# Primitive Attributes: Post-ops¶

oneDNN implements some basic capabilities of operation fusion using the post-ops attributes API. The operation fusion typically reduces the memory bandwidth pressure hence leading to higher performance.

Post-ops are operations that are appended after a primitive. They are implemented using the Primitive Attributes mechanism. If there are multiple post-ops, they are executed in the order they have been appended.

Currently the following post-ops are supported by the library:

Just like Primitive Attributes, the post-ops are represented by an opaque structure (dnnl_post_ops_t in C API and dnnl::post_ops in C++ API) which is copied once it is attached to the attributes using the C++ dnnl::primitive_attr::set_post_ops or C dnnl_primitive_attr_set_post_ops functions. The attributes then must be passed to a primitive descriptor creation function to take effect. Below is a simple skeleton for the C++ API:

dnnl::post_ops po; // default empty post-ops
assert(po.len() == 0); // no post-ops attached

po.append_SOMETHING(params); // append some particular post-op
po.append_SOMETHING_ELSE(other_params); // append one more post-op

// (!) Note that the order in which post-ops are appended matters!
assert(po.len() == 2);

dnnl::primitive_attr attr; // default attributes
attr.set_post_ops(po); // attach the post-ops to the attr

// further po changes would not affect attr

primitive::primitive_desc op_pd(params, attr); // create a pd with the attr

Note

Different post-ops can be chained together by appending one after another. Note that the appending order matters: the sequence of the post operations is executed in the order of appearance. The maximum number of post operations supported in the library is 32.

Warning

Different primitives may have different post-ops support. Each primitive documentation page contains information about what kind of post operations it supports. Moreover, the support might also depend on the actual implementation of a primitive. For instance, the library may not support post-ops for primitive reference implementations (which are typically very slow, so there is no point in doing the actual fusion). Robust code should handle errors accordingly. See the section on attributes error handling.

Note

Post-ops do not change the memory format of the operation destination memory object.

The post-op object can be inspected using the dnnl::post_ops::kind() function that takes an index of the post-op (which must be less than the value returned by dnnl::post_ops::len()), and returns its kind.

## Supported Post-ops¶

### Eltwise Post-op¶

The eltwise post-op enables fusing a primitive with an Eltwise primitive. This is probably one of the most popular kinds of fusion: an eltwise (typically an activation function) with preceding convolution or inner product.

The dnnl::primitive::kind of this post-op is dnnl::primitive::kind::eltwise.

API:

The parameters (C++ API for simplicity):

void dnnl::post_ops::append_eltwise(
float scale, // scaling factor (described below)
algorithm alg, float alpha, float beta // same as in eltwise primitive
);

The alg, alpha, and beta parameters are the same as in Eltwise.

The eltwise post-op replaces:

$\dst[:] = \operatorname{Op}(...)$

with

$\dst[:] = scale \cdot \operatorname{eltwise}( \operatorname{Op}(...) )$

The intermediate result of $$\operatorname{Op}(...)$$ is not preserved. Hence, in most cases this kind of fusion cannot be used during training.

The $$scale$$ factor is supported in INT8 inference only. For all other cases the scale must be 1.0.

### Sum Post-op¶

The sum post-op accumulates the result of a primitive with the existing data. Prior to accumulating the result, the existing value would be multiplied by scale.

The kind of this post-op is dnnl::primitive::kind::sum.

This feature might improve performance for cases like residual learning blocks, where the result of a convolution is accumulated to the previously computed activations. The scale parameter can be used in [INT8](Primitive Attributes: Quantization) inference only when the result and previous activations have different magnitudes. For all other cases the scale must be 1.0.

The sum post-op replaces

$\dst[:] = \operatorname{Op}(...)$

with

$\dst[:] = scale \cdot \dst[:] + \operatorname{Op}(...)$

If the data type parameter is specified, the original destination tensor will be reinterpreted as a tensor with the provided data type. Because it is a reinterpretation, data_type and the destination data type must have the same size. As a result, the computation will be:

$\dst(:) = scale \cdot \operatorname{as_data_type}(\dst(:)) + \operatorname{Op}(...)$

Note

• Currently only a u8/s8 data type parameter is supported. CPU

• No support for different destination and sum data type.

### Depthwise Post-op¶

Appends a Depthwise convolution as a post-op. This post-op can only be fused with 1x1 convolution as generally seen in models (like MobileNet_v1) that use a stack of Separable convolutions: Depthwise convolution followed by 1x1 convolution. The stack of these Separable convolutions (like in MobileNet_v1) provide an opportunity to fuse 1x1-Convolution with bandwidth-limited Depthwise convolution.

The dnnl::primitive::kind of this post-op is dnnl::primitive::kind::convolution.

There are two variants of this post-op: dw_k3s1p1 and dw_k3_s2p1 for stride-1 and and stride-2 respectively.

API:

For better readability, below we assume a 2D convolution and use the following notations:

conv_1x1 Convolution with weights spatial=1 i.e., kh = kw = 1.

conv_dw Depthwise convolution with weights spatial=3 i.e., kh = kw = 3, g = oc = ic and pad_l = pad_r = {1, 1}.

The Depthwise post-op replaces

$dst[:] = Conv_{1x1}(...)$

with

$dst[:] = Conv_{dw}(Conv_{1x1}(...))$

The final output dimensions of the after post-op is defined as

$dst_{conv_dw} = \{ n, oc_{1x1}, \operatorname{ceil}(oh_{conv_{1x1}}/stride), \operatorname{ceil}(ow_{conv_{1x1}}/stride) \}$

where oh_conv_1x1, ow_conv_1x1 are height and width of conv_1x1 destination.

Supported data types

conv 1x1 output data type

depthwise post-op output data type

depthwise post-op weights data type

depthwise post-op bias data type

u8, s8

u8, s8, s32, f32

s8

f32, s32

f32

f32

f32

f32

bf16

bf16, f32

bf16

f32, bf16

Note

• Currently only supported for 2D 1x1 convolution.

• Only eltwise post-op can be part of post-op chain (i.e., sum post-op is not supported)

• The dst_1x1, wei_dw and dst_dw are assumed to be dnnl_format_tag_any.

### Binary Post-op¶

The binary post-op enables fusing a primitive with a Binary primitive.

The dnnl::primitive::kind of this post-op is dnnl::primitive::kind::binary.

API:

The parameters (C++ API for simplicity):

void dnnl::post_ops::append_binary(
algorithm alg, // binary algorithm to apply
const memory::desc &src1 // memory descriptor for a second memory operand
);

The alg and src1 parameters are the same as in Binary.

The binary post-op replaces:

$\dst[:] = \operatorname{Op}(...)$

with

$\dst[:] = \operatorname{binary}(\operatorname{Op}(...), Source\_1[:])$

The intermediate result of $$\operatorname{Op}(...)$$ is not preserved. Hence, in most cases this kind of fusion cannot be used during training.

Currently the following scenarios are supported:

• Per tensor broadcast, when $$Source\_1$$ is represented as a one-element tensor, i.e. {1, 1, 1, 1} for 2D spatial $$\operatorname{Op}(...)$$.

• Per channels (i.e. dimension 1) broadcast, when a dim[1] value of $$Source\_1$$ coincides with a dim[1] value of $$\operatorname{Op}(...)$$, i.e. {1, C, 1, 1} for 2D spatial $$\operatorname{Op}(...)$$.

Scenario when $$Source\_1$$ represents a full tensor as $$\operatorname{Op}(...)$$ is not supported yet.

## Examples of Chained Post-ops¶

Different post-ops can be chained together by appending one after another. Note that the order matters: the post-ops are executed in the order they have been appended.

Let’s consider some examples.

### Sum -> ReLU¶

This pattern is pretty common for the CNN topologies of the ResNet family.

dnnl::post_ops po;
po.append_sum(
/* scale = */ 1.f);
po.append_eltwise(
/* scale     = */ 1.f,
/* alg kind  = */ dnnl::algorithm::eltwise_relu,
/* neg slope = */ 0.f,
/* unused for relu */ 0.f);

dnnl::primitive_attr attr;
attr.set_post_ops(po);

convolution_forward::primitive_desc(conv_d, attr, engine);

This will lead to the following primitive behavior:

$\dst[:] = \operatorname{ReLU}(\dst[:] + \operatorname{conv}(\src[:], \weights[:])$

### Tanh -> Sum -> ScaleShift¶

This is a hypothetical example that illustrates the sequence of operations applied. We also set all the scales to values other than 1.0 and use dnnl::primitive_attr::set_output_scales which will be covered in Primitive Attributes: Quantization.

dnnl::post_ops po;
po.append_eltwise(
/* scale     = */ s_tanh,
/* alg kind  = */ dnnl::algorithm::eltwise_tanh,
/* unused for tanh */ 0.f,
/* unused for tanh */ 0.f);
po.append_sum(
/* scale     = */ s_sum);
po.append_eltwise(
/* scale     = */ s_linear,
/* alg kind  = */ dnnl::algorithm::eltwise_linear,
/* scale     = */ alpha,
/* shift     = */ beta);

dnnl::primitive_attr attr;
attr.set_output_scales(0, {s_conv});
attr.set_post_ops(po);

convolution_forward::primitive_desc(conv_d, attr, engine);

This will lead to the following primitive behavior (for better readability the tensors are designated by their names only; i.e., [:] is omitted):

$\dst = s_{linear} \cdot ( \alpha \cdot ( s_{sum} \cdot \dst + s_{tanh} \cdot \tanh ( s_{conv} \cdot \operatorname{conv}(\src, \weights) ) ) + \beta )$

### Relu -> Depthwise -> Relu¶

An example of fusing depthwise convolution with 1x1 convolution in MobileNet.

dnnl::post_ops po;

po.append_eltwise(
/* scale     = */ 1.f,
/* alg kind  = */ dnnl::algorithm::eltwise_relu,
/* neg slope = */ 0.f,
/* unused for relu */ 0.f);

po.append_dw_k3s1p1( /* or po.append_dw_k3s2p1 for depthwise with stride=2*/
/* depthwise weights data type = */ dnnl::memory::data_type::s8,
/* depthwise bias data type (undef implies no bias) = */ dnnl::memory::data_type::undef,
/* depthwise destination data type = */ dnnl::memory::data_type::u8,
/* output scales for depthwise output = */ scales_depthwise)

po.append_eltwise(
/* scale     = */ 1.f,
/* alg kind  = */ dnnl::algorithm::eltwise_relu,
/* neg slope = */ 0.f,
/* unused for relu */ 0.f);

dnnl::primitive_attr attr;
attr.set_output_scales(0, {output_scales_1x1_conv});
attr.set_post_ops(po);

auto cpd = convolution_forward::primitive_desc(conv_1x1, attr, engine);
auto dw_weight_md = cpd.query(query::exec_arg_md,
DNNL_ARG_ATTR_POST_OP_DW | DNNL_ARG_WEIGHTS);
auto dw_bias_md = cpd.query(query::exec_arg_md,
DNNL_ARG_ATTR_POST_OP_DW | DNNL_ARG_BIAS);

This will lead to the following primitive behaviour:

$dst = ReLU_{depthwise} ( scales_{depthwise} \cdot ( conv_{depthwise} ( ReLU_{1x1} ( scales_{conv_{1x1}} \cdot ( conv_{1x1}() ) ) ) ) )$

### Binary¶

An example of fusing convolution with binary post-op with per channel addition.

dnnl::memory::desc conv_dst_md {MB, C, H, W}; /* 2D conv destination memory desc */

dnnl::post_ops po;

/* Append eltwise post-op prior the binary post-op */
po.append_eltwise(
/* scale     = */ 1.f,
/* alg kind  = */ dnnl::algorithm::eltwise_relu,
/* neg slope = */ 0.f,
/* unused for relu */ 0.f);

/* Note that C coincides with the one from conv_dst_md. Also note that only
* supported memory format for src1 memory is nchw (or abcd) format. */
po.append_binary(
/* alg kind = */ dnnl::algorithm::binary_add,
/* src1_md = */ dnnl::memory::desc(
{1, C, 1, 1},
dnnl::memory::data_type::f32,
dnnl::memory::format_tag::abcd));

dnnl::primitive_attr attr;
attr.set_post_ops(po);

auto cpd = convolution_forward::primitive_desc(conv, attr, engine);

/* To set memory argument for binary post-op, the following should take place: */
std::unordered_map<int, memory> args;

args.insert(DNNL_ARG_SRC, conv_src_memory);
...
int binary_post_op_position = 1; /* hard coded here, but may be queried */
args.insert(
DNNL_ARG_ATTR_MULTIPLE_POST_OP(binary_post_op_position) | DNNL_ARG_SRC_1, /* note parentheses around index */
binary_post_op_src1_memory);