# Words with LLMs

Large Language Models (LLMs), such as GPT-4, represent words using a combination of tokenization, word embeddings, and context information.

1. Tokenization: Tokenization is the process of breaking down the text into smaller units, called tokens. These tokens can be words, subwords, or even characters, depending on the tokenization strategy. For instance, the byte-pair encoding (BPE) used in GPT-2 and GPT-3 splits words into subwords based on the frequency of their occurrence in the training data. The tokenizer helps to convert the input text into a format that can be fed into the neural network for processing.

2. Word embeddings: After tokenization, each token is mapped to a high-dimensional vector called a word embedding. These embeddings capture semantic and syntactic information about words, and they allow the model to understand relationships between words in the text. Word embeddings are usually pre-trained on a large corpus of text and fine-tuned during the training process of the LLM. These embeddings are stored in an embedding matrix, which is used to look up the vector representation for each token in the input text.

3. Context information: LLMs use self-attention mechanisms, such as the Transformer architecture, to capture context information from the surrounding tokens. The self-attention mechanism allows the model to weigh the importance of different tokens in the input sequence while generating embeddings for each token. This contextual information helps the model to disambiguate words with multiple meanings, capture long-range dependencies, and generate more accurate and coherent responses.

In summary, words are represented in Large Language Models through a combination of tokenization, word embeddings, and context information. These representations enable the model to understand and generate meaningful text based on the input it receives.

# Mapping Words

The process of mapping textual information onto vectors suitable for machine learning involves several steps:

1. Tokenization: As mentioned earlier, tokenization is the process of converting the input text into smaller units (tokens) that the model can work with. Tokens can be words, subwords, or characters, depending on the chosen strategy. The tokenized text is then represented as a sequence of integers, where each integer corresponds to a unique token in the model's vocabulary.

2. Embedding: Once the text is tokenized, each token (integer) is mapped to a high-dimensional vector using an embedding matrix. The embedding matrix is a large, learnable parameter matrix that is part of the model's architecture. The rows of the matrix correspond to unique tokens in the vocabulary, and the columns represent the dimensions of the vector space. The matrix is initialized with pre-trained embeddings or random values and is fine-tuned during the training process to capture semantic and syntactic information about the tokens.

3. Positional encoding: In models like the Transformer, which do not have any inherent notion of the order of the input tokens, positional encoding is used to inject information about the position of each token in the sequence. This is done by adding a unique vector, generated by a specific function, to each token's embedding. Positional encoding ensures that the model can account for the order and relationships between tokens in a sequence.

4. Contextualization: After obtaining the embeddings and incorporating positional information, the input vectors are fed into the model's layers. In the case of the Transformer architecture, the self-attention mechanism helps capture contextual information from surrounding tokens. This is achieved by computing attention scores that weigh the importance of different tokens in the input sequence. The model then generates context-aware representations for each token by aggregating information from other tokens based on these attention scores.

The resulting context-aware vectors, which contain information about the words and their relationships within the input text, are then suitable for various machine learning tasks, such as text classification, sentiment analysis, machine translation, and text generation.

In summary, textual information is mapped onto vectors suitable for machine learning through a series of steps involving tokenization, embedding, positional encoding, and contextualization. These steps enable the model to process and learn from the text data effectively.

After tokenization, the input text is represented as a sequence of integers, with each integer corresponding to a unique token in the model's vocabulary. This sequence of integers is then fed into the model as follows:

1. Input layer: The sequence of integers is first passed to the input layer of the model. In deep learning models like the Transformer, this input layer is designed to handle sequences of variable length. The input layer serves as the starting point for processing the text data within the model.

2. Embedding layer: The sequence of integers is passed through an embedding layer, which maps each integer (token ID) to a high-dimensional vector using an embedding matrix. This matrix is a large, learnable parameter matrix in the model's architecture, with rows corresponding to unique tokens in the vocabulary and columns representing the dimensions of the vector space. The embedding layer essentially converts the sequence of integers into a sequence of continuous-valued vectors, which can then be processed by the subsequent layers in the model.

3. Positional encoding (for Transformer models): Since Transformer models do not have any inherent notion of the order of input tokens, positional encoding is used to inject information about the position of each token in the sequence. A unique vector, generated by a specific function, is added to each token's embedding to provide this positional information. This step ensures that the model can account for the order and relationships between tokens in a sequence.

4. Model layers: After obtaining the embeddings with positional information, the sequence of vectors is fed into the model's layers. In the case of the Transformer architecture, the input vectors pass through multiple layers of self-attention and feed-forward sub-layers. These layers capture contextual information from surrounding tokens, compute attention scores that weigh the importance of different tokens in the input sequence, and generate context-aware representations for each token.

The sequence of integers, represented as a sequence of high-dimensional vectors after processing through the embedding layer and (if applicable) the positional encoding, is used as input to the subsequent layers in the model. As the input vectors pass through the layers, the model learns to extract relevant features and patterns from the text data, which can be utilized for various natural language processing tasks such as text classification, sentiment analysis, machine translation, and text generation.

# State and Input Stream Ordering

In the case of sequential models like RNNs (Recurrent Neural Networks) and LSTMs (Long Short-Term Memory networks), the model maintains state and ordering of data by design. These models process tokens sequentially, maintaining a hidden state at each time step that acts as a memory of the information seen so far. The hidden state is updated as each token is fed into the model, and it helps capture the context and relationships between tokens in the sequence.

However, for models like the Transformer, which don't process tokens sequentially, the state and ordering of data are handled differently. The Transformer architecture relies on two primary mechanisms to maintain ordering and contextual information:

1. Positional encoding: As mentioned earlier, Transformer models do not have any inherent notion of the order of input tokens. To address this issue, positional encoding is used to inject information about the position of each token in the sequence. A unique vector, generated by a specific function, is added to each token's embedding. This positional information helps the model account for the order and relationships between tokens in a sequence. The combined embeddings (token embeddings + positional encodings) are then fed into the model's layers as input.

2. Self-attention mechanism: The self-attention mechanism in Transformer models helps capture contextual information from surrounding tokens. It computes attention scores that weigh the importance of different tokens in the input sequence. These attention scores allow the model to relate tokens to each other, regardless of their positions in the sequence. By aggregating information from other tokens based on these attention scores, the model generates context-aware representations for each token. The self-attention mechanism helps the Transformer model maintain state and capture long-range dependencies between tokens, despite processing them in parallel.

In summary, while sequential models like RNNs and LSTMs maintain state and ordering of data inherently through their sequential processing and hidden states, models like the Transformer handle this through the use of positional encoding and the self-attention mechanism. These mechanisms ensure that the model can account for the order and relationships between tokens in a sequence while processing the input text.

# Transformers and Importance

In the Transformer architecture, the importance of a piece of text is determined using the self-attention mechanism. The self-attention mechanism calculates attention scores that weigh the importance of different tokens in the input sequence relative to each other. It allows the model to relate tokens to one another, regardless of their positions in the sequence, and generates context-aware representations for each token by aggregating information from other tokens based on these attention scores.

1. Query, Key, and Value Vectors: For each token in the input sequence, the model generates three vectors: a query vector, a key vector, and a value vector. These vectors are obtained by multiplying the token embeddings (with positional encoding) by three learnable weight matrices, one for each type of vector.

2. Attention Scores: The attention scores are computed by taking the dot product of the query vector of a token with the key vector of all other tokens in the sequence. The dot product measures the similarity between the query and key vectors, and higher scores indicate greater similarity or importance. The resulting attention scores are then divided by a scaling factor (usually the square root of the key vector dimension) to stabilize the gradients during training.

3. Softmax: The attention scores are passed through a softmax function, which normalizes the scores into a probability distribution. This ensures that the sum of the attention scores for a given token is equal to 1. After applying the softmax function, higher scores represent a stronger relationship between the corresponding tokens.

4. Weighted Value Vectors: The softmax-normalized attention scores are used to weigh the value vectors of the tokens in the sequence. Each value vector is multiplied by its corresponding softmax-normalized attention score, resulting in a set of weighted value vectors.

5. Context Vector: The weighted value vectors are summed up to create a context vector for each token. This context vector represents the aggregated information from all other tokens in the sequence, weighted by their importance relative to the current token.

By calculating the self-attention scores and generating context vectors, the Transformer model can judge the importance of different parts of the input text and relate tokens to each other to capture contextual information and dependencies. This mechanism allows the model to understand and process the input text effectively, which can be utilized for various natural language processing tasks such as text classification, sentiment analysis, machine translation, and text generation.

# Transformer Architecture

Implementing a complete Transformer in C without using any external libraries is a complex and lengthy task. However, I can provide you with an outline of the main components and steps involved in building a basic Transformer. You can then use this outline as a starting point for your implementation.

1. Define data structures: Create data structures for matrices, vectors, and any other necessary structures to store the model's parameters, such as the token embeddings, positional encodings, and weight matrices for the multi-head attention mechanism.

2. Implement matrix and vector operations: Implement basic matrix and vector operations like addition, subtraction, multiplication, and dot product without using external libraries. You will need these operations for various calculations within the Transformer model.

3. Tokenization: Implement a simple tokenization function to convert input text into a sequence of integers. Each integer should correspond to a unique token in the model's vocabulary.

4. Embedding layer: Implement an embedding layer that maps each token (integer) to a high-dimensional vector using an embedding matrix. This matrix should be initialized with random values and fine-tuned during the training process.

5. Positional encoding: Implement a function for generating positional encodings and adding them to the token embeddings. You can use the sine and cosine functions, as proposed in the original Transformer paper, or experiment with other positional encoding techniques.

6. Multi-head self-attention mechanism: Implement the multi-head self-attention mechanism, which involves the following steps:

a. Compute query, key, and value vectors by multiplying token embeddings with the corresponding weight matrices.

b. Calculate attention scores by taking the dot product of query and key vectors, and normalize the scores using a softmax function.

c. Multiply the normalized attention scores with the value vectors to obtain weighted value vectors.

d. Sum the weighted value vectors to create the context vector for each token.

e. Repeat this process for each attention head, and concatenate the resulting context vectors.

7. Feed-forward layers: Implement feed-forward layers with activation functions, such as ReLU or GELU, which will process the output of the multi-head self-attention mechanism.

8. Layer normalization and residual connections: Implement layer normalization and residual connections to combine the outputs of the self-attention and feed-forward layers.

9. Training loop: Implement a training loop that fine-tunes the model parameters using backpropagation and optimization techniques like stochastic gradient descent or Adam optimizer.

10. Inference: Implement an inference function to generate predictions from the trained model.

The outline provided above covers the essential components of a basic Transformer model. For a complete implementation, you will need to write the code for each of these components, along with any other necessary functions and utilities for handling data and training the model. Please note that implementing a Transformer from scratch in C is a complex task, and you should be prepared to invest a significant amount of time and effort into the project.

# Vector Size

The size of the vectors in a Large Language Model (LLM) like GPT-4 depends on the dimension of the hidden states or embeddings used in the model. While the specific architecture details of GPT-4 are not publicly available, we can refer to GPT-3 as a point of comparison.

GPT-3 has several versions with varying sizes, and the hidden state dimension in the largest version (GPT-3-175B) is 1,280. This means that each token's embedding vector in this version of GPT-3 is a 1,280-dimensional vector. For GPT-4, the size of the vectors may be similar or even larger, depending on the specific model size and configuration chosen.

In general, as the size of the model increases, the dimensionality of the embeddings and hidden states also tends to increase, which can result in improved performance at the cost of higher computational and memory requirements.