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The `bin/pandoc-wrapper.sh` tool will verify that the ssytem has a recent enough version of `pandoc(1)`. We explain why we insist on `pandoc(1)`. version >= 3.1.12.2 in comments where the $PANDOC_MIN_VERSION is set. Added `--wrap=preserve` as a default argument to `pandoc(1)`. While this change will impact every HTML file generated, we believe this will improve the ability of someone to look at the generated HTML and correlate with the original markdown. Changed `bin/pandoc-wrapper.sh` VERSION from "1.4.2 2024-03-17" to "1.4.3 2024-03-18". Performed `make www` to achieve all of the above and to generate HTML using the new `--wrap=preserve` `pandoc(1)` mode.
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@@ -129,9 +129,9 @@
|
||||
|
||||
<h2 id="author"><a name="author"></a>Author:</h2>
|
||||
<ul>
|
||||
<li>Name: <a href="../../authors.html#Christopher_Mills">Christopher
|
||||
Mills</a><br> Location: <a href="../../location.html#US">US</a> -
|
||||
<em>United States of America</em> (<em>United States</em>) <br><br></li>
|
||||
<li>Name: <a href="../../authors.html#Christopher_Mills">Christopher Mills</a><br>
|
||||
Location: <a href="../../location.html#US">US</a> - <em>United States of America</em> (<em>United States</em>)
|
||||
<br><br></li>
|
||||
</ul>
|
||||
|
||||
<!-- END: next line ends content generated by: bin/output-index-author.sh -->
|
||||
@@ -144,88 +144,65 @@ Mills</a><br> Location: <a href="../../location.html#US">US</a> -
|
||||
<h3 id="bugs-and-misfeatures">Bugs and (Mis)features:</h3>
|
||||
<p>The current status of this entry is:</p>
|
||||
<pre><code>STATUS: INABIAF - please **DO NOT** fix</code></pre>
|
||||
<p>For more detailed information see <a
|
||||
href="../../bugs.html#2019_mills">2019 mills bugs</a>.</p>
|
||||
<p>For more detailed information see <a href="../../bugs.html#2019_mills">2019 mills bugs</a>.</p>
|
||||
<h2 id="to-use">To use:</h2>
|
||||
<div class="sourceCode" id="cb3"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> cpclean</span>
|
||||
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Let this run for about about an hour and then kill it:</span></span>
|
||||
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> Shakespeare.txt</span></code></pre></div>
|
||||
<h2 id="try">Try:</h2>
|
||||
<div class="sourceCode" id="cb4"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./try.sh</span></span></code></pre></div>
|
||||
<p>However, as the binary model files used to produce the output are in
|
||||
an implementation-specific format, your mileage may vary.</p>
|
||||
<p>However, as the binary model files used to produce the output are in an
|
||||
implementation-specific format, your mileage may vary.</p>
|
||||
<h2 id="judges-remarks">Judges’ remarks:</h2>
|
||||
<p>Can a machine learn?</p>
|
||||
<p>Some say so.</p>
|
||||
<p>But can a machine learn to write like Shakespeare? Can it write rules
|
||||
and guidelines for the IOCCC?</p>
|
||||
<p>But can a machine learn to write like Shakespeare? Can it write rules and
|
||||
guidelines for the IOCCC?</p>
|
||||
<p>You decide. :-)</p>
|
||||
<h2 id="authors-remarks">Author’s remarks:</h2>
|
||||
<h3 id="welcome-to-omlet">Welcome to OMLET! 🍳:</h3>
|
||||
<p>OMLET is the <em>Obfuscated Machine Learning Environment
|
||||
Toolkit</em>, a micro-framework for experimenting with <a
|
||||
href="https://en.wikipedia.org/wiki/Recurrent_neural_network">recurrent
|
||||
neural networks</a> (RNN). OMLET lets you build, train and evaluate <a
|
||||
href="https://en.wikipedia.org/wiki/Deep_learning">deep neural
|
||||
networks</a> (DNN). Why invest hours reading documentation and megabytes
|
||||
of disk space on a full-featured DNN framework like <a
|
||||
href="https://www.tensorflow.org">TensorFlow</a> or <a
|
||||
href="http://torch.ch">Torch</a> when you can have full RNN
|
||||
functionality in less than 4 KB!</p>
|
||||
<p>OMLET is the <em>Obfuscated Machine Learning Environment Toolkit</em>, a
|
||||
micro-framework for experimenting with <a href="https://en.wikipedia.org/wiki/Recurrent_neural_network">recurrent neural networks</a> (RNN).
|
||||
OMLET lets you build, train and evaluate <a href="https://en.wikipedia.org/wiki/Deep_learning">deep neural networks</a> (DNN). Why
|
||||
invest hours reading documentation and megabytes of disk space on a
|
||||
full-featured DNN framework like <a href="https://www.tensorflow.org">TensorFlow</a> or <a href="http://torch.ch">Torch</a> when you can have
|
||||
full RNN functionality in less than 4 KB!</p>
|
||||
<p>OMLET has the following features:</p>
|
||||
<ul>
|
||||
<li>User-programmable network configurations and hyperparameters.</li>
|
||||
<li>Support for various types of recurrent and feed-forward neural
|
||||
networks including vanilla RNNs, LSTMs and GRUs of depths of up to 99
|
||||
layers.</li>
|
||||
<li>No limit on parameter size (except for those imposed by the
|
||||
system).</li>
|
||||
<li>Support for various types of recurrent and feed-forward neural networks
|
||||
including vanilla RNNs, LSTMs and GRUs of depths of up to 99 layers.</li>
|
||||
<li>No limit on parameter size (except for those imposed by the system).</li>
|
||||
<li>Training and inference modes, with periodic checkpointing.</li>
|
||||
<li>Advanced <a href="https://arxiv.org/abs/1412.6980">Adam</a>
|
||||
optimizer with <a
|
||||
href="https://www.fast.ai/2018/07/02/adam-weight-decay/">weight
|
||||
decay</a> for simplified training.</li>
|
||||
<li>Hyperparameters support for batch sizing, learning rate schedule,
|
||||
weight decay and gradient clipping.</li>
|
||||
<li>Easily extensible (requires some expertise in the C programming
|
||||
language).</li>
|
||||
<li>Advanced <a href="https://arxiv.org/abs/1412.6980">Adam</a> optimizer with <a href="https://www.fast.ai/2018/07/02/adam-weight-decay/">weight decay</a> for simplified
|
||||
training.</li>
|
||||
<li>Hyperparameters support for batch sizing, learning rate schedule, weight
|
||||
decay and gradient clipping.</li>
|
||||
<li>Easily extensible (requires some expertise in the C programming language).</li>
|
||||
<li>Friendly markdown documentation.</li>
|
||||
</ul>
|
||||
<p>OMLET is based on <a href="https://karpathy.ai">Andrej Karpathy’s</a>
|
||||
<a href="https://github.com/karpathy/char-rnn">character-level language
|
||||
model</a> as described in his blog post <a
|
||||
href="http://karpathy.github.io/2015/05/21/rnn-effectiveness/"><em>The
|
||||
Unreasonable Effectiveness of Recurrent Neural Networks</em></a>. I’ve
|
||||
included a small sample dataset to use for training, but you can have
|
||||
even more fun by downloading some larger datasets:</p>
|
||||
<p>OMLET is based on <a href="https://karpathy.ai">Andrej Karpathy’s</a> <a href="https://github.com/karpathy/char-rnn">character-level language model</a>
|
||||
as described in his blog post <a href="http://karpathy.github.io/2015/05/21/rnn-effectiveness/"><em>The Unreasonable Effectiveness of Recurrent
|
||||
Neural Networks</em></a>. I’ve included a small sample dataset to use for
|
||||
training, but you can have even more fun by downloading some larger datasets:</p>
|
||||
<ul>
|
||||
<li><a
|
||||
href="https://cs.stanford.edu/people/karpathy/char-rnn/linux_input.txt">Linux
|
||||
kernel source</a></li>
|
||||
<li><a
|
||||
href="https://cs.stanford.edu/people/karpathy/char-rnn/warpeace_input.txt"><em>War
|
||||
and Peace</em></a></li>
|
||||
<li><a href="https://github.com/ryanmcdermott/trump-speeches">Donald
|
||||
Trump’s 2016 campaign speeches</a></li>
|
||||
<li><a href="https://cs.stanford.edu/people/karpathy/char-rnn/linux_input.txt">Linux kernel source</a></li>
|
||||
<li><a href="https://cs.stanford.edu/people/karpathy/char-rnn/warpeace_input.txt"><em>War and Peace</em></a></li>
|
||||
<li><a href="https://github.com/ryanmcdermott/trump-speeches">Donald Trump’s 2016 campaign speeches</a></li>
|
||||
</ul>
|
||||
<h3 id="getting-started-with-omlet">Getting started with OMLET</h3>
|
||||
<p>OMLET has three operating modes:</p>
|
||||
<ul>
|
||||
<li><em>Training</em>, which trains a network from scratch.</li>
|
||||
<li><em>Continuation</em>, which trains starting from an existing
|
||||
checkpoint.</li>
|
||||
<li><em>Inference</em>, which uses an existing trained network to make
|
||||
predictions.</li>
|
||||
<li><em>Continuation</em>, which trains starting from an existing checkpoint.</li>
|
||||
<li><em>Inference</em>, which uses an existing trained network to make predictions.</li>
|
||||
</ul>
|
||||
<p>For your first OMLET experiment, we will try training a simple
|
||||
single-level RNN to write some <a
|
||||
href="https://en.wikipedia.org/wiki/William_Shakespeare">Shakespeare</a>
|
||||
plays. Start by typing</p>
|
||||
<p>For your first OMLET experiment, we will try training a simple single-level
|
||||
RNN to write some <a href="https://en.wikipedia.org/wiki/William_Shakespeare">Shakespeare</a> plays. Start by typing</p>
|
||||
<div class="sourceCode" id="cb5"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span></span></code></pre></div>
|
||||
<p>After it builds, train it using</p>
|
||||
<div class="sourceCode" id="cb6"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> Shakespere.txt</span></code></pre></div>
|
||||
<p>This will immediately start outputting gibberish to the output,
|
||||
e.g.</p>
|
||||
<p>This will immediately start outputting gibberish to the output, e.g.</p>
|
||||
<div class="sourceCode" id="cb7"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> Shakespere.txt</span></code></pre></div>
|
||||
<p>produces:</p>
|
||||
<pre><code>sins ohennAu
|
||||
@@ -260,14 +237,13 @@ Vh th no dh foud bobt werw:s Aotnf Fhwi't whe, eusu
|
||||
lhh thele wewcond ary soupfy wind tDont couc ths:
|
||||
er fucwald oncli hen bos, f
|
||||
T0:1% 2.878945</code></pre>
|
||||
<p>The gibberish is the networks attempt to write a play. So far, it’s
|
||||
not very successful! Between the chunks of gibberish are training
|
||||
progress reports that look like</p>
|
||||
<p>The gibberish is the networks attempt to write a play. So far, it’s not very
|
||||
successful! Between the chunks of gibberish are training progress reports
|
||||
that look like</p>
|
||||
<pre><code>T0:1% 2.878945</code></pre>
|
||||
<p>This tells you that we are 1% through training epoch 0, and that the
|
||||
training <a href="https://en.wikipedia.org/wiki/Loss_function">loss</a>
|
||||
is about 2.88. As the training continues, the training loss will reduce
|
||||
and the generated snippets will improve quickly:</p>
|
||||
<p>This tells you that we are 1% through training epoch 0, and that the training
|
||||
<a href="https://en.wikipedia.org/wiki/Loss_function">loss</a> is about 2.88. As the training continues, the training loss will
|
||||
reduce and the generated snippets will improve quickly:</p>
|
||||
<pre><code>ses, kuth
|
||||
LAs of the wish,
|
||||
As, I nos you,
|
||||
@@ -293,12 +269,12 @@ rerytund: tich lon hyivetetgor.
|
||||
VOLUONIA:
|
||||
He brich nom dove worthan then wise,
|
||||
T0:13% 2.254926</code></pre>
|
||||
<p>It’s already started to figure out things about Shakespeare plays –
|
||||
how to spell short English words, how long lines tend to be, and that
|
||||
characters take turns speaking with their names capitalized. The
|
||||
training loss has dropped to 2.25 and the improvement is noticeable.</p>
|
||||
<p>Eventually, we will finish with the training data set and move on to
|
||||
a validation cycle:</p>
|
||||
<p>It’s already started to figure out things about Shakespeare plays – how to
|
||||
spell short English words, how long lines tend to be, and that characters take
|
||||
turns speaking with their names capitalized. The training loss has dropped to
|
||||
2.25 and the improvement is noticeable.</p>
|
||||
<p>Eventually, we will finish with the training data set and move on to a
|
||||
validation cycle:</p>
|
||||
<pre><code>y fath onother,
|
||||
I sucess,
|
||||
For I me the west crare.
|
||||
@@ -333,58 +309,49 @@ Willerity.
|
||||
|
||||
First Cumfol of
|
||||
T1:0% 1.885619</code></pre>
|
||||
<p>Validation cycles are used to test the network to see if it has
|
||||
learned to generalize – how well it performs on data it hasn’t seen
|
||||
before (as opposed to the training data that the network will see many
|
||||
times as it trains). Progress on the validation set is also displayed
|
||||
with a validation progress report that looks like</p>
|
||||
<p>Validation cycles are used to test the network to see if it has learned to
|
||||
generalize – how well it performs on data it hasn’t seen before (as opposed to
|
||||
the training data that the network will see many times as it trains). Progress
|
||||
on the validation set is also displayed with a validation progress report that
|
||||
looks like</p>
|
||||
<pre><code>V0:36% 1.716672</code></pre>
|
||||
<p>which means we are 36% of the way through the validation for epoch 0,
|
||||
and the validation loss is about 1.72. Comparing the validation loss and
|
||||
the training loss will give you an idea of how well the network is
|
||||
learning and can let you know if the network is <a
|
||||
href="https://en.wikipedia.org/wiki/Overfitting">overfitting or
|
||||
underfitting</a>.</p>
|
||||
<p>which means we are 36% of the way through the validation for epoch 0, and the
|
||||
validation loss is about 1.72. Comparing the validation loss and the
|
||||
training loss will give you an idea of how well the network is learning and
|
||||
can let you know if the network is <a href="https://en.wikipedia.org/wiki/Overfitting">overfitting or underfitting</a>.</p>
|
||||
<p>As part of the training process, the data set (which for OMLET is the
|
||||
<a href="Shakespeare.txt">Shakespeare.txt</a> file you gave on the
|
||||
command line) is divided into <a
|
||||
href="https://en.wikipedia.org/wiki/Training,_validation,_and_test_sets">training
|
||||
and validation sets</a> (by default, 95% of the data is used for
|
||||
training, but like most OMLET parameters, you can change this at
|
||||
compile-time).</p>
|
||||
<p>At the end of the validation run, OMLET writes out a checkpoint file
|
||||
with a name like <code>cp01_1.970</code>. This saves the state of the
|
||||
run at the start of the epoch 1, after computing a validation loss of
|
||||
1.970. The checkpoint is helpful if you need to stop and restart
|
||||
training. You can stop training by doing <code>Control-C</code>.</p>
|
||||
<a href="Shakespeare.txt">Shakespeare.txt</a> file you gave on the command line) is divided into
|
||||
<a href="https://en.wikipedia.org/wiki/Training,_validation,_and_test_sets">training and validation sets</a> (by default, 95% of the data is used for
|
||||
training, but like most OMLET parameters, you can change this at compile-time).</p>
|
||||
<p>At the end of the validation run, OMLET writes out a checkpoint file with a
|
||||
name like <code>cp01_1.970</code>. This saves the state of the run at the start of the
|
||||
epoch 1, after computing a validation loss of 1.970. The checkpoint is
|
||||
helpful if you need to stop and restart training. You can stop training by
|
||||
doing <code>Control-C</code>.</p>
|
||||
<p>You can continue training from a previous checkpoint by providing the
|
||||
checkpoint file name as the second parameter, for example:</p>
|
||||
<div class="sourceCode" id="cb13"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> Shakespeare.txt cp01_1.970</span></code></pre></div>
|
||||
<p>After the validation cycle finishes, OMLET begins the next epoch by
|
||||
restarting training at the beginning of the training set. Training
|
||||
continues forever, until you quit it with <code>Control-C</code>. You
|
||||
should monitor the checkpoints to see that the validation loss continues
|
||||
to drop. If it rises, the network has probably started to overfit on the
|
||||
training data.</p>
|
||||
<p>Once you’ve trained the validation loss as low as it will go, you can
|
||||
use OMLET to run the network in inference mode which uses the frozen
|
||||
checkpoint parameters to generate data. Inference mode takes the
|
||||
checkpoint file as <em>standard input</em> (not on the command line) and
|
||||
hence must be run with a command like</p>
|
||||
<div class="sourceCode" id="cb14"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> <span class="op"><</span> cp55_1.807</span></code></pre></div>
|
||||
<p>Running it produces an infinite amount of generated output, until you
|
||||
hit <code>Control-C</code> to stop it.</p>
|
||||
<p>Note that if you decide to change networks or use a different input
|
||||
file, you will want to delete all the checkpoint files because the
|
||||
format depends on both the network and the input – using the wrong
|
||||
checkpoint is likely to cause a crash.</p>
|
||||
<h3 id="experimenting-with-different-networks">Experimenting with
|
||||
different networks</h3>
|
||||
<p>The default network for OMLET (the one you get if you type
|
||||
<code>make</code> with the executable name <code>prog</code>) is the
|
||||
simplest recurrent neural network. It looks like</p>
|
||||
<div class="sourceCode" id="cb13"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> Shakespeare.txt cp01_1.970</span></code></pre></div>
|
||||
<p>After the validation cycle finishes, OMLET begins the next epoch by restarting
|
||||
training at the beginning of the training set. Training continues forever,
|
||||
until you quit it with <code>Control-C</code>. You should monitor the checkpoints to
|
||||
see that the validation loss continues to drop. If it rises, the network has
|
||||
probably started to overfit on the training data.</p>
|
||||
<p>Once you’ve trained the validation loss as low as it will go, you can use
|
||||
OMLET to run the network in inference mode which uses the frozen checkpoint
|
||||
parameters to generate data. Inference mode takes the checkpoint file as
|
||||
<em>standard input</em> (not on the command line) and hence must be run with a
|
||||
command like</p>
|
||||
<div class="sourceCode" id="cb14"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./prog</span> <span class="op"><</span> cp55_1.807</span></code></pre></div>
|
||||
<p>Running it produces an infinite amount of generated output, until you hit
|
||||
<code>Control-C</code> to stop it.</p>
|
||||
<p>Note that if you decide to change networks or use a different input file, you
|
||||
will want to delete all the checkpoint files because the format depends on
|
||||
both the network and the input – using the wrong checkpoint is likely to
|
||||
cause a crash.</p>
|
||||
<h3 id="experimenting-with-different-networks">Experimenting with different networks</h3>
|
||||
<p>The default network for OMLET (the one you get if you type <code>make</code> with the
|
||||
executable name <code>prog</code>) is the simplest recurrent neural network. It looks
|
||||
like</p>
|
||||
<div class="sourceCode" id="cb15"><pre class="sourceCode c"><code class="sourceCode c"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>h <span class="op">=</span> tanh<span class="op">(</span>Wxh <span class="op">*</span> x <span class="op">+</span> Whh <span class="op">*</span> h<span class="ch">' </span><span class="er">+ Bh)</span></span>
|
||||
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> Why <span class="op">*</span> h <span class="op">+</span> By</span></code></pre></div>
|
||||
<p>where</p>
|
||||
@@ -393,36 +360,24 @@ simplest recurrent neural network. It looks like</p>
|
||||
<li><code>y</code> is the <em>output vector</em></li>
|
||||
<li><code>h</code> is the <em>hidden state vector</em></li>
|
||||
<li><code>h'</code> is the previous value of <code>h</code></li>
|
||||
<li><code>Wxh</code>, <code>Whh</code>, and <code>Why</code> are
|
||||
<em>weight matrices</em></li>
|
||||
<li><code>Wxh</code>, <code>Whh</code>, and <code>Why</code> are <em>weight matrices</em></li>
|
||||
<li><code>Bh</code> and <code>By</code> are <em>bias vectors</em>.</li>
|
||||
<li><code>tanh(3)</code> is the <a
|
||||
href="https://en.wikipedia.org/wiki/Hyperbolic_function">hyperbolic
|
||||
tangent function</a></li>
|
||||
<li><code>tanh(3)</code> is the <a href="https://en.wikipedia.org/wiki/Hyperbolic_function">hyperbolic tangent function</a></li>
|
||||
</ul>
|
||||
<p>The <code>W</code>’s and <code>B</code>’s are the trainable
|
||||
parameters of the network, and the process of training is optimizing the
|
||||
values of these parameters to minimize the loss of the network across
|
||||
the training set.</p>
|
||||
<p>The <code>W</code>’s and <code>B</code>’s are the trainable parameters of the network, and the
|
||||
process of training is optimizing the values of these parameters to minimize
|
||||
the loss of the network across the training set.</p>
|
||||
<p>It is the presence of the hidden state vector that allows the RNN to
|
||||
“remember” the past. We can see what would happen if we removed this
|
||||
hidden state. If you type</p>
|
||||
<div class="sourceCode" id="cb16"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> lin1</span></code></pre></div>
|
||||
<p>OMLET will create an <a
|
||||
href="https://en.wikipedia.org/wiki/ADALINE">ADALINE</a> network that
|
||||
does</p>
|
||||
“remember” the past. We can see what would happen if we removed this hidden
|
||||
state. If you type</p>
|
||||
<div class="sourceCode" id="cb16"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> lin1</span></code></pre></div>
|
||||
<p>OMLET will create an <a href="https://en.wikipedia.org/wiki/ADALINE">ADALINE</a> network that does</p>
|
||||
<div class="sourceCode" id="cb17"><pre class="sourceCode c"><code class="sourceCode c"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> Wxy <span class="op">*</span> x <span class="op">+</span> By</span></code></pre></div>
|
||||
<p>This is a simple <a
|
||||
href="https://en.wikipedia.org/wiki/Linear_map">linear</a> <a
|
||||
href="https://en.wikipedia.org/wiki/Feedforward_neural_network">feed-forward
|
||||
network</a>. You can run it with</p>
|
||||
<div class="sourceCode" id="cb18"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lin1</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The linear network won’t be able to get past the gibberish stage,
|
||||
because it lacks history:</p>
|
||||
<div class="sourceCode" id="cb19"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lin1</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>This is a simple <a href="https://en.wikipedia.org/wiki/Linear_map">linear</a> <a href="https://en.wikipedia.org/wiki/Feedforward_neural_network">feed-forward network</a>. You can run it with</p>
|
||||
<div class="sourceCode" id="cb18"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lin1</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The linear network won’t be able to get past the gibberish stage, because it
|
||||
lacks history:</p>
|
||||
<div class="sourceCode" id="cb19"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lin1</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>produces:</p>
|
||||
<pre><code>UERond w,
|
||||
|
||||
@@ -446,92 +401,68 @@ I'delandinarrstath har aksubly s cath Whern t Is, weciss:
|
||||
GLat s; llde.
|
||||
Y aterit dsthence
|
||||
T14:67% 2.465404</code></pre>
|
||||
<p>It is able to guess at what character is likely to follow the current
|
||||
one (by doing a <a
|
||||
href="https://en.wikipedia.org/wiki/Linear_regression">linear
|
||||
regression</a>), but it lacks any history beyond that to guide it.</p>
|
||||
<p>You might be wondering about the role of the <code>tanh(3)</code>
|
||||
function in the RNN. <code>tanh(3)</code> acts as an <a
|
||||
href="https://en.wikipedia.org/wiki/Activation_function">activation
|
||||
function</a> which adds <a
|
||||
href="https://en.wikipedia.org/wiki/Nonlinear_system">nonlinearity</a>
|
||||
<p>It is able to guess at what character is likely to follow the current one
|
||||
(by doing a <a href="https://en.wikipedia.org/wiki/Linear_regression">linear regression</a>), but it lacks any history beyond that to
|
||||
guide it.</p>
|
||||
<p>You might be wondering about the role of the <code>tanh(3)</code> function in the RNN.
|
||||
<code>tanh(3)</code> acts as an <a href="https://en.wikipedia.org/wiki/Activation_function">activation function</a> which adds <a href="https://en.wikipedia.org/wiki/Nonlinear_system">nonlinearity</a>
|
||||
to the network and allows it to solve complicated problems. Without
|
||||
nonlinearity, all of the linear functions would fold together into a
|
||||
single matrix-vector multiply and you’d effectively regress to the
|
||||
linear network above. Alas, even adding a nonlinearity to the
|
||||
feed-forward network (creating a <a
|
||||
href="https://en.wikipedia.org/wiki/Perceptron">perceptron</a>) does not
|
||||
improve the performance because we still lack the history provided by
|
||||
the hidden state vector (although if you want to try it yourself, you
|
||||
can do so with <code>make per1</code> - note that’s not
|
||||
<code>perl</code> the language but <code>per</code> with the digit
|
||||
1).</p>
|
||||
nonlinearity, all of the linear functions would fold together into a single
|
||||
matrix-vector multiply and you’d effectively regress to the linear network
|
||||
above. Alas, even adding a nonlinearity to the feed-forward network
|
||||
(creating a <a href="https://en.wikipedia.org/wiki/Perceptron">perceptron</a>) does not improve the performance because we
|
||||
still lack the history provided by the hidden state vector (although if you
|
||||
want to try it yourself, you can do so with <code>make per1</code> - note that’s not <code>perl</code>
|
||||
the language but <code>per</code> with the digit 1).</p>
|
||||
<h3 id="going-deeper">Going deeper:</h3>
|
||||
<p>We can try to improve the RNN’s performance by stacking RNN modules
|
||||
atop each other:</p>
|
||||
<p>We can try to improve the RNN’s performance by stacking RNN modules atop each
|
||||
other:</p>
|
||||
<div class="sourceCode" id="cb21"><pre class="sourceCode c"><code class="sourceCode c"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>h1 <span class="op">=</span> RNN<span class="op">(</span>h1<span class="ch">',</span><span class="er"> x)</span></span>
|
||||
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>h2 <span class="op">=</span> RNN<span class="op">(</span>h2<span class="ch">',</span><span class="er"> h1)</span></span>
|
||||
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> Why <span class="op">*</span> h2 <span class="op">+</span> By</span></code></pre></div>
|
||||
<p>with <code>RNN(h, x)</code> defined as above. Each RNN module has its
|
||||
own set of parameters and its own hidden state vector. This will improve
|
||||
the network’s performance, at the cost of a much larger parameter
|
||||
space.</p>
|
||||
<p>with <code>RNN(h, x)</code> defined as above. Each RNN module has its own set of
|
||||
parameters and its own hidden state vector. This will improve the network’s
|
||||
performance, at the cost of a much larger parameter space.</p>
|
||||
<hr />
|
||||
<p><strong>IMPORTANT NOTE</strong>: Since OMLET uses the system stack
|
||||
for network storage, larger networks may cause OMLET to crash (typically
|
||||
with a message like <code>Segmentation fault</code>) unless the system
|
||||
stack size is first increased. The exact command for doing so depends on
|
||||
your shell and your system’s hard limits. On
|
||||
<code>sh</code>/<code>ksh</code>/<code>bash</code> shells, you can view
|
||||
the hard limit with <code>ulimit -Hs</code> and set it with
|
||||
<code>ulimit -s 65532</code> (replacing <code>65532</code> with the
|
||||
actual hard limit). On <code>csh</code>/<code>tcsh</code> shells, you
|
||||
can view the hard limit with <code>limit -h stacksize</code> and set it
|
||||
with <code>limit stacksize 65532</code> (replacing <code>65532</code>
|
||||
with the actual hard limit).</p>
|
||||
<p><strong>IMPORTANT NOTE</strong>: Since OMLET uses the system stack for network storage,
|
||||
larger networks may cause OMLET to crash (typically with a message like
|
||||
<code>Segmentation fault</code>) unless the system stack size is first increased.
|
||||
The exact command for doing so depends on your shell and your system’s
|
||||
hard limits. On <code>sh</code>/<code>ksh</code>/<code>bash</code> shells, you can view the hard limit
|
||||
with <code>ulimit -Hs</code> and set it with <code>ulimit -s 65532</code> (replacing <code>65532</code>
|
||||
with the actual hard limit). On <code>csh</code>/<code>tcsh</code> shells, you can view
|
||||
the hard limit with <code>limit -h stacksize</code> and set it with
|
||||
<code>limit stacksize 65532</code> (replacing <code>65532</code> with the actual hard limit).</p>
|
||||
<hr />
|
||||
<p>You can try the deeper network by doing</p>
|
||||
<div class="sourceCode" id="cb22"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> rnn2</span></code></pre></div>
|
||||
<p>(or even <code>make rnn3</code> if you want a three-layer RNN) and
|
||||
train it with</p>
|
||||
<div class="sourceCode" id="cb23"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./rnn2</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The additional depth should allow the network to make better
|
||||
predictions (it can represent more complicated history), but it may take
|
||||
a long time to train -- both because the network (being larger) now
|
||||
requires more time to train and because of the <a
|
||||
href="https://en.wikipedia.org/wiki/Vanishing_gradient_problem">vanishing
|
||||
and exploding gradient problem</a>, which might keep it from ever
|
||||
reaching its potential.</p>
|
||||
<div class="sourceCode" id="cb22"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> rnn2</span></code></pre></div>
|
||||
<p>(or even <code>make rnn3</code> if you want a three-layer RNN) and train it with</p>
|
||||
<div class="sourceCode" id="cb23"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./rnn2</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The additional depth should allow the network to make better predictions (it
|
||||
can represent more complicated history), but it may take a long time to train
|
||||
-- both because the network (being larger) now requires more time to train and
|
||||
because of the <a href="https://en.wikipedia.org/wiki/Vanishing_gradient_problem">vanishing and exploding gradient problem</a>, which might
|
||||
keep it from ever reaching its potential.</p>
|
||||
<h3 id="lstms-and-grus">LSTMs and GRUs</h3>
|
||||
<p>RNNs are particularly hard to train because they are trained using <a
|
||||
href="https://en.wikipedia.org/wiki/Backpropagation_through_time">backpropagation
|
||||
through time</a>. The RNN is trained by effectively converting it into a
|
||||
non-recurrent network by making many copies of it and propagating the
|
||||
hidden state through the copies. During training, the backpropagation
|
||||
through many clones of the network amplifies the gradient, worsening the
|
||||
exploding and vanishing gradient problem.</p>
|
||||
<p><a href="https://en.wikipedia.org/wiki/Long_short-term_memory">Long
|
||||
Short Term Memory</a> networks (also called LSTMs) were developed to
|
||||
solve this problem. Christopher Olah gives a good description of them at
|
||||
his <a
|
||||
href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">blog
|
||||
posting</a>. You can build a two-level LSTM by doing</p>
|
||||
<div class="sourceCode" id="cb24"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> lstm2</span></code></pre></div>
|
||||
<p>RNNs are particularly hard to train because they are trained using
|
||||
<a href="https://en.wikipedia.org/wiki/Backpropagation_through_time">backpropagation through time</a>. The RNN is trained by effectively
|
||||
converting it into a non-recurrent network by making many copies of it
|
||||
and propagating the hidden state through the copies. During training,
|
||||
the backpropagation through many clones of the network amplifies the
|
||||
gradient, worsening the exploding and vanishing gradient problem.</p>
|
||||
<p><a href="https://en.wikipedia.org/wiki/Long_short-term_memory">Long Short Term Memory</a> networks (also called LSTMs) were developed to
|
||||
solve this problem. Christopher Olah gives a good description of them
|
||||
at his <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">blog posting</a>. You can build a two-level LSTM by doing</p>
|
||||
<div class="sourceCode" id="cb24"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> lstm2</span></code></pre></div>
|
||||
<p>and train with it with</p>
|
||||
<div class="sourceCode" id="cb25"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lstm2</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The LSTM is much easier to train because it explicitly decides how to
|
||||
update its hidden state via “gates”. These gates are called</p>
|
||||
<div class="sourceCode" id="cb25"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="ex">./lstm2</span> Shakespeare.txt</span></code></pre></div>
|
||||
<p>The LSTM is much easier to train because it explicitly decides how to update
|
||||
its hidden state via “gates”. These gates are called</p>
|
||||
<ul>
|
||||
<li><em>input gate</em>, which decides what part of the input to pay
|
||||
attention to</li>
|
||||
<li><em>forget gate</em>, which decides what part of the hidden state to
|
||||
forget</li>
|
||||
<li><em>output gate</em>, which decides what part of the hidden state is
|
||||
used to produce the output</li>
|
||||
<li><em>input gate</em>, which decides what part of the input to pay attention to</li>
|
||||
<li><em>forget gate</em>, which decides what part of the hidden state to forget</li>
|
||||
<li><em>output gate</em>, which decides what part of the hidden state is used to
|
||||
produce the output</li>
|
||||
</ul>
|
||||
<p>The basic LSTM equations are</p>
|
||||
<div class="sourceCode" id="cb26"><pre class="sourceCode c"><code class="sourceCode c"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>f <span class="op">=</span> sigmoid<span class="op">(</span>Wxf <span class="op">*</span> x <span class="op">+</span> Whf <span class="op">*</span> h<span class="ch">' </span><span class="er">+ Bf)</span></span>
|
||||
@@ -542,95 +473,70 @@ used to produce the output</li>
|
||||
<p>Where</p>
|
||||
<ul>
|
||||
<li><code>x</code> is the input vector</li>
|
||||
<li><code>h</code> is the hidden state (and the output to the next
|
||||
layer)</li>
|
||||
<li><code>c</code> is the <em>cell state</em> which represents the
|
||||
“memory” of the LSTM</li>
|
||||
<li><code>h'</code> and <code>c'</code> are the previous values of
|
||||
<code>h</code> and <code>c</code> respectively</li>
|
||||
<li><code>f</code> is the <em>forget gate</em> that tells the LSTM what
|
||||
portion of the hidden state to forget</li>
|
||||
<li><code>i</code> is the <em>input gate</em> that tells the LSTM what
|
||||
portion of the input vector to pay attention to</li>
|
||||
<li><code>o</code> is the <em>output gate</em> that tells the LSTM what
|
||||
portion of the cell state to use to generate the hidden state</li>
|
||||
<li><code>Wxf</code>, <code>Whf</code>, <code>Wxi</code>,
|
||||
<code>Whi</code>, <code>Wxo</code>, <code>Who</code>, <code>Wxc</code>,
|
||||
and <code>Whc</code> are trainable parameter matrices</li>
|
||||
<li><code>Bf</code>, <code>Bi</code>, <code>Bo</code>, and
|
||||
<code>Bc</code> are trainable bias vectors</li>
|
||||
<li><code>h</code> is the hidden state (and the output to the next layer)</li>
|
||||
<li><code>c</code> is the <em>cell state</em> which represents the “memory” of the LSTM</li>
|
||||
<li><code>h'</code> and <code>c'</code> are the previous values of <code>h</code> and <code>c</code> respectively</li>
|
||||
<li><code>f</code> is the <em>forget gate</em> that tells the LSTM what portion of the hidden
|
||||
state to forget</li>
|
||||
<li><code>i</code> is the <em>input gate</em> that tells the LSTM what portion of the input
|
||||
vector to pay attention to</li>
|
||||
<li><code>o</code> is the <em>output gate</em> that tells the LSTM what portion of the cell
|
||||
state to use to generate the hidden state</li>
|
||||
<li><code>Wxf</code>, <code>Whf</code>, <code>Wxi</code>, <code>Whi</code>, <code>Wxo</code>, <code>Who</code>, <code>Wxc</code>, and <code>Whc</code> are trainable
|
||||
parameter matrices</li>
|
||||
<li><code>Bf</code>, <code>Bi</code>, <code>Bo</code>, and <code>Bc</code> are trainable bias vectors</li>
|
||||
<li><code>tanh(3)</code> is the hyperbolic tangent function</li>
|
||||
<li><code>sigmoid</code> is the <a
|
||||
href="https://en.wikipedia.org/wiki/Logistic_function">logistic
|
||||
function</a></li>
|
||||
<li><code>sigmoid</code> is the <a href="https://en.wikipedia.org/wiki/Logistic_function">logistic function</a></li>
|
||||
</ul>
|
||||
<p>There are several LSTM variants (see <a
|
||||
href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">C.
|
||||
Olah’s blog post</a> for more examples). One important one is the <a
|
||||
href="https://en.wikipedia.org/wiki/Gated_recurrent_unit">gated
|
||||
recurrent unit</a>. GRUs are simplified versions of an LSTM which
|
||||
combine the gates together, meaning they require fewer learned
|
||||
parameters. This allows them to train faster than a generic LSTM. You
|
||||
can build a two-layer GRU with</p>
|
||||
<div class="sourceCode" id="cb27"><pre
|
||||
class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> gru2</span></code></pre></div>
|
||||
<p>There are several LSTM variants (see <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">C. Olah’s blog post</a> for more
|
||||
examples). One important one is the <a href="https://en.wikipedia.org/wiki/Gated_recurrent_unit">gated recurrent unit</a>. GRUs are
|
||||
simplified versions of an LSTM which combine the gates together, meaning they
|
||||
require fewer learned parameters. This allows them to train faster than a
|
||||
generic LSTM. You can build a two-layer GRU with</p>
|
||||
<div class="sourceCode" id="cb27"><pre class="sourceCode sh"><code class="sourceCode bash"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">make</span> gru2</span></code></pre></div>
|
||||
<h3 id="building-your-own-networks">Building your own networks</h3>
|
||||
<p>The OMLET <code>Makefile</code> comes with one-, two- and three-layer
|
||||
RNNs, LSTMs and GRUs, along with simpler feed-forward networks like
|
||||
multi-layer perceptrons and a linear network. This isn’t the limit of
|
||||
OMLET’s power – you can create your own networks by modifying the
|
||||
<code>Makefile</code>. Networks are passed in on the compiler’s
|
||||
command-line by using <code>-D</code> directives. The network is defined
|
||||
by a <code>-DNW='...'</code> command which consists of a series of
|
||||
comma-separated assignments. For example, the simple one-layer RNN could
|
||||
be defined like</p>
|
||||
<p>The OMLET <code>Makefile</code> comes with one-, two- and three-layer RNNs, LSTMs and
|
||||
GRUs, along with simpler feed-forward networks like multi-layer perceptrons and
|
||||
a linear network. This isn’t the limit of OMLET’s power – you can create your
|
||||
own networks by modifying the <code>Makefile</code>. Networks are passed in on the
|
||||
compiler’s command-line by using <code>-D</code> directives. The network is defined by
|
||||
a <code>-DNW='...'</code> command which consists of a series of comma-separated
|
||||
assignments. For example, the simple one-layer RNN could be defined like</p>
|
||||
<pre class="make"><code>-DNW=' x = I(n), hp = I(128), \
|
||||
h = C(hp, T(A(L(128, x), L(128, hp)))), \
|
||||
y = L(n, h)'</code></pre>
|
||||
<p>The network declares <code>x</code> as an input vector (there must be
|
||||
a declaration for <code>x</code>). It is declared as <code>I(n)</code>,
|
||||
which is an input vector of size <code>n</code>, which is the number of
|
||||
characters of the input alphabet (OMLET computes this from the input
|
||||
file at the start of training). OMLET will arrange to present the input
|
||||
character as a <a
|
||||
href="https://en.wikipedia.org/wiki/One-hot">one-hot</a> vector based on
|
||||
the current input character.</p>
|
||||
<p>The second declaration, <code>hp</code>, declares the previous hidden
|
||||
state vector (what we called <code>h'</code> above). We declare this to
|
||||
be of size 128 – an arbitrary choice. A larger state vector can
|
||||
(theoretically) carry more state, but at a cost of larger parameter
|
||||
matrices and longer training time. You can experiment with increasing
|
||||
the hidden vector size and see.</p>
|
||||
<p>The third line is the core of the RNN. It sets <code>h</code>, the
|
||||
hidden vector output to be the sum of two linear elements specified by
|
||||
<code>L</code>. The <code>L</code> function takes two parameters – the
|
||||
output vector size (which must match the size of <code>h</code>) and the
|
||||
input vector. <code>L</code> will compute <code>y = W * x + B</code>
|
||||
where each <code>L</code> has its own <code>W</code> (weight) and
|
||||
<code>B</code> (bias) training parameters. Both <code>x</code> and
|
||||
<code>hp</code> are sent through <code>L</code> and the result passed
|
||||
through the <code>A</code> function, which does vector addition. That
|
||||
result is passed through <code>T</code> which does element-wise
|
||||
<code>tanh(3)</code> activation.</p>
|
||||
<p>Next, we wrap the whole thing with the <code>C</code> function.
|
||||
<code>C</code> connects <code>hp</code> with <code>h</code>, causing the
|
||||
new value of <code>h</code> to be passed to the <code>hp</code> vector
|
||||
on the next iteration of the algorithm (allowing the RNN to retain state
|
||||
in <code>h</code>).</p>
|
||||
<p>Finally, the whole result is passed through another instance of
|
||||
<code>L</code>, this time producing a vector of size <code>n</code>,
|
||||
which will have the negative log <a
|
||||
href="https://en.wikipedia.org/wiki/Likelihood_function">likelihood</a>
|
||||
function. This is assigned to <code>y</code>, which is the output of the
|
||||
network (and hence must also be declared).</p>
|
||||
<p>OMLET will take the <code>y</code> result and pass it through the <a
|
||||
href="https://en.wikipedia.org/wiki/Softmax_function">softmax</a>
|
||||
function, which converts the log probabilities into a probability
|
||||
distribution. In inference mode, this is used to select the next
|
||||
character to emit. In training mode, this is used to generate the loss
|
||||
which is backpropagated.</p>
|
||||
<p>As an example of a more complicated network, we can look at a
|
||||
two-layer GRU network:</p>
|
||||
<p>The network declares <code>x</code> as an input vector (there must be a declaration for
|
||||
<code>x</code>). It is declared as <code>I(n)</code>, which is an input vector of size <code>n</code>, which
|
||||
is the number of characters of the input alphabet (OMLET computes this from
|
||||
the input file at the start of training). OMLET will arrange to present the
|
||||
input character as a <a href="https://en.wikipedia.org/wiki/One-hot">one-hot</a> vector based on the current input
|
||||
character.</p>
|
||||
<p>The second declaration, <code>hp</code>, declares the previous hidden state vector (what
|
||||
we called <code>h'</code> above). We declare this to be of size 128 – an arbitrary
|
||||
choice. A larger state vector can (theoretically) carry more state, but at
|
||||
a cost of larger parameter matrices and longer training time. You can
|
||||
experiment with increasing the hidden vector size and see.</p>
|
||||
<p>The third line is the core of the RNN. It sets <code>h</code>, the hidden vector output
|
||||
to be the sum of two linear elements specified by <code>L</code>. The <code>L</code> function
|
||||
takes two parameters – the output vector size (which must match the size of
|
||||
<code>h</code>) and the input vector. <code>L</code> will compute <code>y = W * x + B</code> where each <code>L</code>
|
||||
has its own <code>W</code> (weight) and <code>B</code> (bias) training parameters. Both <code>x</code> and
|
||||
<code>hp</code> are sent through <code>L</code> and the result passed through the <code>A</code> function,
|
||||
which does vector addition. That result is passed through <code>T</code> which does
|
||||
element-wise <code>tanh(3)</code> activation.</p>
|
||||
<p>Next, we wrap the whole thing with the <code>C</code> function. <code>C</code> connects <code>hp</code>
|
||||
with <code>h</code>, causing the new value of <code>h</code> to be passed to the <code>hp</code> vector on
|
||||
the next iteration of the algorithm (allowing the RNN to retain state in <code>h</code>).</p>
|
||||
<p>Finally, the whole result is passed through another instance of <code>L</code>, this time
|
||||
producing a vector of size <code>n</code>, which will have the negative log
|
||||
<a href="https://en.wikipedia.org/wiki/Likelihood_function">likelihood</a> function. This is assigned to <code>y</code>, which is the output of
|
||||
the network (and hence must also be declared).</p>
|
||||
<p>OMLET will take the <code>y</code> result and pass it through the <a href="https://en.wikipedia.org/wiki/Softmax_function">softmax</a> function,
|
||||
which converts the log probabilities into a probability distribution. In
|
||||
inference mode, this is used to select the next character to emit. In
|
||||
training mode, this is used to generate the loss which is backpropagated.</p>
|
||||
<p>As an example of a more complicated network, we can look at a two-layer
|
||||
GRU network:</p>
|
||||
<pre class="make"><code>-DHS=128, \
|
||||
-DNW=' x = I(n), \
|
||||
y = L(n, MD(MD(x)))' \
|
||||
@@ -641,167 +547,116 @@ two-layer GRU network:</p>
|
||||
zc = OG(1, -1, z), \
|
||||
h = C(hp, A(M(zc, hp), M(z, c))), \
|
||||
y = h'</code></pre>
|
||||
<p>We are using a few new tricks here – first, we are defining
|
||||
<code>HS</code> as the size of the hidden and cell vectors. There’s
|
||||
nothing special about this name, it’s just convenient to specify it so
|
||||
we don’t have a bunch of constants in the code. Second, the network
|
||||
itself is very simple – it declares <code>x</code> and has the matrix
|
||||
that converts the <code>HS</code>-sized hidden vector back to the
|
||||
<code>n</code>-sized alphabet vector… but it now calls <code>MD</code>,
|
||||
which is the user-definable module (here we are using it twice, to have
|
||||
two cascaded GRU blocks). The <code>MD</code> function performs the
|
||||
sub-network defined by the <code>BK</code> compile-time parameter
|
||||
(specified in the <code>-DBK='...'</code> setting). This sub-module
|
||||
again takes an <code>x</code> parameter and produces a <code>y</code>
|
||||
output. Inside it, we declare <code>hp</code> and <code>h</code>, the
|
||||
previous and current state vector, plus equations for the various GRU
|
||||
gates (these use <code>S</code> for the sigmoid activation function).
|
||||
One final new call is <code>OG</code> which does offset and gain,
|
||||
performing <code>y = offset + gain * x</code> where <code>offset</code>
|
||||
(the first parameter) and <code>gain</code> (the second) are constants.
|
||||
We are using this here to compute <code>(1 - z)</code> for the GRU’s
|
||||
linear interpolator.</p>
|
||||
<p>We are using a few new tricks here – first, we are defining <code>HS</code> as the size
|
||||
of the hidden and cell vectors. There’s nothing special about this name, it’s
|
||||
just convenient to specify it so we don’t have a bunch of constants in the
|
||||
code. Second, the network itself is very simple – it declares <code>x</code> and has
|
||||
the matrix that converts the <code>HS</code>-sized hidden vector back to the <code>n</code>-sized
|
||||
alphabet vector… but it now calls <code>MD</code>, which is the user-definable
|
||||
module (here we are using it twice, to have two cascaded GRU blocks). The
|
||||
<code>MD</code> function performs the sub-network defined by the <code>BK</code> compile-time
|
||||
parameter (specified in the <code>-DBK='...'</code> setting). This sub-module again
|
||||
takes an <code>x</code> parameter and produces a <code>y</code> output. Inside it, we declare
|
||||
<code>hp</code> and <code>h</code>, the previous and current state vector, plus equations for the
|
||||
various GRU gates (these use <code>S</code> for the sigmoid activation function).
|
||||
One final new call is <code>OG</code> which does offset and gain, performing
|
||||
<code>y = offset + gain * x</code> where <code>offset</code> (the first parameter) and <code>gain</code> (the
|
||||
second) are constants. We are using this here to compute <code>(1 - z)</code> for the
|
||||
GRU’s linear interpolator.</p>
|
||||
<p>The full set of available function blocks follows:</p>
|
||||
<ul>
|
||||
<li><code>I(s)</code>: declares a vector (input or state) of size
|
||||
<code>s</code></li>
|
||||
<li><code>L(s, x)</code>: learnable linear function
|
||||
<code>y = W * x + B</code> with an output vector size of
|
||||
<code>s</code></li>
|
||||
<li><code>CM(x)</code>: learnable element-wise gain function
|
||||
<code>y = W * x</code></li>
|
||||
<li><code>I(s)</code>: declares a vector (input or state) of size <code>s</code></li>
|
||||
<li><code>L(s, x)</code>: learnable linear function <code>y = W * x + B</code> with an output vector
|
||||
size of <code>s</code></li>
|
||||
<li><code>CM(x)</code>: learnable element-wise gain function <code>y = W * x</code></li>
|
||||
<li><code>A(a, b)</code>: element-wise add: <code>y = a + b</code></li>
|
||||
<li><code>M(a, b)</code>: element-wise multiply:
|
||||
<code>y = a * b</code></li>
|
||||
<li><code>S(x)</code>: sigmoid activation function
|
||||
<code>y = sigmoid(x)</code></li>
|
||||
<li><code>T(x)</code>: hyperbolic tangent activation function
|
||||
<code>y = tanh(x)</code></li>
|
||||
<li><code>C(xp, x)</code>: copy <code>x</code> to <code>xp</code> in the
|
||||
next time step (propagate through time)</li>
|
||||
<li><code>OG(o, g, x)</code>: apply a constant offset and gain:
|
||||
<code>y = o + g * x</code></li>
|
||||
<li><code>MD(x)</code>: apply the sub-network specified by
|
||||
<code>BK</code></li>
|
||||
<li><code>M(a, b)</code>: element-wise multiply: <code>y = a * b</code></li>
|
||||
<li><code>S(x)</code>: sigmoid activation function <code>y = sigmoid(x)</code></li>
|
||||
<li><code>T(x)</code>: hyperbolic tangent activation function <code>y = tanh(x)</code></li>
|
||||
<li><code>C(xp, x)</code>: copy <code>x</code> to <code>xp</code> in the next time step (propagate through
|
||||
time)</li>
|
||||
<li><code>OG(o, g, x)</code>: apply a constant offset and gain: <code>y = o + g * x</code></li>
|
||||
<li><code>MD(x)</code>: apply the sub-network specified by <code>BK</code></li>
|
||||
</ul>
|
||||
<p>Note: even if you don’t use <code>MD</code> in your network, you
|
||||
should still define <code>BK</code> by adding <code>-DBK='y=x'</code> to
|
||||
the command line, otherwise you will get a compile-time error.</p>
|
||||
<p>Note: even if you don’t use <code>MD</code> in your network, you should still define
|
||||
<code>BK</code> by adding <code>-DBK='y=x'</code> to the command line, otherwise you will get a
|
||||
compile-time error.</p>
|
||||
<h3 id="hyperparameters">Hyperparameters</h3>
|
||||
<p>OMLET has a large number of training and inference parameters which
|
||||
can be changed by the user. All of these are set by <code>-D</code> on
|
||||
the compile command line. The list of hyperparameters follows:</p>
|
||||
<p>OMLET has a large number of training and inference parameters which can be
|
||||
changed by the user. All of these are set by <code>-D</code> on the compile command line.
|
||||
The list of hyperparameters follows:</p>
|
||||
<ul>
|
||||
<li><code>TP</code>: Temperature parameter for use in inference mode.
|
||||
This divides the log probabilities before softmax. A low temperature
|
||||
makes the model choose safer but more boring choices. A high temperature
|
||||
takes more risks but makes more mistakes. Default is 1.0, which uses the
|
||||
computed probabilities.</li>
|
||||
<li><code>N</code>: Batch size. This is the number of times the RNN is
|
||||
unrolled, so it controls how far back in the past the RNN can see. The
|
||||
default is 50. Larger batch sizes update the weights less frequently and
|
||||
allow the RNN to see farther back in time, but at a cost of
|
||||
proportionally more memory.</li>
|
||||
<li><code>TR</code>: The percentage of batches in the input data set
|
||||
that will be used for training. The default value of 0.95 sets this as
|
||||
95%.</li>
|
||||
<li><code>LR</code>: The initial learning rate, the default is
|
||||
0.002.</li>
|
||||
<li><code>LE</code>: The epoch where the learning rate will start
|
||||
decaying. Defaults to epoch 10.</li>
|
||||
<li><code>LD</code>: Learning rate decay, per epoch (after
|
||||
<code>LE</code> epochs). The learning rate is scaled by this number.
|
||||
Default is 0.97</li>
|
||||
<li><code>WD</code>: Weight-decay parameter, to promote <a
|
||||
href="https://en.wikipedia.org/wiki/Regularization_(mathematics)">regularization</a>.
|
||||
The default is 0.00008.</li>
|
||||
<li><code>RS</code>: The random scale for weight initialization. Weight
|
||||
parameters will be initialized to be between <code>-RS</code> to
|
||||
<code>+RS</code>. The default is 0.15.</li>
|
||||
<li><code>CL</code>: Clamp value for gradients. Gradients will be
|
||||
limited to the range <code>-CL</code> to <code>+CL</code>. Default is
|
||||
5.</li>
|
||||
<li><code>B1</code>: Momentum mean parameter for Adam optimizer. Set to
|
||||
0.9.</li>
|
||||
<li><code>B2</code>: Momentum variance parameter for Adam optimizer, Set
|
||||
to 0.999.</li>
|
||||
<li><code>EP</code>: Epsilon parameter for Adam, to provide numerical
|
||||
stability. Set to 0.00000001.</li>
|
||||
<li><code>DI</code>: How often to print a training or validation
|
||||
progress message and inference snippet. The default prints every 100
|
||||
training batches.</li>
|
||||
<li><code>SL</code>: The number of characters to print when doing an
|
||||
inference snippet. Default is 200.</li>
|
||||
<li><code>PF</code>: Format string for the checkpoint filename. The
|
||||
default is <code>"cp%02d_%.3f"</code> which includes the epoch and
|
||||
validation loss. You may wish to add a subdirectory to the name to keep
|
||||
checkpoint files out of the current directory.</li>
|
||||
<li><code>TP</code>: Temperature parameter for use in inference mode. This divides the
|
||||
log probabilities before softmax. A low temperature makes the model choose
|
||||
safer but more boring choices. A high temperature takes more risks but
|
||||
makes more mistakes. Default is 1.0, which uses the computed
|
||||
probabilities.</li>
|
||||
<li><code>N</code>: Batch size. This is the number of times the RNN is unrolled, so it
|
||||
controls how far back in the past the RNN can see. The default is 50.
|
||||
Larger batch sizes update the weights less frequently and allow the RNN to
|
||||
see farther back in time, but at a cost of proportionally more memory.</li>
|
||||
<li><code>TR</code>: The percentage of batches in the input data set that will be used
|
||||
for training. The default value of 0.95 sets this as 95%.</li>
|
||||
<li><code>LR</code>: The initial learning rate, the default is 0.002.</li>
|
||||
<li><code>LE</code>: The epoch where the learning rate will start decaying. Defaults to
|
||||
epoch 10.</li>
|
||||
<li><code>LD</code>: Learning rate decay, per epoch (after <code>LE</code> epochs). The learning
|
||||
rate is scaled by this number. Default is 0.97</li>
|
||||
<li><code>WD</code>: Weight-decay parameter, to promote <a href="https://en.wikipedia.org/wiki/Regularization_(mathematics)">regularization</a>. The default
|
||||
is 0.00008.</li>
|
||||
<li><code>RS</code>: The random scale for weight initialization. Weight parameters will
|
||||
be initialized to be between <code>-RS</code> to <code>+RS</code>. The default is 0.15.</li>
|
||||
<li><code>CL</code>: Clamp value for gradients. Gradients will be limited to the range
|
||||
<code>-CL</code> to <code>+CL</code>. Default is 5.</li>
|
||||
<li><code>B1</code>: Momentum mean parameter for Adam optimizer. Set to 0.9.</li>
|
||||
<li><code>B2</code>: Momentum variance parameter for Adam optimizer, Set to 0.999.</li>
|
||||
<li><code>EP</code>: Epsilon parameter for Adam, to provide numerical stability. Set to
|
||||
0.00000001.</li>
|
||||
<li><code>DI</code>: How often to print a training or validation progress message and
|
||||
inference snippet. The default prints every 100 training batches.</li>
|
||||
<li><code>SL</code>: The number of characters to print when doing an inference snippet.
|
||||
Default is 200.</li>
|
||||
<li><code>PF</code>: Format string for the checkpoint filename. The default is
|
||||
<code>"cp%02d_%.3f"</code> which includes the epoch and validation loss. You may
|
||||
wish to add a subdirectory to the name to keep checkpoint files out of
|
||||
the current directory.</li>
|
||||
</ul>
|
||||
<h2 id="copyright-and-cc-by-sa-4.0-license">Copyright and CC BY-SA 4.0
|
||||
License:</h2>
|
||||
<p>This file is Copyright (c) 2023 by Landon Curt Noll. All Rights
|
||||
Reserved. You are free to share and adapt this file under the terms of
|
||||
this license:</p>
|
||||
<h2 id="copyright-and-cc-by-sa-4.0-license">Copyright and CC BY-SA 4.0 License:</h2>
|
||||
<p>This file is Copyright (c) 2023 by Landon Curt Noll. All Rights Reserved.
|
||||
You are free to share and adapt this file under the terms of this license:</p>
|
||||
<pre><code>Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)</code></pre>
|
||||
<p>For more information, see:
|
||||
https://creativecommons.org/licenses/by-sa/4.0/</p>
|
||||
<p>For more information, see: https://creativecommons.org/licenses/by-sa/4.0/</p>
|
||||
|
||||
<!-- END: this line ends content for HTML phase 21 by: bin/pandoc-wrapper.sh via bin/md2html.sh -->
|
||||
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|
||||
|
||||
<!-- START: this line starts content generated by: bin/output-index-inventory.sh -->
|
||||
|
||||
<h1 id="inventory-for-2019mills"><a name="inventory"></a>Inventory for
|
||||
2019/mills</h1>
|
||||
<h1 id="inventory-for-2019mills"><a name="inventory"></a>Inventory for 2019/mills</h1>
|
||||
<p><a href="#top">Jump to top</a></p>
|
||||
<h2 id="primary-files">Primary files</h2>
|
||||
<ul>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/prog.c">prog.c</a>
|
||||
- entry source</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/Makefile">Makefile</a>
|
||||
- entry Makefile</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/prog.orig.c">prog.orig.c</a>
|
||||
- original source</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/try.sh">try.sh</a>
|
||||
- how to run</li>
|
||||
<li><a href="2019_mills.tar.bz2">2019_mills.tar.bz2</a> - download entry
|
||||
source</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/prog.c">prog.c</a> - entry source</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/Makefile">Makefile</a> - entry Makefile</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/prog.orig.c">prog.orig.c</a> - original source</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/try.sh">try.sh</a> - how to run</li>
|
||||
<li><a href="2019_mills.tar.bz2">2019_mills.tar.bz2</a> - download entry source</li>
|
||||
</ul>
|
||||
<h2 id="secondary-files">Secondary files</h2>
|
||||
<ul>
|
||||
<li><a href="index.html">index.html</a> - entry home page</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/.entry.json">.entry.json</a>
|
||||
- description of entry in JSON</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/.gitignore">.gitignore</a>
|
||||
- list of files that should not be committed under git</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/.entry.json">.entry.json</a> - description of entry in JSON</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/.gitignore">.gitignore</a> - list of files that should not be committed under git</li>
|
||||
<li><a href=".path">.path</a> - directory path from top directory</li>
|
||||
<li><a href="Eugene_Onegin.cp11_1.188">Eugene_Onegin.cp11_1.188</a> -
|
||||
training data from Eugene Onegin poetry</li>
|
||||
<li><a href="Eugene_Onegin.txt.gz">Eugene_Onegin.txt.gz</a> - compressed
|
||||
Eugene Onegin poetry</li>
|
||||
<li><a
|
||||
href="IOCCC-Rules-Guidelines.cp98_0.175">IOCCC-Rules-Guidelines.cp98_0.175</a>
|
||||
- training data from IOCCC 1984-2019 rules guidelines</li>
|
||||
<li><a
|
||||
href="IOCCC-Rules-Guidelines.txt.gz">IOCCC-Rules-Guidelines.txt.gz</a> -
|
||||
compressed IOCCC rules and guidelines 1984-2019</li>
|
||||
<li><a href="IOCCC-hints.cp09_1.809">IOCCC-hints.cp09_1.809</a> -
|
||||
training data from IOCCC hints file text for 1984-2018</li>
|
||||
<li><a href="IOCCC-hints.txt.gz">IOCCC-hints.txt.gz</a> - compressed
|
||||
IOCCC hints for 1984-2018</li>
|
||||
<li><a
|
||||
href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/README.md">README.md</a>
|
||||
- markdown source for index.html</li>
|
||||
<li><a href="Shakespeare.cp04_1.633">Shakespeare.cp04_1.633</a> -
|
||||
training data from Shakespeare text</li>
|
||||
<li><a href="Shakespeare.txt.gz">Shakespeare.txt.gz</a> - compressed
|
||||
Shakespeare text</li>
|
||||
<li><a href="Eugene_Onegin.cp11_1.188">Eugene_Onegin.cp11_1.188</a> - training data from Eugene Onegin poetry</li>
|
||||
<li><a href="Eugene_Onegin.txt.gz">Eugene_Onegin.txt.gz</a> - compressed Eugene Onegin poetry</li>
|
||||
<li><a href="IOCCC-Rules-Guidelines.cp98_0.175">IOCCC-Rules-Guidelines.cp98_0.175</a> - training data from IOCCC 1984-2019 rules guidelines</li>
|
||||
<li><a href="IOCCC-Rules-Guidelines.txt.gz">IOCCC-Rules-Guidelines.txt.gz</a> - compressed IOCCC rules and guidelines 1984-2019</li>
|
||||
<li><a href="IOCCC-hints.cp09_1.809">IOCCC-hints.cp09_1.809</a> - training data from IOCCC hints file text for 1984-2018</li>
|
||||
<li><a href="IOCCC-hints.txt.gz">IOCCC-hints.txt.gz</a> - compressed IOCCC hints for 1984-2018</li>
|
||||
<li><a href="https://github.com/ioccc-src/temp-test-ioccc/blob/master/2019/mills/README.md">README.md</a> - markdown source for index.html</li>
|
||||
<li><a href="Shakespeare.cp04_1.633">Shakespeare.cp04_1.633</a> - training data from Shakespeare text</li>
|
||||
<li><a href="Shakespeare.txt.gz">Shakespeare.txt.gz</a> - compressed Shakespeare text</li>
|
||||
</ul>
|
||||
|
||||
<!-- END: next line ends content generated by: bin/output-index-inventory.sh -->
|
||||
|
||||
Reference in new issue
Block a user