{"id":106,"date":"2025-09-05T23:51:39","date_gmt":"2025-09-05T21:51:39","guid":{"rendered":"https:\/\/mlatilikzsolt.hu\/?p=106"},"modified":"2025-09-06T18:46:44","modified_gmt":"2025-09-06T16:46:44","slug":"intro-to-neural-networks_part3","status":"publish","type":"post","link":"https:\/\/mlatilikzsolt.hu\/en\/2025\/09\/05\/intro-to-neural-networks_part3\/","title":{"rendered":"Introduction to the World of Neural Networks Part 3"},"content":{"rendered":"

In the previous<\/a> section, we saw how a single artificial neuron works. But a neuron on its own isn't very useful. Its true usefulness comes when you connect multiple neurons together to form a layer. In this section, we'll look at that in a little more detail.<\/p>\n\n\n\n

What Is a Layer?<\/h2>\n\n\n\n

In simple terms, a layer is a bunch of neurons that work with the same input data, but each neuron processes that data with different weights and biases. This data can come directly from the input or from a previous layer. Thanks to the different weights and offsets, each neuron can recognize different patterns in the same data.<\/p>\n\n\n\n

For example, if we analyze an image with a neural network, some neurons can recognize vertical lines, others horizontal lines, and still others oblique lines. By combining these appropriately, it becomes possible to recognize more complex shapes. This is how Facebook's feature that recognizes faces in photos works, for example. <\/p>\n\n\n\n

Let's look at an example.<\/h2>\n\n\n\n

For the sake of illustration, let's build a simple layer with:<\/p>\n\n\n\n

    \n
  • 4 inputs: x1<\/sub>, x2<\/sub>, x3<\/sub>, x4<\/sub><\/li>\n\n\n\n
  • 3 neurons<\/li>\n<\/ul>\n\n\n\n

    Each neuron uses four weights (one for each input) and a bias, from which it calculates its own output value.<\/p>\n\n\n\n

    z_j= w_{j1} \\cdot x_1 + w_{j2} \\cdot x_2 + w_{j3} \\cdot x_3 + w_{j4} \\cdot x_4 + b_j<\/pre><\/div>\n\n\n\n
    In this formula, j refers to each neuron (1, 2, 3). After the calculations are done, the output of the layer will be a three-element vector: [z1<\/sub>, z2<\/sub>, z3<\/sub>]. This can be either the input to a next layer or a final result that is not processed further.<\/p>\n\n\n\n
    \"\"<\/figure>\n\n\n\n
    Python example: calculating the output of a layer<\/h2>\n\n\n\n
    Let's see how we can program the above example in Python. <\/p>\n\n\n\n
    Important: in this example we do not use an activation function, we only calculate the \u201craw\u201d output data.<\/p>\n\n\n\n