## Artificial Intelligence :

Artificial intelligence (AI) has been at the forefront of technology over the last few years and has made its way into mainstream applications, such as expert systems, personalized applications on mobile devices, machine translation in natural language processing, chatbots, self-driving cars, and so on. The definition of AI, however, has been a subject of dispute for quite a while. This is primarily because of the so-called AI effect that categorizes work that has already been solved through AI in the past as non-AI. According to the famous computer scientist, Larry Tesler, “Intelligence is whatever machines haven't done yet.”

Building an intelligent system that could play chess was considered AI until the IBM computer Deep Blue defeated Gary Kasparov in 1996. Similarly, problems dealing with vision, speech, and natural language were once considered complex, but due to the AI effect, they would now only be considered computation rather than true AI.

Recently, AI has become capable of solving complex mathematical problems, composing music, and creating abstract paintings; these capabilities of AI are ever increasing. The point in the future at which AI systems will equal human levels of intelligence has been referred to by scientists as the AI singularity. The question of whether machines will ever actually reach human levels of intelligence is very intriguing and debatable.

Many would argue that machines will never reach human levels of intelligence, since the AI logic by which they learn or perform intelligent tasks is programmed by humans, and they lack the consciousness and self-awareness that humans possess. However, several researchers have proposed the alternative idea that human consciousness and self-awareness are like infinite loop programs that learn from their surroundings through feedback.

Hence, it may be possible to program consciousness and self-awareness into machines, too. For now, however, we will leave this philosophical side of AI for another day, and will simply discuss AI as we know it.

Put simply, AI can be defined as the ability of a machine (generally, a computer or robot) to perform tasks with human-like intelligence, possessing such attributes as the ability to reason, learn from experience, generalize, decipher meanings, and possess visual perception.

While there may be debates about what AI can achieve and what it cannot, recent success stories of AI-based systems have been overwhelming. A few of the more recent mainstream applications of AI are depicted in the following diagram:

 Applications of Artificial Intelligence (AI)

In this article, we will briefly touch upon the concept of neural networks and how they are integral to AI.

## Neural networks :

Neural networks are machine learning models that are inspired by the human brain. They consist of neural processing units that are interconnected with one another in a hierarchical fashion. These neural processing units are called artificial neurons, and they perform the same function as axons in a human brain.

In a human brain, dendrites receive input from neighbouring neurons and attenuate or magnify the input before transmitting it on to the soma of the neuron. In the soma of the neuron, these modified signals are added together and passed on to the axon of the neuron. If the input to the axon is over a specified threshold, then the signal is passed on to the dendrites of the neighbouring neurons.

An artificial neuron loosely works perhaps on the same logic as that of a biological neuron. It receives input from neighbouring neurons. The input is scaled by the input connections of the neurons and then added together. Finally, the summed input is passed through an activation function whose output is passed on to the neurons in the next layer.

A biological neuron and an artificial neuron are illustrated in the following diagrams for comparison:

 Biological Neuron

An artificial neuron is illustrated in the following diagram:

 Artificial Neuron

Now, let's look at the structure of an artificial neural network:

 Artificial Neural Network Structure

The input, $\inline&space;\boldsymbol{x&space;\epsilon&space;R^{N}}$, passes through successive layers of neural units, arranged in a hierarchical fashion. Each neuron in a specific layer receives an input from the neurons of the preceding layers, attenuated or amplified by the weights of the connections between them.

The weight, $\inline&space;\boldsymbol{w^{(l)}_{ij}}$, corresponds to the weight connection between the $\inline&space;\boldsymbol{i^{th}}$ neuron in layer $\inline&space;\boldsymbol{(l)}$ and the $\inline&space;\boldsymbol{j^{th}}$ neuron in layer $\inline&space;\boldsymbol{(l+1)}$. Also, each neuron unit, $\inline&space;\boldsymbol{i}$, in a specific layer, $\inline&space;\boldsymbol{l}$, is accompanied by a bias,$\inline&space;\boldsymbol{b^{(l)}_{i}}$. The neural network predicts the output, $\inline&space;\boldsymbol{\hat{y}}$, for the input vector, $\inline&space;\boldsymbol{x&space;\epsilon&space;R^{N}}$. If the actual label of the data is $\inline&space;\boldsymbol{y}$, where $\inline&space;\boldsymbol{y}$ takes continuous values, then the neuron network learns the weights and biases by minimizing the prediction error,$\inline&space;\boldsymbol{(y-\hat{y})^2}$

Of course, the error has to be minimized for all of the labelled data points: $\inline&space;\boldsymbol{(x_i,&space;y_i)&space;\forall&space;i&space;\epsilon&space;1,&space;2,&space;.&space;.&space;.&space;m}$.

If we denote the set of weights and biases by one common vector,$\inline&space;\boldsymbol{W}$, and the total error in the prediction is represented by $\inline&space;\boldsymbol{C}$, then through the training process, the estimated $\inline&space;\boldsymbol{W}$ can be expressed as follows:

$\large&space;\hat{W}&space;=&space;\underbrace{argmin}_W&space;C&space;=&space;\underbrace{argmin}_W&space;\sum_{i}&space;(y=\hat{y}_i)^2$

Also, the predicted output, $\inline&space;\boldsymbol{\hat{y}}$, can be represented by a function of the input, $\inline&space;\boldsymbol{x}$, parameterized by the weight vector, $\inline&space;\boldsymbol{W}$, as follows:

$\inline&space;\huge&space;\hat{y}&space;=&space;f_W(x)$

Such a formula for predicting the continuous values of the output is called a regression problem.

For a two-class binary classification, the cross-entropy loss is minimized instead of the squared error loss, and the network outputs the probability of the positive class instead of the output. The cross-entropy loss can be represented as follows:

$\inline&space;\huge&space;C&space;=&space;-&space;\sum_{i}&space;[y_i\log{p_i}&space;+&space;(1&space;+&space;y_i)&space;\log(1&space;-&space;p_i)]$

Here, $\inline&space;\boldsymbol{p_i}$ is the predicted probability of the output class, given the input $\inline&space;\boldsymbol{x}$, and can be represented as a function of the input, $\inline&space;\boldsymbol{x}$, parameterized by the weight vector, as follows:

$\inline&space;\huge&space;p&space;=&space;P&space;(y=1/x;W)&space;=&space;f_W(x)$

In general, for multi-class classification problems (say, of $\inline&space;\boldsymbol{n}$ classes), the cross-entropy loss is given via the following:

$\inline&space;\huge&space;C&space;=&space;-\sum_{i}&space;y_{i}^{(j)}&space;\log(P_i^{(j)})$

Here, $\inline&space;\boldsymbol{y_i^{(j)}}$ is the output label of the $\inline&space;\boldsymbol{j^{th}}$ class, for the $\inline&space;\boldsymbol{i^{th}}$ data point.

Hope you enjoyed reading this article on neural networks, albeit article gives a very basic overview. However, you can always refer to Intelligent Projects Using Python for more in-depth coverage of the underlying concepts, including GANs, Transfer Learning, Reinforcement Learning, and others. Intelligent Projects Using Python is a must-read for data scientists, machine learning professionals, and deep learning practitioners who are ready to extend their knowledge and potential in AI.

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