Module 27 — Complete Transformer Pipeline

The Transformer Pipeline describes the complete mathematical workflow of a Transformer model, starting from raw text and ending with generated output tokens.

Every modern Transformer model—including BERT, GPT, T5, ViT, LLaMA, Gemma, Mistral, Qwen, DeepSeek, and Phi—follows this general pipeline with architecture-specific variations.

Topics

Tokenization
Embedding
Positional Encoding
Self Attention
Multi-Head Attention
Feed Forward
Encoder
Decoder
Linear Projection
Softmax
Token Generation

1. Tokenization

The input text is converted into discrete tokens.

Formula

Text \rightarrow [t_1,t_2,\ldots,t_n]

where

$t_i$ = Token
$n$ = Sequence Length

2. Token IDs

Each token is mapped to a vocabulary index.

Formula

IDs = [id_1,id_2,\ldots,id_n]

where

id_i \in Vocabulary

3. Token Embedding

Each token ID is converted into a dense vector.

Formula

E = Embedding(IDs)

E = XV

where

$V$ = Embedding Matrix

4. Positional Encoding

Positional information is added to token embeddings.

Formula

X = E + PE

For sinusoidal encoding,

PE(pos,2i) = \sin \left( \frac{pos} {10000^{2i/d}} \right)

PE(pos,2i+1) = \cos \left( \frac{pos} {10000^{2i/d}} \right)

5. Query, Key and Value

The input embeddings are projected into Query, Key, and Value matrices.

Query

Q = XW_Q

Key

K = XW_K

Value

V = XW_V

6. Self Attention

The attention weights are computed as

Attention(Q,K,V) = Softmax \left( \frac {QK^T} {\sqrt{d_k}} \right) V

This enables every token to attend to every other token.

7. Multi-Head Attention

Multiple attention heads capture different relationships in parallel.

Formula

head_i = Attention(Q_i,K_i,V_i)

The outputs are concatenated.

MultiHead = Concat (head_1,\ldots,head_h) W_O

8. Residual Connection

The attention output is added back to the input.

Formula

x' = x + MultiHead(x)

9. Layer Normalization

The residual output is normalized.

Formula

y = LayerNorm(x')

10. Feed Forward Network

Each token passes through a position-wise neural network.

Formula

FFN(x) = W_2 ( GELU ( W_1x+b_1 ) ) +b_2

11. Encoder Block

A Transformer encoder layer consists of

Encoder(x) = LayerNorm ( x + FFN ( MHA(x) ) )

Multiple encoder layers are stacked.

Encoder = Layer_N ( \cdots Layer_2 ( Layer_1(x) ) )

12. Decoder Block

The decoder contains

Masked Self Attention
Cross Attention
Feed Forward Network

Formula

Decoder ( Q, K, V )

Cross attention

Attention ( Q_d, K_e, V_e )

13. Linear Projection

The decoder output is projected into the vocabulary space.

Formula

Logits = HW^T+b

where

$H$ = Hidden Representation
$W$ = Vocabulary Projection Matrix

14. Softmax

The logits are converted into probabilities.

Formula

P = Softmax(Logits)

Expanded,

P_i = \frac {e^{z_i}} {\sum_j e^{z_j}}

15. Token Generation

The next token is selected using a decoding strategy.

Greedy Search

\hat y = argmax(P)

Beam Search

Score = \sum \log P

Top-k Sampling

x_t \in TopK(P)

Top-p Sampling

\sum_{i=1}^{k} P_i \ge p

16. Complete End-to-End Transformer Pipeline

The complete workflow is

T e x t \to T o k e n i z a t i o n \to T o k e n I D s \to E m b e d d i n g \to P o s i t i o n E n c o d i n g \to Q u e r y / K e y / V a l u e \to S e l f A t t e n t i o n \to M u l t i H e a d A t t e n t i o n \to R e s i d u a l \to L a y e r N o r m \to F e e d F o r w a r

17. Matrix Dimensions

Suppose

Sequence Length = $n$
Hidden Dimension = $d$
Vocabulary Size = $|V|$

Input Embedding

X \in \mathbb{R}^{n\times d}

Query

Q \in \mathbb{R}^{n\times d}

Key

K \in \mathbb{R}^{n\times d}

Value

V \in \mathbb{R}^{n\times d}

Attention Matrix

A \in \mathbb{R}^{n\times n}

Hidden Representation

H \in \mathbb{R}^{n\times d}

Logits

Logits \in \mathbb{R}^{n\times |V|}

Probability

P \in \mathbb{R}^{n\times |V|}

18. Complete Mathematical Pipeline

Stage	Formula
Tokenization	$Text\rightarrow Tokens$
Token IDs	$Tokens\rightarrow IDs$

19. Applications

The complete Transformer pipeline forms the foundation of

BERT
GPT
GPT-2
GPT-3
GPT-4
T5
ViT
LLaMA
Gemma
Qwen
Mistral
DeepSeek
Phi
Claude
Gemini
Modern Large Language Models (LLMs)
Vision-Language Models (VLMs)
Multimodal AI Systems

Summary

The complete Transformer pipeline converts raw text into meaningful predictions through a sequence of mathematical operations: tokenization, embedding, positional encoding, self-attention, multi-head attention, feed-forward networks, encoder-decoder processing, output projection, softmax, and token generation. These components together form the foundation of nearly every modern Transformer-based AI model.