1、Convnets in TensorFlowCS 20: TensorFlow for Deep Learning ResearchLecture 72/7/201712AgendaConvolutions without trainingConvnet with MNIST!tf.layers3Understanding convolutions4Convolutions in math and physics5a function derived from two given functions by integration that expresses how the shape of

2、one is modified by the otherConvolutions in math and physics6Brian Amberg derivative work (Wikipedia)Convolutions in math and physics7How an input is transformed by a kernel* *also called filter/feature mapConvolutions in machine learning8We can use one single convolutional layer to modify a certain

3、 imageConvolutions in machine learning9 Kernel for blurring100.06250.1250.06250.1250.250.1250.06250.1250.0625Matrix multiplication of this kernel with a 3 x 3 patch of an image is a weighted sum of neighboring pixels= blurring effectConvolution without training110.06250.1250.06250.1250.250.1250.0625

4、0.1250.0625tf.nn.conv2dinputKernel for blurringoutputConvolutions in TensorFlow12We can use one single convolutional layer to modify a certain imagetf.nn.conv2d( input, filter, strides, padding, use_cudnn_on_gpu=True, data_format=NHWC, dilations=1, 1, 1, 1, name=None)Convolutions in TensorFlow13We c

5、an use one single convolutional layer to modify a certain imagetf.nn.conv2d( input,Batch size (N) x Height (H) x Width (W) x Channels (C) filter,Height x Width x Input Channels x Output Channels strides,4 element 1-D tensor, strides in each direction padding,SAME or VALID use_cudnn_on_gpu=True, data

6、_format=NHWC, dilations=1, 1, 1, 1, name=None)Convolutions in TensorFlow14We can use one single convolutional layer to modify a certain imagetf.nn.conv2d( image, kernel, strides=1, 3, 3, 1, padding=SAME,)Some basic kernels15inputsharpenedgetop sobelembossSee kernels.py and 07_run_kernels.pySome basi

7、c kernels16inputsharpenedgetop sobelembossConvolutions in machine learning17Dont hard-code the values of your kernels.Learn the optimal kernels through training!ConvNet with MNIST18Model1928x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x

8、32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10Strides for all convolutional layers: 1, 1, 1, 1Convolutional layer2028x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 6

9、41 x 10241 x 10conv = tf.nn.conv2d(images,kernel,strides=1, 1, 1, 1,padding=SAME)Convolutional layer: padding21Input width = 13Filter width = 6Stride = 5Convolutional layer: Dimension2228x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x

10、647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10(WF+2P)/S+ 1W: input width/depthF: filter width/depthP: paddingS: strideConvolutional layer: Dimension23(WF+2P)/S+ 1W: input width/depthF: filter width/depthP: paddingS: strideImage credit: CS231n Lecture 7Convolutional layer: Dimension

11、2428x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10(WF+2P)/S+ 1(28 - 5 + 2*2)/1 + 1 = 28W: input width/depthF: filter width/depthP: paddingS: strideConvolutional layer: D

12、imension2528x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10(WF+2P)/S+ 1(28 - 5 + 2*2)/1 + 1 = 28W: input width/depthF: filter width/depthP: paddingS: strideTF computes pa

13、dding for us!Maxpooling2628x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10pool1 = tf.nn.max_pool(conv1,ksize=1, 2, 2, 1,strides=1, 2, 2, 1,padding=SAME)Maxpooling27Slide

14、credit: CS231n Lecture 71124567832101234Single depth slicexymax pool with 2x2 filters and stride 26834Maxpooling: Dimension2828x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241

15、x 10(WK+2P)/S+ 1W: input width/depthK: window width/depthP: paddingS: strideMaxpooling: Dimension2928x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10(WK+2P)/S+ 1(28 - 2 +

16、2*0) / 2 + 1 = 14W: input width/depthK: window width/depthP: paddingS: strideFully connected3028x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10fc = tf.matmul(pool2, w) +

17、bSoftmax3128x28x15x5x1x32Conv + relu28x28x32Maxpool (2x2x1)Conv + reluMaxpool (2x2x1)Fully + reluFully + softmaxWeight5x5x32x647*7*64 x 10241024 x 1014x14x3214x14x647 x 7 x 641 x 10241 x 10Loss functiontf.nn.softmax_cross_entropy_with_logits(labels=Y, logits=logits)Predicttf.nn.softmax(logits_batch)

18、Interactive coding3207_convnet_mnist_starter.py from GitHub!Update utils.py33Training progress34Test accuracy increases while training loss decreases!Accuracy35EpochsAccuracy10.913120.936330.947850.9573100.971250.9818tf.layers36tf.layers37Weve been learning it the hard waytf.layers.conv2d38conv1 = tf.layers.conv2d(inputs=self.img, filters=32, kernel_size=5, 5, padding=SAME, activation=tf.nn.relu, name=con