如何使 Keras 密集层处理 3D 张量作为此 Softmax 全连接层的输入？
How to make a Keras Dense Layer deal with 3D tensor as input for this Softmax Fully Connected Layer?
我正在处理一个自定义问题，我必须更改全连接层（Dense with softmax），我的模型代码是这样的（使用 Keras 框架）：
.......
batch_size = 8
inputs = tf.random.uniform(shape=[batch_size,1024,256],dtype=tf.dtypes.float32)
preds = Dense(num_classes,activation='softmax')(x) #final layer with softmax activation
....
model = Model(inputs=base_model.input,outputs=preds)
所以，我必须更改密集层代码以输出形状为 [batch_size、1024、num_classes] 的概率张量，而不使用 for 循环，我需要它有待优化而不是耗时函数
我要更改的密集代码版本：
class Dense(Layer):
"""Just your regular densely-connected NN layer.
`Dense` implements the operation:
`output = activation(dot(input, kernel) + bias)`
where `activation` is the element-wise activation function
passed as the `activation` argument, `kernel` is a weights matrix
created by the layer, and `bias` is a bias vector created by the layer
(only applicable if `use_bias` is `True`).
Note: if the input to the layer has a rank greater than 2, then
it is flattened prior to the initial dot product with `kernel`.
# Example
```python
# as first layer in a sequential model:
model = Sequential()
model.add(Dense(32, input_shape=(16,)))
# now the model will take as input arrays of shape (*, 16)
# and output arrays of shape (*, 32)
# after the first layer, you don't need to specify
# the size of the input anymore:
model.add(Dense(32))
```
# Arguments
units: Positive integer, dimensionality of the output space.
activation: Activation function to use
(see [activations](../activations.md)).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
kernel_initializer: Initializer for the `kernel` weights matrix
(see [initializers](../initializers.md)).
bias_initializer: Initializer for the bias vector
(see [initializers](../initializers.md)).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see [regularizer](../regularizers.md)).
bias_regularizer: Regularizer function applied to the bias vector
(see [regularizer](../regularizers.md)).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see [regularizer](../regularizers.md)).
kernel_constraint: Constraint function applied to
the `kernel` weights matrix
(see [constraints](../constraints.md)).
bias_constraint: Constraint function applied to the bias vector
(see [constraints](../constraints.md)).
# Input shape
nD tensor with shape: `(batch_size, ..., input_dim)`.
The most common situation would be
a 2D input with shape `(batch_size, input_dim)`.
# Output shape
nD tensor with shape: `(batch_size, ..., units)`.
For instance, for a 2D input with shape `(batch_size, input_dim)`,
the output would have shape `(batch_size, units)`.
"""
def __init__(self, units,
activation=None,
use_bias=True,
kernel_initializer='glorot_uniform',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
**kwargs):
if 'input_shape' not in kwargs and 'input_dim' in kwargs:
kwargs['input_shape'] = (kwargs.pop('input_dim'),)
super(Dense, self).__init__(**kwargs)
self.units = units
self.activation = activations.get(activation)
self.use_bias = use_bias
self.kernel_initializer = initializers.get(kernel_initializer)
self.bias_initializer = initializers.get(bias_initializer)
self.kernel_regularizer = regularizers.get(kernel_regularizer)
self.bias_regularizer = regularizers.get(bias_regularizer)
self.activity_regularizer = regularizers.get(activity_regularizer)
self.kernel_constraint = constraints.get(kernel_constraint)
self.bias_constraint = constraints.get(bias_constraint)
self.input_spec = InputSpec(min_ndim=2)
self.supports_masking = True
def build(self, input_shape):
assert len(input_shape) >= 2
input_dim = input_shape[-1]
self.kernel = self.add_weight(shape=(input_dim, self.units),
initializer=self.kernel_initializer,
name='kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint)
if self.use_bias:
self.bias = self.add_weight(shape=(self.units,),
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint)
else:
self.bias = None
self.input_spec = InputSpec(min_ndim=2, axes={-1: input_dim})
self.built = True
def call(self, inputs):
output = K.dot(inputs, self.kernel)
if self.use_bias:
output = K.bias_add(output, self.bias)
if self.activation is not None:
output = self.activation(output)
return output
def compute_output_shape(self, input_shape):
assert input_shape and len(input_shape) >= 2
assert input_shape[-1]
output_shape = list(input_shape)
output_shape[-1] = self.units
return tuple(output_shape)
def get_config(self):
config = {
'units': self.units,
'activation': activations.serialize(self.activation),
'use_bias': self.use_bias,
'kernel_initializer': initializers.serialize(self.kernel_initializer),
'bias_initializer': initializers.serialize(self.bias_initializer),
'kernel_regularizer': regularizers.serialize(self.kernel_regularizer),
'bias_regularizer': regularizers.serialize(self.bias_regularizer),
'activity_regularizer': regularizers.serialize(self.activity_regularizer),
'kernel_constraint': constraints.serialize(self.kernel_constraint),
'bias_constraint': constraints.serialize(self.bias_constraint)
}
base_config = super(Dense, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
可以通过三种不同的方式来完成（我能想到）。如果你想要一个单一的致密层，将一个包含 256 个元素的向量映射到一个包含 num_classes 个元素的向量，并将它应用到你的整批数据中（也就是说，使用相同的 256 x num_classes 矩阵每个样本的权重），那么你不需要做任何特殊的事情，只需使用常规 Dense 层：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import Dense
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = Dense(num_classes, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2570
另一种方法是拥有一个巨大的 Dense 层，它同时获取所有 1024 * 256 值并在输出端产生所有 1024 * num_classes 值，即，具有形状为 (1024 * 256) x (1024 * num_classes) 的权重矩阵的层（如果内存为千兆字节！）。这也很容易做到，尽管它似乎不太可能是您需要的：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import Flatten, Dense, Reshape, Softmax
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
res = Flatten()(inp)
# This takes _a lot_ of memory!
layer = Dense(1024 * num_classes, activation=None)
out_res = layer(res)
# Apply softmax after reshaping
out_preact = Reshape((-1, num_classes))(out_res)
out = Softmax()(out_preact)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2684364800
最后，您可能想要一组 1024 个权重矩阵，每个矩阵都应用于输入中的相应样本，这意味着权重数组的形状为 (1024, 256, num_classes)。我不认为这可以通过标准 Keras 层之一完成（或者不知道如何）1，但是基于 [= 编写自定义层很容易17=] 这样做：
import tensorflow as tf
from tensorflow.keras.layers import Dense, InputSpec
class Dense2D(Dense):
def __init__(self, *args, **kwargs):
super(Dense2D, self).__init__(*args, **kwargs)
def build(self, input_shape):
assert len(input_shape) >= 3
input_dim1 = input_shape[-2]
input_dim2 = input_shape[-1]
self.kernel = self.add_weight(shape=(input_dim1, input_dim2, self.units),
initializer=self.kernel_initializer,
name='kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint)
if self.use_bias:
self.bias = self.add_weight(shape=(input_dim1, self.units),
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint)
else:
self.bias = None
self.input_spec = InputSpec(min_ndim=3, axes={-2: input_dim1, -1: input_dim2})
self.built = True
def call(self, inputs):
# Multiply each set of weights with each input element
output = tf.einsum('...ij,ijk->...ik', inputs, self.kernel)
if self.use_bias:
output += self.bias
if self.activation is not None:
output = self.activation(output)
return output
def compute_output_shape(self, input_shape):
assert input_shape and len(input_shape) >= 3
assert input_shape[-1]
output_shape = list(input_shape)
output_shape[-1] = self.units
return tuple(output_shape)
然后你会像这样使用它：
import tensorflow as tf
from tensorflow.keras import Input
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = Dense2D(num_classes, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2631680
1：作为 today points out in the comments, you can actually use a LocallyConnected1D 层来执行我尝试对 Dense2D 层执行的操作。就这么简单：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import LocallyConnected1D
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = LocallyConnected1D(num_classes, 1, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2631680
我正在处理一个自定义问题，我必须更改全连接层（Dense with softmax），我的模型代码是这样的（使用 Keras 框架）：
.......
batch_size = 8
inputs = tf.random.uniform(shape=[batch_size,1024,256],dtype=tf.dtypes.float32)
preds = Dense(num_classes,activation='softmax')(x) #final layer with softmax activation
....
model = Model(inputs=base_model.input,outputs=preds)
所以，我必须更改密集层代码以输出形状为 [batch_size、1024、num_classes] 的概率张量，而不使用 for 循环，我需要它有待优化而不是耗时函数
我要更改的密集代码版本：
class Dense(Layer):
"""Just your regular densely-connected NN layer.
`Dense` implements the operation:
`output = activation(dot(input, kernel) + bias)`
where `activation` is the element-wise activation function
passed as the `activation` argument, `kernel` is a weights matrix
created by the layer, and `bias` is a bias vector created by the layer
(only applicable if `use_bias` is `True`).
Note: if the input to the layer has a rank greater than 2, then
it is flattened prior to the initial dot product with `kernel`.
# Example
```python
# as first layer in a sequential model:
model = Sequential()
model.add(Dense(32, input_shape=(16,)))
# now the model will take as input arrays of shape (*, 16)
# and output arrays of shape (*, 32)
# after the first layer, you don't need to specify
# the size of the input anymore:
model.add(Dense(32))
```
# Arguments
units: Positive integer, dimensionality of the output space.
activation: Activation function to use
(see [activations](../activations.md)).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
kernel_initializer: Initializer for the `kernel` weights matrix
(see [initializers](../initializers.md)).
bias_initializer: Initializer for the bias vector
(see [initializers](../initializers.md)).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see [regularizer](../regularizers.md)).
bias_regularizer: Regularizer function applied to the bias vector
(see [regularizer](../regularizers.md)).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see [regularizer](../regularizers.md)).
kernel_constraint: Constraint function applied to
the `kernel` weights matrix
(see [constraints](../constraints.md)).
bias_constraint: Constraint function applied to the bias vector
(see [constraints](../constraints.md)).
# Input shape
nD tensor with shape: `(batch_size, ..., input_dim)`.
The most common situation would be
a 2D input with shape `(batch_size, input_dim)`.
# Output shape
nD tensor with shape: `(batch_size, ..., units)`.
For instance, for a 2D input with shape `(batch_size, input_dim)`,
the output would have shape `(batch_size, units)`.
"""
def __init__(self, units,
activation=None,
use_bias=True,
kernel_initializer='glorot_uniform',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
**kwargs):
if 'input_shape' not in kwargs and 'input_dim' in kwargs:
kwargs['input_shape'] = (kwargs.pop('input_dim'),)
super(Dense, self).__init__(**kwargs)
self.units = units
self.activation = activations.get(activation)
self.use_bias = use_bias
self.kernel_initializer = initializers.get(kernel_initializer)
self.bias_initializer = initializers.get(bias_initializer)
self.kernel_regularizer = regularizers.get(kernel_regularizer)
self.bias_regularizer = regularizers.get(bias_regularizer)
self.activity_regularizer = regularizers.get(activity_regularizer)
self.kernel_constraint = constraints.get(kernel_constraint)
self.bias_constraint = constraints.get(bias_constraint)
self.input_spec = InputSpec(min_ndim=2)
self.supports_masking = True
def build(self, input_shape):
assert len(input_shape) >= 2
input_dim = input_shape[-1]
self.kernel = self.add_weight(shape=(input_dim, self.units),
initializer=self.kernel_initializer,
name='kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint)
if self.use_bias:
self.bias = self.add_weight(shape=(self.units,),
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint)
else:
self.bias = None
self.input_spec = InputSpec(min_ndim=2, axes={-1: input_dim})
self.built = True
def call(self, inputs):
output = K.dot(inputs, self.kernel)
if self.use_bias:
output = K.bias_add(output, self.bias)
if self.activation is not None:
output = self.activation(output)
return output
def compute_output_shape(self, input_shape):
assert input_shape and len(input_shape) >= 2
assert input_shape[-1]
output_shape = list(input_shape)
output_shape[-1] = self.units
return tuple(output_shape)
def get_config(self):
config = {
'units': self.units,
'activation': activations.serialize(self.activation),
'use_bias': self.use_bias,
'kernel_initializer': initializers.serialize(self.kernel_initializer),
'bias_initializer': initializers.serialize(self.bias_initializer),
'kernel_regularizer': regularizers.serialize(self.kernel_regularizer),
'bias_regularizer': regularizers.serialize(self.bias_regularizer),
'activity_regularizer': regularizers.serialize(self.activity_regularizer),
'kernel_constraint': constraints.serialize(self.kernel_constraint),
'bias_constraint': constraints.serialize(self.bias_constraint)
}
base_config = super(Dense, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
可以通过三种不同的方式来完成（我能想到）。如果你想要一个单一的致密层，将一个包含 256 个元素的向量映射到一个包含 num_classes 个元素的向量，并将它应用到你的整批数据中（也就是说，使用相同的 256 x num_classes 矩阵每个样本的权重），那么你不需要做任何特殊的事情，只需使用常规 Dense 层：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import Dense
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = Dense(num_classes, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2570
另一种方法是拥有一个巨大的 Dense 层，它同时获取所有 1024 * 256 值并在输出端产生所有 1024 * num_classes 值，即，具有形状为 (1024 * 256) x (1024 * num_classes) 的权重矩阵的层（如果内存为千兆字节！）。这也很容易做到，尽管它似乎不太可能是您需要的：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import Flatten, Dense, Reshape, Softmax
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
res = Flatten()(inp)
# This takes _a lot_ of memory!
layer = Dense(1024 * num_classes, activation=None)
out_res = layer(res)
# Apply softmax after reshaping
out_preact = Reshape((-1, num_classes))(out_res)
out = Softmax()(out_preact)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2684364800
最后，您可能想要一组 1024 个权重矩阵，每个矩阵都应用于输入中的相应样本，这意味着权重数组的形状为 (1024, 256, num_classes)。我不认为这可以通过标准 Keras 层之一完成（或者不知道如何）1，但是基于 [= 编写自定义层很容易17=] 这样做：
import tensorflow as tf
from tensorflow.keras.layers import Dense, InputSpec
class Dense2D(Dense):
def __init__(self, *args, **kwargs):
super(Dense2D, self).__init__(*args, **kwargs)
def build(self, input_shape):
assert len(input_shape) >= 3
input_dim1 = input_shape[-2]
input_dim2 = input_shape[-1]
self.kernel = self.add_weight(shape=(input_dim1, input_dim2, self.units),
initializer=self.kernel_initializer,
name='kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint)
if self.use_bias:
self.bias = self.add_weight(shape=(input_dim1, self.units),
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint)
else:
self.bias = None
self.input_spec = InputSpec(min_ndim=3, axes={-2: input_dim1, -1: input_dim2})
self.built = True
def call(self, inputs):
# Multiply each set of weights with each input element
output = tf.einsum('...ij,ijk->...ik', inputs, self.kernel)
if self.use_bias:
output += self.bias
if self.activation is not None:
output = self.activation(output)
return output
def compute_output_shape(self, input_shape):
assert input_shape and len(input_shape) >= 3
assert input_shape[-1]
output_shape = list(input_shape)
output_shape[-1] = self.units
return tuple(output_shape)
然后你会像这样使用它：
import tensorflow as tf
from tensorflow.keras import Input
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = Dense2D(num_classes, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2631680
1：作为 today points out in the comments, you can actually use a LocallyConnected1D 层来执行我尝试对 Dense2D 层执行的操作。就这么简单：
import tensorflow as tf
from tensorflow.keras import Input
from tensorflow.keras.layers import LocallyConnected1D
batch_size = 8
num_classes = 10
inp = Input(shape=(1024, 256))
layer = LocallyConnected1D(num_classes, 1, activation='softmax')
out = layer(inp)
print(out.shape)
# (None, 1024, 10)
print(layer.count_params())
# 2631680