Describe the architecture and functionality of a Transformer network, and explain how it addresses the limitations of Recurrent Neural Networks in natural language processing tasks.

The Transformer network is a neural network architecture that has revolutionized the field of natural language processing (NLP). Introduced in the paper "Attention is All You Need" by Vaswani et al. in 2017, the Transformer departs from the sequential processing paradigm of recurrent neural networks (RNNs) and instead relies entirely on attention mechanisms to model relationships between words in a sequence. This allows the Transformer to process sequences in parallel, leading to significant improvements in training speed and performance, especially for long sequences. Architecture of the Transformer: The Transformer architecture consists of an encoder and a decoder, both of which are composed of multiple identical layers. Encoder: The encoder's role is to process the input sequence and generate a contextualized representation of each word. It consists of N identical layers, where N is a hyperparameter (typically 6). Each layer has two sub-layers: Multi-Head Self-Attention: This sub-layer computes attention weights between each word in the input sequence and all other words in the sequence, including itself. It uses multiple "attention heads" to capture different aspects of the relationships between words. Feed Forward Network: This sub-layer applies a fully connected feed forward network to each word in the sequence independently. It helps to transform and refine the representations generated by the attention mechanism. Each sub-layer also includes residual connections and layer normalization to improve training stability and performance. The output of each sub-layer is added to its input (residual connection), and then the result is normalized (layer normalization). Decoder: The decoder's role is to generate the output sequence, one word at a time, based on the encoder's output and the previously generated words. It also consists of N identical layers, where N is a hyperparameter (typically 6). Each layer has three sub-layers: Masked Multi-Head Self-Attention: This sub-layer is similar to the multi-head self-attention in the encoder, but it includes a mask that prevents the decoder from attending to future words in the sequence. This is necessary to ensure that the decoder only uses information from the previously generated words to predict the next word. Multi-Head Attention: This sub-layer computes attention weights between the decoder's output and the encoder's output. It allows the decoder to attend to relevant parts of the input sequence when generating the next word. Feed Forward Network: This sub-layer is identical to the feed forward network in the encoder. As in the encoder, each sub-layer also includes residual connections and layer normalization. Functionality of the Transformer: The Transformer works by processing the input sequence through the encoder and the decoder. Encoder: The encoder first embeds the input words into a high-dimensional vector space. These embeddings are then passed through the N encoder layers. Each layer applies multi-head self-attention to compute attention weights between the words in the sequence, and then applies a feed forward network to transform the representations. The output of the encoder is a contextualized representation of each word in the sequence. Decoder: The decoder starts with a start-of-sequence token and generates the output sequence one word at a time. At each step, the decoder applies masked multi-head self-attention to the previously generated words, and then applies multi-head attention to the encoder's output. This allows the decoder to attend to relevant parts of the input sequence when generating the next word. Finally, the decoder applies a feed forward network and a softmax layer to predict the next word. The process is repeated until the decoder generates an end-of-sequence token. Attention Mechanism: The core component of the Transformer is the attention mechanism, which allows the model to focus on the most relevant parts of the input sequence when processing each word. The attention mechanism computes a weighted sum of the values of all the words in the sequence, where the weights are determined by the relevance of each word to the current word. The attention mechanism takes three inputs: queries, k....