Deep Neural Networks are a type of mathematical models in the field of machine learning and artificial intelligence, whose structure and function are inspired by the way the human brain works. These networks are composed of multiple layers and use similar approaches to recognize patterns and complex features in input data such as images, texts, numerical data, speech, etc.

The formation of a deep neural network mainly consists of two main elements:

1. Hidden Layers: These layers are responsible for extracting and converting input data. Each hidden layer consists of a number of neurons (or processing units) and extract more complex feature information from the input data. These layers are activated by non-linear functions (activation functions) such as ReLU (Rectified Linear Unit).

2. Weights and parameters: Each connection between neurons has a weight. These weights are randomly initialized and then updated by optimization algorithms such as backpropagation. Neural network parameters include these weights and other values such as biases.

The operation of deep neural networks is that at first the input information is processed through hidden layers and different features are extracted from the input data. These features are obtained gradually and deeper from layer to layer. Then, these features are processed by the output layers to produce the final result.

Deep neural networks have high power in learning data representation and the ability to embed patterns and complex features. This allows the network to perform extremely well in various problems such as image recognition, machine translation, natural language processing, and other complex problems. For example, in image recognition, a deep neural network can automatically recognize many image features such as edges, faces, and objects.

Overall, deep neural networks have been heavily processed as one of the first options in solving complex data-driven and machine learning problems in recent decades, and have provided performance improvements in a wide variety of applications and industries.

In learning operations in deep neural networks, iterative steps and matching the model to the input data are very important. These steps generally include the following:

1. Initialization of weights: Initially, the weights are initialized randomly. These weights represent the influence of each connection between neurons.

2. Calculate the output of the model: As training data enters the network, the information is processed from layer to layer and the outputs predicted by the model are produced.

3. Error calculation: The outputs produced by the model are compared with the expected outputs to calculate the difference (error) between them. This error is usually calculated using different loss functions.

4. Backpropagation: This is a fundamental process in learning deep models. In this process, the error is transferred from the output layers to the input layers and the weights are updated. This optimization allows the network to better adapt to the input data and reduce the error.

5. Update weights: Using optimization algorithms such as Gradient Descent and its more advanced versions, the weights and parameters of the network are updated to reduce the error and improve the performance of the model in future predictions.

6. Repeat steps 2 to 5: These steps are executed iteratively so that the model reaches an optimal and desirable performance in predicting new data.

The main goal of this learning process is to improve the performance of the model in predicting new data and to better adapt to the diversity and complexity of the input data. By repeating the learning steps, the neural network gradually acquires more capabilities in extracting and displaying more complex features from the input data and, as a result, performs more accurately in prediction.