1 Question 1 A Deep Neural Network is shown in Figure 1. The aim of this network is to classify human and dog. 1. Calculate the initial error of the Deep Neural Network by feeding the following input: X₁ = 5, X₂ = 2. The X₁ indicates the length of the tail and X₂ indicates the number of eyes. 2. Update the layer 2 weights (ws,we, w7 ws) of the Deep Neural Network shown in Figure 1 for a single iteration. The learning rate is set to a = 1 and there are no biases in the neurons. 3. Recalculate the error with the updated weights of layer 2 and report its improvement with respect to the initial error (percentage wise). 4. (Bonus Question) Update and report the layer 1 weights (w₁,w₂, 3, 4) of the network and estimate the improvement to the error. Input /₂ = 0 Layer 1 3/₂ /₂0 Layer 2 Predicted Output Real Output 1 0 BE Figure 1: A Deep Neural Network designed for dog or human detection
1 Question 1 A Deep Neural Network is shown in Figure 1. The aim of this network is to classify human and dog. 1. Calculate the initial error of the Deep Neural Network by feeding the following input: X₁ = 5, X₂ = 2. The X₁ indicates the length of the tail and X₂ indicates the number of eyes. 2. Update the layer 2 weights (ws,we, w7 ws) of the Deep Neural Network shown in Figure 1 for a single iteration. The learning rate is set to a = 1 and there are no biases in the neurons. 3. Recalculate the error with the updated weights of layer 2 and report its improvement with respect to the initial error (percentage wise). 4. (Bonus Question) Update and report the layer 1 weights (w₁,w₂, 3, 4) of the network and estimate the improvement to the error. Input /₂ = 0 Layer 1 3/₂ /₂0 Layer 2 Predicted Output Real Output 1 0 BE Figure 1: A Deep Neural Network designed for dog or human detection
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![1 Question 1
A Deep Neural Network is shown in Figure 1. The aim of this network is to classify human and dog.
1. Calculate the initial error of the Deep Neural Network by feeding the following input: X₁ = 5, X₂ = 2.
The X₁ indicates the length of the tail and X₂ indicates the number of eyes.
2. Update the layer 2 weights (ws,we,w7,ws) of the Deep Neural Network shown in Figure 1 for a single
iteration. The learning rate is set to a = 1 and there are no biases in the neurons.
3. Recalculate the error with the updated weights of layer 2 and report its improvement with respect to
the initial error (percentage wise).
4. (Bonus Question) Update and report the layer 1 weights (w₁,₂,3,w₁) of the network and estimate
the improvement to the error..
Input
X₁-5
X₂-2
W₂-0
W₂=0
w₂ = 0
W₁=0
Layer 1
3₁
W₁=0
₂0
w₂0
Layer 2
Predicted
Output
Real
Output
1
0
Figure 1: A Deep Neural Network designed for dog or human detection](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F948596cc-5887-46b7-a7b7-05d78b1fa3eb%2Fcca36ac4-e455-4f28-8f66-9526c201aa80%2Fm6s9o6_processed.png&w=3840&q=75)
Transcribed Image Text:1 Question 1
A Deep Neural Network is shown in Figure 1. The aim of this network is to classify human and dog.
1. Calculate the initial error of the Deep Neural Network by feeding the following input: X₁ = 5, X₂ = 2.
The X₁ indicates the length of the tail and X₂ indicates the number of eyes.
2. Update the layer 2 weights (ws,we,w7,ws) of the Deep Neural Network shown in Figure 1 for a single
iteration. The learning rate is set to a = 1 and there are no biases in the neurons.
3. Recalculate the error with the updated weights of layer 2 and report its improvement with respect to
the initial error (percentage wise).
4. (Bonus Question) Update and report the layer 1 weights (w₁,₂,3,w₁) of the network and estimate
the improvement to the error..
Input
X₁-5
X₂-2
W₂-0
W₂=0
w₂ = 0
W₁=0
Layer 1
3₁
W₁=0
₂0
w₂0
Layer 2
Predicted
Output
Real
Output
1
0
Figure 1: A Deep Neural Network designed for dog or human detection
![Formula Sheet
The ANN neurons function is described as below:
(1)
where w, b, X and o(2) are the weight, bias, input and activation function respectively. Sigmoid function
o(z)= is widely used as an activation function (outputs 0-1).
The error function can also be shown as the following:
n
y = o(w₂X₁ + bi)
i=1
JE₁
E =
Əw(L)
i=1
y(2) = $ (z(L))
The parital derivative of error, with respect of the weight for layer (L) is calculated as below:
(3 - 9)²
- = y(L-1) ó' (z(L)) 2 (y(L) — ŷ),
where the derivative of the sigmoid activation function is o' (z(2)) = 6 (z(¹)) ((1 − 6 (z(¹²))).
For each iteration, the weight can then be updated by the following:
JE
'dw'
where learning rate a dictates how fast the weights need to be adjusted.
ww-a-
(2)
(3)
(4)
(5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F948596cc-5887-46b7-a7b7-05d78b1fa3eb%2Fcca36ac4-e455-4f28-8f66-9526c201aa80%2Fu7z7jli_processed.png&w=3840&q=75)
Transcribed Image Text:Formula Sheet
The ANN neurons function is described as below:
(1)
where w, b, X and o(2) are the weight, bias, input and activation function respectively. Sigmoid function
o(z)= is widely used as an activation function (outputs 0-1).
The error function can also be shown as the following:
n
y = o(w₂X₁ + bi)
i=1
JE₁
E =
Əw(L)
i=1
y(2) = $ (z(L))
The parital derivative of error, with respect of the weight for layer (L) is calculated as below:
(3 - 9)²
- = y(L-1) ó' (z(L)) 2 (y(L) — ŷ),
where the derivative of the sigmoid activation function is o' (z(2)) = 6 (z(¹)) ((1 − 6 (z(¹²))).
For each iteration, the weight can then be updated by the following:
JE
'dw'
where learning rate a dictates how fast the weights need to be adjusted.
ww-a-
(2)
(3)
(4)
(5)
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