Flash Attention derived and coded from first principles with Triton (Python)

In this monologue podcast, Umar Jamil explores Flash Attention, detailing its derivation and coding, emphasizing a first-principles approach using

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Umar Jamil

Introduction to Flash Attention

Prerequisites and Motivation for Flash Attention

Softmax and Numerical Instability

Solution for Numerical Stability and Softmax Algorithm

Optimizing Softmax Computation: Fusing Operations

Proof by Induction for the Optimized Softmax Algorithm

Block Matrix Multiplication

Block Matrix Multiplication Applied to Attention

Restoring the Softmax Operation with a Twist

Online Softmax and Normalization Factor

Applying Normalization and Flash Attention Forward Pass

Introduction to GPUs and CUDA

CUDA Kernels and Thread Management

Block Processing in CUDA

Matrix Addition in CUDA

Tensor Layouts and Strides

Introduction to Triton and Vector Addition

Implementing Flash Attention Forward Pass in Triton

Triton Kernel and Block Pointer

Online Softmax and Forward Pass Algorithm

Flash Attention Forward Pass and Normalization

GPU Architecture and CUDA Programming Model

Derivatives, Gradients, and Jacobians

Autograd and Computation Graphs

Gradient of Matrix Multiplication

Gradient Through Softmax

Jacobian Matrix and Online Softmax

Flash Attention Backward Pass Algorithm

Implementing the Backward Pass in Triton

Implementing the Inner Loops

Computing and Storing Gradients

Completing the Backward Pass and Auto-Tuning

Software Pipelining

Flash Attention derived and coded from first principles with Triton (Python)

Umar Jamil

00:00Introduction to Flash Attention

Introduction to Flash Attention

02:22Prerequisites and Motivation for Flash Attention

Prerequisites and Motivation for Flash Attention

12:51Softmax and Numerical Instability

Softmax and Numerical Instability

21:26Solution for Numerical Stability and Softmax Algorithm

Solution for Numerical Stability and Softmax Algorithm

27:03Optimizing Softmax Computation: Fusing Operations

Optimizing Softmax Computation: Fusing Operations

39:44Proof by Induction for the Optimized Softmax Algorithm

Proof by Induction for the Optimized Softmax Algorithm

47:28Block Matrix Multiplication

Block Matrix Multiplication

55:07Block Matrix Multiplication Applied to Attention

Block Matrix Multiplication Applied to Attention

1:05:08Restoring the Softmax Operation with a Twist

Restoring the Softmax Operation with a Twist

1:23:08Online Softmax and Normalization Factor

Online Softmax and Normalization Factor

1:37:57Applying Normalization and Flash Attention Forward Pass

Applying Normalization and Flash Attention Forward Pass

1:47:28Introduction to GPUs and CUDA

Introduction to GPUs and CUDA

1:55:15CUDA Kernels and Thread Management

CUDA Kernels and Thread Management

2:06:48Block Processing in CUDA

Block Processing in CUDA

2:17:31Matrix Addition in CUDA

Matrix Addition in CUDA

2:27:28Tensor Layouts and Strides

Tensor Layouts and Strides

2:47:28Introduction to Triton and Vector Addition

Introduction to Triton and Vector Addition

3:05:15Implementing Flash Attention Forward Pass in Triton

Implementing Flash Attention Forward Pass in Triton

3:23:35Triton Kernel and Block Pointer

Triton Kernel and Block Pointer

3:47:00Online Softmax and Forward Pass Algorithm

Online Softmax and Forward Pass Algorithm

4:07:06Flash Attention Forward Pass and Normalization

Flash Attention Forward Pass and Normalization

4:27:28GPU Architecture and CUDA Programming Model

GPU Architecture and CUDA Programming Model

4:45:00Derivatives, Gradients, and Jacobians

Derivatives, Gradients, and Jacobians

4:57:56Autograd and Computation Graphs

Autograd and Computation Graphs

5:05:15Gradient of Matrix Multiplication

Gradient of Matrix Multiplication

5:16:17Gradient Through Softmax

Gradient Through Softmax

5:23:30Jacobian Matrix and Online Softmax

Jacobian Matrix and Online Softmax

5:47:00Flash Attention Backward Pass Algorithm

Flash Attention Backward Pass Algorithm

6:07:00Implementing the Backward Pass in Triton

Implementing the Backward Pass in Triton

6:26:25Implementing the Inner Loops

Implementing the Inner Loops

6:47:00Computing and Storing Gradients

Computing and Storing Gradients

7:06:00Completing the Backward Pass and Auto-Tuning

Completing the Backward Pass and Auto-Tuning

7:23:30Software Pipelining

Software Pipelining