我想用带有Tensorflow后端的Keras构建一个神经网络，它输出一个L2归一化向量。我尝试了以下但由于某种原因它没有使输出没有通过：
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)
所以这里的输出是一个3D矢量，我想确保这个矢量的长度为1.有人可以帮帮我吗？你能告诉我为什么我的解决方案失败了吗？
例：
output: [ 8.27677908e-08 2.64180613e-07 -2.81542953e-07]
required: [ 0.20961709 0.6690619 -0.71303362]
型号摘要：
____________________________________________________________________________________________________
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
我发现了问题！
所以我使用tensorflow作为支持，K.l2_normalize（x，axis）调用tf.nn.l2_normalize（x，dim，epsilon = 1e-12，name = None）。请注意，此方法有一个额外的参数epsilon。这个方法看起来如下：
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)
因此，如果网络的输出包含的数字低于epsilon（默认情况下设置为1e-12），那么它没有正确规范化，这就是我的情况。