Convolutional Neural Networks (CNN) Explained

Convolutional neural networks power image classification, face recognition, medical image analysis, defect detection on production lines and the vision systems of self driving cars. They are a special kind of neural network whose structure matches the way images are organised: nearby pixels are related, and the same pattern can appear anywhere in the picture.

Why convolutional neural networks were needed

A 224 × 224 colour image has 224 × 224 × 3 = 150 528 input values. A fully connected layer with just 64 neurons would need over 9.6 million weights, and it would have to learn the same edge detector separately for every location. Goodfellow, Bengio and Courville describe three ideas that make convolution better suited:

• Sparse interactions: each output depends only on a small patch of the input, not on every pixel.
• Parameter sharing: the same kernel weights are used at every position, so a feature is learned once.
• Equivariance to translation: if the object moves in the image, its feature moves the same way in the feature map.

How a convolutional layer works

A kernel is a small grid of weights, typically 3 × 3 or 5 × 5, extending through all input channels. It is placed on a patch of the input, each weight is multiplied by the value under it, the products are summed and a bias is added. The kernel then slides by a step called the stride and repeats. The grid of results is a feature map. Strictly, deep learning libraries compute cross correlation (the kernel is not flipped), but it is still called convolution.

Download diagram (WebP)

Stride, padding and output size

Padding adds a border of zeros around the input so that the kernel can be centred on edge pixels. With a 3 × 3 kernel, a padding of 1 and a stride of 1 keep the output the same size as the input (“same” padding). Without padding (“valid”) the output shrinks. For input width W, kernel size K, padding P and stride S, the output width is:

$$W_\text{out} = \left\lfloor \frac{W - K + 2P}{S} \right\rfloor + 1$$

Channels and parameters

Each kernel spans all C_in input channels, so it has K × K × C_in weights plus one bias. A layer with C_out kernels produces C_out feature maps and has:

$$N_\text{params} = (K \times K \times C_\text{in} + 1) \times C_\text{out}$$

The number of parameters does not depend on the image size, which is the key saving compared with a dense layer.

Activation, pooling and dense layers

• Activation: after each convolution a nonlinear function, usually ReLU (max(0, x)), is applied element by element. Without it, stacked layers would collapse into one linear operation.
• Pooling: a max pooling layer takes the largest value in each small window, typically 2 × 2 with stride 2, halving the width and height. It reduces computation and makes features less sensitive to small shifts. Many modern networks use strided convolutions instead.
• Dense layers and output: at the end, feature maps are flattened or averaged (global average pooling) and passed to fully connected layers. A softmax output gives class probabilities.

Early layers learn simple features such as edges and colour blobs; deeper layers combine them into textures, parts and whole objects. Training uses backpropagation and gradient descent, like other neural networks, and needs care to avoid overfitting, usually with data augmentation, dropout and weight decay.

Key formulas for convolutional neural networks

Landmark CNN architectures

• LeNet-5 (1998): LeCun and colleagues used convolution and subsampling layers to read handwritten digits, establishing the basic CNN pattern.
• AlexNet (2012): trained on GPUs with ReLU and dropout, it won the ImageNet challenge with a top 5 error of 15.3%, against 26.2% for the next entry, and started the deep learning boom in vision.
• VGG (2014): showed that deep stacks of simple 3 × 3 convolutions work well.
• ResNet (2015): added skip (residual) connections that let the signal bypass layers, making networks of 152 layers trainable; it won the 2015 ImageNet challenge.

Applications of convolutional neural networks

CNNs are used for image classification, object detection and segmentation (compared in classification vs detection vs segmentation), optical inspection in machine vision systems, medical imaging, satellite image analysis and, in one dimensional form, vibration and sensor signals for predictive maintenance. In many vision tasks, transformer based models now compete with CNNs, and hybrid designs use both.

Convolutional neural networks interview and viva questions

1. What is parameter sharing in a CNN? The same kernel weights are applied at every position of the input, so a feature is learned once and detected anywhere, with far fewer parameters.
2. How do you calculate the output size of a convolutional layer? Use W_out = ⌊(W − K + 2P) ÷ S⌋ + 1, where W is input size, K kernel size, P padding and S stride.
3. What does max pooling do? It keeps the largest value in each small window, reducing the spatial size and making features less sensitive to small shifts.
4. Why is ReLU used after convolution? It adds nonlinearity so that stacked layers can learn complex functions, and it is cheap to compute.
5. What problem do residual connections in ResNet solve? They let the signal and gradients bypass layers, which makes very deep networks easier to train.