Using transformers with embeddings.

Learning Outcomes:

How are transformers the engine which make embeddings work?
Provide mathematical and code structural foundations

Lecture: Using Transformers with Embeddings in AI

Welcome to today's lecture on how we use transformers with embeddings in artificial intelligence (AI).
The transformer architecture has revolutionized the way we process sequential data.
In particular, natural language processing (NLP) has greatly benefited from these advancements. Today, we're going to explore the mathematical and the code structural foundations.

Part 1: Introduction to Embeddings

What are Embeddings?
{Algebraic Matrix} Embeddings are dense vectors of floating points, usually in a high-dimensional space, that are used to represent discrete variables like words, sentences, or entities in an AI model.
The concept behind embeddings is to capture semantic meaning and relationships in a geometric space; entities with similar meanings are placed closer together.

Part 2: Understanding Transformers

The Birth of Transformers
Transformers were introduced in the paper "Attention is All You Need" by Vaswani et al.
They are a type of neural network architecture designed specifically for handling sequential data.
Unlike previous approaches such as recurrent neural networks (RNNs) and long short-term memory (LSTM) networks, transformers do not process data in sequence but instead use a mechanism called 'attention' to weigh the influence of different parts of the input data.
Key Components of Transformers
Transformers consist of two main parts: the encoder and the decoder.
Each of these parts is made up of layers that typically contain multi-head self-attention mechanisms and position-wise feed-forward networks. {The foundation of the programming patterns of forward propogation and backward propogation.}
Self-Attention: Allows the model to weigh the importance of different parts of the input data irrespective of their position in the sequence.
Positional Encoding: Since the model does not process data sequentially, positional encodings are added to give the model information about the order of the sequence.
Multi-Head Attention: An extension of self-attention that allows the model to jointly process information at different positions from different representational spaces.
Feed-Forward Networks: These are fully connected networks applied to each position separately and identically.

Part 3: Transformers & Embeddings

Transformers integrate with embeddings as the initial step in processing input data.
The input embeddings transform discrete data into continuous vectors that the transformer can process.
These embeddings also include positional encodings to give the transformer information about sequence order.

Part 4: Mathematical Foundations

The transformer model involves several key equations and concepts:
Attention Function: Attention(Q, K, V) = softmax((QK^T) / √(d_k)) V
Multi-Head Attention: MultiHead(Q, K, V) = Concat(head_1,...,head_h)W^O where head_i = Attention(QW^Q_i, KW^K_i, VW^V_i)
Positional Encoding: PE(pos, 2i) = sin(pos / 10000^(2i/d_model)) for even i
Feed-Forward Network: FFN(x) = max(0, xW_1 + b_1)W_2 + b_2

Part 5: Code Structural Foundations

Now let's move on to a hands-on lab exercise to see transformers and embeddings in action using Python and the transformers library by Hugging Face.
Lab Exercise 1: Building and Training a Transformer Model

from transformers import BertTokenizer, BertModel
import torch

# Initialize the tokenizer and the model
tokenizer = BertTokenizer.from_pretrained('bert-base-uncased')
model = BertModel.from_pretrained('bert-base-uncased')

# Tokenize the input text and convert to input IDs
inputs = tokenizer("Hello, my dog is cute", return_tensors="pt")

# Forward pass, get the model's output
outputs = model(**inputs)

# The last hidden-state is the sequence of hidden-states at the output of the last layer of the model
last_hidden_states = outputs.last_hidden_state

Lab Exercise 2: Exploring Embeddings

# Getting the embeddings for the input text
embedding_output = outputs.embedding_output

# Exploring the embeddings
print(embedding_output.shape) # The shape of embeddings
print(embedding_output) # The actual embeddings
This concludes our lecture and lab exercises on transformers and embeddings! Remember, the transformer architecture coupled with embeddings provides a powerful tool for capturing complex dependencies and relationships in sequential data. Keep experimenting and building upon these foundations to master transformers in AI.
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