### Complete Training Loop Example

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Demonstrates a full training setup for Pause Transformer on character-level data. Includes model configuration, optimizer setup, training loop with loss computation and gradient updates, and evaluation with entropy-based adaptive pausing. The final inference uses the last pause step's logits.

```python
import torch
import torch.optim as optim
from pause_transformer import PauseTransformer

# Model configuration
model = PauseTransformer(
    num_tokens=256,           # Byte-level vocabulary
    dim=512,
    depth=6,
    max_pause_length=2,
    dim_head=64,
    heads=8,
    ff_mult=4
)

# Setup optimizer
optimizer = optim.AdamW(model.parameters(), lr=1e-4, weight_decay=0.01)

# Training loop
model.train()
for step in range(1000):
    # Generate random training data (replace with real data)
    x = torch.randint(0, 256, (8, 512))

    # Forward pass with loss
    loss = model(x, return_loss=True)

    # Backward pass
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if step % 100 == 0:
        print(f"Step {step}, Loss: {loss.item():.4f}")

# Evaluation with entropy-based adaptive pausing
model.eval()
with torch.no_grad():
    test_x = torch.randint(0, 256, (1, 256))

    # Get entropy to guide pause allocation
    entropy = model(test_x, arrest_pausing=True, return_logit_entropy=True)

    # Allocate more pause steps to high-entropy (uncertain) tokens
    pause_lengths = torch.clamp((entropy * 2).long(), 0, 2)

    # Final inference with adaptive computation
    logits = model(test_x, pause_lengths=pause_lengths)
    predictions = logits[:, :, -1, :].argmax(dim=-1)  # Use last pause step
    print(f"Prediction shape: {predictions.shape}")
```

--------------------------------

### Initialize and Use PauseTransformer Model

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Initializes the PauseTransformer model with specified parameters and performs a forward pass. Use this for basic model setup and inference.

```python
import torch
from pause_transformer import PauseTransformer

# Initialize the Pause Transformer model
model = PauseTransformer(
    num_tokens=256,           # Vocabulary size (e.g., 256 for byte-level)
    dim=512,                  # Model embedding dimension
    depth=6,                  # Number of transformer layers
    max_pause_length=2,       # Maximum thinking steps per token
    dim_head=64,              # Dimension per attention head
    heads=8,                  # Number of attention heads
    ff_mult=4                 # Feedforward expansion multiplier
)

# Create sample input sequence
x = torch.randint(0, 256, (1, 1024))  # (batch_size, sequence_length)

# Forward pass - returns logits with pause dimension
logits = model(x)
# Output shape: (batch, seq_len, max_pause_length + 1, num_tokens)
print(f"Logits shape: {logits.shape}")  # torch.Size([1, 1024, 3, 256])
```

--------------------------------

### Logit Entropy for Adaptive Computation

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Returns the entropy of the output logits instead of the logits themselves using `return_logit_entropy=True`. This can be used for adaptive computation, where tokens with high entropy (uncertainty) are allocated more pause steps. Ensure `arrest_pausing=True` is set for the initial pass to get entropy without pausing.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=2
)

x = torch.randint(0, 256, (1, 128))

# First pass: get entropy without pausing to identify uncertain tokens
entropy = model(x, arrest_pausing=True, return_logit_entropy=True)
print(f"Entropy shape: {entropy.shape}")  # torch.Size([1, 128])
print(f"Mean entropy: {entropy.mean().item():.4f}")

# Use entropy to determine which tokens need more thinking
# Higher entropy = more uncertain = needs more pause steps
threshold = entropy.median()
pause_lengths = (entropy > threshold).long() * 2  # 0 or 2 pause steps
print(f"Adaptive pause lengths: {pause_lengths}")

# Second pass: run with adaptive pause lengths
logits = model(x, pause_lengths=pause_lengths)
```

--------------------------------

### Independent Pause Training (no_prev_pause_integration)

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Disables the integration of previous token's pause information during training via `no_prev_pause_integration=True`. This forces each token to develop its thinking capability independently, useful for specific training curricula. Compare results with `no_prev_pause_integration=False`.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=2
)

x = torch.randint(0, 256, (4, 256))

# Training without previous pause integration
# Each token's thinking is independent of neighbors
loss = model(x, return_loss=True, no_prev_pause_integration=True)
print(f"Loss (independent pause): {loss.item():.4f}")

# Compare with integrated pause training
loss_integrated = model(x, return_loss=True, no_prev_pause_integration=False)
print(f"Loss (integrated pause): {loss_integrated.item():.4f}")
```

--------------------------------

### Random Uniform Pausing for Training Regularization

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Enables random pause lengths sampled uniformly from [0, max_pause_length] during training. This acts as a regularization technique, encouraging the model to learn variable computation depths. Each forward pass with `rand_uniform_pausing=True` will use different random pause configurations.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=3
)

x = torch.randint(0, 256, (4, 256))

# Training with random uniform pause lengths per token
loss = model(x, return_loss=True, rand_uniform_pausing=True)
print(f"Loss (random pause): {loss.item():.4f}")

# Each forward pass uses different random pause configurations
for i in range(3):
    loss = model(x, return_loss=True, rand_uniform_pausing=True)
    print(f"Iteration {i+1} loss: {loss.item():.4f}")
```

--------------------------------

### Train PauseTransformer with Automatic Loss

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Trains the PauseTransformer model using automatic cross-entropy loss computation. The model handles label shifting internally, simplifying the training loop.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=2
)

# Training mode - model automatically creates labels from shifted input
x = torch.randint(0, 256, (4, 512))  # (batch_size, sequence_length)

# Compute loss directly
loss = model(x, return_loss=True)
print(f"Training loss: {loss.item():.4f}")

# Backpropagation
loss.backward()
```

--------------------------------

### Fast Inference with arrest_pausing

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Performs fast inference or training by disabling pause token processing using `arrest_pausing=True`. The model behaves like a standard causal transformer, outputting logits without the pause dimension.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=2
)

x = torch.randint(0, 256, (1, 1024))

# Fast inference without pause processing
logits = model(x, arrest_pausing=True)
# Output shape: (batch, seq_len, num_tokens) - no pause dimension
print(f"Logits shape (no pause): {logits.shape}")  # torch.Size([1, 1024, 256])

# Training without pause computation
loss = model(x, return_loss=True, arrest_pausing=True)
print(f"Loss (no pause): {loss.item():.4f}")
```

--------------------------------

### Custom Pause Lengths Per Token

Source: https://context7.com/lucidrains/pause-transformer/llms.txt

Utilizes the `pause_lengths` parameter to specify variable thinking steps for each token, enabling fine-grained adaptive computation. This is useful for controlling computational allocation per token.

```python
import torch
from pause_transformer import PauseTransformer

model = PauseTransformer(
    num_tokens=256,
    dim=512,
    depth=6,
    max_pause_length=4  # Allow up to 4 thinking steps
)

batch_size, seq_len = 2, 128
x = torch.randint(0, 256, (batch_size, seq_len))

# Define custom pause lengths per token
# Each token can think for 0 to max_pause_length steps
pause_lengths = torch.randint(0, 5, (batch_size, seq_len))

# Forward with custom pause distribution
logits = model(x, pause_lengths=pause_lengths)

# Training with custom pause lengths
loss = model(x, return_loss=True, pause_lengths=pause_lengths)
print(f"Loss with custom pause: {loss.item():.4f}")
```

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