A Complete Roadmap with Deep Algorithmic Understanding

Transformer Mastery Course: From DSA to Generative AI

A Complete Roadmap with Deep Algorithmic Understanding

Course Title

"Transformers: The Algorithmic Engine of Modern AI"
Data Structures, Algorithms, and Generative Intelligence

Course Overview

This course transforms Data Structures & Algorithms (DSA) students into Transformer experts by teaching the core algorithms behind GPT, BERT, Llama, and beyond — without black-box magic.

Goal: Understand how Transformers work at the algorithmic level, implement them from scratch, and optimize them using DSA principles.

Course Roadmap (12 Weeks)

Week	Module	Core DSA Focus	Project
1	Math & Tensors	Arrays, Matrices, Vector Ops	NumPy → PyTorch
2	Attention is All You Need	Graphs, Hashing	Build Scaled Dot-Product Attention
3	Multi-Head & Self-Attention	Parallelism, Divide & Conquer	Multi-Head from Scratch
4	Positional Encoding	Hash Functions, Signal Processing	Sinusoidal vs Learned PE
5	Feedforward & Residuals	Dynamic Programming, Memoization	LayerNorm + Residual
6	Decoder-Only Architecture	Autoregressive DP, Caching	Mini-GPT (64-dim)
7	Training Loop & Backprop	Gradient Descent, Computation Graph	Train on TinyShakespeare
8	Inference & KV Cache	Memoization, Space Optimization	10x Faster Generation
9	Beam Search & Sampling	Priority Queues, Heaps	Top-k, Nucleus Sampling
10	Tokenization & Vocabulary	Tries, Hash Maps	BPE from Scratch
11	Scaling Laws & Optimization	Big-O, Parallelism	FlashAttention, LoRA
12	Capstone: Build Your GPT	Full Stack	124M GPT from Scratch

Core Algorithm: Transformer Step-by-Step (Pseudocode + DSA)

# ========================================
# TRANSFORMER ALGORITHM (Decoder-Only)
# ========================================
def transformer_forward(input_ids, past_kv=None):
    """
    DSA: Arrays, Hashing, Graphs, DP (KV Cache)
    """
    # 1. Token → Embedding (O(V) → O(d) via Hash Map)
    x = embedding_lookup(input_ids) * sqrt(d_model)
    
    # 2. Add Positional Encoding (Deterministic Hash: pos → vector)
    x = x + positional_encoding(seq_len)
    
    # 3. For each layer: Attention + FFN
    new_kv_cache = []
    for layer in transformer_layers:
        # === SELF-ATTENTION (Graph Algorithm) ===
        Q, K, V = linear_project(x)           # O(n * d)
        scores = matmul(Q, K.T) / sqrt(d_k)    # O(n²) → Adjacency Matrix
        mask = causal_triangle_mask()         # Lower triangular
        probs = softmax(scores + mask)
        context = matmul(probs, V)            # Weighted sum
        
        x = residual_add(x, context)
        x = layer_norm(x)
        
        # === FEEDFORWARD (Dense Array Ops) ===
        x = residual_add(x, ffn(x))
        x = layer_norm(x)
        
        # Cache K, V for next token (DP Memoization)
        new_kv_cache.append((K, V))
    
    # 4. Final LM Head
    logits = linear(x, vocab_size)
    return logits, new_kv_cache

Key DSA Concepts in Transformers

Transformer Part	DSA Concept	Why It Matters
`input_ids → embeddings`	Hash Map (Dict)	O(1) token lookup
`QKV Projection`	Matrix Multiplication	O(n²d) bottleneck
`Attention Scores`	Adjacency Matrix (Graph)	Tokens = nodes, attention = edges
`Causal Mask`	Triangular Array	Enforces autoregression
`KV Cache`	Memoization (DP)	Avoid recomputing past
`Beam Search`	Min-Heap (Priority Queue)	Track top-k sequences
`BPE Tokenization`	Trie + Greedy	Subword merging
`LayerNorm`	Statistics on Arrays	Stabilize training

Week-by-Week Breakdown

Week 1: Math & Tensors

# Task: Implement matmul from scratch
def matmul(A, B):
    return [[sum(a*b for a,b in zip(row, col)) 
             for col in zip(*B)] for row in A]

Arrays, Broadcasting, Einstein Summation
PyTorch Tensors → torch.einsum

Week 2: Attention Mechanism

def scaled_dot_product_attention(Q, K, V, mask=None):
    d_k = Q.size(-1)
    scores = Q @ K.transpose(-2,-1) / sqrt(d_k)  # Graph weights
    if mask: scores = scores.masked_fill(mask == 0, -inf)
    probs = softmax(scores)
    return probs @ V

Graph Interpretation: Attention = weighted graph
Time Complexity: O(n²)

Week 3: Multi-Head Attention

# DSA: Parallel Processing (like MapReduce)
heads = [attention_head_i(x) for i in range(h)]
output = concat(heads) @ W_o

Split → Compute → Merge (Divide & Conquer)

Week 4: Positional Encoding

# Hash Function: position → unique vector
pe[pos, 2i]   = sin(pos / 10000^{2i/d})
pe[pos, 2i+1] = cos(pos / 10000^{2i/d})

No learning needed → deterministic
Alternative: Learned PE (trainable array)

Week 6: Build Mini-GPT

class MiniGPT(nn.Module):
    def __init__(self, vocab=1000, d_model=64, n_layer=4):
        self.token_emb = nn.Embedding(vocab, d_model)
        self.pos_emb = nn.Parameter(torch.zeros(1, 128, d_model))
        self.blocks = nn.ModuleList([Block() for _ in range(n_layer)])
        self.ln_f = nn.LayerNorm(d_model)
        self.head = nn.Linear(d_model, vocab)

Train on TinyShakespeare (1MB text)

Week 8: KV Cache (Speed Hack)

# Before: O(n²) per token
# After: O(n) per token → 100x faster!
if past_kv is not None:
    past_k, past_v = past_kv
    K = torch.cat([past_k, K], dim=1)
    V = torch.cat([past_v, V], dim=1)

Week 9: Beam Search with Heap

import heapq
heap = []  # (score, sequence)
heapq.heappush(heap, (-prob, [token]))
best = heapq.nsmallest(k, heap)

Week 10: BPE Tokenization (Trie + Greedy)

def get_stats(ids):
    counts = {}
    for pair in zip(ids, ids[1:]):
        counts[pair] = counts.get(pair, 0) + 1
    return counts  # Hash Map

Capstone Project: Build Your Own GPT

Component	Implementation
Model	124M GPT (like GPT-2 small)
Tokenizer	BPE from scratch
Training	100K steps on OpenWebText
Inference	KV Cache + Beam Search
Optimization	FlashAttention, LoRA

Learning Resources

Resource	Link
Original Paper	Attention is All You Need
Annotated	The Illustrated Transformer
Code	`nanoGPT` by Andrej Karpathy
Course	Stanford CS224N, MIT 6.S191

Assessment & Certification

Task	Weight
Weekly Quizzes (DSA in Transformers)	20%
3 Coding Assignments	30%
Midterm: Build BERT Tokenizer + Attention	20%
Final Project: Train & Deploy GPT	30%

Certificate: Certified Transformer Architect (with GitHub portfolio)

Final Words

"Transformers are not magic — they are algorithms built on arrays, graphs, and heaps."

This course turns DSA students into AI builders.

Bonus: One-Page Cheat Sheet

TRANSFORMER = Embedding
            + Positional Encoding
            + N × (MultiHeadAttention + FFN + Residual + LayerNorm)
            + LM Head

ATTENTION(Q,K,V) = softmax(QK^T / √d_k) × V

GENERATION:
  while not EOS:
      logits, kv_cache = model(token, kv_cache)
      token = sample(logits)

DSA MAP:
  Token → Hash Map
  Position → Sinusoid Hash
  Attention → Graph
  KV Cache → DP Memo
  Beam → Min-Heap
  BPE → Trie + Greedy

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Full syllabus PDF
Slide deck
Jupyter notebooks
C++ version
Interview prep kit

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