Contents

Scaled Dot-Product Attention (SDPA)

Overview

Scaled Dot-Product Attention (SDPA) is introduced in [1] as the core operation of Transformer block which now becomes the backbone of many language models and generative models (BERT, Stable Diffusion, GPT, etc.).

The input of SDPA consists of query (Q), key (K), and value (V). The attention output is computed as:

\[attention(Q,K,V) = V \cdot softmax(\frac{QK^T}{\sqrt{d_k}})\]

\(d_k\) is the dimension size of K. Other notations used in the document:

  • N: the mini-batch size.

  • H: the number of multi-head.

  • S: the sequence length.

  • D: the size of each head.

SDPA patterns

oneDNN supports SDPA and its optimization through Graph API [2] by defining the SDPA graph, getting partition from the graph, and optimizing the kernels underneath. In general, an SDPA pattern is defined as a directional acyclic graph (DAG) using oneDNN Graph API.

Floating-point SDPA

oneDNN defines floating-point (f32, bf16, or f16) SDPA as follows. The blue nodes are required when defining an SDPA pattern while the brown parts are optional.

SDPA pattern

  1. The first MatMul calculates the dot products between Query and Key. See MatMul operation in Graph API.

  2. The Scale node is optional and is used to scale the output of the first MatMul with a scaling factor. It can be constructed by Multiply or Divide operation in Graph API. The scaling factor is given by users as an input of SDPA. \(\sqrt{d_k}\) in the formula is not considered as part of the SDPA pattern as it is constant.

  3. The Mask node is optional and is used to apply an attention mask to the output of the previous Scale node. It can be constructed by Add or Select operation in Graph API for different mask policies (eg. causal mask or padding mask). When Add operation is used to apply the mask, the input mask is usually an upper triangular matrix with all the elements above the diagonal filled with -inf and zeroes elsewhere. The -inf entries will become zero probability after Softmax is applied in the next step. Alternately, a Select operation may be used. In this case, the input is a boolean tensor (for example, with true on and below the diagonal, and false above the diagonal). A false element in the mask forces the corresponding element of the scaled output to -inf, while a true element leaves it unchanged.

    SDPA-mask-1 SDPA-mask-2

  4. The SoftMax operation takes the masked output and transforms it into probabilities between 0 and 1. See SoftMax operation in Graph API.

  5. The second MatMul calculates the dot products between the probabilities after SoftMax and Value.

  6. The Reorder node is optional and used to reshape or transpose the attention output for cases where the attention output is transformed from shape (N, H, S, D) to (N, S, H, D) or (N, S, H * D). The node can be constructed by the combinations of StaticTranspose and StaticReshape operation in Graph API.

    SDPA-Reorder

Data Types

oneDNN supports the floating-point SDPA pattern with data types f32, bf16, and f16. You can specify the data type via the input and output logical tensors’ data type fields for each operation. oneDNN does not support mixing different floating data types in a floating-point SDPA pattern.

oneDNN supports the quantized SDPA pattern with int8-f32 mixed precision, int8-bf16 mixed precision, and int8-f16 mixed precision data types.

The definition of the data types and support status on different CPU and GPU platforms follow the general description in Data Types.

Implementation limitations

  1. oneDNN primitive-based SDPA is implemented as the reference implementation on both Intel Architecture Processors and Intel Graphics Products. In this case, floating-point SDPA patterns are usually implemented with f32, bf16, or f16 matmul (with post-ops) and softmax primitives, while quantized SDPA patterns are implemented with int8 matmul (with post-ops) and f32, bf16, or f16 softmax primitives. The reference implementation requires memory to store the intermediate results of the dot products between Query and Key which takes \(O(S^2)\) memory. It may lead to out-of-memory error when computing long sequence length input on platforms with limited memory.

  2. The SDPA patterns functionally supports all input shapes meeting the shape requirements of each operation in the graph. For example, Add, Multiply, Divide, and Select operations require the input tensors to have the same shape or the shapes can be properly broadcasted based on the operation attribute.

  3. CPU

    • Optimized implementation is available for 4D Q/K/V tensors with shape defined as (N, H, S, D).

    • Optimized implementation is available for OpenMP runtime and Threadpool runtime on Intel Architecture Processors.

    • Specifically for OpenMP runtime, the optimized implementation requires N * H > 2 * thread number to get enough parallelism.

  4. GPU

    • Optimized implementation is available for 4D Q/K/V tensors with shape defined as (N, H, S, D).

    • Optimized implementation is available for floating-point SDPA with f16 data type and D <= 256 on Intel Graphics Products with Intel(R) Xe Matrix Extensions (Intel(R) XMX) support.

Example

oneDNN provides an SDPA example demonstrating how to construct a typical floating-point SDPA pattern with oneDNN Graph API on CPU and GPU with different runtimes.

oneDNN also provides a MQA (Multi-Query Attention) example [3] demonstrating how to construct a floating-point MQA pattern with the same pattern structure as in the SDPA example but different head number in Key and Value tensors. In MQA, the head number of Key and Value is always one.

References

[1] Attention is all you need, https://arxiv.org/abs/1706.03762v7

[2] oneDNN Graph API documentation, https://oneapi-src.github.io/oneDNN/graph_extension.html

[3] Fast Transformer Decoding: One Write-Head is All You Need, https://arxiv.org/abs/1911.02150