How to make a Keras Dense Layer deal with 3D tensor as input for this Softmax Fully Connected Layer?

Question

I am working on a custom problem, and i have to change the fully connected layer (Dense with softmax), My model code is something like this (with Keras Framework):

.......
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)

So, i have to change the Code of Dense Layer to output a Tensor of probabilities with the shape of [batch_size, 1024, num_classes], without using a for loop, i need it to be optimized and not a consuming time function

The Dense code version that i want to change:

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()))

Answer 1

There are three different ways in which this can be done (that I can think of). If you want to have a single dense layer, that maps a vector of 256 elements to a vector of num_classes elements, and apply it all across your batch of data (that is, use the same 256 x num_classes matrix of weights for every sample), then you don't need to do anything special, just use a regular Dense layer:

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

Another way would be to have a single huge Dense layer that takes all 1024 * 256 values in at the same time and produces all 1024 * num_classes values at the output, that is, a layer with a matrix of weights with shape (1024 * 256) x (1024 * num_classes) (in the order if gigabytes of memory!). This is easy to do too, although it seems unlikely to be what you need:

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

Finally, you may want to have a set of 1024 weight matrices, each one applied to the corresponding sample in the input, which would imply an array of weights with shape (1024, 256, num_classes). I don't think this can be done with one of the standard Keras layers (or don't know how to)¹, but it's easy enough to write a custom layer based on Dense to do that:

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)

You would then use it like this:

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: As today points out in the comments, you can actually use a LocallyConnected1D layer to do the same that I tried to do with my Dense2D layer. It is as simple as this:

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