KERNELIZED

Max Kernel: Forward and Backward Pass (MATH)

AI

Compute

Autograd

MATH

\(A \in \mathbb{R}^{s_2 s_1}\) where \(s_2\) and \(s_1\) are the index set, for example in a 5D tensor \(A \in \mathbb{R}^{ijklm}\) a possible index set could be \(s_2 = \{…

SoftMax Kernel: Forward and Backward Pass (MATH)

AI

Compute

Autograd

MATH

\(A \in \mathbb{R}^{s_2 s_1}\) where \(s_2\) and \(s_1\) are the index set, for example in a 5D tensor \(A \in \mathbb{R}^{ijklm}\) a possible index set could be \(s_2 = \{…

FlashAttention Kernel: Forward Pass (MATH)

FlashAttention

Transformers

Attention

Compute

Autograd

MATH

\(A \in \mathbb{R}^{s_2 s_1}\) where \(s_2\) and \(s_1\) are the index set, for example in a 5D tensor \(A \in \mathbb{R}^{ijklm}\) a possible index set could be \(s_2 = \{…

FlashAttention Kernel: Backward Pass (MATH)

FlashAttention

Transformers

Attention

Compute

Autograd

MATH

\(A \in \mathbb{R}^{s_2 s_1}\) where \(s_2\) and \(s_1\) are the index set, for example in a 5D tensor \(A \in \mathbb{R}^{ijklm}\) a possible index set could be \(s_2 = \{…