Transformer Decoder_positional encoding: since transformers lack inher

A Transformer Decoder is a key component of the Transformer architecture, which was introduced in the paper "Attention is All You Need" by Vaswani et al. in 2017 and has revolutionized the field of Natural Language Processing (NLP). The Transformer Decoder is primarily used in sequence-to-sequence tasks like machine translation, text generation, summarization, and more.

In the context of the Transformer model, the Decoder is responsible for generating output sequences (e.g., translating a sentence from one language to another or producing a summary) based on the encoded input sequence and any previous generated tokens in the output sequence. It consists of several key elements:

1. Self-Attention Layers: These layers allow each output token to attend to all the other output tokens that have been generated so far, enabling the decoder to consider the entire context while predicting the next token.

2. Masked Self-Attention: To prevent future tokens from influencing present ones during training (since they're not available at prediction time), the decoder uses masked self-attention where positions beyond the current position are masked out.

3. Encoder-Decoder Attention Layers: In addition to attending to its own outputs, the decoder also attends to the output of the Transformer Encoder. This cross-attention mechanism allows it to condition its predictions on the input sequence.

4. Position-wise Feedforward Networks (FFNs): Each attention layer is followed by a feedforward network that applies non-linear transformations independently to each position.

5. Residual Connections and Layer Normalization: Both are used after each sub-layer (self-attention and FFN) to ease the training process and stabilize gradients.

6. Positional Encoding: Since the Transformer does not have inherent sequential information due to its parallel processing nature, positional encoding is added to the input embeddings to incorporate the order of the tokens.

The overall structure of the Transformer Decoder enables it to capture long-range dependencies effectively and produce high-quality outputs in various NLP tasks.

1.Self-Attention Layers

In the context of the Transformer Decoder, the Self-Attention mechanism empowers each output token to consider the entire context of the previously generated tokens.

Here's a more detailed breakdown:

In a Self-Attention layer within the Decoder, each token in the sequence computes its representation by attending to all other tokens that have already been generated. This is done through three matrices – Queries, Keys, and Values.

1. Queries: Each token in the sequence is transformed into a query vector, which will be used to query the rest of the sequence for relevant information.

2. Keys and Values: Concurrently, every token is also transformed into both a key vector (used for measuring relevance) and a value vector (which holds the actual information content).

3. Attention Weights: Each query vector compares itself to all key vectors, resulting in a set of attention weights. These weights reflect the importance of each token in the sequence for the current token being generated.

4. Contextual Representation: The attention weights are then used to compute a weighted sum of the value vectors. This results in a new contextual representation for the current token, taking into account the entire history of generated tokens.

By doing so, the Self-Attention layer in the Decoder ensures that each predicted token is informed not only by its own embedding but also by the entire context of the partially constructed output sequence. This makes Transformers extremely powerful for modeling long-range dependencies and generating coherent and accurate sequences, especially in tasks like text generation and machine translation.

However, it's worth noting that the Decoder's Self-Attention is slightly different from the Encoder's; in the Decoder, there's a masking technique applied to prevent tokens from peeking into their future positions during training, maintaining causality in the output sequence generation process.

2.Masked Self-Attention

Masked Self-Attention is a critical adaptation of the vanilla Self-Attention mechanism specifically tailored for the Transformer Decoder.

In the standard Self-Attention process, each token in a sequence can attend to all other tokens in the sequence. However, this would violate the autoregressive property required for many sequence generation tasks where the model should predict the next token based solely on the previously generated tokens, without any lookahead.

To enforce this constraint, the Transformer Decoder employs Masked Self-Attention. During training, it masks out (i.e., sets to zero or assigns a very large negative value) the attention scores between a token and all tokens that appear after it in the sequence. As a result, when the softmax function is applied to calculate the attention weights, future tokens receive near-zero attention, essentially rendering them invisible to the current token being processed.

In practice, this means that when the Decoder is generating the nth token, it can only attend to the first n-1 tokens. Thus, the model learns to predict each token conditioned on its past context, ensuring that predictions are made in a causal, left-to-right order consistent with the requirements of tasks like text generation, machine translation, and others where the output depends on previously generated elements.

3.Encoder-Decoder Attention Layers 

Encoder-Decoder Attention Layers form a crucial part of the Transformer architecture, particularly in the Decoder component. They serve as the bridge between the Encoder's understanding of the input sequence and the Decoder's generation of the output sequence.

In the context of sequence-to-sequence tasks such as machine translation, the Encoder processes the input sequence and produces a contextualized representation of the source text. The Decoder, then, generates the target sequence word by word, but it needs to make use of the information encoded by the Encoder.

How Encoder-Decoder Attention Works:

Each step of the Decoder involves an Encoder-Decoder Attention Layer. Here's how it functions:

1. Query-Key-Value Attention: At each decoding step, the current hidden state of the decoder serves as the query. This query interacts with the set of key-value pairs coming from the final states of the Encoder.

   • Keys: Representations of the input tokens provided by the Encoder.
   • Values: Contextualized representations corresponding to those keys.

2. Scaled Dot-Product Attention: The query and keys go through a dot-product operation, scaled down by the square root of the key dimension to avoid large values when computing the softmax. This operation determines the degree of relevance of each input token to the current decoding step.

3. Context Vector: The result of this attention mechanism is a weighted sum of the values, where the weights are the attention scores. This weighted sum is called the context vector and represents the relevant parts of the input sequence needed to predict the next output token.

4. Combination with Decoder's Hidden State: The Decoder combines this context vector with its own internal state (usually via concatenation or summation) before feeding it into the Position-wise Feedforward Network (FFN) and subsequent layers.

This way, the Decoder can selectively focus on different parts of the input sequence depending on what it's currently trying to generate in the output sequence, making the model highly adaptable and effective in handling complex dependencies across sequences.

Indeed, the Encoder-Decoder Attention Layers play a pivotal role within the Transformer architecture by establishing a direct connection between the encoded input and the decoded output. Here's a detailed explanation:

In the Transformer, the Encoder takes the input sequence and processes it through a series of self-attention and feed-forward neural network layers to create a rich, contextually aware representation. Each word in the input sequence gets mapped to a higher-dimensional space where it carries information about its relationship with every other word in the sequence.

On the other hand, the Decoder generates the output sequence token by token. However, it cannot directly access the original input sequence once the Encoder has processed it. This is where Encoder-Decoder Attention comes into play.

During each decoding step, the Decoder generates a 'query' using its own current hidden state. This query is then compared against all 'keys' produced by the Encoder – these keys encapsulate the essence of the input sequence. Through a process often referred to as "attention", the Decoder calculates a weight for each key based on how well its corresponding 'value' (the Encoder's representation of the input token) aligns with the current query.

The Decoder then aggregates the values from the Encoder, weighted by these attention scores, to form a context vector. This context vector effectively condenses the Encoder's understanding of the input sequence and focuses it according to the Decoder's current needs – i.e., what's relevant for generating the next output token.

By incorporating this context vector into its computation, the Decoder is able to utilize the full knowledge of the input sequence while generating the output, thereby ensuring coherence and accuracy in tasks like machine translation, summarization, and question answering. This two-way interaction, facilitated by the Encoder-Decoder Attention Layers, is a hallmark feature of the Transformer's ability to handle complex dependencies in natural language processing tasks.

4.Position-wise Feedforward Networks (FFNs)

Position-wise Feedforward Networks (FFNs) are essential components in the Transformer architecture. After each multi-head attention layer (whether self-attention or encoder-decoder attention), there's a position-wise feedforward network.

4.1 The purpose of the FFN

The purpose of the FFN is to add more complexity and non-linearity to the model’s learning capacity, allowing it to learn more intricate patterns in the data.

The Position-wise Feedforward Networks (FFNs) act as a complementary component to the attention layers within the Transformer architecture. While the attention layers capture global dependencies and contextual relationships among tokens in the sequence, the FFNs serve to increase the model's ability to learn local, position-specific, and potentially more abstract features.

The non-linear activation functions within the FFNs enable the model to learn complex and non-linear mappings between the input and output representations. This boosts the model's capacity to recognize and encode intricate patterns in the data, patterns that may not be efficiently captured by the linear operations alone.

Furthermore, the FFNs contribute to the diversity of the functional forms learned by the model, which is particularly beneficial in tasks where the relationship between input and output might not be simple or linearly separable. This complexity enhances the Transformer's expressiveness and improves its performance across a variety of NLP tasks. The combination of attention and FFNs is a cornerstone of the Transformer's success in handling sequential data.

4.2 The distinction between attention mechanisms and FFNs

Unlike the attention mechanisms which operate across all positions simultaneously, the FFNs work independently on each position in the sequence.

The distinction between attention mechanisms and Position-wise Feedforward Networks (FFNs) within the Transformer is profound:

• Attention Mechanisms: Operate globally over the entire sequence, allowing each position to interact with every other position. They calculate attention weights, which determine how much influence each position should have on the current position's representation. This global view enables the model to understand the context and dependencies across the sequence.

• Position-wise Feedforward Networks (FFNs): On the other hand, apply the same feedforward network architecture to each position in the sequence independently. This means that each position's representation is updated based on the specific FFN transformation without considering the context from other positions. This independence enables the model to learn complex, non-linear, and position-specific features that augment the context-aware representations created by the attention layers.

While attention layers focus on capturing inter-token relationships, FFNs concentrate on enriching individual token representations, adding extra layers of abstraction and complexity to the model's understanding of the data. Together, these components create a synergistic effect that powers the Transformer's remarkable performance in dealing with sequential data.

5. Residual Connections and Layer Normalization

Indeed, Residual Connections and Layer Normalization are crucial techniques employed in the Transformer architecture to improve training stability and performance.

Residual Connections: Inspired by the success of residual networks (ResNets) in computer vision tasks, residual connections allow the gradient to flow more easily through deep neural networks. In the Transformer, after each sub-layer (self-attention or position-wise feedforward network), the original input is added back to the output of that sub-layer. This is mathematically expressed as:

y = LayerSublayer(x) + x

where LayerSublayer(x) represents the operation performed by the self-attention layer or the feedforward network, and x is the input to that sub-layer. By adding the input directly to the output, residual connections help mitigate the vanishing gradient problem, allowing the model to train deeper networks without significant degradation in performance.

Layer Normalization: Layer Normalization normalizes the activations of the inputs entering a layer. It adjusts the scale and shift of the inputs to have zero mean and unit variance, which stabilizes the distribution of inputs and speeds up the training process. In the Transformer, layer normalization is applied before each sub-layer computation. The normalization is calculated separately for each position in the sequence, hence the term "layer" rather than "batch" normalization.

Applying Layer Normalization before residual connections standardizes the inputs to the sub-layers, improving their signal-to-noise ratio and promoting faster convergence during training. Additionally, it ensures that the magnitude of the inputs does not explode or vanish as they pass through multiple nonlinear transformations.

Together, residual connections and layer normalization make the Transformer more robust to training instability, allowing it to leverage the benefits of increased depth and width in its architecture, leading to improved performance in various NLP tasks.

6. Postional Encoding

Positional Encoding adds information about the relative or absolute position of each token in the sequence to its corresponding embedding. This is necessary because the attention mechanism treats all input tokens equally and does not differentiate them based on their position. Without positional encoding, the model would lose the ability to understand that the meaning of a word can change depending on its position within a sentence.

Positional Encoding is a technique implemented in the Transformer model to inject information about the position of each token within the input sequence into its respective embedding. This is particularly important since Transformers lack an inherent notion of sequence order due to their parallel processing nature.

In the Transformer architecture, each token is initially embedded and then combined with its positional encoding before being processed by the model's layers. The positional encoding is designed to ensure that the model can distinguish between tokens that are otherwise identical but occupy different positions in the sequence.

There are different ways to implement positional encoding, but in the original Transformer paper, sinusoidal functions were used to create a fixed-length vector for each position. These sinusoidal functions have varying frequencies across different dimensions, which theoretically allows the model to capture both short-term and long-term dependencies.

The mathematical formulation of the positional encoding usually includes sine and cosine functions with different wavelengths across the dimensions of the embedding space. When concatenated with the token embeddings, this positional information enables the Transformer to maintain awareness of the sequence structure throughout the computation, even though the self-attention mechanism operates without considering the sequential order. This fusion of positional information with token semantics empowers the Transformer to excel in tasks that heavily rely on the order of words, phrases, or symbols, such as machine translation, sentiment analysis, and text generation.