Question

A Convolutional Neural Network (CNN) has 3 consecutive 5×5 convolutional layers with a stride of 1 without pooling. What is the size of the receptive field for a neuron (the set of input image pixels which activate the neuron) in the 3rd convolutional layer?

A. 5.

B. 9.

C. 13.

D. 125.

Answer 1

Solution:-

Let the receptive field of a layer is given by Rl, where l is the number of layer

Let Jl be the jump (or in simpler words distance between the two consecutive features)

Let the stride be s

Let the kernel size be k

so Jl = J(l-1)*s

Rl = (R(l-1) + (k-1)*J(l-1))

The initial condition for Input layer = R0 = 1, J0 = 1

For conv layer 1 = J1 = J0*s = 1*1 = 1

R1 = R0 + (k-1)*J0 = 1 + (5-1)*1 = 5

For conv layer 2 = J2 = J1*s = 1*1 = 1

R2 = R1 + (k-1)*J1 = 5 + (5-1)*1 = 9

For conv layer 3 = J3 = J2*s = 1*1 = 1

R3 = R2 + (k-1)*J2 = 9 + (5-1)*1 = 13

So answer will be C.

I hope it solves your problem and if you have any doubt please ask in the comments and if you liked the solution please upvote. Thanks.

Answer 2

Given:

• Kernel size (K) = $5\times 5$ for all layers.

• Stride (S) = 1 for all layers.

• No pooling layers (only convolutions).

Receptive Field (RF) Formula for Consecutive Layers:

$$R{F}_{\text{new}}=R{F}_{\text{prev}}+(K-1)\times S_{\text{prev}}$$

 

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Step-by-Step Calculation:

1. Layer 1 (First Conv):

• Input RF = 1 (single pixel).

• Output RF:

  $$R{F}_1=1+(5-1)\times 1=5$$

2. Layer 2 (Second Conv):

• Input RF = 5.

• Output RF:

  $$R{F}_2=5+(5-1)\times 1=9$$

3. Layer 3 (Third Conv):

• Input RF = 9.

• Output RF:

  $$R{F}_3=9+(5-1)\times 1=13$$

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Final Answer:

The receptive field in the 3rd layer is 13 pixels (Option C).