long-context

# Long Context: Extending Transformer Context Windows

## When to Use This Skill

Use Long Context techniques when you need to:
- **Process long documents** (32k, 64k, 128k+ tokens) with transformer models
- **Extend context windows** of pre-trained models (LLaMA, Mistral, etc.)
- **Implement efficient positional encodings** (RoPE, ALiBi)
- **Train models** with length extrapolation capabilities
- **Deploy models** that handle variable-length inputs efficiently
- **Fine-tune** existing models for longer contexts with minimal compute

**Key Techniques**: RoPE (Rotary Position Embeddings), YaRN, ALiBi (Attention with Linear Biases), Position Interpolation

**Papers**: RoFormer (arXiv 2104.09864), YaRN (arXiv 2309.00071), ALiBi (arXiv 2108.12409), Position Interpolation (arXiv 2306.15595)

## Installation

```bash
# HuggingFace Transformers (includes RoPE, YaRN support)
pip install transformers torch

# For custom implementations
pip install einops  # Tensor operations
pip install rotary-embedding-torch  # Standalone RoPE

# Optional: FlashAttention for efficiency
pip install flash-attn --no-build-isolation
```

## Quick Start

### RoPE (Rotary Position Embeddings)

```python
import torch
import torch.nn as nn

class RotaryEmbedding(nn.Module):
    """Rotary Position Embeddings (RoPE)."""

    def __init__(self, dim, max_seq_len=8192, base=10000):
        super().__init__()
        # Compute inverse frequencies
        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float() / dim))
        self.register_buffer("inv_freq", inv_freq)
        self.max_seq_len = max_seq_len

    def forward(self, seq_len, device):
        # Position indices
        t = torch.arange(seq_len, device=device).type_as(self.inv_freq)

        # Compute frequencies
        freqs = torch.outer(t, self.inv_freq)  # (seq_len, dim/2)

        # Compute sin and cos
        emb = torch.cat((freqs, freqs), dim=-1)  # (seq_len, dim)
        return emb.cos(), emb.sin()

def rotate_half(x):
    """Rotate half the hidden dimensions."""
    x1, x2 = x.chunk(2, dim=-1)
    return torch.cat((-x2, x1), dim=-1)

def apply_rotary_pos_emb(q, k, cos, sin):
    """Apply rotary embeddings to queries and keys."""
    # q, k shape: (batch, heads, seq_len, dim)
    q_embed = (q * cos) + (rotate_half(q) * sin)
    k_embed = (k * cos) + (rotate_half(k) * sin)
    return q_embed, k_embed

# Usage
rope = RotaryEmbedding(dim=64, max_seq_len=8192)
cos, sin = rope(seq_len=2048, device='cuda')

# In attention layer
q_rotated, k_rotated = apply_rotary_pos_emb(query, key, cos, sin)
```

### ALiBi (Attention with Linear Biases)

```python
def get_alibi_slopes(num_heads):
    """Get ALiBi slope values for each attention head."""
    def get_slopes_power_of_2(n):
        start = 2 ** (-(2 ** -(math.log2(n) - 3)))
        ratio = start
        return [start * (ratio ** i) for i in range(n)]

    if math.log2(num_heads).is_integer():
        return get_slopes_power_of_2(num_heads)
    else:
        # Closest power of 2
        closest_power = 2 ** math.floor(math.log2(num_heads))
        slopes = get_slopes_power_of_2(closest_power)
        # Add extra slopes
        extra = get_slopes_power_of_2(2 * closest_power)
        slopes.extend(extra[0::2][:num_heads - closest_power])
        return slopes

def create_alibi_bias(seq_len, num_heads):
    """Create ALiBi attention bias."""
    # Distance matrix
    context_position = torch.arange(seq_len)
    memory_position = torch.arange(seq_len)
    relative_position = memory_position[None, :] - context_position[:, None]

    # Get slopes
    slopes = torch.tensor(get_alibi_slopes(num_heads))

    # Apply slopes to distances
    alibi = slopes[:, None, None] * relative_position[None, :, :]
    return alibi  # (num_heads, seq_len, seq_len)

# Usage in attention
num_heads = 8
seq_len = 2048
alibi_bias = create_alibi_bias(seq_len, num_heads).to('cuda')

# Add bias to attention scores
# attn_scores shape: (batch, num_heads, seq_len, seq_len)
attn_scores = attn_scores + alibi_bias
attn_weights = torch.softmax(attn_scores, dim=-1)
```

### Position Interpolation for LLaMA

```python
from transformers import LlamaForCausalLM, LlamaTokenizer

# Original context: 2048 tokens
model = LlamaForCausalLM.from_pretrained("meta-llama/Llama-2-7b-hf")

# Extend to 32k with position interpolation
# Modify RoPE base frequency
model.config.rope_scaling = {
    "type": "linear",
    "factor": 16.0  # 2048 * 16 = 32768
}

# Or use dynamic scaling
model.config.rope_scaling = {
    "type": "dynamic",
    "factor": 16.0
}

# Fine-tune with long documents (minimal steps needed)
# Position interpolation works out-of-the-box after this config change
```

## Core Concepts

### 1. RoPE (Rotary Position Embeddings)

**How it works:**
- Encodes absolute position via rotation matrix
- Provides relative position dependency in attention
- Enables length extrapolation

**Mathematical formulation:**
```
q_m = (W_q * x_m) * e^(imθ)
k_n = (W_k * x_n) * e^(inθ)

where θ_j = base^(-2j/d) for j ∈ [0, d/2)
```

**Advantages:**
- Decaying inter-token dependency with distance
- Compatible with linear attention
- Better extrapolation than absolute position encodings

### 2. YaRN (Yet another RoPE extensioN)

**Key innovation:**
- NTK-aware interpolation (Neural Tangent Kernel)
- Attention temperature scaling
- Efficient context extension (10× less tokens vs baselines)

**Parameters:**
```python
# YaRN configuration
yarn_config = {
    "scale": 16,                    # Extension factor
    "original_max_position": 2048,  # Base context
    "extrapolation_factor": 1.0,    # NTK parameter
    "attn_factor": 1.0,             # Attention scaling
    "beta_fast": 32,                # High-frequency scale
    "beta_slow": 1,                 # Low-frequency scale
}
```

**Performance:**
- Extends LLaMA to 128k tokens
- 2.5× less training steps than baselines
- State-of-the-art context window extension

### 3. ALiBi (Attention with Linear Biases)

**Core idea:**
-