Deep Neural Network Library (DNNL)  1.2.0
Performance library for Deep Learning
Matrix Multiplication

API Reference

The matrix multiplication (MatMul) primitive computes the product of two 2D tensors with optional bias addition:

$dst(m, n) = \sum_{k=0}^{K} \left( src(m, k) \cdot weights(k, n) \right) + bias(m, n)$

The MatMul primitive also supports batching multiple independent matrix multiplication operations, in which case the tensors must be 3D:

$dst(mb, m, n) = \sum_{k=0}^{K} \left( src(mb, m, k) \cdot weights(mb, k, n) \right) + bias(mb, m, n)$

The bias tensor is optional and supports implicit broadcast semantics: any of its dimensions can be 1 and the same value would be used across the corresponding dimension. However, $$bias$$ must have the same number of dimensions as the $$dst$$.

Implementation Details

General Notes

1. The MatMul primitive supports input and output tensors with run-time specified shapes and memory formats. The run-time specified dimensions or strides are specified using the DNNL_RUNTIME_DIM_VAL wildcard value during the primitive initialization and creation stage. At the execution stage, the user must pass fully specified memory objects so that the primitive is able to perform the computations. Note that the less information about shapes or format is available at the creation stage, the less performant execution will be. In particular, if the shape is not known at creation stage, one cannot use the special format tag dnnl::memory::format_tag::any to enable an implementation to choose the most appropriate memory format for the corresponding input or output shapes. On the other hand, run-time specified shapes enable users to create a primitive once and use it in different situations.

Please check tutorials below to see DNNL_RUNTIME_DIM_VAL support in use.

Data Types

The MatMul primitive supports the following combinations of data types for source, destination, weights, and bias tensors:

Source Weights Destination Bias
f32 f32 f32 f32
f16 f16 f16 f16
bf16 bf16 bf16 bf16, f32
u8, s8 s8, u8 u8, s8, s32, f32 u8, s8, s32, f32

Data Representation

The MatMul primitive expects the following tensors:

Dims Source Weights Destination Bias
2D $$M \times K$$ $$K \times N$$ $$M \times N$$ None or $$(M \text{ or } 1) \times (N \text{ or } 1)$$
3D $$MB \times M \times K$$ $$MB \times K \times N$$ $$MB \times M \times N$$ None or $$(MB \text{ or } 1) \times (M \text{ or } 1) \times (N \text{ or } 1)$$

The MatMul primitive is generally optimized for the case in which memory objects use plain memory formats (with some restrictions; see the table below). However, it is recommended to use the placeholder memory format dnnl::memory::format_tag::any if an input tensor is reused across multiple executions. In this case, the primitive will set the most appropriate memory format for the corresponding input tensor.

The table below shows the combinations of memory formats for which the MatMul primitive is optimized. The memory format of the destination tensor should always be dnnl::memory::format_tag::ab for the 2D case and dnnl::memory::format_tag::abc for the 3D one.

Dims Logical tensors MatMul is optimized for the following memory formats
2D Source: $$M \times K$$
Weights: $$K \times N$$
Source: dnnl_ab or dnnl_ba
Weights: dnnl_ab or dnnl_ba
3D Source: $$MB \times M \times K$$
Weights: $$MB \times K \times N$$
Source: dnnl_abc or dnnl_acb
Weights: dnnl_abc or dnnl_acb

Attributes and Post-ops

Attributes and post-ops enable modifying the behavior of the MatMul primitive. The following attributes and post-ops are supported:

Type Operation Restrictions Description
Attribute Output scales Scales the result by given scale factor(s)
Attribute Zero points Int8 computations only Sets zero point(s) for the corresponding tensors
Post-op Eltwise Applies an Eltwise operation to the result
Post-op Sum Adds the operation result to the destination tensor instead of overwriting it

To facilitate dynamic quantization, the primitive supports run-time output scales. That means a user could configure attributes with output scales set to the DNNL_RUNTIME_F32_VAL wildcard value instead of the actual scales, if the scales are not known at the primitive descriptor creation stage. In this case, the user must provide the scales as an additional input memory object with argument DNNL_ARG_ATTR_OUTPUT_SCALES during the execution stage.

Similarly to run-time output scales, the primitive supports run-time zero points. The wildcard value for zero points is DNNL_RUNTIME_S32_VAL. During the execution stage, the corresponding memory object needs to be passed in the argument with index set to (DNNL_ARG_ATTR_ZERO_POINTS | DNNL_ARG_\${MEMORY_INDEX}).

• For instance, source tensor zero points memory argument would be passed with index (DNNL_ARG_ATTR_ZERO_POINTS | DNNL_ARG_SRC).
Please check tutorials below to see run-time attributes in use.

Implementation Limitations

1. Check Data Types.
2. The CPU engine doesn't support u8 data type for weights.

Performance Tips

• Use dnnl::memory::format_tag::any for either of the input tensors if and only if the shape of the corresponding tensor is fully known at creation time and it is possible to cache reordered tensors across multiple primitive executions. For instance, a good candidate for reuse are the weights tensors during inference: their shapes and data types are known in advance; thus they can be reordered during the first inference pass and can be reused during the subsequent passes. However, if any of the input tensors cannot be reused, it is best to force the primitive to use the same format as that used by the tensors.

Tutorials

CPU MatMul Tutorial: Comparison with SGEMM

C++ API example demonstrating MatMul as a replacement for SGEMM functions.

Concepts:

CPU/GPU MatMul Tutorial: INT8 Inference

C++ API example demonstrating how one can use MatMul fused with ReLU in INT8 inference.

Concepts:

CPU MatMul Tutorial: Quantization

C++ API example demonstrating how one can perform reduced precision matrix-matrix multiplication using MatMul and the accuracy of the result compared to the floating point computations.

Concepts: