>
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<p>
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In our discussions of ordinary differential equations and partial
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differential equations using neural networks. Here we will discuss how
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we can solve say ordinary differential equations and eigenvalue
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problems using RNNs. Eigenvalue problems can be solved using RNNs by
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rewriting such a problems as a non-linear differential equation.
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<p>
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Instead of starting with a well-known ordinary differential equation,
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we start directly with an eigenvaule problem.
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</section>
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<section>
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<h2 id="___sec3">Long-Short Time Memory </h2>
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<p>
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Discussions about dynamic unrolling through time. discuss memory cells, input and output
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