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doc/pub/Recurrent/html/._Recurrent-bs000.html
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<center><h4>Dec 17, 2019</h4></center> <!-- date -->
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<h2 id="___sec0" class="anchor">Recurrent neural networks: Overarching view </h2>
<p>
Till now our focus has been, including convolutional neural networks
as well, on feedforward neural networks. The output or the activations
flow only in one direction, from the input layer to the output layer.
<p>
A recurrent neural network (RNN) looks very much like a feedforward
neural network, except that it also has connections pointing
backward.
<p>
RNNs are used to analyze time series data such as stock prices, and
tell you when to buy or sell. In autonomous driving systems, they can
anticipate car trajectories and help avoid accidents. More generally,
they can work on sequences of arbitrary lengths, rather than on
fixed-sized inputs like all the nets we have discussed so far. For
example, they can take sentences, documents, or audio samples as
input, making them extremely useful for natural language processing
systems such as automatic translation and speech-to-text.
<p>
<b>The text here is under development</b>. Planned finished mid Jan 2020.
<p>
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<h2 id="___sec1" class="anchor">Set up of an RNN </h2>
<p>
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at a given time \( t \) and outputs \( y_t \). Introducing time as a variable
offers an intutitive way of understanding these networks. In addition
to the inputs \( x_t \), the layer at a time \( t \) receives also as input
the output from the previous layer \( t-1 \), that is \( y_{t1} \).
<p>
This means also that we need to have weights that link both the inputs
\( x_t \) to the outputs \( y_t \) as well as weights that link the output
from the previous time \( y_{t-1} \) and \( y_t \). The figure here shows an
example of a simple RNN.
<p>
<p>
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<!-- navigation toc: --> <li><a href="._Recurrent-bs001.html#___sec0" style="font-size: 80%;">Recurrent neural networks: Overarching view</a></li>
<!-- navigation toc: --> <li><a href="._Recurrent-bs002.html#___sec1" style="font-size: 80%;">Set up of an RNN</a></li>
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<p>
In our discussions of ordinary differential equations and partial
differential equations using neural networks. Here we will discuss how
we can solve say ordinary differential equations and eigenvalue
problems using RNNs. Eigenvalue problems can be solved using RNNs by
rewriting such a problems as a non-linear differential equation.
<p>
Instead of starting with a well-known ordinary differential equation,
we start directly with an eigenvaule problem.
<p>
<p>
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<a class="navbar-brand" href="Recurrent-bs.html">Data Analysis and Machine Learning: Recurrent neural networks</a>
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<!-- navigation toc: --> <li><a href="._Recurrent-bs001.html#___sec0" style="font-size: 80%;">Recurrent neural networks: Overarching view</a></li>
<!-- navigation toc: --> <li><a href="._Recurrent-bs002.html#___sec1" style="font-size: 80%;">Set up of an RNN</a></li>
<!-- navigation toc: --> <li><a href="._Recurrent-bs003.html#___sec2" style="font-size: 80%;">Solving differential equations and eigenvalue problems with RNNs</a></li>
<!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">Long-Short Time Memory</a></li>
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<h2 id="___sec3" class="anchor">Long-Short Time Memory </h2>
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Discussions about dynamic unrolling through time. discuss memory cells, input and output
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