Summary  
This chapter introduces the core concept of feedforward neural networks trained via supervised learning, showing how layers of interconnected “neurons” learn patterns from labeled examples to perform classification tasks.

General domain of usage  
Image recognition (e.g., distinguishing drawings of cats and dogs)

## Introduction

Imagine learning to translate English into Spanish. You memorize words, phrases, and their context — and soon you can translate sentences you’ve never seen before.
A neural network works the same way: it **learns from examples** such as text, images, or audio, and uses discovered patterns to make predictions.

Just as people learn to distinguish cats from dogs by seeing many examples, a neural network learns to perform tasks like **classification**, **regression**, or **generation** by analyzing labeled data. This process is called **supervised learning**, the most common way neural networks are trained.

During training, the network sees examples with known answers (**labels**) and adjusts itself to match them. Later, when given new **unlabeled** inputs, it applies what it has learned to make predictions on its own.

Note

Below is a simple demonstration of a neural network trained to **recognize drawings of cats and dogs**.
Draw something and see how the model classifies it:

* **LMB** – draw
* **Shift + LMB** – erase


<!DOCTYPE html>
<html lang="en">
  <head>
    <style>
      * {
        box-sizing: border-box;
      }

      :root {
        --dark-blue: #1e2635;
        --blue: #4f5e77;
        --orange: #ff8a00;
        --grey: #f4f4f4;
      }

      /* body {
          width: 713px;
          border: 1px solid;
        } */

      ul {
        list-style-type: none;
        padding: 0;
      }

      li {
        margin: 0.5rem 0;
        text-align: center;
      }

      a {
        text-decoration: none;
      }

      .custom-parent-container {
        display: flex;
        justify-content: space-between;
      }

      /* >>>>>>>>>>> CANVAS <<<<<<<<<<<<<<<<<< */
      .canvas {
        width: 256px;
        height: 256px;
        border-radius: 5px;
        border: 3px solid var(--orange);
        box-shadow: 4px 4px 4px 0px rgba(0, 0, 0, 0.25);
        background-color: var(--grey);
      }

      .tools-wrapper {
        width: 256px;
        display: flex;
        border-bottom-left-radius: 10px;
        border-bottom-right-radius: 10px;
        padding-top: 15px;
      }

      .customize-btn {
        background-color: var(--grey);
        color: var(--orange);
        font-size: 20px;
        border: 3px solid var(--orange);
        border-radius: 5px;
        padding: 5px 11px;
        font-family: "Hind Siliguri";
        font-weight: 700;
        cursor: pointer;
        transition: 0.5s ease-in-out;
      }

      .customize-btn:hover,
      .customize-btn:focus {
        background-color: var(--orange);
        color: #fff;
      }

      .cat-btn {
        margin-left: 5px;
      }

      .clear-btn {
        margin-left: auto;
      }

      /* >>>>>>>>>>>>>>>> SQUARES <<<<<<<<<<<<<*/
      .layers-section {
        width: 340px;
        height: 310px;
        display: flex;
        flex-direction: row;
        align-items: center;
        margin-left: 20px;
      }

      .square {
        margin: 10px 0;
        width: 30px;
        height: 30px;
        border-radius: 2px;
        border: 3px solid var(--orange);
        background: transparent;
        position: relative;
        display: flex;
        align-items: flex-end;
        justify-content: center;
      }

      .lines-wrapper {
        top: 0;
        position: relative;
        width: 100%;
        height: 300px;
      }

      .svg-icon {
        position: absolute;
      }

      .square-filler {
        width: 100%;
        background-color: var(--orange);
        margin: 1px;
        transition: height 1s;
      }

      /* IMAGES */

      .images-section {
        display: flex;
        flex-direction: column;
        justify-content: center;
        padding-bottom: 20px;
      }

      .custom-image:not(:last-child) {
        margin-bottom: 10px;
      }

      .custom-image {
        transition: width 1s;
      }
    </style>
  </head>
  <body>
    <div class="custom-parent-container">
      
      <div class="section">
        <canvas
          onmousedown="handleCanvasMouseDown(event)"
          onmousemove="handleCanvasMouseMove(event)"
          onmouseup="handleCanvasMouseUp(event)"
          class="canvas js-canvas"
          width="256"
          height="256"
          id="canvas"
        ></canvas>

        <div class="tools-wrapper">
          <button type="button" class="customize-btn js-dog-btn" onclick="handleDogBtnClick()">
            Dog
          </button>
          <button
            type="button"
            class="customize-btn cat-btn js-cat-btn"
            onclick="handleCatBtnClick()"
          >
            Cat
          </button>
          <button
            type="button"
            class="customize-btn clear-btn js-clear-btn"
            onclick="handleClearClick()"
          >
            Clear
          </button>
        </div>
      </div>
      
      <div class="layers-section js-layers-section"></div>
      
      <div class="images-section">
        <img
          class="custom-image"
          src="https://staging-content-media-cdn.codefinity.com/courses/c1087363-9025-4c37-8d5e-983a32a007e9/other-section/oleh-s_tests/cat.png"
          alt="Cat Illustration"
          width="30px"
          style="width: 30px"
          id="class_cat"
        />
        <img
          class="custom-image"
          src="https://staging-content-media-cdn.codefinity.com/courses/c1087363-9025-4c37-8d5e-983a32a007e9/other-section/oleh-s_tests/dog.png"
          alt="Dog Illustration"
          width="30px"
          style="width: 30px"
          id="class_dog"
        />
      </div>
    </div>
    
    
    <script>
      // Canvas properties
      window.penSize = 2;
      window.isDrawing = false;
      window.penColor = "black";
      window.lastX = undefined;
      window.lastY = undefined;
    </script>
    
    <script>
      function handleCanvasMouseDown(e) {
        const canvasContext = document.querySelector(".js-canvas").getContext("2d");

        isDrawing = true;
        lastX = e.offsetX;
        lastY = e.offsetY;

        if (e.shiftKey) {
          // If Shift key is held down, start clearing mode
          clearPixels(lastX, lastY);
        } else {
          canvasContext.beginPath();
          canvasContext.moveTo(lastX, lastY);
        }
      }

      function handleCanvasMouseUp() {
        isDrawing = false;
        lastX = undefined;
        lastY = undefined;
      }

      function handleCanvasMouseMove(e) {
        const canvasContext = document.querySelector(".js-canvas").getContext("2d");

        if (isDrawing) {
          const currentX = e.offsetX;
          const currentY = e.offsetY;

          if (e.shiftKey) {
            // If Shift key is held down and in clearing mode, clear the pixels
            clearPixels(currentX, currentY);
          } else {
            canvasContext.lineTo(currentX, currentY);
            canvasContext.strokeStyle = penColor;
            canvasContext.lineWidth = penSize * 2;
            canvasContext.stroke();
          }

          lastX = currentX;
          lastY = currentY;
        }
      }

      function clearPixels(x, y) {
        const canvasContext = document.querySelector(".js-canvas").getContext("2d");
        canvasContext.clearRect(x - penSize, y - penSize, penSize * 2, penSize * 2);
      }

      function handleClearClick() {
        const canvas = document.querySelector(".js-canvas");
        const canvasContext = canvas.getContext("2d");
        canvasContext.clearRect(0, 0, canvas.width, canvas.height);
      }
    </script>

    
    
    <script>
      window.nn_data = [
        [
          { id: "neuron_0_0", fill: 50 },
          { id: "neuron_0_1", fill: 50 },
          { id: "neuron_0_2", fill: 50 },
          { id: "neuron_0_3", fill: 50 },
        ],
        [
          { id: "neuron_1_0", fill: 50 },
          { id: "neuron_1_1", fill: 50 },
          { id: "neuron_1_2", fill: 50 },
        ],
        [
          { id: "neuron_2_0", fill: 50 },
          { id: "neuron_2_1", fill: 50 },
          { id: "neuron_2_2", fill: 50 },
          { id: "neuron_2_3", fill: 50 },
          { id: "neuron_2_4", fill: 50 },
          { id: "neuron_2_5", fill: 50 },
          { id: "neuron_2_6", fill: 50 },
          { id: "neuron_2_7", fill: 50 },
        ],
        [
          { id: "neuron_3_0", fill: 50 },
          { id: "neuron_3_1", fill: 50 },
          { id: "neuron_3_2", fill: 50 },
          { id: "neuron_3_3", fill: 50 },
          { id: "neuron_3_4", fill: 50 },
          { id: "neuron_3_5", fill: 50 },
        ],
        [
          { id: "neuron_4_0", fill: 50 },
          { id: "neuron_4_1", fill: 50 },
        ],
      ];
      window.points = {
        1: [150],
        2: [130, 170],
        3: [110, 150, 190],
        4: [90, 130, 170, 210],
        5: [70, 110, 150, 190, 230],
        6: [50, 90, 130, 170, 210, 250],
        7: [30, 70, 110, 150, 190, 230, 270],
        8: [10, 50, 90, 130, 170, 210, 250, 290],
      };
    </script>
    

    
    <script src="https://staging-content-media-cdn.codefinity.com/courses/c1087363-9025-4c37-8d5e-983a32a007e9/other-section/andrii_test/scripts/index_ww.js"></script>

    <script>
      function handleLoad() {
        const layersSectionElement = document.querySelector(".js-layers-section");

        // Generate columns and sets of lines dynamically
        for (let i = 0; i < nn_data.length; i++) {
          const column = buildColumnSquares(nn_data[i]);
          layersSectionElement.appendChild(column);

          if (i < nn_data.length - 1) {
            const setOfLines = createDots(nn_data[i].length, nn_data[i + 1].length);
            layersSectionElement.appendChild(setOfLines);
          }
        }

        if (isMobile()) {
          //console.log('Mobile Detected');
          document.getElementsByClassName("custom-parent-container")[0].style.display = "none";
        } else {
          //console.log('Mobile Not Detected');
          start_nn();
        }
      }

      function buildColumnSquares(squaresArray) {
        const columnParentElement = document.createElement("div");
        columnParentElement.setAttribute("class", "layer");

        const columnSquaresMarkup = squaresArray
          .map(
            ({ id, fill }) => `
                <div class="square" id="${id}">
                  <div class="square-filler" style="height: ${(22 * fill) / 100}px;"></div>
                </div>
              `
          )
          .join("");

        columnParentElement.innerHTML = columnSquaresMarkup;
        return columnParentElement;
      }

      function createDots(...keys) {
        if (keys.includes(0)) {
          return;
        }
        const linesParentElement = document.createElement("div");
        linesParentElement.setAttribute("class", "lines-wrapper");

        const combinations = [];

        // Generate all combinations of points from different arrays
        for (let i = 0; i < keys.length; i++) {
          const key1 = keys[i];
          const linePoints1 = points[key1];

          for (let j = i + 1; j < keys.length; j++) {
            const key2 = keys[j];
            const linePoints2 = points[key2];

            // Loop through all combinations of points from different arrays
            for (const point1 of linePoints1) {
              for (const point2 of linePoints2) {
                combinations.push({ point1, point2 });
              }
            }
          }
        }

        // Create SVG elements and append them to the container
        for (const combination of combinations) {
          const svgElement = createLine(combination.point1, combination.point2);
          linesParentElement.innerHTML += svgElement;
        }

        return linesParentElement; // Return the container
      }

      function createLine(point1, point2) {
        return `
            <svg width="100%" height="100%" class="svg-icon">
              <line
                x1="0"
                y1="${point1}"
                x2="100%"
                y2="${point2}"
                stroke="#ff8a00"
                stroke-width="1"
              />
            </svg>
          `;
      }

      function isMobile() {
        var a;
        if (
          navigator.userAgent.match(/Android/i) ||
          navigator.userAgent.match(/webOS/i) ||
          navigator.userAgent.match(/iPhone/i) ||
          navigator.userAgent.match(/iPad/i) ||
          navigator.userAgent.match(/iPod/i) ||
          navigator.userAgent.match(/BlackBerry/i) ||
          navigator.userAgent.match(/Windows Phone/i)
        ) {
          a = true;
        } else {
          a = false;
        }
        return a;
      }

      window.onload = handleLoad();
    </script>
  </body>
</html>

Neural networks are powerful algorithms inspired by the structure of the human brain that are used to solve complex machine learning problems. You will build your own Neural Network from scratch to understand how it works. After this course, you will be able to create neural networks for solving classification and regression problems using the scikit-learn library.

First, we will discuss what a neural network is and how it works. And also consider the scope of its application.

Next, we will try to build our own neural network and see how efficiently it copes with learning. We will also consider a ready-made solution from the scikit-learn library.

Finally, we will give you some additional useful information on how to understand which model to use and what types of neural networks there are. To complete the course, you will be tested on your acquired knowledge.

What is a Neural Network?

Introduction

Neural Network Example