Note
Click here to download the full example code
DS-CNN/KWS inference
This tutorial illustrates how to build a basic speech recognition Akida network that recognizes thirty-two different words.
The model will be first defined as a CNN and trained in Keras, then converted using the CNN2SNN toolkit.
This example uses a Keyword Spotting Dataset prepared using TensorFlow audio recognition example utils.
The words to recognize are first converted to spectrogram images that allows us to use a model architecture that is typically used for image recognition tasks.
1. Load the preprocessed dataset
The TensorFlow speech_commands dataset is used for training and validation. All keywords except “backward”, “follow” and “forward”, are retrieved. These three words are kept to illustrate the edge learning in this edge example. The data are not directly used for training. They are preprocessed, transforming the audio files into MFCC features, well-suited for CNN networks. A pickle file containing the preprocessed data is available on our data server.
import pickle
from tensorflow.keras.utils import get_file
# Fetch pre-processed data for 32 keywords
fname = get_file(
fname='kws_preprocessed_all_words_except_backward_follow_forward.pkl',
origin="http://data.brainchip.com/dataset-mirror/kws/kws_preprocessed_all_words_except_backward_follow_forward.pkl",
cache_subdir='datasets/kws')
with open(fname, 'rb') as f:
[_, _, x_valid, y_valid, _, _, word_to_index, _] = pickle.load(f)
# Preprocessed dataset parameters
num_classes = len(word_to_index)
print("Wanted words and labels:\n", word_to_index)
Downloading data from http://data.brainchip.com/dataset-mirror/kws/kws_preprocessed_all_words_except_backward_follow_forward.pkl
8192/62628765 [..............................] - ETA: 0s
180224/62628765 [..............................] - ETA: 18s
524288/62628765 [..............................] - ETA: 13s
917504/62628765 [..............................] - ETA: 10s
1318912/62628765 [..............................] - ETA: 9s
1835008/62628765 [..............................] - ETA: 8s
2408448/62628765 [>.............................] - ETA: 7s
2998272/62628765 [>.............................] - ETA: 7s
3440640/62628765 [>.............................] - ETA: 7s
3842048/62628765 [>.............................] - ETA: 7s
4300800/62628765 [=>............................] - ETA: 7s
4702208/62628765 [=>............................] - ETA: 7s
5144576/62628765 [=>............................] - ETA: 7s
5562368/62628765 [=>............................] - ETA: 6s
6021120/62628765 [=>............................] - ETA: 6s
6463488/62628765 [==>...........................] - ETA: 6s
6938624/62628765 [==>...........................] - ETA: 6s
7389184/62628765 [==>...........................] - ETA: 6s
7880704/62628765 [==>...........................] - ETA: 6s
8355840/62628765 [===>..........................] - ETA: 6s
8847360/62628765 [===>..........................] - ETA: 6s
9355264/62628765 [===>..........................] - ETA: 6s
9838592/62628765 [===>..........................] - ETA: 6s
10330112/62628765 [===>..........................] - ETA: 5s
10838016/62628765 [====>.........................] - ETA: 5s
11378688/62628765 [====>.........................] - ETA: 5s
11862016/62628765 [====>.........................] - ETA: 5s
11968512/62628765 [====>.........................] - ETA: 5s
12189696/62628765 [====>.........................] - ETA: 5s
12345344/62628765 [====>.........................] - ETA: 6s
12591104/62628765 [=====>........................] - ETA: 6s
12787712/62628765 [=====>........................] - ETA: 6s
12992512/62628765 [=====>........................] - ETA: 6s
13213696/62628765 [=====>........................] - ETA: 6s
13443072/62628765 [=====>........................] - ETA: 6s
13680640/62628765 [=====>........................] - ETA: 6s
13926400/62628765 [=====>........................] - ETA: 6s
14188544/62628765 [=====>........................] - ETA: 6s
14450688/62628765 [=====>........................] - ETA: 6s
14729216/62628765 [======>.......................] - ETA: 6s
15024128/62628765 [======>.......................] - ETA: 6s
15294464/62628765 [======>.......................] - ETA: 6s
15589376/62628765 [======>.......................] - ETA: 6s
15908864/62628765 [======>.......................] - ETA: 6s
16236544/62628765 [======>.......................] - ETA: 6s
16547840/62628765 [======>.......................] - ETA: 6s
16900096/62628765 [=======>......................] - ETA: 6s
17235968/62628765 [=======>......................] - ETA: 6s
17588224/62628765 [=======>......................] - ETA: 6s
17965056/62628765 [=======>......................] - ETA: 6s
18317312/62628765 [=======>......................] - ETA: 6s
18702336/62628765 [=======>......................] - ETA: 6s
19095552/62628765 [========>.....................] - ETA: 6s
19488768/62628765 [========>.....................] - ETA: 6s
19898368/62628765 [========>.....................] - ETA: 5s
20291584/62628765 [========>.....................] - ETA: 5s
20701184/62628765 [========>.....................] - ETA: 5s
21110784/62628765 [=========>....................] - ETA: 5s
21536768/62628765 [=========>....................] - ETA: 5s
21921792/62628765 [=========>....................] - ETA: 5s
22364160/62628765 [=========>....................] - ETA: 5s
22814720/62628765 [=========>....................] - ETA: 5s
23240704/62628765 [==========>...................] - ETA: 5s
23691264/62628765 [==========>...................] - ETA: 5s
23920640/62628765 [==========>...................] - ETA: 5s
24305664/62628765 [==========>...................] - ETA: 5s
24657920/62628765 [==========>...................] - ETA: 5s
24993792/62628765 [==========>...................] - ETA: 5s
25370624/62628765 [===========>..................] - ETA: 5s
25755648/62628765 [===========>..................] - ETA: 5s
26132480/62628765 [===========>..................] - ETA: 4s
26542080/62628765 [===========>..................] - ETA: 4s
26951680/62628765 [===========>..................] - ETA: 4s
27361280/62628765 [============>.................] - ETA: 4s
27787264/62628765 [============>.................] - ETA: 4s
28221440/62628765 [============>.................] - ETA: 4s
28663808/62628765 [============>.................] - ETA: 4s
29130752/62628765 [============>.................] - ETA: 4s
29573120/62628765 [=============>................] - ETA: 4s
30056448/62628765 [=============>................] - ETA: 4s
30531584/62628765 [=============>................] - ETA: 4s
31023104/62628765 [=============>................] - ETA: 4s
31506432/62628765 [==============>...............] - ETA: 4s
32014336/62628765 [==============>...............] - ETA: 4s
32325632/62628765 [==============>...............] - ETA: 4s
32776192/62628765 [==============>...............] - ETA: 3s
33161216/62628765 [==============>...............] - ETA: 3s
33529856/62628765 [===============>..............] - ETA: 3s
33931264/62628765 [===============>..............] - ETA: 3s
34308096/62628765 [===============>..............] - ETA: 3s
34725888/62628765 [===============>..............] - ETA: 3s
35135488/62628765 [===============>..............] - ETA: 3s
35561472/62628765 [================>.............] - ETA: 3s
35987456/62628765 [================>.............] - ETA: 3s
36429824/62628765 [================>.............] - ETA: 3s
36864000/62628765 [================>.............] - ETA: 3s
37298176/62628765 [================>.............] - ETA: 3s
37732352/62628765 [=================>............] - ETA: 3s
38174720/62628765 [=================>............] - ETA: 3s
38625280/62628765 [=================>............] - ETA: 3s
39108608/62628765 [=================>............] - ETA: 3s
39600128/62628765 [=================>............] - ETA: 2s
40108032/62628765 [==================>...........] - ETA: 2s
40615936/62628765 [==================>...........] - ETA: 2s
41082880/62628765 [==================>...........] - ETA: 2s
41385984/62628765 [==================>...........] - ETA: 2s
41639936/62628765 [==================>...........] - ETA: 2s
41861120/62628765 [===================>..........] - ETA: 2s
42041344/62628765 [===================>..........] - ETA: 2s
42188800/62628765 [===================>..........] - ETA: 2s
42336256/62628765 [===================>..........] - ETA: 2s
42483712/62628765 [===================>..........] - ETA: 2s
42647552/62628765 [===================>..........] - ETA: 2s
42745856/62628765 [===================>..........] - ETA: 2s
42852352/62628765 [===================>..........] - ETA: 2s
42950656/62628765 [===================>..........] - ETA: 2s
43048960/62628765 [===================>..........] - ETA: 2s
43163648/62628765 [===================>..........] - ETA: 2s
43270144/62628765 [===================>..........] - ETA: 2s
43401216/62628765 [===================>..........] - ETA: 2s
43540480/62628765 [===================>..........] - ETA: 2s
43687936/62628765 [===================>..........] - ETA: 2s
43843584/62628765 [====================>.........] - ETA: 2s
43941888/62628765 [====================>.........] - ETA: 2s
44056576/62628765 [====================>.........] - ETA: 2s
44154880/62628765 [====================>.........] - ETA: 2s
44261376/62628765 [====================>.........] - ETA: 2s
44376064/62628765 [====================>.........] - ETA: 2s
44507136/62628765 [====================>.........] - ETA: 2s
44654592/62628765 [====================>.........] - ETA: 2s
44810240/62628765 [====================>.........] - ETA: 2s
44974080/62628765 [====================>.........] - ETA: 2s
45146112/62628765 [====================>.........] - ETA: 2s
45334528/62628765 [====================>.........] - ETA: 2s
45514752/62628765 [====================>.........] - ETA: 2s
45694976/62628765 [====================>.........] - ETA: 2s
45907968/62628765 [====================>.........] - ETA: 2s
46112768/62628765 [=====================>........] - ETA: 2s
46333952/62628765 [=====================>........] - ETA: 2s
46563328/62628765 [=====================>........] - ETA: 2s
46800896/62628765 [=====================>........] - ETA: 2s
47054848/62628765 [=====================>........] - ETA: 2s
47308800/62628765 [=====================>........] - ETA: 2s
47562752/62628765 [=====================>........] - ETA: 2s
47849472/62628765 [=====================>........] - ETA: 2s
48128000/62628765 [======================>.......] - ETA: 2s
48414720/62628765 [======================>.......] - ETA: 2s
48726016/62628765 [======================>.......] - ETA: 2s
49020928/62628765 [======================>.......] - ETA: 2s
49348608/62628765 [======================>.......] - ETA: 2s
49668096/62628765 [======================>.......] - ETA: 2s
50012160/62628765 [======================>.......] - ETA: 1s
50339840/62628765 [=======================>......] - ETA: 1s
50708480/62628765 [=======================>......] - ETA: 1s
51036160/62628765 [=======================>......] - ETA: 1s
51404800/62628765 [=======================>......] - ETA: 1s
51781632/62628765 [=======================>......] - ETA: 1s
52125696/62628765 [=======================>......] - ETA: 1s
52477952/62628765 [========================>.....] - ETA: 1s
52871168/62628765 [========================>.....] - ETA: 1s
53116928/62628765 [========================>.....] - ETA: 1s
53452800/62628765 [========================>.....] - ETA: 1s
53747712/62628765 [========================>.....] - ETA: 1s
54059008/62628765 [========================>.....] - ETA: 1s
54386688/62628765 [=========================>....] - ETA: 1s
54722560/62628765 [=========================>....] - ETA: 1s
55058432/62628765 [=========================>....] - ETA: 1s
55402496/62628765 [=========================>....] - ETA: 1s
55746560/62628765 [=========================>....] - ETA: 1s
56115200/62628765 [=========================>....] - ETA: 1s
56500224/62628765 [==========================>...] - ETA: 0s
56868864/62628765 [==========================>...] - ETA: 0s
57065472/62628765 [==========================>...] - ETA: 0s
57303040/62628765 [==========================>...] - ETA: 0s
57458688/62628765 [==========================>...] - ETA: 0s
57606144/62628765 [==========================>...] - ETA: 0s
57753600/62628765 [==========================>...] - ETA: 0s
57917440/62628765 [==========================>...] - ETA: 0s
58097664/62628765 [==========================>...] - ETA: 0s
58277888/62628765 [==========================>...] - ETA: 0s
58466304/62628765 [===========================>..] - ETA: 0s
58654720/62628765 [===========================>..] - ETA: 0s
58867712/62628765 [===========================>..] - ETA: 0s
59097088/62628765 [===========================>..] - ETA: 0s
59326464/62628765 [===========================>..] - ETA: 0s
59547648/62628765 [===========================>..] - ETA: 0s
59613184/62628765 [===========================>..] - ETA: 0s
59785216/62628765 [===========================>..] - ETA: 0s
59883520/62628765 [===========================>..] - ETA: 0s
59998208/62628765 [===========================>..] - ETA: 0s
60121088/62628765 [===========================>..] - ETA: 0s
60194816/62628765 [===========================>..] - ETA: 0s
60284928/62628765 [===========================>..] - ETA: 0s
60366848/62628765 [===========================>..] - ETA: 0s
60456960/62628765 [===========================>..] - ETA: 0s
60571648/62628765 [============================>.] - ETA: 0s
60686336/62628765 [============================>.] - ETA: 0s
60817408/62628765 [============================>.] - ETA: 0s
60964864/62628765 [============================>.] - ETA: 0s
61120512/62628765 [============================>.] - ETA: 0s
61284352/62628765 [============================>.] - ETA: 0s
61464576/62628765 [============================>.] - ETA: 0s
61652992/62628765 [============================>.] - ETA: 0s
61849600/62628765 [============================>.] - ETA: 0s
62062592/62628765 [============================>.] - ETA: 0s
62275584/62628765 [============================>.] - ETA: 0s
62480384/62628765 [============================>.] - ETA: 0s
62628765/62628765 [==============================] - 11s 0us/step
Wanted words and labels:
{'six': 23, 'three': 25, 'seven': 21, 'bed': 1, 'eight': 6, 'yes': 31, 'cat': 3, 'on': 18, 'one': 19, 'stop': 24, 'two': 27, 'house': 11, 'five': 7, 'down': 5, 'four': 8, 'go': 9, 'up': 28, 'learn': 12, 'no': 16, 'bird': 2, 'zero': 32, 'nine': 15, 'visual': 29, 'wow': 30, 'sheila': 22, 'marvin': 14, 'off': 17, 'right': 20, 'left': 13, 'happy': 10, 'dog': 4, 'tree': 26, '_silence_': 0}
2. Load a pre-trained native Keras model
The model consists of:
a first convolutional layer accepting dense inputs (images),
several separable convolutional layers preserving spatial dimensions,
a global pooling reducing the spatial dimensions to a single pixel,
a last separable convolutional to reduce the number of outputs
a final fully connected layer to classify words
All layers are followed by a batch normalization and a ReLU activation.
This model was obtained with unconstrained float weights and activations after 16 epochs of training.
from tensorflow.keras.models import load_model
# Retrieve the model file from the BrainChip data server
model_file = get_file("ds_cnn_kws.h5",
"http://data.brainchip.com/models/ds_cnn/ds_cnn_kws.h5",
cache_subdir='models')
# Load the native Keras pre-trained model
model_keras = load_model(model_file)
model_keras.summary()
Downloading data from http://data.brainchip.com/models/ds_cnn/ds_cnn_kws.h5
8192/162912 [>.............................] - ETA: 0s
162912/162912 [==============================] - 0s 0us/step
Model: "ds_cnn_kws"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
input (InputLayer) [(None, 49, 10, 1)] 0
rescaling (Rescaling) (None, 49, 10, 1) 0
conv_0 (Conv2D) (None, 25, 5, 64) 1600
conv_0/BN (BatchNormalizati (None, 25, 5, 64) 256
on)
conv_0/relu (ReLU) (None, 25, 5, 64) 0
separable_1 (SeparableConv2 (None, 25, 5, 64) 4672
D)
separable_1/BN (BatchNormal (None, 25, 5, 64) 256
ization)
separable_1/relu (ReLU) (None, 25, 5, 64) 0
separable_2 (SeparableConv2 (None, 25, 5, 64) 4672
D)
separable_2/BN (BatchNormal (None, 25, 5, 64) 256
ization)
separable_2/relu (ReLU) (None, 25, 5, 64) 0
separable_3 (SeparableConv2 (None, 25, 5, 64) 4672
D)
separable_3/BN (BatchNormal (None, 25, 5, 64) 256
ization)
separable_3/relu (ReLU) (None, 25, 5, 64) 0
separable_4 (SeparableConv2 (None, 25, 5, 64) 4672
D)
separable_4/global_avg (Glo (None, 64) 0
balAveragePooling2D)
separable_4/BN (BatchNormal (None, 64) 256
ization)
separable_4/relu (ReLU) (None, 64) 0
reshape_1 (Reshape) (None, 1, 1, 64) 0
flatten (Flatten) (None, 64) 0
dense_5 (Dense) (None, 33) 2145
act_softmax (Activation) (None, 33) 0
=================================================================
Total params: 23,713
Trainable params: 23,073
Non-trainable params: 640
_________________________________________________________________
import numpy as np
from sklearn.metrics import accuracy_score
# Check Keras Model performance
potentials_keras = model_keras.predict(x_valid)
preds_keras = np.squeeze(np.argmax(potentials_keras, 1))
accuracy = accuracy_score(y_valid, preds_keras)
print("Accuracy: " + "{0:.2f}".format(100 * accuracy) + "%")
1/308 [..............................] - ETA: 33s
49/308 [===>..........................] - ETA: 0s
95/308 [========>.....................] - ETA: 0s
141/308 [============>.................] - ETA: 0s
189/308 [=================>............] - ETA: 0s
239/308 [======================>.......] - ETA: 0s
286/308 [==========================>...] - ETA: 0s
308/308 [==============================] - 0s 1ms/step
Accuracy: 92.85%
3. Load a pre-trained quantized Keras model satisfying Akida NSoC requirements
The above native Keras model is quantized and fine-tuned to get a quantized Keras model satisfying the Akida NSoC requirements. The first convolutional layer uses 8 bits weights, but other layers use 4 bits weights.
All activations are 4 bits except for the final Separable Convolutional that uses binary activations.
Pre-trained weights were obtained after a few training episodes:
we train the model with quantized activations only, with weights initialized from those trained in the previous episode (native Keras model),
then, we train the model with quantized weights, with both weights and activations initialized from those trained in the previous episode,
finally, we train the model with quantized weights and activations and by gradually increasing quantization in the last layer.
The table below summarizes the results obtained when preparing the weights stored under http://data.brainchip.com/models/ds_cnn/ :
Episode |
Weights Quant. |
Activ. Quant. / last layer |
Accuracy |
Epochs |
|---|---|---|---|---|
1 |
N/A |
N/A |
93.06 % |
16 |
2 |
N/A |
4 bits / 4 bits |
92.30 % |
16 |
3 |
8/4 bits |
4 bits / 4 bits |
92.11 % |
16 |
4 |
8/4 bits |
4 bits / 3 bits |
92.38 % |
16 |
5 |
8/4 bits |
4 bits / 2 bits |
92.23 % |
16 |
6 |
8/4 bits |
4 bits / 1 bit |
92.22 % |
16 |
from akida_models import ds_cnn_kws_pretrained
# Load the pre-trained quantized model
model_keras_quantized = ds_cnn_kws_pretrained()
model_keras_quantized.summary()
# Check Model performance
potentials_keras_q = model_keras_quantized.predict(x_valid)
preds_keras_q = np.squeeze(np.argmax(potentials_keras_q, 1))
accuracy_q = accuracy_score(y_valid, preds_keras_q)
print("Accuracy: " + "{0:.2f}".format(100 * accuracy_q) + "%")
Downloading data from http://data.brainchip.com/models/ds_cnn/ds_cnn_kws_iq8_wq4_aq4_laq1.h5.
0/135784 [..............................] - ETA: 0s
135784/135784 [==============================] - 0s 0us/step
Model: "ds_cnn_kws"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
input (InputLayer) [(None, 49, 10, 1)] 0
rescaling (Rescaling) (None, 49, 10, 1) 0
conv_0 (QuantizedConv2D) (None, 25, 5, 64) 1664
conv_0/relu (ActivationDisc (None, 25, 5, 64) 0
reteRelu)
separable_1 (QuantizedSepar (None, 25, 5, 64) 4736
ableConv2D)
separable_1/relu (Activatio (None, 25, 5, 64) 0
nDiscreteRelu)
separable_2 (QuantizedSepar (None, 25, 5, 64) 4736
ableConv2D)
separable_2/relu (Activatio (None, 25, 5, 64) 0
nDiscreteRelu)
separable_3 (QuantizedSepar (None, 25, 5, 64) 4736
ableConv2D)
separable_3/relu (Activatio (None, 25, 5, 64) 0
nDiscreteRelu)
separable_4 (QuantizedSepar (None, 25, 5, 64) 4736
ableConv2D)
separable_4/global_avg (Glo (None, 64) 0
balAveragePooling2D)
separable_4/relu (Activatio (None, 64) 0
nDiscreteRelu)
reshape_1 (Reshape) (None, 1, 1, 64) 0
flatten (Flatten) (None, 64) 0
dense_5 (QuantizedDense) (None, 33) 2145
act_softmax (Activation) (None, 33) 0
=================================================================
Total params: 22,753
Trainable params: 22,753
Non-trainable params: 0
_________________________________________________________________
1/308 [..............................] - ETA: 1:14
34/308 [==>...........................] - ETA: 0s
68/308 [=====>........................] - ETA: 0s
102/308 [========>.....................] - ETA: 0s
135/308 [============>.................] - ETA: 0s
169/308 [===============>..............] - ETA: 0s
202/308 [==================>...........] - ETA: 0s
234/308 [=====================>........] - ETA: 0s
265/308 [========================>.....] - ETA: 0s
296/308 [===========================>..] - ETA: 0s
308/308 [==============================] - 1s 2ms/step
Accuracy: 91.43%
4. Conversion to Akida
We convert the model to Akida and then evaluate the performances on the dataset.
from cnn2snn import convert
# Convert the model
model_akida = convert(model_keras_quantized)
model_akida.summary()
Model Summary
______________________________________________
Input shape Output shape Sequences Layers
==============================================
[49, 10, 1] [1, 1, 33] 1 6
______________________________________________
_______________________________________________________
Layer (type) Output shape Kernel shape
============= SW/conv_0-dense_5 (Software) ============
conv_0 (InputConv.) [25, 5, 64] (5, 5, 1, 64)
_______________________________________________________
separable_1 (Sep.Conv.) [25, 5, 64] (3, 3, 64, 1)
_______________________________________________________
(1, 1, 64, 64)
_______________________________________________________
separable_2 (Sep.Conv.) [25, 5, 64] (3, 3, 64, 1)
_______________________________________________________
(1, 1, 64, 64)
_______________________________________________________
separable_3 (Sep.Conv.) [25, 5, 64] (3, 3, 64, 1)
_______________________________________________________
(1, 1, 64, 64)
_______________________________________________________
separable_4 (Sep.Conv.) [1, 1, 64] (3, 3, 64, 1)
_______________________________________________________
(1, 1, 64, 64)
_______________________________________________________
dense_5 (Fully.) [1, 1, 33] (1, 1, 64, 33)
_______________________________________________________
# Check Akida model performance
preds_akida = model_akida.predict_classes(x_valid, num_classes=num_classes)
accuracy = accuracy_score(y_valid, preds_akida)
print("Accuracy: " + "{0:.2f}".format(100 * accuracy) + "%")
# For non-regression purpose
assert accuracy > 0.9
Accuracy: 91.34%
5. Confusion matrix
The confusion matrix provides a good summary of what mistakes the network is making.
Per scikit-learn convention it displays the true class in each row (ie on each row you can see what the network predicted for the corresponding word).
Please refer to the Tensorflow audio recognition example for a detailed explanation of the confusion matrix.
import itertools
import matplotlib.pyplot as plt
from sklearn.metrics import confusion_matrix
# Create confusion matrix
cm = confusion_matrix(y_valid, preds_akida,
labels=list(word_to_index.values()))
# Normalize
cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
# Display confusion matrix
plt.rcParams["figure.figsize"] = (16, 16)
plt.figure()
title = 'Confusion matrix'
cmap = plt.cm.Blues
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(word_to_index))
plt.xticks(tick_marks, word_to_index, rotation=45)
plt.yticks(tick_marks, word_to_index)
thresh = cm.max() / 2.
for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
plt.text(j,
i,
format(cm[i, j], '.2f'),
horizontalalignment="center",
color="white" if cm[i, j] > thresh else "black")
plt.ylabel('True label')
plt.xlabel('Predicted label')
plt.autoscale()
plt.show()
Total running time of the script: ( 0 minutes 18.388 seconds)