Building a GPT - companion notebook annotated

# Download the tiny shakespeare dataset
#!wget https://raw.githubusercontent.com/karpathy/char-rnn/master/data/tinyshakespeare/input.txt

# read it in to inspect it
with open('input.txt', 'r', encoding='utf-8') as f:
    text = f.read()

# print the length of the dataset
print("length of dataset in characters: ", len(text))

# let's look at the first 1000 characters
print(text[:1000])

# here are all the unique characters that occur in this text
chars = sorted(list(set(text)))
vocab_size = len(chars)
print(''.join(chars))
print(vocab_size)

# create a mapping from characters to integers
stoi = { ch:i for i,ch in enumerate(chars) }
itos = { i:ch for i,ch in enumerate(chars) }
encode = lambda s: [stoi[c] for c in s] # encoder: take a string, output a list of integers
decode = lambda l: ''.join([itos[i] for i in l]) # decoder: take a list of integers, output a string

print(encode("hii there"))
print(decode(encode("hii there")))

# let's now encode the entire text dataset and store it into a torch.Tensor
import torch # we use PyTorch: [https://pytorch.org](https://pytorch.org)
data = torch.tensor(encode(text), dtype=torch.long)
print(data.shape, data.dtype)
print(data[:1000]) # the 1000 characters we looked at earier will to the GPT look like this

# split up the data into train and validation sets
n = int(0.9*len(data)) # first 90% will be train, rest val
train_data = data[:n]
val_data = data[n:]

block_size = 8
train_data[:block_size+1]

x = train_data[:block_size]
y = train_data[1:block_size+1]
for t in range(block_size):
    context = x[:t+1]
    target = y[t]
    print(f"when input is {context} the target: {target}")

torch.manual_seed(1337)
batch_size = 4 # how many independent sequences will we process in parallel?
block_size = 8 # what is the maximum context length for predictions?

def get_batch(split):
    # generate a small batch of data of inputs x and targets y
    data = train_data if split == 'train' else val_data
    ix = torch.randint(len(data) - block_size, (batch_size,))
    x = torch.stack([data[i:i+block_size] for i in ix])
    y = torch.stack([data[i+1:i+block_size+1] for i in ix])
    return x, y

xb, yb = get_batch('train')
print('inputs:')
print(xb.shape)
print(xb)
print('targets:')
print(yb.shape)
print(yb)

print('----')

for b in range(batch_size): # batch dimension
    for t in range(block_size): # time dimension
        context = xb[b, :t+1]
        target = yb[b,t]
        print(f"when input is {context.tolist()} the target: {target}")

# define the bigram language model
import torch
import torch.nn as nn
from torch.nn import functional as F
torch.manual_seed(1337)

class BigramLanguageModel(nn.Module):
    def __init__(self, vocab_size):
        super().__init__()
        self.token_embedding_table = nn.Embedding(vocab_size, vocab_size)

    def forward(self, idx, targets=None):
        # idx and targets are both (B,T) tensor of integers
        logits = self.token_embedding_table(idx) # (B,T,C)

        if targets is None:
            loss = None
        else:
            B, T, C = logits.shape
            logits = logits.view(B*T, C)
            targets = targets.view(B*T)
            loss = F.cross_entropy(logits, targets)

        return logits, loss

    def generate(self, idx, max_new_tokens):
        # idx is (B, T) array of indices in the current context
        for _ in range(max_new_tokens):
            # get the predictions
            logits, loss = self(idx)
            # focus only on the last time step
            logits = logits[:, -1, :] # becomes (B, C)
            # apply softmax to get probabilities
            probs = F.softmax(logits, dim=-1) # (B, C)
            # sample from the distribution
            idx_next = torch.multinomial(probs, num_samples=1) # (B, 1)
            # append sampled index to the running sequence
            idx = torch.cat((idx, idx_next), dim=1) # (B, T+1)
        return idx

m = BigramLanguageModel(vocab_size)
logits, loss = m(xb, yb) # xb/yb are from the previous cell (B=4, T=8)
print(logits.shape) # Expected: (B, T, C) = (4, 8, 65)
print(loss) # Expected: Around 4.17

print(decode(m.generate(idx = torch.zeros((1, 1), dtype=torch.long), max_new_tokens=100)[0].tolist()))

optimizer = torch.optim.AdamW(m.parameters(), lr=1e-3)

batch_size = 32 # Redefine batch size for training
for steps in range(100): # # sample a batch of data
    xb, yb = get_batch('train')

    # evaluate the loss
    logits, loss = m(xb, yb)
    optimizer.zero_grad(set_to_none=True)
    loss.backward()
    optimizer.step()

print(loss.item())

print(decode(m.generate(idx = torch.zeros((1, 1), dtype=torch.long), max_new_tokens=500)[0].tolist()))

torch.manual_seed(42)
a = torch.tril(torch.ones(3, 3)) # Lower triangular matrix of 1s
a = a / torch.sum(a, 1, keepdim=True) # Normalize rows to sum to 1
b = torch.randint(0,10,(3,2)).float() # Some data
c = a @ b # Matrix multiply
print('a=')
print(a)
print('--')
print('b=')
print(b)
print('--')
print('c=')
print(c)

# consider the following toy example:
torch.manual_seed(1337)
B,T,C = 4,8,2 # batch, time, channels
x = torch.randn(B,T,C)
x.shape

# We want x[b,t] = mean_{i<=t} x[b,i]
xbow = torch.zeros((B,T,C)) # x bag-of-words (running average)
for b in range(B):
    for t in range(T):
        xprev = x[b,:t+1] # Select vectors from start up to time t: shape (t+1, C)
        xbow[b,t] = torch.mean(xprev, 0) # Compute mean along the time dimension (dim 0)

# Create the averaging weight matrix
wei = torch.tril(torch.ones(T, T))
wei = wei / wei.sum(1, keepdim=True) # Normalize rows to sum to 1
# Perform batched matrix multiplication
xbow2 = wei @ x # (T, T) @ (B, T, C) -> (B, T, C) via broadcasting
torch.allclose(xbow, xbow2) # Check if results are identical

tril = torch.tril(torch.ones(T, T))
wei = torch.zeros((T,T))
# Mask out future positions by setting them to -infinity before softmax
wei = wei.masked_fill(tril == 0, float('-inf'))
# Apply softmax to get row-wise probability distributions (weights)
wei = F.softmax(wei, dim=-1)
# Perform weighted aggregation
xbow3 = wei @ x
torch.allclose(xbow, xbow3) # Check if results are identical

torch.manual_seed(1337)
B,T,C = 4,8,32 # batch, time, channels (embedding dimension)
x = torch.randn(B,T,C)

# let's see a single Head perform self-attention
head_size = 16
key = nn.Linear(C, head_size, bias=False)
query = nn.Linear(C, head_size, bias=False)
value = nn.Linear(C, head_size, bias=False)
k = key(x)   # (B, T, head_size)
q = query(x) # (B, T, head_size)
# Compute attention scores ("affinities")
wei = q @ k.transpose(-2, -1) # (B, T, hs) @ (B, hs, T) ---> (B, T, T)

# Scale the scores
# Note: Karpathy uses C**-0.5 here (sqrt(embedding_dim)). Standard Transformer uses sqrt(head_size).
wei = wei * (C**-0.5)

# Apply causal mask
tril = torch.tril(torch.ones(T, T))
#wei = torch.zeros((T,T)) # This line is commented out in original, was from softmax demo
wei = wei.masked_fill(tril == 0, float('-inf')) # Mask future tokens

# Apply softmax to get attention weights
wei = F.softmax(wei, dim=-1) # (B, T, T)

# Perform weighted aggregation of Values
v = value(x) # (B, T, head_size)
out = wei @ v # (B, T, T) @ (B, T, hs) ---> (B, T, hs)
#out = wei @ x # This would aggregate original x, not the projected values 'v'

out.shape # Expected: (B, T, head_size) = (4, 8, 16)

wei[0] # Show attention weights for the first sequence in the batch

# Demonstrate variance without scaling
k_unscaled = torch.randn(B,T,head_size)
q_unscaled = torch.randn(B,T,head_size)
wei_unscaled = q_unscaled @ k_unscaled.transpose(-2, -1)
print(f"k var: {k_unscaled.var():.4f}, q var: {q_unscaled.var():.4f}, wei (unscaled) var: {wei_unscaled.var():.4f}")

# Demonstrate variance *with* scaling (using head_size for illustration)
k = torch.randn(B,T,head_size)
q = torch.randn(B,T,head_size)
wei = q @ k.transpose(-2, -1) * head_size**-0.5 # Scale by sqrt(head_size)
print(f"k var: {k.var():.4f}, q var: {q.var():.4f}, wei (scaled) var: {wei.var():.4f}") # Variance should be closer to 1

k.var() # Should be close to 1

q.var() # Should be close to 1

wei.var() # With scaling, should be closer to 1 than head_size (16)

# Softmax with small inputs (diffuse distribution)
torch.softmax(torch.tensor([0.1, -0.2, 0.3, -0.2, 0.5]), dim=-1)

# Softmax with large inputs (simulating unscaled attention scores) -> peaks
torch.softmax(torch.tensor([0.1, -0.2, 0.3, -0.2, 0.5])*8, dim=-1) # gets too peaky, converges to one-hot

class LayerNorm1d: # (used to be BatchNorm1d)
    def __init__(self, dim, eps=1e-5, momentum=0.1): # Momentum is not used in typical LayerNorm
        self.eps = eps
        # Learnable scale and shift parameters, initialized to 1 and 0
        self.gamma = torch.ones(dim)
        self.beta = torch.zeros(dim)

    def __call__(self, x):
        # calculate the forward pass
        # Calculate mean over the *last* dimension (features/embedding)
        xmean = x.mean(1, keepdim=True) # batch mean (shape B, 1, C if input B, T, C) --> Needs adjustment for (B,C) input shape here. Assumes input is (B, dim)
        # Correction: x is (32, 100). dim=1 is correct for features. Shape (32, 1)
        xvar = x.var(1, keepdim=True) # batch variance (shape 32, 1)
        # Normalize each feature vector independently
        xhat = (x - xmean) / torch.sqrt(xvar + self.eps) # normalize to unit variance
        # Apply scale and shift
        self.out = self.gamma * xhat + self.beta
        return self.out

    def parameters(self):
        # Expose gamma and beta as learnable parameters
        return [self.gamma, self.beta]

torch.manual_seed(1337)
module = LayerNorm1d(100) # Create LayerNorm for 100 features
x = torch.randn(32, 100) # batch size 32 of 100-dimensional vectors
x = module(x)
x.shape # Should be (32, 100)

# Mean and std of the first feature *across the batch*. Not expected to be 0 and 1.
x[:,0].mean(), x[:,0].std()

# Mean and std *across features* for the first item in the batch. Expected to be ~0 and ~1.
x[0,:].mean(), x[0,:].std()

# <--------- ENCODE ------------------><--------------- DECODE ----------------->
# les réseaux de neurones sont géniaux! <START> neural networks are awesome!<END>

# Import necessary PyTorch modules
import torch
import torch.nn as nn
from torch.nn import functional as F

# ===== HYPERPARAMETERS =====
batch_size = 16       # Number of sequences per batch (Smaller than Bigram training)
block_size = 32       # Context length (Larger than Bigram demo)
max_iters = 5000      # Total training iterations (More substantial training) TODO change to 5000 later
eval_interval = 100   # How often to check validation loss
learning_rate = 1e-3  # Optimizer learning rate
eval_iters = 200      # Number of batches to average for validation loss estimate
n_embd = 64           # Embedding dimension (Size of token vectors)
n_head = 4            # Number of attention heads
n_layer = 4           # Number of Transformer blocks (layers)
dropout = 0.0         # Dropout probability (0.0 means no dropout here)
# ==========================

# Device selection: MPS (Apple Silicon) > CUDA > CPU
if torch.backends.mps.is_available():
    device = torch.device("mps")   # Apple Silicon GPU
elif torch.cuda.is_available():
    device = torch.device("cuda")  # NVIDIA GPU
else:
    device = torch.device("cpu")   # CPU fallback
print(f"Using device: {device}")

# Set random seed for reproducibility
torch.manual_seed(1337)
if device.type == 'cuda':
    torch.cuda.manual_seed(1337)
elif device.type == 'mps':
    torch.mps.manual_seed(1337)

# Load and read the training text (assuming input.txt is available)
with open('input.txt', 'r', encoding='utf-8') as f:
    text = f.read()

# ===== DATA PREPROCESSING =====
chars = sorted(list(set(text)))
vocab_size = len(chars)
stoi = { ch:i for i,ch in enumerate(chars) }   # string to index
itos = { i:ch for i,ch in enumerate(chars) }   # index to string
encode = lambda s: [stoi[c] for c in s]   # convert string to list of integers
decode = lambda l: ''.join([itos[i] for i in l])   # convert list of integers to string

# Split data into training and validation sets
data = torch.tensor(encode(text), dtype=torch.long)
n = int(0.9*len(data))   # first 90% for training
train_data = data[:n]
val_data = data[n:]
# =============================

# ===== DATA LOADING FUNCTION =====
def get_batch(split):
    """Generate a batch of data for training or validation."""
    data = train_data if split == 'train' else val_data
    ix = torch.randint(len(data) - block_size, (batch_size,))
    x = torch.stack([data[i:i+block_size] for i in ix])
    y = torch.stack([data[i+1:i+block_size+1] for i in ix])
    x, y = x.to(device), y.to(device) # Move data to the target device
    return x, y
# ================================

# ===== LOSS ESTIMATION FUNCTION =====
@torch.no_grad()   # Disable gradient calculation for efficiency
def estimate_loss():
    """Estimate the loss on training and validation sets."""
    out = {}
    model.eval()   # Set model to evaluation mode
    for split in ['train', 'val']:
        losses = torch.zeros(eval_iters)
        for k in range(eval_iters):
            X, Y = get_batch(split)
            logits, loss = model(X, Y)
            losses[k] = loss.item()
        out[split] = losses.mean()
    model.train()  # Set model back to training mode
    return out
# ===================================

# ===== ATTENTION HEAD IMPLEMENTATION =====
class Head(nn.Module):
    """Single head of self-attention."""
    
    def __init__(self, head_size):
        super().__init__()
        # Linear projections for Key, Query, Value
        self.key = nn.Linear(n_embd, head_size, bias=False)
        self.query = nn.Linear(n_embd, head_size, bias=False)
        self.value = nn.Linear(n_embd, head_size, bias=False)
        # Causal mask (tril). 'register_buffer' makes it part of the model state but not a parameter to be trained.
        self.register_buffer('tril', torch.tril(torch.ones(block_size, block_size)))
        # Dropout layer (applied after softmax)
        self.dropout = nn.Dropout(dropout)

    def forward(self, x):
        B,T,C = x.shape # C here is n_embd
        # Project input to K, Q, V
        k = self.key(x)   # (B,T,head_size)
        q = self.query(x) # (B,T,head_size)
        # Compute attention scores, scale, mask, softmax
        # Note the scaling by C**-0.5 (sqrt(n_embd)) as discussed before
        wei = q @ k.transpose(-2,-1) * C**-0.5   # (B, T, T)
        wei = wei.masked_fill(self.tril[:T, :T] == 0, float('-inf'))   # Use dynamic slicing [:T, :T] for flexibility if T < block_size
        wei = F.softmax(wei, dim=-1)   # (B, T, T)
        wei = self.dropout(wei) # Apply dropout to attention weights
        # Weighted aggregation of values
        v = self.value(x) # (B,T,head_size)
        out = wei @ v # (B, T, T) @ (B, T, head_size) -> (B, T, head_size)
        return out
# ========================================

# ===== MULTI-HEAD ATTENTION =====
class MultiHeadAttention(nn.Module):
    """Multiple heads of self-attention in parallel."""
    
    def __init__(self, num_heads, head_size):
        super().__init__()
        self.heads = nn.ModuleList([Head(head_size) for _ in range(num_heads)])
        # Linear layer after concatenating heads
        self.proj = nn.Linear(n_embd, n_embd) # Projects back to n_embd dimension
        self.dropout = nn.Dropout(dropout)

    def forward(self, x):
        # Compute attention for each head and concatenate results
        out = torch.cat([h(x) for h in self.heads], dim=-1) # Shape (B, T, num_heads * head_size) = (B, T, n_embd)
        # Apply final projection and dropout
        out = self.dropout(self.proj(out))
        return out
# ===============================

# ===== FEED-FORWARD NETWORK =====
class FeedFoward(nn.Module):
    """Simple position-wise feed-forward network with one hidden layer."""
    
    def __init__(self, n_embd):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(n_embd, 4 * n_embd),   # Expand dimension (common practice)
            nn.ReLU(),                      # Non-linearity
            nn.Linear(4 * n_embd, n_embd),   # Project back to original dimension
            nn.Dropout(dropout),
        )

    def forward(self, x):
        return self.net(x)
# ==============================

# ===== TRANSFORMER BLOCK =====
class Block(nn.Module):
    """Transformer block: communication (attention) followed by computation (FFN)."""
    
    def __init__(self, n_embd, n_head):
        super().__init__()
        head_size = n_embd // n_head   # Calculate size for each head
        self.sa = MultiHeadAttention(n_head, head_size) # Self-Attention layer
        self.ffwd = FeedFoward(n_embd) # Feed-Forward layer
        self.ln1 = nn.LayerNorm(n_embd) # LayerNorm for Attention input
        self.ln2 = nn.LayerNorm(n_embd) # LayerNorm for FFN input

    def forward(self, x):
        # Pre-Normalization variant: Norm -> Sublayer -> Residual
        x = x + self.sa(self.ln1(x))  # Attention block
        x = x + self.ffwd(self.ln2(x)) # Feed-forward block
        return x
# ============================

# ===== LANGUAGE MODEL =====
class BigramLanguageModel(nn.Module):
    """GPT-like language model using Transformer blocks."""
    
    def __init__(self):
        super().__init__()
        # Token Embedding Table: Maps character index to embedding vector. (vocab_size, n_embd)
        self.token_embedding_table = nn.Embedding(vocab_size, n_embd)
        # Position Embedding Table: Maps position index (0 to block_size-1) to embedding vector. (block_size, n_embd)
        self.position_embedding_table = nn.Embedding(block_size, n_embd)
        # Sequence of Transformer Blocks
        self.blocks = nn.Sequential(*[Block(n_embd, n_head=n_head) for _ in range(n_layer)])
        # Final Layer Normalization (applied after blocks)
        self.ln_f = nn.LayerNorm(n_embd)   # Final layer norm
        # Linear Head: Maps final embedding back to vocabulary size to get logits. (n_embd, vocab_size)
        self.lm_head = nn.Linear(n_embd, vocab_size)

    def forward(self, idx, targets=None):
        B, T = idx.shape
        
        # Get token embeddings from indices: (B, T) -> (B, T, n_embd)
        tok_emb = self.token_embedding_table(idx)
        # Get position embeddings: Create indices 0..T-1, look up embeddings -> (T, n_embd)
        pos_emb = self.position_embedding_table(torch.arange(T, device=device))
        # Combine token and position embeddings by addition: (B, T, n_embd). Broadcasting handles the addition.
        x = tok_emb + pos_emb   # (B,T,C)
        # Pass through Transformer blocks: (B, T, n_embd) -> (B, T, n_embd)
        x = self.blocks(x)
        # Apply final LayerNorm
        x = self.ln_f(x)
        # Map to vocabulary logits: (B, T, n_embd) -> (B, T, vocab_size)
        logits = self.lm_head(x)

        # Calculate loss if targets are provided (same as before)
        if targets is None:
            loss = None
        else:
            # Reshape for cross_entropy: (B*T, vocab_size) and (B*T)
            B, T, C = logits.shape
            logits = logits.view(B*T, C)
            targets = targets.view(B*T)
            loss = F.cross_entropy(logits, targets)

        return logits, loss

    def generate(self, idx, max_new_tokens):
        """Generate new text given a starting sequence."""
        for _ in range(max_new_tokens):
            # Crop context `idx` to the last `block_size` tokens. Important as position embeddings only go up to block_size.
            idx_cond = idx[:, -block_size:]
            # Get predictions (logits) from the model
            logits, loss = self(idx_cond)
            # Focus on the logits for the *last* time step: (B, C)
            logits = logits[:, -1, :]
            # Convert logits to probabilities via softmax
            probs = F.softmax(logits, dim=-1)   # (B, C)
            # Sample next token index from the probability distribution
            idx_next = torch.multinomial(probs, num_samples=1)   # (B, 1)
            # Append the sampled index to the running sequence
            idx = torch.cat((idx, idx_next), dim=1)   # (B, T+1)
        return idx
# =========================

# ===== MODEL INITIALIZATION AND TRAINING =====
# Create model instance and move it to the selected device
model = BigramLanguageModel()
m = model.to(device)
# Print number of parameters (useful for understanding model size)
print(sum(p.numel() for p in m.parameters())/1e6, 'M parameters') # Calculate and print M parameters

# Create optimizer (AdamW again)
optimizer = torch.optim.AdamW(model.parameters(), lr=learning_rate)

# Training loop
for iter in range(max_iters):
    # Evaluate loss periodically
    if iter % eval_interval == 0 or iter == max_iters - 1:
        losses = estimate_loss() # Get train/val loss using the helper function
        print(f"step {iter}: train loss {losses['train']:.4f}, val loss {losses['val']:.4f}") # Print losses

    # Sample a batch of data
    xb, yb = get_batch('train')

    # Forward pass: Evaluate loss
    logits, loss = model(xb, yb)
    # Backward pass: Calculate gradients
    optimizer.zero_grad(set_to_none=True) # Zero gradients
    loss.backward() # Backpropagation
    # Update parameters
    optimizer.step() # Optimizer step

# Generate text from the trained model
context = torch.zeros((1, 1), dtype=torch.long, device=device) # Starting context: [[0]]
print(decode(m.generate(context, max_new_tokens=2000)[0].tolist()))
# ============================================