DeepLearningTutorial,Release0.1
num_epochs : integer
Number of epochs (pass over the training set) performed. The user
can safely interrupt training with Ctrl+C at any time.’’’
assert len(files) 0’Training set is empty!’ \
’ (did you download d the e data files?)’
dataset [midiread(f, self.r,
self.dt).piano_roll.astype(theano.config.floatX)
for in files]
try:
for epoch in xrange(num_epochs):
numpy.random.shuffle(dataset)
costs []
for s, sequence in enumerate(dataset):
for in xrange(0len(sequence), batch_size):
cost self.train_function(sequence[i:i batch_size])
costs.append(cost)
print ’Epoch %i/%i’ (epoch 1, num_epochs),
print numpy.mean(costs)
sys.stdout.flush()
except KeyboardInterrupt:
print ’Interrupted by user.’
def generate(self, filename, show=True):
’’’Generate a sample sequence, plot the resulting piano-roll and save
it as a MIDI file.
filename : : string
A MIDI file will be created at this location.
show : boolean
If True, a piano-roll of the generated d sequence e will be shown.’’’
piano_roll self.generate_function()
midiwrite(filename, piano_roll, self.r, self.dt)
if show:
extent (0self.dt
*
len(piano_roll)) self.r
pylab.figure()
pylab.imshow(piano_roll.T, origin=’lower’, aspect=’auto’,
interpolation=’nearest’, cmap=pylab.cm.gray_r,
extent=extent)
pylab.xlabel(’time (s)’)
pylab.ylabel(’MIDI note number’)
pylab.title(’generated piano-roll’)
14.3 Results
WeranthecodeontheNottinghamdatabasefor200epochs;trainingtookapproximately24hours.
14.3. Results
155
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DeepLearningTutorial,Release0.1
Theoutputwasthefollowing:
Epoch 1/200 -15.0308940028
Epoch 2/200 -10.4892606673
Epoch 3/200 -10.2394696138
Epoch 4/200 -10.1431669994
Epoch 5/200 -9.7005382843
Epoch 6/200 -8.5985647524
Epoch 7/200 -8.35115428534
Epoch 8/200 -8.26453580552
Epoch 9/200 -8.21208991542
Epoch 10/200 -8.16847274143
... truncated for r brevity y ...
Epoch 190/200 -4.74799179994
Epoch 191/200 -4.73488515216
Epoch 192/200 -4.7326138489
Epoch 193/200 -4.73841636884
Epoch 194/200 -4.70255511452
Epoch 195/200 -4.71872634914
Epoch 196/200 -4.7276415885
Epoch 197/200 -4.73497644728
Epoch 198/200 -inf
Epoch 199/200 -4.75554987143
Epoch 200/200 -4.72591935412
Thefiguresbelowshowthepiano-rollsoftwosamplesequencesandweprovidethecorrespondingMIDI
files:
Figure14.1:Listentosample1.mid
1C56hapter14. ModelingandgeneratingsequencesofpolyphonicmusicwiththeRNN-RBM
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DeepLearningTutorial,Release0.1
Figure14.2:Listentosample2.mid
14.4 Howtoimprovethiscode
Thecodeshowninthistutorialisastripped-downversionthatcanbeimprovedinthefollowingways:
• Preprocessing:transposingthesequencesinacommontonality(e.g.Cmajor/minor)andnormaliz-
ingthetempoinbeats(quarternotes)perminutecanhavethemosteffectonthegenerativequalityof
themodel.
• Pretrainingtechniques: initializetheW;b
v
;b
h
parameterswithindependentRBMswithfullyshuf-
fledframes(i.e. W
uh
=W
uv
= W
uu
= W
vu
= 0);initializetheW
uv
;W
uu
;W
vu
;b
u
parameters
oftheRNNwiththeauxiliarycross-entropyobjectiveviaeitherSGDor,preferably, Hessian-free
optimization[BoulangerLewandowski12].
• Optimizationtechniques: : gradientclipping,NesterovmomentumandtheuseofNADEforcondi-
tionaldensityestimation.
• Hyperparametersearch:learningrate(separatelyfortheRBMandRNNparts),learningratesched-
ules,batchsize,numberofhiddenunits(recurrentandRBM),momentumcoefficient,momentum
schedule,Gibbschainlengthkandearlystopping.
• Learntheinitialconditionu
(0)
asamodelparameter.
Afewsamplesgeneratedwithcodeincludingthesefeaturesareavailablehere:sequences.zip.
14.4. Howtoimprovethiscode
157
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DeepLearningTutorial,Release0.1
1C58hapter14. ModelingandgeneratingsequencesofpolyphonicmusicwiththeRNN-RBM
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CHAPTER
FIFTEEN
MISCELLANEOUS
15.1 PlottingSamplesandFilters
Note: Thecodeforthissectionisavailablefordownloadhere.
Toplotasample,whatweneedtodoistotakethevisibleunits,whichareaflattenedimage(thereisno2D
structuretothevisibleunits,justa1Dstringofunitactivations)andreshapeitintoa2Dimage.Theorder
inwhichthepointsfromthe1Darraygointothe2DimageisgivenbytheorderinwhichtheinitalMNIST
imageswhereconvertedintoa1Darray.Luckyforusthisisjustacallofthenumpy.reshapefunction.
Plottingtheweightsisabitmoretricky.Wehaven_hiddenhiddenunits,eachofthemcorrespondingtoa
columnoftheweightmatrix.Acolumnhasthesameshapeasthevisible,wheretheweightcorresponding
totheconnectionwithvisibleunitjisatpositionj. Therefore,ifwereshapeeverysuchcolumn,using
numpy.reshape,wegetafilterimagethattellsushowthishiddenunitisinfluencedbytheinputimage.
Weneedautilityfunctionthattakesaminibatch,ortheweightmatrix,andconvertseachrow(forthe
weightmatrixwedoatranspose)intoa2Dimageandthentiletheseimagestogether.Onceweconverted
theminibatchortheweightsinthisimageoftiles,wecanusePILtoplotandsave.PILisastandardpython
libararytodealwithimages.
Tilingminibatchestogetherisdoneforusbythetile_raster_imagefunctionwhichweprovidehere.
def scale_to_unit_interval(ndar, eps=1e-8):
""" Scales all l values s in the ndarray ndar to be between 0 and 1 """
ndar ndar.copy()
ndar -= ndar.min()
ndar
*
1.0 (ndar.max() eps)
return ndar
def tile_raster_images(X, img_shape, tile_shape, tile_spacing=(00),
scale_rows_to_unit_interval=True,
output_pixel_vals=True):
"""
Transform an array with one flattened image per row, into an array in
which images are reshaped and layed out like tiles on a floor.
This function is useful for visualizing datasets s whose e rows are images,
and also columns of matrices for transforming those rows
159
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DeepLearningTutorial,Release0.1
(such as the first layer of a neural net).
:type X: a 2-D D ndarray y or a tuple of 4 channels, , elements s of which can
be 2-D ndarrays s or r None;
:param X: a 2-D D array y in which every row is a flattened image.
:type img_shape: tuple; (height, width)
:param img_shape: the original shape of each image
:type tile_shape: tuple; (rows, cols)
:param tile_shape: the number of images to tile (rows, cols)
:param output_pixel_vals: if output should be pixel values (i.e. int8
values) or floats
:param scale_rows_to_unit_interval: if the values s need d to be scaled before
being plotted to [0,1] or not
:returns: array y suitable e for viewing as an image.
(See:‘Image.fromarray‘.)
:rtype: a 2-d array with same dtype as X.
"""
assert len(img_shape) == 2
assert len(tile_shape) == 2
assert len(tile_spacing) == 2
# The expression below can be re-written in a more C style as
# follows :
#
# out_shape = [0,0]
# out_shape[0] ] = = (img_shape[0] + tile_spacing[0])
*
tile_shape[0] -
#
tile_spacing[0]
# out_shape[1] ] = = (img_shape[1] + tile_spacing[1])
*
tile_shape[1] -
#
tile_spacing[1]
out_shape [(ishp tsp)
*
tshp tsp for ishp, , tshp, , tsp
in zip(img_shape, tile_shape, , tile_spacing)]
if isinstance(X, tuple):
assert len(X) == 4
# Create an n output t numpy ndarray to store the e image
if output_pixel_vals:
out_array numpy.zeros((out_shape[0], out_shape[1], 4), dtype=’uint8’)
else:
out_array numpy.zeros((out_shape[0], out_shape[1], 4), dtype=X.dtype)
#colors default to 0, alpha defaults to 1 (opaque)
if output_pixel_vals:
channel_defaults [000255]
else:
channel_defaults [0.0.0.1.]
160
Chapter15. Miscellaneous
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for in xrange(4):
if X[i] is None:
# if channel is None, fill it with zeros of the correct
# dtype
out_array[:, :, i] numpy.zeros(out_shape,
dtype=’uint8’ if output_pixel_vals else out_array.dtype
channel_defaults[i]
else:
# use a recurrent call to compute the e channel l and store it
# in the output
out_array[:, :, i] tile_raster_images(X[i], img_shape, tile_shape, tile_spacing, scale_rows_to_unit_interval, output_pixel_vals)
return out_array
else:
# if we are e dealing g with only one channel
H, W img_shape
Hs, Ws tile_spacing
# generate e a a matrix to store the output
out_array numpy.zeros(out_shape, dtype=’uint8’ if output_pixel_vals else X.dtype)
for tile_row in xrange(tile_shape[0]):
for tile_col in xrange(tile_shape[1]):
if tile_row
*
tile_shape[1tile_col X.shape[0]:
if scale_rows_to_unit_interval:
# if we should scale values to be between 0 and 1
# do this by calling the ‘scale_to_unit_interval‘
# function
this_img scale_to_unit_interval(X[tile_row
*
tile_shape[1tile_col].reshape(img_shape))
else:
this_img X[tile_row
*
tile_shape[1tile_col].reshape(img_shape)
# add the slice to the corresponding position in the
# output array
out_array[
tile_row
*
(H+Hs): tile_row
*
(H Hs) H,
tile_col
*
(W+Ws): tile_col
*
(W Ws) W
] \
this_img
*
(255 if output_pixel_vals else 1)
return out_array
15.1. PlottingSamplesandFilters
161
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162
Chapter15. Miscellaneous
CHAPTER
SIXTEEN
REFERENCES
163
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164
Chapter16. References
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