L2 normalised output with keras
Question:
I would like to build a neural net with Keras with Tensorflow backend which outputs an L2 normalized vector. I have tried the following but for some reason it does not normalize the output:
import keras.backend as K
input = Input(shape=input_shape)
...
dense7 = Dense(output_dim=3)(flatten6)
l2_norm = Lambda(lambda x: K.l2_normalize(x,axis=1))(dense7)
return Model(input=input, output=l2_norm)
So here the output is a 3D vector and I would like to make sure that the length of this vector is 1. Can anybody help me out? Also can you tell me why my solution fails?
Example:
output: [ 8.27677908e-08 2.64180613e-07 -2.81542953e-07]
required: [ 0.20961709 0.6690619 -0.71303362]
Model summary:
____________________________________________________________________________________________________
Layer (type) Output Shape Param # Connected to
====================================================================================================
input_1 (InputLayer) (None, 224, 224, 3) 0
____________________________________________________________________________________________________
convolution2d_1 (Convolution2D) (None, 112, 112, 64) 9472 input_1[0][0]
____________________________________________________________________________________________________
batchnormalization_1 (BatchNormal(None, 112, 112, 64) 128 convolution2d_1[0][0]
____________________________________________________________________________________________________
maxpooling2d_1 (MaxPooling2D) (None, 56, 56, 64) 0 batchnormalization_1[0][0]
____________________________________________________________________________________________________
convolution2d_2 (Convolution2D) (None, 56, 56, 64) 4160 maxpooling2d_1[0][0]
____________________________________________________________________________________________________
batchnormalization_2 (BatchNormal(None, 56, 56, 64) 128 convolution2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_3 (Convolution2D) (None, 56, 56, 192) 110784 batchnormalization_2[0][0]
____________________________________________________________________________________________________
batchnormalization_3 (BatchNormal(None, 56, 56, 192) 384 convolution2d_3[0][0]
____________________________________________________________________________________________________
maxpooling2d_2 (MaxPooling2D) (None, 28, 28, 192) 0 batchnormalization_3[0][0]
____________________________________________________________________________________________________
convolution2d_5 (Convolution2D) (None, 28, 28, 96) 18528 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_7 (Convolution2D) (None, 28, 28, 16) 3088 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
maxpooling2d_3 (MaxPooling2D) (None, 28, 28, 192) 0 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_4 (Convolution2D) (None, 28, 28, 64) 12352 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_6 (Convolution2D) (None, 28, 28, 128) 110720 convolution2d_5[0][0]
____________________________________________________________________________________________________
convolution2d_8 (Convolution2D) (None, 28, 28, 32) 12832 convolution2d_7[0][0]
____________________________________________________________________________________________________
convolution2d_9 (Convolution2D) (None, 28, 28, 32) 6176 maxpooling2d_3[0][0]
____________________________________________________________________________________________________
merge_1 (Merge) (None, 28, 28, 256) 0 convolution2d_4[0][0]
convolution2d_6[0][0]
convolution2d_8[0][0]
convolution2d_9[0][0]
____________________________________________________________________________________________________
convolution2d_11 (Convolution2D) (None, 28, 28, 96) 24672 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_13 (Convolution2D) (None, 28, 28, 32) 8224 merge_1[0][0]
____________________________________________________________________________________________________
maxpooling2d_4 (MaxPooling2D) (None, 28, 28, 256) 0 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_10 (Convolution2D) (None, 28, 28, 64) 16448 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_12 (Convolution2D) (None, 28, 28, 128) 110720 convolution2d_11[0][0]
____________________________________________________________________________________________________
convolution2d_14 (Convolution2D) (None, 28, 28, 64) 51264 convolution2d_13[0][0]
____________________________________________________________________________________________________
convolution2d_15 (Convolution2D) (None, 28, 28, 64) 16448 maxpooling2d_4[0][0]
____________________________________________________________________________________________________
merge_2 (Merge) (None, 28, 28, 320) 0 convolution2d_10[0][0]
convolution2d_12[0][0]
convolution2d_14[0][0]
convolution2d_15[0][0]
____________________________________________________________________________________________________
convolution2d_16 (Convolution2D) (None, 28, 28, 128) 41088 merge_2[0][0]
____________________________________________________________________________________________________
convolution2d_18 (Convolution2D) (None, 28, 28, 32) 10272 merge_2[0][0]
____________________________________________________________________________________________________
convolution2d_17 (Convolution2D) (None, 14, 14, 256) 295168 convolution2d_16[0][0]
____________________________________________________________________________________________________
convolution2d_19 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_18[0][0]
____________________________________________________________________________________________________
maxpooling2d_5 (MaxPooling2D) (None, 14, 14, 320) 0 merge_2[0][0]
____________________________________________________________________________________________________
merge_3 (Merge) (None, 14, 14, 640) 0 convolution2d_17[0][0]
convolution2d_19[0][0]
maxpooling2d_5[0][0]
____________________________________________________________________________________________________
convolution2d_21 (Convolution2D) (None, 14, 14, 96) 61536 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_23 (Convolution2D) (None, 14, 14, 32) 20512 merge_3[0][0]
____________________________________________________________________________________________________
maxpooling2d_6 (MaxPooling2D) (None, 14, 14, 640) 0 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_20 (Convolution2D) (None, 14, 14, 256) 164096 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_22 (Convolution2D) (None, 14, 14, 192) 166080 convolution2d_21[0][0]
____________________________________________________________________________________________________
convolution2d_24 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_23[0][0]
____________________________________________________________________________________________________
convolution2d_25 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_6[0][0]
____________________________________________________________________________________________________
merge_4 (Merge) (None, 14, 14, 640) 0 convolution2d_20[0][0]
convolution2d_22[0][0]
convolution2d_24[0][0]
convolution2d_25[0][0]
____________________________________________________________________________________________________
convolution2d_27 (Convolution2D) (None, 14, 14, 112) 71792 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_29 (Convolution2D) (None, 14, 14, 32) 20512 merge_4[0][0]
____________________________________________________________________________________________________
maxpooling2d_7 (MaxPooling2D) (None, 14, 14, 640) 0 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_26 (Convolution2D) (None, 14, 14, 224) 143584 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_28 (Convolution2D) (None, 14, 14, 224) 226016 convolution2d_27[0][0]
____________________________________________________________________________________________________
convolution2d_30 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_29[0][0]
____________________________________________________________________________________________________
convolution2d_31 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_7[0][0]
____________________________________________________________________________________________________
merge_5 (Merge) (None, 14, 14, 640) 0 convolution2d_26[0][0]
convolution2d_28[0][0]
convolution2d_30[0][0]
convolution2d_31[0][0]
____________________________________________________________________________________________________
convolution2d_33 (Convolution2D) (None, 14, 14, 128) 82048 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_35 (Convolution2D) (None, 14, 14, 32) 20512 merge_5[0][0]
____________________________________________________________________________________________________
maxpooling2d_8 (MaxPooling2D) (None, 14, 14, 640) 0 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_32 (Convolution2D) (None, 14, 14, 192) 123072 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_34 (Convolution2D) (None, 14, 14, 256) 295168 convolution2d_33[0][0]
____________________________________________________________________________________________________
convolution2d_36 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_35[0][0]
____________________________________________________________________________________________________
convolution2d_37 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_8[0][0]
____________________________________________________________________________________________________
merge_6 (Merge) (None, 14, 14, 640) 0 convolution2d_32[0][0]
convolution2d_34[0][0]
convolution2d_36[0][0]
convolution2d_37[0][0]
____________________________________________________________________________________________________
convolution2d_39 (Convolution2D) (None, 14, 14, 144) 92304 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_41 (Convolution2D) (None, 14, 14, 32) 20512 merge_6[0][0]
____________________________________________________________________________________________________
maxpooling2d_9 (MaxPooling2D) (None, 14, 14, 640) 0 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_38 (Convolution2D) (None, 14, 14, 160) 102560 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_40 (Convolution2D) (None, 14, 14, 288) 373536 convolution2d_39[0][0]
____________________________________________________________________________________________________
convolution2d_42 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_41[0][0]
____________________________________________________________________________________________________
convolution2d_43 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_9[0][0]
____________________________________________________________________________________________________
merge_7 (Merge) (None, 14, 14, 640) 0 convolution2d_38[0][0]
convolution2d_40[0][0]
convolution2d_42[0][0]
convolution2d_43[0][0]
____________________________________________________________________________________________________
convolution2d_44 (Convolution2D) (None, 14, 14, 160) 102560 merge_7[0][0]
____________________________________________________________________________________________________
convolution2d_46 (Convolution2D) (None, 14, 14, 64) 41024 merge_7[0][0]
____________________________________________________________________________________________________
convolution2d_45 (Convolution2D) (None, 7, 7, 256) 368896 convolution2d_44[0][0]
____________________________________________________________________________________________________
convolution2d_47 (Convolution2D) (None, 7, 7, 128) 204928 convolution2d_46[0][0]
____________________________________________________________________________________________________
maxpooling2d_10 (MaxPooling2D) (None, 7, 7, 640) 0 merge_7[0][0]
____________________________________________________________________________________________________
merge_8 (Merge) (None, 7, 7, 1024) 0 convolution2d_45[0][0]
convolution2d_47[0][0]
maxpooling2d_10[0][0]
____________________________________________________________________________________________________
convolution2d_49 (Convolution2D) (None, 7, 7, 192) 196800 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_51 (Convolution2D) (None, 7, 7, 48) 49200 merge_8[0][0]
____________________________________________________________________________________________________
maxpooling2d_11 (MaxPooling2D) (None, 7, 7, 1024) 0 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_48 (Convolution2D) (None, 7, 7, 384) 393600 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_50 (Convolution2D) (None, 7, 7, 384) 663936 convolution2d_49[0][0]
____________________________________________________________________________________________________
convolution2d_52 (Convolution2D) (None, 7, 7, 128) 153728 convolution2d_51[0][0]
____________________________________________________________________________________________________
convolution2d_53 (Convolution2D) (None, 7, 7, 128) 131200 maxpooling2d_11[0][0]
____________________________________________________________________________________________________
merge_9 (Merge) (None, 7, 7, 1024) 0 convolution2d_48[0][0]
convolution2d_50[0][0]
convolution2d_52[0][0]
convolution2d_53[0][0]
____________________________________________________________________________________________________
convolution2d_55 (Convolution2D) (None, 7, 7, 192) 196800 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_57 (Convolution2D) (None, 7, 7, 48) 49200 merge_9[0][0]
____________________________________________________________________________________________________
maxpooling2d_12 (MaxPooling2D) (None, 7, 7, 1024) 0 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_54 (Convolution2D) (None, 7, 7, 384) 393600 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_56 (Convolution2D) (None, 7, 7, 384) 663936 convolution2d_55[0][0]
____________________________________________________________________________________________________
convolution2d_58 (Convolution2D) (None, 7, 7, 128) 153728 convolution2d_57[0][0]
____________________________________________________________________________________________________
convolution2d_59 (Convolution2D) (None, 7, 7, 128) 131200 maxpooling2d_12[0][0]
____________________________________________________________________________________________________
merge_10 (Merge) (None, 7, 7, 1024) 0 convolution2d_54[0][0]
convolution2d_56[0][0]
convolution2d_58[0][0]
convolution2d_59[0][0]
____________________________________________________________________________________________________
averagepooling2d_1 (AveragePoolin(None, 1, 1, 1024) 0 merge_10[0][0]
____________________________________________________________________________________________________
flatten_1 (Flatten) (None, 1024) 0 averagepooling2d_1[0][0]
____________________________________________________________________________________________________
dense_1 (Dense) (None, 3) 3075 flatten_1[0][0]
____________________________________________________________________________________________________
lambda_1 (Lambda) (None, 3) 0 dense_1[0][0]
====================================================================================================
Total params: 7328819
Answers:
I found the problem!
So I am using tensorflow as a backed and K.l2_normalize(x, axis) calls the tf.nn.l2_normalize(x, dim, epsilon=1e-12, name=None). Notice that this method has one extra parameter epsilon. And this method looks as follows:
with ops.name_scope(name, "l2_normalize", [x]) as name:
x = ops.convert_to_tensor(x, name="x")
square_sum = math_ops.reduce_sum(math_ops.square(x), dim, keep_dims=True)
x_inv_norm = math_ops.rsqrt(math_ops.maximum(square_sum, epsilon))
return math_ops.mul(x, x_inv_norm, name=name)
So if the output of the net contains numbers lower then epsilon (which is set to 1e-12 by default) then it is not normalized correctly which is what happens in my case.
You can use the function, which is called by tensorflow.keras.backend.l2_normalize to set the epsilon value:
from tensorflow.python.ops import nn
nn.l2_normalize(x, axis=None, epsilon=1e-12)
@thebeancounter
You can define your own L2 Layer.
For example to support masking: if there follow layers after the L2 Normalization, which depend on masking you should use the following:
class L2Layer(tf.keras.layers.Layer):
def __init__(self):
super(L2Layer, self).__init__()
self.supports_masking = True
def call(self, inputs, mask=None):
return K.l2_normalize(inputs, axis=2)
I think you could use a final layer like this one:
tf.keras.layers.Lambda(lambda x: tf.math.l2_normalize(x, axis=1))
I would like to build a neural net with Keras with Tensorflow backend which outputs an L2 normalized vector. I have tried the following but for some reason it does not normalize the output:
import keras.backend as K
input = Input(shape=input_shape)
...
dense7 = Dense(output_dim=3)(flatten6)
l2_norm = Lambda(lambda x: K.l2_normalize(x,axis=1))(dense7)
return Model(input=input, output=l2_norm)
So here the output is a 3D vector and I would like to make sure that the length of this vector is 1. Can anybody help me out? Also can you tell me why my solution fails?
Example:
output: [ 8.27677908e-08 2.64180613e-07 -2.81542953e-07]
required: [ 0.20961709 0.6690619 -0.71303362]
Model summary:
____________________________________________________________________________________________________
Layer (type) Output Shape Param # Connected to
====================================================================================================
input_1 (InputLayer) (None, 224, 224, 3) 0
____________________________________________________________________________________________________
convolution2d_1 (Convolution2D) (None, 112, 112, 64) 9472 input_1[0][0]
____________________________________________________________________________________________________
batchnormalization_1 (BatchNormal(None, 112, 112, 64) 128 convolution2d_1[0][0]
____________________________________________________________________________________________________
maxpooling2d_1 (MaxPooling2D) (None, 56, 56, 64) 0 batchnormalization_1[0][0]
____________________________________________________________________________________________________
convolution2d_2 (Convolution2D) (None, 56, 56, 64) 4160 maxpooling2d_1[0][0]
____________________________________________________________________________________________________
batchnormalization_2 (BatchNormal(None, 56, 56, 64) 128 convolution2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_3 (Convolution2D) (None, 56, 56, 192) 110784 batchnormalization_2[0][0]
____________________________________________________________________________________________________
batchnormalization_3 (BatchNormal(None, 56, 56, 192) 384 convolution2d_3[0][0]
____________________________________________________________________________________________________
maxpooling2d_2 (MaxPooling2D) (None, 28, 28, 192) 0 batchnormalization_3[0][0]
____________________________________________________________________________________________________
convolution2d_5 (Convolution2D) (None, 28, 28, 96) 18528 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_7 (Convolution2D) (None, 28, 28, 16) 3088 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
maxpooling2d_3 (MaxPooling2D) (None, 28, 28, 192) 0 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_4 (Convolution2D) (None, 28, 28, 64) 12352 maxpooling2d_2[0][0]
____________________________________________________________________________________________________
convolution2d_6 (Convolution2D) (None, 28, 28, 128) 110720 convolution2d_5[0][0]
____________________________________________________________________________________________________
convolution2d_8 (Convolution2D) (None, 28, 28, 32) 12832 convolution2d_7[0][0]
____________________________________________________________________________________________________
convolution2d_9 (Convolution2D) (None, 28, 28, 32) 6176 maxpooling2d_3[0][0]
____________________________________________________________________________________________________
merge_1 (Merge) (None, 28, 28, 256) 0 convolution2d_4[0][0]
convolution2d_6[0][0]
convolution2d_8[0][0]
convolution2d_9[0][0]
____________________________________________________________________________________________________
convolution2d_11 (Convolution2D) (None, 28, 28, 96) 24672 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_13 (Convolution2D) (None, 28, 28, 32) 8224 merge_1[0][0]
____________________________________________________________________________________________________
maxpooling2d_4 (MaxPooling2D) (None, 28, 28, 256) 0 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_10 (Convolution2D) (None, 28, 28, 64) 16448 merge_1[0][0]
____________________________________________________________________________________________________
convolution2d_12 (Convolution2D) (None, 28, 28, 128) 110720 convolution2d_11[0][0]
____________________________________________________________________________________________________
convolution2d_14 (Convolution2D) (None, 28, 28, 64) 51264 convolution2d_13[0][0]
____________________________________________________________________________________________________
convolution2d_15 (Convolution2D) (None, 28, 28, 64) 16448 maxpooling2d_4[0][0]
____________________________________________________________________________________________________
merge_2 (Merge) (None, 28, 28, 320) 0 convolution2d_10[0][0]
convolution2d_12[0][0]
convolution2d_14[0][0]
convolution2d_15[0][0]
____________________________________________________________________________________________________
convolution2d_16 (Convolution2D) (None, 28, 28, 128) 41088 merge_2[0][0]
____________________________________________________________________________________________________
convolution2d_18 (Convolution2D) (None, 28, 28, 32) 10272 merge_2[0][0]
____________________________________________________________________________________________________
convolution2d_17 (Convolution2D) (None, 14, 14, 256) 295168 convolution2d_16[0][0]
____________________________________________________________________________________________________
convolution2d_19 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_18[0][0]
____________________________________________________________________________________________________
maxpooling2d_5 (MaxPooling2D) (None, 14, 14, 320) 0 merge_2[0][0]
____________________________________________________________________________________________________
merge_3 (Merge) (None, 14, 14, 640) 0 convolution2d_17[0][0]
convolution2d_19[0][0]
maxpooling2d_5[0][0]
____________________________________________________________________________________________________
convolution2d_21 (Convolution2D) (None, 14, 14, 96) 61536 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_23 (Convolution2D) (None, 14, 14, 32) 20512 merge_3[0][0]
____________________________________________________________________________________________________
maxpooling2d_6 (MaxPooling2D) (None, 14, 14, 640) 0 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_20 (Convolution2D) (None, 14, 14, 256) 164096 merge_3[0][0]
____________________________________________________________________________________________________
convolution2d_22 (Convolution2D) (None, 14, 14, 192) 166080 convolution2d_21[0][0]
____________________________________________________________________________________________________
convolution2d_24 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_23[0][0]
____________________________________________________________________________________________________
convolution2d_25 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_6[0][0]
____________________________________________________________________________________________________
merge_4 (Merge) (None, 14, 14, 640) 0 convolution2d_20[0][0]
convolution2d_22[0][0]
convolution2d_24[0][0]
convolution2d_25[0][0]
____________________________________________________________________________________________________
convolution2d_27 (Convolution2D) (None, 14, 14, 112) 71792 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_29 (Convolution2D) (None, 14, 14, 32) 20512 merge_4[0][0]
____________________________________________________________________________________________________
maxpooling2d_7 (MaxPooling2D) (None, 14, 14, 640) 0 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_26 (Convolution2D) (None, 14, 14, 224) 143584 merge_4[0][0]
____________________________________________________________________________________________________
convolution2d_28 (Convolution2D) (None, 14, 14, 224) 226016 convolution2d_27[0][0]
____________________________________________________________________________________________________
convolution2d_30 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_29[0][0]
____________________________________________________________________________________________________
convolution2d_31 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_7[0][0]
____________________________________________________________________________________________________
merge_5 (Merge) (None, 14, 14, 640) 0 convolution2d_26[0][0]
convolution2d_28[0][0]
convolution2d_30[0][0]
convolution2d_31[0][0]
____________________________________________________________________________________________________
convolution2d_33 (Convolution2D) (None, 14, 14, 128) 82048 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_35 (Convolution2D) (None, 14, 14, 32) 20512 merge_5[0][0]
____________________________________________________________________________________________________
maxpooling2d_8 (MaxPooling2D) (None, 14, 14, 640) 0 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_32 (Convolution2D) (None, 14, 14, 192) 123072 merge_5[0][0]
____________________________________________________________________________________________________
convolution2d_34 (Convolution2D) (None, 14, 14, 256) 295168 convolution2d_33[0][0]
____________________________________________________________________________________________________
convolution2d_36 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_35[0][0]
____________________________________________________________________________________________________
convolution2d_37 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_8[0][0]
____________________________________________________________________________________________________
merge_6 (Merge) (None, 14, 14, 640) 0 convolution2d_32[0][0]
convolution2d_34[0][0]
convolution2d_36[0][0]
convolution2d_37[0][0]
____________________________________________________________________________________________________
convolution2d_39 (Convolution2D) (None, 14, 14, 144) 92304 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_41 (Convolution2D) (None, 14, 14, 32) 20512 merge_6[0][0]
____________________________________________________________________________________________________
maxpooling2d_9 (MaxPooling2D) (None, 14, 14, 640) 0 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_38 (Convolution2D) (None, 14, 14, 160) 102560 merge_6[0][0]
____________________________________________________________________________________________________
convolution2d_40 (Convolution2D) (None, 14, 14, 288) 373536 convolution2d_39[0][0]
____________________________________________________________________________________________________
convolution2d_42 (Convolution2D) (None, 14, 14, 64) 51264 convolution2d_41[0][0]
____________________________________________________________________________________________________
convolution2d_43 (Convolution2D) (None, 14, 14, 128) 82048 maxpooling2d_9[0][0]
____________________________________________________________________________________________________
merge_7 (Merge) (None, 14, 14, 640) 0 convolution2d_38[0][0]
convolution2d_40[0][0]
convolution2d_42[0][0]
convolution2d_43[0][0]
____________________________________________________________________________________________________
convolution2d_44 (Convolution2D) (None, 14, 14, 160) 102560 merge_7[0][0]
____________________________________________________________________________________________________
convolution2d_46 (Convolution2D) (None, 14, 14, 64) 41024 merge_7[0][0]
____________________________________________________________________________________________________
convolution2d_45 (Convolution2D) (None, 7, 7, 256) 368896 convolution2d_44[0][0]
____________________________________________________________________________________________________
convolution2d_47 (Convolution2D) (None, 7, 7, 128) 204928 convolution2d_46[0][0]
____________________________________________________________________________________________________
maxpooling2d_10 (MaxPooling2D) (None, 7, 7, 640) 0 merge_7[0][0]
____________________________________________________________________________________________________
merge_8 (Merge) (None, 7, 7, 1024) 0 convolution2d_45[0][0]
convolution2d_47[0][0]
maxpooling2d_10[0][0]
____________________________________________________________________________________________________
convolution2d_49 (Convolution2D) (None, 7, 7, 192) 196800 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_51 (Convolution2D) (None, 7, 7, 48) 49200 merge_8[0][0]
____________________________________________________________________________________________________
maxpooling2d_11 (MaxPooling2D) (None, 7, 7, 1024) 0 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_48 (Convolution2D) (None, 7, 7, 384) 393600 merge_8[0][0]
____________________________________________________________________________________________________
convolution2d_50 (Convolution2D) (None, 7, 7, 384) 663936 convolution2d_49[0][0]
____________________________________________________________________________________________________
convolution2d_52 (Convolution2D) (None, 7, 7, 128) 153728 convolution2d_51[0][0]
____________________________________________________________________________________________________
convolution2d_53 (Convolution2D) (None, 7, 7, 128) 131200 maxpooling2d_11[0][0]
____________________________________________________________________________________________________
merge_9 (Merge) (None, 7, 7, 1024) 0 convolution2d_48[0][0]
convolution2d_50[0][0]
convolution2d_52[0][0]
convolution2d_53[0][0]
____________________________________________________________________________________________________
convolution2d_55 (Convolution2D) (None, 7, 7, 192) 196800 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_57 (Convolution2D) (None, 7, 7, 48) 49200 merge_9[0][0]
____________________________________________________________________________________________________
maxpooling2d_12 (MaxPooling2D) (None, 7, 7, 1024) 0 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_54 (Convolution2D) (None, 7, 7, 384) 393600 merge_9[0][0]
____________________________________________________________________________________________________
convolution2d_56 (Convolution2D) (None, 7, 7, 384) 663936 convolution2d_55[0][0]
____________________________________________________________________________________________________
convolution2d_58 (Convolution2D) (None, 7, 7, 128) 153728 convolution2d_57[0][0]
____________________________________________________________________________________________________
convolution2d_59 (Convolution2D) (None, 7, 7, 128) 131200 maxpooling2d_12[0][0]
____________________________________________________________________________________________________
merge_10 (Merge) (None, 7, 7, 1024) 0 convolution2d_54[0][0]
convolution2d_56[0][0]
convolution2d_58[0][0]
convolution2d_59[0][0]
____________________________________________________________________________________________________
averagepooling2d_1 (AveragePoolin(None, 1, 1, 1024) 0 merge_10[0][0]
____________________________________________________________________________________________________
flatten_1 (Flatten) (None, 1024) 0 averagepooling2d_1[0][0]
____________________________________________________________________________________________________
dense_1 (Dense) (None, 3) 3075 flatten_1[0][0]
____________________________________________________________________________________________________
lambda_1 (Lambda) (None, 3) 0 dense_1[0][0]
====================================================================================================
Total params: 7328819
I found the problem!
So I am using tensorflow as a backed and K.l2_normalize(x, axis) calls the tf.nn.l2_normalize(x, dim, epsilon=1e-12, name=None). Notice that this method has one extra parameter epsilon. And this method looks as follows:
with ops.name_scope(name, "l2_normalize", [x]) as name:
x = ops.convert_to_tensor(x, name="x")
square_sum = math_ops.reduce_sum(math_ops.square(x), dim, keep_dims=True)
x_inv_norm = math_ops.rsqrt(math_ops.maximum(square_sum, epsilon))
return math_ops.mul(x, x_inv_norm, name=name)
So if the output of the net contains numbers lower then epsilon (which is set to 1e-12 by default) then it is not normalized correctly which is what happens in my case.
You can use the function, which is called by tensorflow.keras.backend.l2_normalize to set the epsilon value:
from tensorflow.python.ops import nn
nn.l2_normalize(x, axis=None, epsilon=1e-12)
@thebeancounter
You can define your own L2 Layer.
For example to support masking: if there follow layers after the L2 Normalization, which depend on masking you should use the following:
class L2Layer(tf.keras.layers.Layer):
def __init__(self):
super(L2Layer, self).__init__()
self.supports_masking = True
def call(self, inputs, mask=None):
return K.l2_normalize(inputs, axis=2)
I think you could use a final layer like this one:
tf.keras.layers.Lambda(lambda x: tf.math.l2_normalize(x, axis=1))