make make cpclean # Let this run for about about an hour and then kill it ./prog Shakespeare.txt ./prog < $(< ls -1tr cp* | tail -1) | head -100
# If you are on a 64-bit system: make test-64bit less IOCCC-Rules-Guidelines.output.txt less IOCCC-hints.output.txt less Eugene_Onegin.output.txt # However, as the binary model files used to produce the output are in an implementation-specific format, # your mileage may vary.
Can a machine learn?
Some say so.
But can a machine learn to write like Shakespeare,
or tweet like Trump?
Can it write rules and guidelines for the IOCCC?
You decide. :-)
OMLET is the Obfuscated Machine Learning Environment Toolkit, a micro-framework for experimenting with recurrent neural networks. OMLET lets you build, train and evaluate deep neural networks. Why invest hours reading documentation and megabytes of disk space on a full-featured DNN framework like TensorFlow or Torch when you can have full RNN functionality in less than 4 KB!
OMLET has the following features:
OMLET is based on Andrej Karpathy’s character-level language model as described in his blog post The Unreasonable Effectiveness of Recurrent Neural Networks. I’ve included a small sample dataset to use for training, but you can have even more fun by downloading some larger datasets:
OMLET has three operating modes:
For your first OMLET experiment, we will try training a simple single-level RNN to write some Shakespere plays. Start by typing
After it builds, train it using
This will immediately start outputting gibberish to the output, e.g.
./prog shakespere.txt sins ohennAu T-teooclelp tiThoWy g nlakuafy e sselW usnsofueB Aoee pasfUsuslhe ooM ot Wou moy me neltAl -no IoyI mhuyakse inT-l chu ghenn ffo? fnsoe yhyye ue nnfrlass heUthole saounlcesyee pee t, T0:0% 3.210888 o',,vU An ,hTf lnm Far rur:s moilt WoEgrv wonds mith Aog thernw Rni So co Nnd : For an bImy pgafoun: Wf'r hom wortiverita int fod mous Eheledet, Tho he theket nonS wnu-ang dorlaMSp nrocWiSe tflg 'o. T0:0% 2.995950 d whecedhencrysesil yr bn, we hh y thiwt hut fithlot, Fmdy s he alt 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
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
This tells you that we are 1% through training epoch 0, and that the training loss is about 2.88. As the training continues, the training loss will reduce and the generated snippets will improve quickly:
ses, kuth LAs of the wish, As, I nos you, Yov not to nalll, Tr tot wonds. First Sondy, llt lrte, our, tw. First. BRUTUS: Helsting the kith gops of hoch Whay, fars surd what to, The cownens golt te. T0:12% 2.259114 eplerrotrur tandans one wiok thy or thach and cullice ded yourssting And wours: Whed ur surt. SINENIUS: On we lain bith rerytund: tich lon hyivetetgor. VOLUONIA: He brich nom dove worthan then wise, T0:13% 2.254926
It’s already started to figure out things about Shakespere 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.
Eventually, we will finish with the training data set and move on to a validation cycle:
y fath onother, I sucess, For I me the west crare. TRANIO: Whow and'd have not to had you you one in my lapteny she very ame come me a gut and shourd aghir you as ignested; shend to make I strem To h T0:99% 1.924063 notnce gaud and is nicked thou day, ha the dusing you disaid: in thim, you things in ere thee thus erile Iht that tare theme my hast thesp thou shay: thou not eaten-or-ho-bess resing: I the but had d T0:99% 1.923128 V0:0% 1.678907 V0:9% 1.700527 V0:18% 1.733179 V0:27% 1.714891 V0:36% 1.716672 V0:45% 1.782946 V0:54% 1.835629 V0:63% 1.876108 V0:72% 1.906814 V0:81% 1.924096 V0:90% 1.954492 V0:99% 1.969287 serfs you'll alliencseard: We got you? before I say. Farstred dentlentecaly, sir, I it one bosticield All me the backnour mino, Whith capitaned mid! but stell the ifvemion Willerity. First Cumfol of T1:0% 1.885619
Validation cycles are used to test the network to see if it has learned to generalize – how well 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
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 overfitting or underfitting.
As part of the training process, the data set (which for OMLET is the
shakespere.txt file you gave on the command line) is divided into
training and validation sets (by default, 95% of the data is used for
training, but like most OMLET parameters, you can change this at compile-time).
At the end of the validation run, OMLET writes out a checkpoint file with a
cp01_1.970. 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
You can continue training from a previous checkpoint by providing the checkpoint file name as the second parameter, for example:
./prog shakespere.txt cp01_1.970
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
Control-C. 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.
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 standard input (not on the command line) and hence must be run with a command like
./prog < cp55_1.807
Running it produces an infinite amount of generated output, until you hit
Control-C to stop it.
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.
The default network for OMLET (the one you get if you type
make with the
prog) is the simplest recurrent neural network. It looks
h = tanh(Wxh * x + Whh * h' + Bh) y = Why * h + By
xis the input vector
yis the output vector
his the hidden state vector
h'is the previous value of
Whyare weight matrices
Byare bias vectors.
tanhis the hyperbolic tangent function
B’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.
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
OMLET will create an ADALINE network that does
y = Wxy * x + By
This simple linear feed-forward network. You can run it with
The linear network won’t be able to get past the gibberish stage, because it lacks history:
./lin1 shakespeare.txt UERond w, Gir: KINof s, mesther s thouth. E: KINTret, at fu, GOMy t, as sth kesewit sooos atse ang k, ck, Sotheouserivesthecowhet been's, t he, h nre; t and, har wiread of pincer cedst sur has, ut: T14:67% 2.465115 UKESpan, NGaromy soreate e m esewfoure pamitherarjulthengeoly tl. NG s at e! w. WAllinoully? Wamisw ofilem: I'delandinarrstath har aksubly s cath Whern t Is, weciss: GLat s; llde. Y aterit dsthence T14:67% 2.465404
It is able to guess at what character is likely to follow the current one (by doing a linear regression), but it lacks any history beyond that to guide it.
You might be wondering about the role of the
tanh function in the RNN.
tanh acts as an activation function which adds nonlinearity
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 perceptron) 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
We can try to improve the RNN’s performance by stacking RNN modules atop each other:
h1 = RNN(h1', x) h2 = RNN(h2', h1) y = Why * h2 + By
RNN(h, x) 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
IMPORTANT NOTE: Since OMLET uses the system stack for network storage, larger networks may cause OMLET to crash (typically with a message like
Segmentation fault) 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
bashshells, you can view the hard limit with
ulimit -Hsand set it with
ulimit -s 65532(replacing
65532with the actual hard limit). On
tcshshells, you can view the hard limit with
limit -h stacksizeand set it with
limit stacksize 65532(replacing
65532with the actual hard limit).
You can try the deeper network by doing
make rnn3 if you want a three-layer RNN) and train it with
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 vanishing and exploding gradient problem, which might keep it from ever reaching its potential.
RNNs are particularly hard to train because the they are trained using bankpropagation through time. 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.
Long Short Term Memory networks (also called LSTMs) were developed to solve this problem. Christopher Olah gives a good description of them at his blog posting. You can build a two-level LSTM by doing
and train with it with
The LSTM is much easier to train because it explicitly decides how to update its hidden state via “gates”. These gates are called
The basic LSTM equations are
f = sigmoid(Wxf * x + Whf * h' + Bf) i = sigmoid(Wxi * x + Whi * h' + Bi) o = sigmoid(Wxo * x + Who * h' + Bo) c = f * c' + i * tanh(Wxc * x + Whc * h' + Bc) h = o * tanh(c)
xis the input vector
his the hidden state (and the output to the next layer)
cis the cell state which represents the “memory” of the LSTM
c‘ are the previous values of
fis the forget gate that tells the LSTM what portion of the hidden state to forget
iis the input gate that tells the LSTM what portion of the input vector to pay attention to
ois the output gate that tells the LSTM what portion of the cell state to use to generate the hidden state
Whcare trainable parameter matrices
Bcare trainable bias vectors
tanhis the hyperbolic tangent function
sigmoidis the logistic function
There are several LSTM variants (see C. Olah’s blog post for more examples). One important one is the gated recurrent unit. 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
Makefile 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
Makefile. Networks are passed in on the
compiler’s command-line by using
-D directives. The network is defined by
-DNW='...' command which consists of a series of comma-separated
assignments. For example, the simple one-layer RNN could be defined like
-DNW=` x = I(n), hp = I(128), \ h = C(hp, T(A(L(128, x), L(128, hp)))), \ y = L(n, h)'
The network declares
x as an input vector (there must be a declaration for
x). It is declared as
I(n), which is an input vector of size
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 one-hot vector based on the current input
The second declaration,
hp, declares the previous hidden state vector (what
h' 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.
The third line is the core of the RNN. It sets
h, the hidden vector output
to be the sum of two linear elements specified by
takes two parameters – the output vector size (which must match the size of
h) and the input vector.
L will compute
y = W * x + B where each
has its own
W (weight) and
B (bias) training parameters. Both
hp are sent through
L and the result passed through the
which does vector addition. That result is passed through
T which does
Next, we wrap the whole thing with the
h, causing the new value of
h to be passed to the
hp vector on
the next iteration of the algorithm (allowing the RNN to retain state in
Finally, the whole result is passed through another instance of
L, this time
producing a vector of size
n, which will have the negative log
likelihood function. This is assigned to
y, which is the output of
the network (and hence must also be declared).
OMLET will take the
y result and pass it through the softmax 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.
As an example of a more complicated network, we can look at a two-layer GRU network:
-DHS=128, \ -DNW=' x = I(n), \ y = L(n, MD(MD(x)))' \ -DBK=' hp = I(HS), \ z = S(A(L(HS, x), L(HS, hp))), \ r = S(A(L(HS, x), L(HS, hp))), \ c = T(A(L(HS, x), L(HS, hp))), \ zc = OG(1, -1, z), \ h = C(hp, A(M(zc, hp), M(z, c))), \ y = h'
We are using a few new tricks here – first, we are defining
HS as the size
of the hidden and cell vectors. There’s nothing special about this name, its
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
x and has
the matrix that converts the
HS-sized hidden vector back to the
alphabet vector… but it now calls
MD, which is the user-definable
module (here we are using it twice, to have two cascaded GRU blocks). The
MD function performs the sub-network defined by the
parameter (specified in the
-DBK='...' setting). This sub-module again
x parameter and produces a
y output. Inside it, we declare
h, the previous and current state vector, plus equations for the
various GRU gates (these use
S for the sigmoid activation function).
One final new call is
OG which does offset and gain, performing
y = offset + gain * x where
offset (the first parameter) and
second) are constants. We are using this here to compute
(1 - z) for the
GRU’s linear interpolator.
The full set of available function blocks follows:
I(s): declares a vector (input or state) of size
L(s, x): learnable linear function
y = W * x + Bwith an output vector size of
CM(x): learnable element-wise gain function
y = W * x
A(a, b): element-wise add:
y = a + b
M(a, b): element-wise multiply:
y = a * b
S(x): sigmoid activation function
y = sigmoid(x)
T(x): hyperbolic tangent activation function
y = tanh(x)
C(xp, x): copy
xpin the next time step (propagate through time)
OG(o, g, x): apply a constant offset and gain:
y = o + g * x
MD(x): apply the sub-network specified by
Note: even if you don’t use
MD in your network, you should still define
BK by adding
-DBK='y=x' to the command line, otherwise you will get a
OMLET has a large number of training and inference parameters which can be
changed by the user. All of these are set by
-D on the compile command line.
The list of hyperparameters follows:
TP: 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.
TR: 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%.
LR: The initial learning rate, The default is 0.002.
LE: The epoch where the learning rate will start decaying. Defaults to epoch 10.
LD: Learning rate decay, per epoch (after
LEepochs). The learning rate is scaled by this number. Default is 0.97
WD: Weight-decay parameter, to promote regularizaiton. The default is 0.00008.
RS: The random scale for weight initialization. Weight parameters will be initialized to be between
+RS. The default is 0.15.
CL: Clamp value for gradients. Gradients will be limited to the range
+CL. Default is 5.
B1: Momentum mean parameter for Adam optimizer. Set to 0.9.
B2: Momentum variance parameter for Adam optimizer, Set to 0.999.
EP: Epsilon parameter for Adam, to provide numerical stability. Set to 0.00000001.
DI: How often to print a training or validation progress message and inference snippet. The default prints every 100 training batches.
SL: The number of characters to print when doing an inference snippet. Default is 200.
PF: Format string for the checkpoint filename. The default is
"cp%02d_%.3f"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.
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Leo Broukhis, Simon Cooper, Landon Curt Noll
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