# Inner Product#

The inner product primitive (sometimes called fully connected layer) treats each activation in the minibatch as a vector and computes its product with a weights 2D tensor producing a 2D tensor as an output.

## Forward#

Let $$\src$$, $$\weights$$, $$\bias$$ and $$\dst$$ be $$N \times IC$$, $$OC \times IC$$, $$OC$$, and $$N \times OC$$ tensors, respectively. Variable names follow the standard Conventions. Then:

$\dst(n, oc) = \bias(oc) + \sum_{ic=0}^{IC-1} \src(n, ic) \cdot \weights(oc, ic)$

In cases where the $$\src$$ and $$\weights$$ tensors have spatial dimensions, they are flattened to 2D. For example, if they are 4D $$N \times IC' \times IH \times IW$$ and $$OC \times IC' \times KH \times KW$$ tensors, then the formula above is applied with $$IC = IC' \cdot IH \cdot IW$$. In such cases, the $$\src$$ and $$\weights$$ tensors must have equal spatial dimensions (e.g. $$KH = IH$$ and $$KW = IW$$ for 4D tensors).

### Difference Between Forward Training and Forward Inference#

There is no difference between the forward_training and forward_inference propagation kinds.

## Backward#

The backward propagation computes $$\diffsrc$$ based on $$\diffdst$$ and $$\weights$$.

The weights update computes $$\diffweights$$ and $$\diffbias$$ based on $$\diffdst$$ and $$\src$$.

Note

The optimized memory formats $$\src$$ and $$\weights$$ might be different on forward propagation, backward propagation, and weights update.

### 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

$$\weights$$

DNNL_ARG_WEIGHTS

$$\bias$$

DNNL_ARG_BIAS

$$\dst$$

DNNL_ARG_DST

$$\diffsrc$$

DNNL_ARG_DIFF_SRC

$$\diffweights$$

DNNL_ARG_DIFF_WEIGHTS

$$\diffbias$$

DNNL_ARG_DIFF_BIAS

$$\diffdst$$

DNNL_ARG_DIFF_DST

N/A

## Data Types Support#

Inner product primitive supports the following combination of data types for source, destination, weights, and bias.

Note

Here we abbreviate data types names for readability. For example, dnnl::memory::data_type::f32 is abbreviated to f32.

Propagation

Source

Weights

Destination

Bias

forward / backward

f32

f32

f32

f32

forward

f16

f16

f16

f16

forward

s8

forward

bf16

bf16

backward

bf16

bf16

weights update

bf16

bf16

## Data Representation#

Like other CNN primitives, the inner product primitive expects the following tensors:

Spatial

Source

Destination

Weights

1D

$$N \times C \times W$$

$$N \times C$$

$$OC \times IC \times KW$$

2D

$$N \times C \times H \times W$$

$$N \times C$$

$$OC \times IC \times KH \times KW$$

3D

$$N \times C \times D \times H \times W$$

$$N \times C$$

$$OC \times IC \times KD \times KH \times KW$$

Memory format of data and weights memory objects is critical for inner product primitive performance. In the oneDNN programming model, inner product primitive is one of the few primitives that support the placeholder format any and can define data and weight memory objects formats based on the primitive parameters. When using any it is necessary to first create an inner product primitive descriptor and then query it for the actual data and weight memory objects formats.

The table below shows the combinations for which plain memory formats the inner product primitive is optimized for. For the destination tensor (which is always $$N \times C$$) the memory format is always nc (ab).

Spatial

Source / Weights logical tensor

Implementation optimized for memory formats

0D

NC / OI

0D

NC / OI

1D

NCW / OIW

1D

NCW / OIW

2D

NCHW / OIHW

2D

NCHW / OIHW

3D

NCDHW / OIDHW

3D

NCDHW / OIDHW

## Post-ops and Attributes#

The following post-ops should be supported by inner product primitives:

Type

Operation

Description

Restrictions

Attribute

Scales

Sets scale(s) for the corresponding tensor(s)

Int8 computations only

Attribute

Zero points

Sets zero point(s) for the corresponding tensors

Int8 computations only

Post-op

Eltwise

Applies an elementwise operation to the result

Post-op

Binary

Applies a binary operation to the result

Post-op

Sum

Adds the operation result to the destination tensor instead of overwriting it

## API#

struct inner_product_forward : public dnnl::primitive#

Inner product forward propagation primitive.

Public Functions

inner_product_forward()#

Default constructor. Produces an empty object.

inner_product_forward(const primitive_desc &pd)#

Constructs an inner product forward propagation primitive.

Parameters:

pd – Primitive descriptor for an inner product forward propagation primitive.

struct primitive_desc : public dnnl::primitive_desc#

Primitive descriptor for an inner product forward propagation primitive.

Public Functions

primitive_desc() = default#

Default constructor. Produces an empty object.

primitive_desc(const engine &aengine, prop_kind aprop_kind, const memory::desc &src_desc, const memory::desc &weights_desc, const memory::desc &bias_desc, const memory::desc &dst_desc, const primitive_attr &attr = default_attr(), bool allow_empty = false)#

Constructs a primitive descriptor for an inner product forward propagation primitive with bias.

Note

All the memory descriptors may be initialized with the dnnl::memory::format_tag::any value of format_tag.

Parameters:
• aengine – Engine to use.

• aprop_kind – Propagation kind. Possible values are dnnl::prop_kind::forward_training, and dnnl::prop_kind::forward_inference.

• src_desc – Memory descriptor for src.

• weights_desc – Memory descriptor for weights.

• bias_desc – Memory descriptor for bias.

• dst_desc – Memory descriptor for dst.

• attr – Primitive attributes to use. Attributes are optional and default to empty attributes.

• allow_empty – A flag signifying whether construction is allowed to fail without throwing an exception. In this case an empty object will be produced. This flag is optional and defaults to false.

primitive_desc(const engine &aengine, prop_kind aprop_kind, const memory::desc &src_desc, const memory::desc &weights_desc, const memory::desc &dst_desc, const primitive_attr &attr = default_attr(), bool allow_empty = false)#

Constructs a primitive descriptor for an inner product forward propagation primitive.

Note

All the memory descriptors may be initialized with the dnnl::memory::format_tag::any value of format_tag.

Parameters:
• aengine – Engine to use.

• aprop_kind – Propagation kind. Possible values are dnnl::prop_kind::forward_training, and dnnl::prop_kind::forward_inference.

• src_desc – Memory descriptor for src.

• weights_desc – Memory descriptor for weights.

• dst_desc – Memory descriptor for dst.

• attr – Primitive attributes to use. Attributes are optional and default to empty attributes.

• allow_empty – A flag signifying whether construction is allowed to fail without throwing an exception. In this case an empty object will be produced. This flag is optional and defaults to false.

memory::desc src_desc() const#

Returns a source memory descriptor.

Returns:

Source memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a source parameter.

memory::desc weights_desc() const#

Returns a weights memory descriptor.

Returns:

Weights memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a weights parameter.

memory::desc dst_desc() const#

Returns a destination memory descriptor.

Returns:

Destination memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a destination parameter.

memory::desc bias_desc() const#

Returns the bias memory descriptor.

Returns:

The bias memory descriptor.

Returns:

A zero memory descriptor of the primitive does not have a bias parameter.

prop_kind get_prop_kind() const#

Returns a propagation kind.

Returns:

A propagation kind.

Returns:

dnnl::prop_kind::undef if the primitive does not have a propagation parameter.

struct inner_product_backward_data : public dnnl::primitive#

Inner product backward propagation primitive.

Public Functions

inner_product_backward_data()#

Default constructor. Produces an empty object.

inner_product_backward_data(const primitive_desc &pd)#

Constructs an inner product backward propagation primitive.

Parameters:

pd – Primitive descriptor for an inner product backward propagation primitive.

struct primitive_desc : public dnnl::primitive_desc#

Primitive descriptor for an inner product backward propagation primitive.

Public Functions

primitive_desc() = default#

Default constructor. Produces an empty object.

primitive_desc(const engine &aengine, const memory::desc &diff_src_desc, const memory::desc &weights_desc, const memory::desc &diff_dst_desc, const inner_product_forward::primitive_desc &hint_fwd_pd, const primitive_attr &attr = default_attr(), bool allow_empty = false)#

Constructs a primitive descriptor for an inner product backward propagation primitive.

Note

All the memory descriptors may be initialized with the dnnl::memory::format_tag::any value of format_tag.

Parameters:
• aengine – Engine to use.

• diff_src_desc – Memory descriptor for diff src.

• weights_desc – Memory descriptor for weights.

• diff_dst_desc – Memory descriptor for diff dst.

• hint_fwd_pd – Primitive descriptor for an inner product forward propagation primitive. It is used as a hint for deciding which memory format to use.

• attr – Primitive attributes to use. Attributes are optional and default to empty attributes.

• allow_empty – A flag signifying whether construction is allowed to fail without throwing an exception. In this case an empty object will be produced. This flag is optional and defaults to false.

memory::desc diff_src_desc() const#

Returns a diff source memory descriptor.

Returns:

Diff source memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a diff source memory with.

memory::desc weights_desc() const#

Returns a weights memory descriptor.

Returns:

Weights memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a weights parameter.

memory::desc diff_dst_desc() const#

Returns a diff destination memory descriptor.

Returns:

Diff destination memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a diff destination parameter.

prop_kind get_prop_kind() const#

Returns a propagation kind.

Returns:

A propagation kind.

Returns:

dnnl::prop_kind::undef if the primitive does not have a propagation parameter.

struct inner_product_backward_weights : public dnnl::primitive#

Inner product weights gradient primitive.

Public Functions

inner_product_backward_weights()#

Default constructor. Produces an empty object.

inner_product_backward_weights(const primitive_desc &pd)#

Constructs an inner product weights gradient primitive.

Parameters:

pd – Primitive descriptor for an inner product weights gradient primitive.

struct primitive_desc : public dnnl::primitive_desc#

Primitive descriptor for an inner product weights gradient primitive.

Public Functions

primitive_desc() = default#

Default constructor. Produces an empty object.

primitive_desc(const engine &aengine, const memory::desc &src_desc, const memory::desc &diff_weights_desc, const memory::desc &diff_bias_desc, const memory::desc &diff_dst_desc, const inner_product_forward::primitive_desc &hint_fwd_pd, const primitive_attr &attr = default_attr(), bool allow_empty = false)#

Constructs a primitive descriptor for an inner product weights update primitive with bias.

Note

All the memory descriptors may be initialized with the dnnl::memory::format_tag::any value of format_tag.

Parameters:
• aengine – Engine to use.

• src_desc – Memory descriptor for src.

• diff_weights_desc – Memory descriptor for diff weights.

• diff_bias_desc – Memory descriptor for diff bias.

• diff_dst_desc – Memory descriptor for diff dst.

• hint_fwd_pd – Primitive descriptor for an inner product forward propagation primitive. It is used as a hint for deciding which memory format to use.

• attr – Primitive attributes to use. Attributes are optional and default to empty attributes.

• allow_empty – A flag signifying whether construction is allowed to fail without throwing an exception. In this case an empty object will be produced. This flag is optional and defaults to false.

primitive_desc(const engine &aengine, const memory::desc &src_desc, const memory::desc &diff_weights_desc, const memory::desc &diff_dst_desc, const inner_product_forward::primitive_desc &hint_fwd_pd, const primitive_attr &attr = default_attr(), bool allow_empty = false)#

Constructs a primitive descriptor for an inner product weights update primitive.

Note

All the memory descriptors may be initialized with the dnnl::memory::format_tag::any value of format_tag.

Parameters:
• aengine – Engine to use.

• src_desc – Memory descriptor for src.

• diff_weights_desc – Memory descriptor for diff weights.

• diff_dst_desc – Memory descriptor for diff dst.

• attr – Primitive attributes to use. Attributes are optional and default to empty attributes.

• hint_fwd_pd – Primitive descriptor for an inner product forward propagation primitive. It is used as a hint for deciding which memory format to use.

• allow_empty – A flag signifying whether construction is allowed to fail without throwing an exception. In this case an empty object will be produced. This flag is optional and defaults to false.

memory::desc src_desc() const#

Returns a source memory descriptor.

Returns:

Source memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a source parameter.

memory::desc diff_weights_desc() const#

Returns a diff weights memory descriptor.

Returns:

Diff weights memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a diff weights parameter.

memory::desc diff_dst_desc() const#

Returns a diff destination memory descriptor.

Returns:

Diff destination memory descriptor.

Returns:

A zero memory descriptor if the primitive does not have a diff destination parameter.

memory::desc diff_bias_desc() const#

Returns the diff bias memory descriptor.

Returns:

The diff bias memory descriptor.

Returns:

A zero memory descriptor of the primitive does not have a diff bias parameter.

prop_kind get_prop_kind() const#

Returns a propagation kind.

Returns:

A propagation kind.

Returns:

dnnl::prop_kind::undef if the primitive does not have a propagation parameter.