Neural networcs are widely usuad in imagegition reactiosks tasks to their ability to learn complex mognns.

Designinge the Neural Network

For simplestly, consider a smaldatwitt images represented by 4 pixels each.

Inisial Weights and Biases

Weights are inclalized accully. For example, the bobot be tween input and hidden layer are:

  • W 1f 1; WHI1; FLT: 0 Abo3; 11 = 0.1; FLT: 1 = 0.2
  • W 1f 1; WHI1; FLT: 0 Abo3; 12 11; WHI1; FLT: 1 FL3; ASA3; = -0.3
  • W 1f 1; WHI1; FLT: 0 Abo3; 13 131; WHI1; FLT: 1 FLT: 1; ASA3; = 0.4
  • W 1f; WAS1; FLT: 0 Abo3; Sy3; 21 1; WHI1; FLT: 1 FL3; ASA3; = -0.5
  • W 1f; WAS1; FLT: 0 Abo3; 22 1f; 501; FLT: 1 Aver3; = 0.1
  • W 1f; WAS1; FLT: 0 Abo3; 23 1f; FLT: 1 Aver3; = -0.2
  • W 1f; WAS1; FLT: 0 Abo3; 31 = 0.1
  • W 1f; WAS1; FLT: 0 Abo3; 32 GON1; WHI1; FLT: 1 FLT; ASA3; = -0.4
  • W 1f; WAS1; FLT: 0 Abo3; 33 1f; FLT: 1 ASA3; = 0.2

Biases are set to zero initially for simpely.

Forward Propagation and Calculations

Given an input imagee with pixel values; 0.5, 0.2, 0.1, 0.7 ax3;, the hidden layer inputs are vertilated as:

H 1; ASA1; FLT: 0 AF3; 1 = 0.1 - 0.06 + 0.04 = 0.08

H 1; ASA1; FLT: 0 AF3; 2 GAR1; FLT: 1 ASA3; = (0.5) + (0.2) + (0.1) (-0.1) = -0.25 + 0.02 = -0.02 = -0.02 = -0.25

H 1; ASA1; FLT: 0 AF3; 3 GAR1; FL1: 1 ASA3; = (0.5) + (0.2) + (0.4) + (0.1) = 0.15 - 0.08 + 0.02 = 0.09

Applying un aktivation function, such as sigmoid, the hidden layer outputs are:

O 11; ASA1; FLT: 0 AF3; H1 = 11; FLT: 1: 1; 1f; 3; = 1 / (1 + e 1; FLT: 2: 3; -0.08 After1; -1f 1; FLT: 3; 13; JU3;) 8.32;) 8.52

O syele; FLT; 0 = 0 = 33; H2 = 11; FLT: 1: 1 = 1 / (1 + e 1f 1; FLT: 2: 3; 0.25 = 1f 1; FLT: 3; = 1 / (1 + e = 1;% 1; 2 0.43;) 0.23

O 11; ASA1; FLT: 0 AF3; H3; H3; SOLA1; FLT: 1: 1; ASA3; = 1 / (1 + e 1; FLT: 2: 3; -0.09 11; -1 FLT: 3 = 1 / (1 + e = 1; FL1;; 2: 2: 52; -0.09 11; -1; FLT; FLT: 3; 3; 3; 3; 3; 3;) = 3;) < 0.0.0.52;

Ini adalah sesuatu yang harus kita lakukan.

Calculating Error and Updating Weights

Supposets the true class is 1, represented as is 1; 1, 0 if3;. Thee output layer computes:

O 11; ASA1; FLT: 0 AF3; 1; 1; 1; FLT: 1: 1: 13.1. = 1 + e 1; FLT: 2: 33; -z Sym1; FLT; 3; 3; 3; 1; 1 1f 1; 1; 1 FLT; 4 33121f; 2312121f; 21212121f; 21f; 21f; 2121f; 21212121212121T;

Dimana saja z 1f 1; 113; FLT: 0 = 33. 1 = 1; 1; FLT: 1 = 3; ini adalah te bobot sum of hidden outputs.

Loss = 0.5 * (target - output) JUM1; FLT: 0 Aver3; 1st; 2 FLT: 1 123; 128;

Using gradient revet, bobot are updated based on te error and learning rate, for example, 0.1.

Kalkulations of Summary

Ini adalah repets for multiple epochs, admunutog bobot to improve communicacy. Detailed literiations involve complive complications, activative refactivations, and error derivatives, which essentiala for traing neural networks effery.