Create an animation video to explain indepth about transformers with complete in depth maths intuition and mechanism explanation

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Welcome to our deep dive into Transformer architecture! Transformers have revolutionized natural language processing by replacing traditional recurrent neural networks with attention mechanisms. The key innovation is parallel processing capability and superior long-range dependency capture. The architecture consists of an encoder stack that processes input sequences and a decoder stack that generates output sequences. Let's explore how this groundbreaking model works. Now let's dive into the heart of transformers: the self-attention mechanism. Self-attention allows each position in a sequence to attend to all other positions, capturing complex relationships between words regardless of their distance. The mechanism works by computing three matrices: Query, Key, and Value from the input embeddings. The attention formula shows how we compute attention weights by taking the dot product of queries and keys, scaling by the square root of the key dimension, applying softmax, and then multiplying by values to get the final output. Multi-head attention is a key innovation that allows the model to jointly attend to information from different representation subspaces at different positions. Instead of using a single attention function, we run multiple attention heads in parallel. Each head learns to focus on different aspects of the relationships between tokens. The outputs from all heads are concatenated and linearly transformed to produce the final result. This parallel processing enables the model to capture various types of dependencies simultaneously, making it much more expressive than single-head attention. Two crucial components complete the transformer architecture. First, positional encoding solves the problem that attention mechanisms have no inherent notion of sequence order. We add sinusoidal positional encodings to word embeddings, using different frequencies for each dimension. This allows the model to learn relative positions. Second, the feed-forward network processes each position independently through two linear transformations with ReLU activation in between. This adds non-linearity and increases the model's capacity to learn complex patterns. These components work together to create the powerful transformer architecture. The final piece of the transformer puzzle involves training techniques and applications. Residual connections and layer normalization are crucial for stable training of deep networks. The residual connections allow gradients to flow directly through the network, preventing vanishing gradients. Layer normalization stabilizes training by normalizing inputs to each layer. Transformers are typically pre-trained on large text corpora using self-supervised objectives, then fine-tuned for specific tasks. This has revolutionized NLP, enabling breakthroughs in machine translation, text summarization, question answering, and language generation. The transformer architecture has become the foundation for modern language models.