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What is FlashAttention and FlashAttention 2

FlashAttention Explained Simply and Mathematically

For Kids: How FlashAttention Works 🧠

Regular Attention (Like Making Pizza 🍕)

Imagine making pizza for your whole class:

  1. Ask everyone what toppings they want (Query)
  2. Check all possible toppings (Key)
  3. Make a giant list of everyone's choices (big Score matrix)
  4. Choose most popular toppings (Softmax)
  5. Combine them into final pizzas (Value)

This takes lots of paper (memory) to track all choices!

FlashAttention (Smart Pizza Making)

FlashAttention is smarter:

  1. Split class into small groups 🧑🤝🧑
  2. Track favorites per group 📝
  3. Keep running total of toppings ➕
  4. Combine group totals at end 🤝

Uses less paper and finishes faster! 🚀

FlashAttention 2 (Supercharged Version)

Even better improvements:

  • Organize toppings first 🥦🍗
  • Reduce repetitive counting 🔄
  • Work on multiple groups at once 👯

2-3x faster than original FlashAttention! ⚡

For Scientists: Mathematical Details 🔬

Standard Attention

For input matrices \( Q, K, V \in \mathbb{R}^{N \times d} \):

\[ S = \frac{QK^T}{\sqrt{d}}, \quad P = \text{softmax}(S), \quad O = PV \]

Memory: \( O(N^2) \) for storing \( S \) and \( P \).

FlashAttention Algorithm

Tiling with block matrices \( Q_i, K_j, V_j \):

  1. Compute block scores: \[ S_{ij} = \frac{Q_i K_j^T}{\sqrt{d}} \]
  2. Online softmax with: \[ m_{ij} = \max(m_{i(j-1)}, \text{rowmax}(S_{ij})) \] \[ l_{ij} = e^{m_{i(j-1)} - m_{ij}} l_{i(j-1)} + \sum e^{S_{ij} - m_{ij}} \]
  3. Output blocks: \[ O_i = \sum_j \frac{e^{S_{ij} - m_{ij}}}{l_{ij}} V_j \]

Memory: \( O(N) \) using streaming.

FlashAttention 2 Optimizations

Key improvements:

  • Loop reordering over \( K,V \) blocks first
  • Reduced non-matmul FLOPs: \[ \text{FLOPs}_{\text{FA2}} = \frac{\text{FLOPs}_{\text{FA1}}}{1 + \frac{\text{Non-Matmul}}{\text{Matmul}}} \]
  • Parallel computation strategy

Backward Pass

Gradient computation via recomputation:

\[ \frac{\partial L}{\partial Q} = \frac{1}{\sqrt{d}} \left( \text{softmax}(S) \odot (dV) \right) K \]

Only store block statistics \( m_{ij}, l_{ij} \).

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