Reduction

API Reference

General

The reduction primitive performs reduction operation on arbitrary data. Each element in the destination is the result of reduction operation with specified algorithm along one or multiple source tensor dimensions:

\[ \dst(f) = \mathop{reduce\_op}\limits_{r}\src(r), \]

where \(reduce\_op\) can be max, min, sum, mul, mean, Lp-norm and Lp-norm-power-p, \(f\) is an index in an idle dimension and \(r\) is an index in a reduction dimension.

Mean:

\[ \dst(f) = \frac{\sum\limits_{r}\src(r)} {R}, \]

where \(R\) is the size of a reduction dimension.

Lp-norm:

\[ \dst(f) = \root p \of {\mathop{eps\_op}(\sum\limits_{r}|src(r)|^p, eps)}, \]

where \(eps\_op\) can be max and sum.

Lp-norm-power-p:

\[ \dst(f) = \mathop{eps\_op}(\sum\limits_{r}|src(r)|^p, eps), \]

where \(eps\_op\) can be max and sum.

Notes

• The reduction primitive requires the source and destination tensors to have the same number of dimensions.
• Reduction dimensions are of size 1 in a destination tensor.
• The reduction primitive does not have a notion of forward or backward propagations.

Execution Arguments

When executed, the inputs and outputs should be mapped to an execution argument index as specified by the following table.

Primitive input/output	Execution argument index
\(\src\)	DNNL_ARG_SRC
\(\dst\)	DNNL_ARG_DST

Implementation Details

General Notes

• The \(\dst\) memory format can be either specified explicitly or by dnnl::memory::format_tag::any (recommended), in which case the primitive will derive the most appropriate memory format based on the format of the source tensor.

Data Type Support

The source and destination tensors may have f32, bf16, or int8 data types. See Data Types page for more details.

Data Representation

Sources, Destination

The reduction primitive works with arbitrary data tensors. There is no special meaning associated with any of the dimensions of a tensor.

Implementation Limitations

1. Refer to Data Types for limitations related to data types support.

Performance Tips

1. Whenever possible, avoid specifying different memory formats for source and destination tensors.

Examples

Engine	Name	Com
CPU/GPU	Reduction Primitive Example	This C++ API example demonstrates how to create and execute a Reduction primitive.