.. index:: pair: page; Pooling .. _doxid-dev_guide_pooling: Pooling ======= :ref:`API Reference ` General ~~~~~~~ The pooling primitive performs forward or backward max or average pooling operation on 1D, 2D, or 3D spatial data. Forward ------- The pooling operation is defined by the following formulas. We show formulas only for 2D spatial data which are straightforward to generalize to cases of higher and lower dimensions. Variable names follow the standard :ref:`Naming Conventions `. Max pooling: .. math:: \dst(n, c, oh, ow) = \max\limits_{kh, kw} \left( \src(n, c, oh \cdot SH + kh \cdot (DH + 1) - PH_L, ow \cdot SW + kw \cdot (DW + 1) - PW_L) \right) Average pooling: .. math:: \dst(n, c, oh, ow) = \frac{1}{DENOM} \sum\limits_{kh, kw} \src(n, c, oh \cdot SH + kh \cdot (DH + 1) - PH_L, ow \cdot SW + kw \cdot (DW + 1) - PW_L) Here output spatial dimensions are calculated similarly to how they are done in :ref:`Convolution `. Average pooling supports two algorithms: * :ref:`dnnl_pooling_avg_include_padding `, in which case :math:`DENOM = KH \cdot KW`, * :ref:`dnnl_pooling_avg_exclude_padding `, in which case :math:`DENOM` equals to the size of overlap between an averaging window and images. TODO: a picture would be nice here. Difference Between Forward Training and Forward Inference +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ * Max pooling requires a ``workspace`` for the :ref:`dnnl_forward_training ` propagation kind, and does not require it for :ref:`dnnl_forward_inference ` (see details below). Backward -------- The backward propagation computes :math:`\diffsrc(n, c, h, w)`, based on :math:`\diffdst(n, c, h, w)` and (in case of max pooling) ``workspace``. Execution Arguments ~~~~~~~~~~~~~~~~~~~ When executed, the inputs and outputs should be mapped to an execution argument index as specified by the following table. ========================================================== ================================================================================================================================================================= ============= Argument Index Type ========================================================== ================================================================================================================================================================= ============= :math:`\src` DNNL_ARG_SRC Input :math:`\dst` DNNL_ARG_DST Output workspace DNNL_ARG_WORKSPACE Input/Output :math:`\diffsrc` DNNL_ARG_DIFF_SRC Output :math:`\diffdst` DNNL_ARG_DIFF_DST Input :math:`\text{binary post-op}` :ref:`DNNL_ARG_ATTR_MULTIPLE_POST_OP(binary_post_op_position) ` | DNNL_ARG_SRC_1 Input \ :ref:`DNNL_ARG_ATTR_MULTIPLE_POST_OP(binary_post_op_position) ` | DNNL_ARG_SRC_2 Input :ref:`scratchpad ` DNNL_ARG_SCRATCHPAD Output ========================================================== ================================================================================================================================================================= ============= Implementation Details ~~~~~~~~~~~~~~~~~~~~~~ General Notes ------------- #. During training, max pooling requires a workspace on forward (:ref:`dnnl_forward_training `) and backward passes to save indices where a maximum was found. The workspace format is opaque, and the indices cannot be restored from it. However, one can use backward pooling to perform up-sampling (used in some detection topologies). The workspace can be created via ``workspace_desc()`` from the pooling primitive descriptor. #. A user can use memory format tag :ref:`dnnl_format_tag_any ` for ``dst`` memory descriptor when creating pooling forward propagation. The library would derive the appropriate format from the ``src`` memory descriptor. However, the ``src`` itself must be defined. Similarly, a user can use memory format tag :ref:`dnnl_format_tag_any ` for the ``diff_src`` memory descriptor when creating pooling backward propagation. Data Type Support ----------------- The pooling primitive supports the following combinations of data types: =================== ======= ============ ======================================================= Propagation Source Destination Accumulation data type (used for average pooling only) =================== ======= ============ ======================================================= forward / backward f32 f32 f32 forward / backward f64 f64 f64 forward / backward bf16 bf16 bf16 forward / backward f16 f16 f32 forward s8 s8 s32 forward u8 u8 s32 forward s32 s32 s32 forward inference s8 u8 s32 forward inference u8 s8 s32 forward inference s8 f16 f32 forward inference u8 f16 f32 forward inference f16 s8 f32 forward inference f16 u8 f32 forward inference s8 f32 f32 forward inference u8 f32 f32 forward inference f32 s8 f32 forward inference f32 u8 f32 =================== ======= ============ ======================================================= .. warning:: There might be hardware and/or implementation specific restrictions. Check :ref:`Implementation Limitations ` section below. Data Representation ------------------- Source, Destination, and Their Gradients ++++++++++++++++++++++++++++++++++++++++ Like other CNN primitives, the pooling primitive expects data to be an :math:`N \times C \times W` tensor for the 1D spatial case, an :math:`N \times C \times H \times W` tensor for the 2D spatial case, and an :math:`N \times C \times D \times H \times W` tensor for the 3D spatial case. The pooling primitive is optimized for the following memory formats: ======== =============== ============ =========================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================== Spatial Logical tensor Data type Implementations optimized for memory formats ======== =============== ============ =========================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================== 1D NCW f32 :ref:`dnnl_ncw ` ( :ref:`dnnl_abc ` ), :ref:`dnnl_nwc ` ( :ref:`dnnl_acb ` ), *optimized^* 1D NCW s32, s8, u8 :ref:`dnnl_nwc ` ( :ref:`dnnl_acb ` ), *optimized^* 2D NCHW f32 :ref:`dnnl_nchw ` ( :ref:`dnnl_abcd ` ), :ref:`dnnl_nhwc ` ( :ref:`dnnl_acdb ` ), *optimized^* 2D NCHW s32, s8, u8 :ref:`dnnl_nhwc ` ( :ref:`dnnl_acdb ` ), *optimized^* 3D NCDHW f32 :ref:`dnnl_ncdhw ` ( :ref:`dnnl_abcde ` ), :ref:`dnnl_ndhwc ` ( :ref:`dnnl_acdeb ` ), *optimized^* 3D NCDHW s32, s8, u8 :ref:`dnnl_ndhwc ` ( :ref:`dnnl_acdeb ` ), *optimized^* ======== =============== ============ =========================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================== Here optimized^ means the format that :ref:`comes out ` of any preceding compute-intensive primitive. Post-Ops and Attributes ----------------------- ============ ======== ================================================================================== ===================================================================================== ==================================== Propagation Type Operation Description Restrictions ============ ======== ================================================================================== ===================================================================================== ==================================== Forward Post-op :ref:`Binary ` Applies a :ref:`Binary ` operation to the result General binary post-op restrictions Forward Post-op :ref:`Eltwise ` Applies an :ref:`Eltwise ` operation to the result. ============ ======== ================================================================================== ===================================================================================== ==================================== :target:`doxid-dev_guide_pooling_1dg_pool_impl_limits` Implementation Limitations ~~~~~~~~~~~~~~~~~~~~~~~~~~ #. Refer to :ref:`Data Types ` for limitations related to data types support. #. GPU * :ref:`dnnl_pooling_max ` for ``f64`` data type will return ``-FLT_MAX`` as an output value instead of ``-DBL_MAX`` in scenarios when pooling kernel is applied to a completely padded area. Performance Tips ~~~~~~~~~~~~~~~~ N/A Examples ~~~~~~~~ See :ref:`Examples and Tutorials ` page for a complete list. Pooling examples are listed in the :ref:`Pooling and Sampling ` section.