# Param count in last layer high, how can I decrease?

Not sure where to put this... I am trying to create a convolutional architecture for a DQN in keras, and I want to know why my param count is so high for my last layer compared to the rest of the network. I've tried slowly decreasing the dimensions of the layers above it, but it performs quite poorly. I want to know if there's anything I can do to decrease the param count of that last layer, besides the above.

Code:

#Import statements.
import random
import numpy as np
import tensorflow as tf
import tensorflow.keras.layers as L
from collections import deque
import layers as mL
import tensorflow.keras.optimizers as O
import optimizers as mO
import tensorflow.keras.backend as K

#Conv function.
def conv(x, units, kernel, stride, noise=False, padding='valid'):
if noise:
y = mL.PGaussian()(y)
return y

#Network
x_input = L.Input(shape=self.state)
x_goal = L.Input(shape=self.state)
x = L.Concatenate(-1)([x_input, x_goal])
x_list = []
for i in range(2):
x = conv(x, 4, (7,7), 1)
for i in range(2):
x = conv(x, 8, (5,5), 2)
for i in range(10):
x = conv(x, 6, (3,3), 1, noise=True)
x = L.Conv2D(1, (3,3), 1)(x)
x_shape = K.int_shape(x)
x = L.Reshape((x_shape[1], x_shape[2]))(x)
x = L.Flatten()(x)
crit = L.Dense(1, trainable=False)(x)
critic = tf.keras.models.Model([x_input, x_goal], crit)
act1 = L.Dense(self.action, trainable=False)(x)
act2 = L.Dense(self.action2, trainable=False)(x)
act1 = L.Softmax()(act1)
act2 = L.Softmax()(act2)
actor = tf.keras.models.Model([x_input, x_goal], [act1, act2])
actor.summary()



actor.summary():

________________________________________________________________
Layer (type)                    Output Shape         Param #     Connected to
==================================================================================================
input_2 (InputLayer)            [(None, 300, 300, 3) 0
__________________________________________________________________________________________________
input_3 (InputLayer)            [(None, 300, 300, 3) 0
__________________________________________________________________________________________________
concatenate (Concatenate)       (None, 300, 300, 6)  0           input_2[0][0]
input_3[0][0]
__________________________________________________________________________________________________
conv2d_52 (Conv2D)              (None, 294, 294, 4)  1180        concatenate[0][0]
__________________________________________________________________________________________________
conv2d_53 (Conv2D)              (None, 288, 288, 4)  788         conv2d_52[0][0]
__________________________________________________________________________________________________
conv2d_54 (Conv2D)              (None, 142, 142, 8)  808         conv2d_53[0][0]
__________________________________________________________________________________________________
conv2d_55 (Conv2D)              (None, 69, 69, 8)    1608        conv2d_54[0][0]
__________________________________________________________________________________________________
conv2d_56 (Conv2D)              (None, 67, 67, 6)    438         conv2d_55[0][0]
__________________________________________________________________________________________________
p_gaussian (PGaussian)          (None, 67, 67, 6)    1           conv2d_56[0][0]
__________________________________________________________________________________________________
conv2d_57 (Conv2D)              (None, 65, 65, 6)    330         p_gaussian[0][0]
__________________________________________________________________________________________________
p_gaussian_1 (PGaussian)        (None, 65, 65, 6)    1           conv2d_57[0][0]
__________________________________________________________________________________________________
conv2d_58 (Conv2D)              (None, 63, 63, 6)    330         p_gaussian_1[0][0]
__________________________________________________________________________________________________
p_gaussian_2 (PGaussian)        (None, 63, 63, 6)    1           conv2d_58[0][0]
__________________________________________________________________________________________________
conv2d_59 (Conv2D)              (None, 61, 61, 6)    330         p_gaussian_2[0][0]
__________________________________________________________________________________________________
p_gaussian_3 (PGaussian)        (None, 61, 61, 6)    1           conv2d_59[0][0]
__________________________________________________________________________________________________
conv2d_60 (Conv2D)              (None, 59, 59, 6)    330         p_gaussian_3[0][0]
__________________________________________________________________________________________________
p_gaussian_4 (PGaussian)        (None, 59, 59, 6)    1           conv2d_60[0][0]
__________________________________________________________________________________________________
conv2d_61 (Conv2D)              (None, 57, 57, 6)    330         p_gaussian_4[0][0]
__________________________________________________________________________________________________
p_gaussian_5 (PGaussian)        (None, 57, 57, 6)    1           conv2d_61[0][0]
__________________________________________________________________________________________________
conv2d_62 (Conv2D)              (None, 55, 55, 6)    330         p_gaussian_5[0][0]
__________________________________________________________________________________________________
p_gaussian_6 (PGaussian)        (None, 55, 55, 6)    1           conv2d_62[0][0]
__________________________________________________________________________________________________
conv2d_63 (Conv2D)              (None, 53, 53, 6)    330         p_gaussian_6[0][0]
__________________________________________________________________________________________________
p_gaussian_7 (PGaussian)        (None, 53, 53, 6)    1           conv2d_63[0][0]
__________________________________________________________________________________________________
conv2d_64 (Conv2D)              (None, 51, 51, 6)    330         p_gaussian_7[0][0]
__________________________________________________________________________________________________
p_gaussian_8 (PGaussian)        (None, 51, 51, 6)    1           conv2d_64[0][0]
__________________________________________________________________________________________________
conv2d_65 (Conv2D)              (None, 49, 49, 6)    330         p_gaussian_8[0][0]
__________________________________________________________________________________________________
p_gaussian_9 (PGaussian)        (None, 49, 49, 6)    1           conv2d_65[0][0]
__________________________________________________________________________________________________
conv2d_66 (Conv2D)              (None, 47, 47, 1)    55          p_gaussian_9[0][0]
__________________________________________________________________________________________________
reshape (Reshape)               (None, 47, 47)       0           conv2d_66[0][0]
__________________________________________________________________________________________________
flatten (Flatten)               (None, 2209)         0           reshape[0][0]
__________________________________________________________________________________________________
dense_1 (Dense)                 (None, 2000)         4420000     flatten[0][0]
__________________________________________________________________________________________________
dense_2 (Dense)                 (None, 200)          442000      flatten[0][0]
__________________________________________________________________________________________________
softmax (Softmax)               (None, 2000)         0           dense_1[0][0]
__________________________________________________________________________________________________
softmax_1 (Softmax)             (None, 200)          0           dense_2[0][0]
==================================================================================================
Total params: 4,869,857
Trainable params: 7,857
Non-trainable params: 4,862,000
__________________________________________________________________________________________________


If I understood correctly you want to decrease the parameters count on the last layer (dense_2 layer right?). It would be nice to know why you want to decrease the number of parameters in the last layers... But I'll proceed with what I see.

Firstly, the dense layers (or fully connected in literature) have a deterministic number of parameters (or weights) to learn according to the size of the input and output tensor. The relation is the following:

$$N_{params} = Y_{output} \cdot (X_{input} +1) = 200 \cdot (2209 +1) = 442000$$

Where:

• $$Y_{output}$$: Output tensor shape (act2=200 which is the output of dense_2 layer)
• $$X_{input}$$: Input tensor shape (x=2209which is the ouput of flatten layer)

So if you want to decrease the number of parameters you can:

• Decrease the input tensor: your self.action2 which I guess is the action space so you might not be able to decrease it
• Decrease the output tensor: maybe? I would need more context (code) to know if that is even possible

So, in short: if you are not willing to change your the input or output tensor to the Dense layers, then no, you can not decrease the number of parameters.

BONUS: In case you missed it, I have noticed you have set your dense layers to trainable=False. So in principle you should not care about decreasing number of parameters (which in most cases is motivated to reduce training time) since they are already not being trained. You can check that in the Keras summary output:

Total params: 4,869,857
Trainable params: 7,857
Non-trainable params: 4,862,000


Where the non-trainable parameters are $$4862000 = 4420000 + 442000$$, which are the number of parameters of your 2 dense layers.

• If I froze the action layer, would it degrade performance? Likewise, if I bottlenecked the layer above the action layers, wouldn't there be a loss of information? – ZeroMaxinumXZ Jan 28 at 21:47
• What is the action layer you are referring to?... I mean, you already froze the 2 dense layers which outputs act1 and act2 by setting trainable=False. Why did you freeze them? I you posted more code I would be able to get the context of it. – JVGD Jan 29 at 9:50