The following describes the semantics of operations defined in the ComputationBuilder
interface. Typically, these operations map onetoone to operations defined in the RPC interface in xla_data.proto
.
A note on nomenclature: the generalized data type XLA deals with is an Ndimensional array holding elements of some uniform type (such as 32bit float). Throughout the documentation, array is used to denote an arbitrarydimensional array. For convenience, special cases have more specific and familiar names; for example a vector is a 1dimensional array and a matrix is a 2dimensional array.
See also ComputationBuilder::BatchNormGrad
and the original batch normalization paper for a detailed description of the algorithm.
Calculates gradients of batch norm.
BatchNormGrad(operand, scale, mean, variance, grad_output, epsilon, feature_index)
Arguments  Type  Semantics 

operand  ComputationDataHandle  n dimensional array to be normalized (x) 
scale  ComputationDataHandle  1 dimensional array (\(\gamma\)) 
mean  ComputationDataHandle  1 dimensional array (\(\mu\)) 
variance  ComputationDataHandle  1 dimensional array (\(\sigma^2\)) 
grad_output  ComputationDataHandle  Gradients passed to BatchNormTraining (\( \nabla y\)) 
epsilon  float  Epsilon value (\(\epsilon\)) 
feature_index  int64  Index to feature dimension in operand

For each feature in the feature dimension (feature_index
is the index for the feature dimension in operand
), the operation calculates the gradients with respect to operand
, offset
and scale
across all the other dimensions. The feature_index
must be a valid index for the feature dimension in operand
.
The three gradients are defined by the following formulas (Assuming a 4dimensional tensor as operand
and (l) is the index for feature dimension):
\( coef_l = \frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h (\nabla y_{ijkl} * (x_{ijkl}  \mu_l) / (\sigma^2_{l}+\epsilon)) \)
\( \nabla x_{ijkl} = \gamma_{l} * (1/\sqrt{\sigma^2_{l}+\epsilon}) * [\nabla y_{ijkl}  mean(\nabla y)  (x_{ijkl}  \mu_{l}) * coef_l] \)
\( \nabla \beta_l = \sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h \nabla y_{ijkl} \)
\( \nabla \gamma_l = \sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h \nabla y_{ijkl} * ((x_{ijkl}  \mu_l) / \sqrt{\sigma^2_{l}+\epsilon}) \)
The inputs mean
and variance
represents moments value across batch and spatial dimensions.
The output type is a tuple of three handles:
Outputs  Type  Semantics 

grad_operand  ComputationDataHandle  gradient with respect to input 
operand (\( \nabla x\))  grad_scale  ComputationDataHandle 
grad_offset  ComputationDataHandle  gradient with respect to input offset (\( \nabla \beta\)) 
See also ComputationBuilder::BatchNormInference
and the original batch normalization paper for a detailed description of the algorithm.
Normalizes an array across batch and spatial dimensions.
BatchNormInference(operand, scale, offset, mean, variance, epsilon, feature_index)
Arguments  Type  Semantics 

operand  ComputationDataHandle  n dimensional array to be normalized 
scale  ComputationDataHandle  1 dimensional array 
offset  ComputationDataHandle  1 dimensional array 
mean  ComputationDataHandle  1 dimensional array 
variance  ComputationDataHandle  1 dimensional array 
epsilon  float  Epsilon value 
feature_index  int64  Index to feature dimension in operand

For each feature in the feature dimension (feature_index
is the index for the feature dimension in operand
), the operation calculates the mean and variance across all the other dimensions and uses the mean and variance to normalize each element in operand
. The feature_index
must be a valid index for the feature dimension in operand
.
BatchNormInference
is equivalent to calling BatchNormTraining
without computing mean
and variance
for each batch. It uses the input mean
and variance
instead as estimated values. The purpose of this op is to reduce latency in inference, hence the name BatchNormInference
.
The output is an ndimensional, normalized array with the same shape as input operand
.
See also ComputationBuilder::BatchNormTraining
and the original batch normalization paper
for a detailed description of the algorithm.
Normalizes an array across batch and spatial dimensions.
BatchNormTraining(operand, scale, offset, epsilon, feature_index)
Arguments  Type  Semantics 

operand  ComputationDataHandle  n dimensional array to be normalized (x) 
scale  ComputationDataHandle  1 dimensional array (\(\gamma\)) 
offset  ComputationDataHandle  1 dimensional array (\(\beta\)) 
epsilon  float  Epsilon value (\(\epsilon\)) 
feature_index  int64  Index to feature dimension in operand

For each feature in the feature dimension (feature_index
is the index for the feature dimension in operand
), the operation calculates the mean and variance across all the other dimensions and uses the mean and variance to normalize each element in operand
. The feature_index
must be a valid index for the feature dimension in operand
.
The algorithm goes as follows for each batch in operand
\(x\) that contains m
elements with w
and h
as the size of spatial dimensions (assuming operand
is an 4 dimensional array):
Calculates batch mean \(\mu_l\) for each feature l
in feature dimension: \(\mu_l=\frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h x_{ijkl}\)
Calculates batch variance \(\sigma^2_l\): \(\sigma^2_l=\frac{1}{mwh}\sum_{i=1}^m\sum_{j=1}^w\sum_{k=1}^h (x_{ijkl}  \mu_l)^2\)
Normalizes, scales and shifts: \(y_{ijkl}=\frac{\gamma_l(x_{ijkl}\mu_l)}{\sqrt[2]{\sigma^2_l+\epsilon}}+\beta_l\)
The epsilon value, usually a small number, is added to avoid dividebyzero errors.
The output type is a tuple of three ComputationDataHandle
s:
Outputs  Type  Semantics 

output  ComputationDataHandle  n dimensional array with the same shape as input operand (y) 
batch_mean  ComputationDataHandle  1 dimensional array (\(\mu\)) 
batch_var  ComputationDataHandle  1 dimensional array (\(\sigma^2\)) 
The batch_mean
and batch_var
are moments calculated across the batch and spatial dimensions using the formulas above.
See also ComputationBuilder::BitcastConvertType
.
Similar to a tf.bitcast
in TensorFlow, performs an elementwise bitcast operation from a data shape to a target shape. The dimensions must match, and the conversion is an elementwise one; e.g. s32
elements become f32
elements via bitcast routine. Bitcast is implemented as a lowlevel cast, so machines with different floatingpoint representations will give different results.
BitcastConvertType(operand, new_element_type)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T with dims D 
new_element_type  PrimitiveType  type U 
The dimensions of the operand and the target shape must match. The bitwidth of the source and destination element types must be equal. The source and destination element types must not be tuples.
See also ComputationBuilder::Broadcast
.
Adds dimensions to an array by duplicating the data in the array.
Broadcast(operand, broadcast_sizes)
Arguments  Type  Semantics 

operand  ComputationDataHandle  The array to duplicate 
broadcast_sizes  ArraySlice<int64>  The sizes of the new dimensions 
The new dimensions are inserted on the left, i.e. if broadcast_sizes
has values {a0, ..., aN}
and the operand shape has dimensions {b0, ..., bM}
then the shape of the output has dimensions {a0, ..., aN, b0, ..., bM}
.
The new dimensions index into copies of the operand, i.e.
output[i0, ..., iN, j0, ..., jM] = operand[j0, ..., jM]
For example, if operand
is a scalar f32
with value 2.0f
, and broadcast_sizes
is {2, 3}
, then the result will be an array with shape f32[2, 3]
and all the values in the result will be 2.0f
.
See also ComputationBuilder::Call
.
Invokes a computation with the given arguments.
Call(computation, args...)
Arguments  Type  Semantics 

computation  Computation  computation of type T_0, T_1, ..., T_N > S with N parameters of arbitrary type 
args  sequence of N ComputationDataHandle s  N arguments of arbitrary type 
The arity and types of the args
must match the parameters of the computation
. It is allowed to have no args
.
See also ComputationBuilder::Clamp
.
Clamps an operand to within the range between a minimum and maximum value.
Clamp(min, operand, max)
Arguments  Type  Semantics 

min  ComputationDataHandle  array of type T 
operand  ComputationDataHandle  array of type T 
max  ComputationDataHandle  array of type T 
Given an operand and minimum and maximum values, returns the operand if it is in the range between the minimum and maximum, else returns the minimum value if the operand is below this range or the maximum value if the operand is above this range. That is, clamp(a, x, b) = min(max(a, x), b)
.
All three arrays must be the same shape. Alternatively, as a restricted form of broadcasting, min
and/or max
can be a scalar of type T
.
Example with scalar min
and max
:
let operand: s32[3] = {1, 5, 9}; let min: s32 = 0; let max: s32 = 6; ==> Clamp(min, operand, max) = s32[3]{0, 5, 6};
See also ComputationBuilder::Collapse
and the tf.reshape
operation.
Collapses dimensions of an array into one dimension.
Collapse(operand, dimensions)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T 
dimensions 
int64 vector  inorder, consecutive subset of T's dimensions. 
Collapse replaces the given subset of the operand's dimensions by a single dimension. The input arguments are an arbitrary array of type T and a compiletimeconstant vector of dimension indices. The dimension indices must be an inorder (low to high dimension numbers), consecutive subset of T's dimensions. Thus, {0, 1, 2}, {0, 1}, or {1, 2} are all valid dimension sets, but {1, 0} or {0, 2} are not. They are replaced by a single new dimension, in the same position in the dimension sequence as those they replace, with the new dimension size equal to the product of original dimension sizes. The lowest dimension number in dimensions
is the slowest varying dimension (most major) in the loop nest which collapses these dimension, and the highest dimension number is fastest varying (most minor). See the tf.reshape
operator if more general collapse ordering is needed.
For example, let v be an array of 24 elements:
let v = f32[4x2x3] { { {10, 11, 12}, {15, 16, 17}}, { {20, 21, 22}, {25, 26, 27}}, { {30, 31, 32}, {35, 36, 37}}, { {40, 41, 42}, {45, 46, 47}}}; // Collapse to a single dimension, leaving one dimension. let v012 = Collapse(v, {0,1,2}); then v012 == f32[24] {10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 45, 46, 47}; // Collapse the two lower dimensions, leaving two dimensions. let v01 = Collapse(v, {0,1}); then v01 == f32[4x6] { {10, 11, 12, 15, 16, 17}, {20, 21, 22, 25, 26, 27}, {30, 31, 32, 35, 36, 37}, {40, 41, 42, 45, 46, 47}}; // Collapse the two higher dimensions, leaving two dimensions. let v12 = Collapse(v, {1,2}); then v12 == f32[8x3] { {10, 11, 12}, {15, 16, 17}, {20, 21, 22}, {25, 26, 27}, {30, 31, 32}, {35, 36, 37}, {40, 41, 42}, {45, 46, 47}};
See also ComputationBuilder::ConcatInDim
.
Concatenate composes an array from multiple array operands. The array is of the same rank as each of the input array operands (which must be of the same rank as each other) and contains the arguments in the order that they were specified.
Concatenate(operands..., dimension)
Arguments  Type  Semantics 

operands  sequence of N ComputationDataHandle
 N arrays of type T with dimensions [L0, L1, ...]. Requires N >= 1. 
dimension  int64  A value in the interval [0, N) that names the dimension to be concatenated between the operands . 
With the exception of dimension
all dimensions must be the same. This is because XLA does not support "ragged" arrays. Also note that rank0 values cannot be concatenated (as it's impossible to name the dimension along which the concatenation occurs).
1dimensional example:
Concat({ {2, 3}, {4, 5}, {6, 7}}, 0) >>> {2, 3, 4, 5, 6, 7}
2dimensional example:
let a = { {1, 2}, {3, 4}, {5, 6}, }; let b = { {7, 8}, }; Concat({a, b}, 0) >>> { {1, 2}, {3, 4}, {5, 6}, {7, 8}, }
Diagram:
See also ComputationBuilder::Conditional
.
Conditional(pred, true_operand, true_computation, false_operand, false_computation)
Arguments  Type  Semantics 

pred  ComputationDataHandle  Scalar of type PRED

true_operand  ComputationDataHandle  Argument of type T_0

true_computation  Computation  Computation of type T_0 > S

false_operand  ComputationDataHandle  Argument of type T_1

false_computation  Computation  Computation of type T_1 > S

Executes true_computation
if pred
is true
, false_computation
if pred
is false
, and returns the result.
The true_computation
must take in a single argument of type T_0
and will be invoked with true_operand
which must be of the same type. The false_computation
must take in a single argument of type T_1
and will be invoked with false_operand
which must be of the same type. The type of the returned value of true_computation
and false_computation
must be the same.
Note that only one of true_computation
and false_computation
will be executed depending on the value of pred
.
See also ComputationBuilder::Conv
.
As ConvWithGeneralPadding, but the padding is specified in a shorthand way as either SAME or VALID. SAME padding pads the input (lhs
) with zeroes so that the output has the same shape as the input when not taking striding into account. VALID padding simply means no padding.
See also ComputationBuilder::ConvWithGeneralPadding
.
Computes a convolution of the kind used in neural networks. Here, a convolution can be thought of as a ndimensional window moving across a ndimensional base area and a computation is performed for each possible position of the window.
Arguments  Type  Semantics 

lhs  ComputationDataHandle  rank n+2 array of inputs 
rhs  ComputationDataHandle  rank n+2 array of kernel weights 
window_strides  ArraySlice<int64>  size n array of kernel strides 
padding  ArraySlice<pair<int64, int64>>  size n array of (low, high) padding 
lhs_dilation  ArraySlice<int64>  size n lhs dilation factor 
: : : array  
rhs_dilation  ArraySlice<int64>  size n rhs dilation factor 
: : : array 
Let n be the number of spatial dimensions. The lhs
argument is a rank n+2 array describing the base area. This is called the input, even though of course the rhs is also an input. In a neural network, these are the input activations. The n+2 dimensions are, in this order:
batch
: Each coordinate in this dimension represents an independent input for which convolution is carried out.z/depth/features
: Each (y,x) position in the base area has a vector associated to it, which goes into this dimension.spatial_dims
: Describes the n
spatial dimensions that define the base area that the window moves across.The rhs
argument is a rank n+2 array describing the convolutional filter/kernel/window. The dimensions are, in this order:
outputz
: The z
dimension of the output.inputz
: The size of this dimension should equal the size of the z
dimension in lhs.spatial_dims
: Describes the n
spatial dimensions that define the nd window that moves across the base area.The window_strides
argument specifies the stride of the convolutional window in the spatial dimensions. For example, if the stride in the first spatial dimension is 3, then the window can only be placed at coordinates where the first spatial index is divisible by 3.
The padding
argument specifies the amount of zero padding to be applied to the base area. The amount of padding can be negative  the absolute value of negative padding indicates the number of elements to remove from the specified dimension before doing the convolution. padding[0]
specifies the padding for dimension y
and padding[1]
specifies the padding for dimension x
. Each pair has the low padding as the first element and the high padding as the second element. The low padding is applied in the direction of lower indices while the high padding is applied in the direction of higher indices. For example, if padding[1]
is (2,3)
then there will be a padding by 2 zeroes on the left and by 3 zeroes on the right in the second spatial dimension. Using padding is equivalent to inserting those same zero values into the input (lhs
) before doing the convolution.
The lhs_dilation
and rhs_dilation
arguments specify the dilation factor to be applied to the lhs and rhs, respectively, in each spatial dimension. If the dilation factor in a spatial dimension is d, then d1 holes are implicitly placed between each of the entries in that dimension, increasing the size of the array. The holes are filled with a noop value, which for convolution means zeroes.
Dilation of the rhs is also called atrous convolution. For more details, see tf.nn.atrous_conv2d
. Dilation of the lhs is also called transposed convolution. For more details, see tf.nn.conv2d_transpose
.
The output shape has these dimensions, in this order:
batch
: Same size as batch
on the input (lhs
).z
: Same size as outputz
on the kernel (rhs
).spatial_dims
: One value for each valid placement of the convolutional window.The valid placements of the convolutional window are determined by the strides and the size of the base area after padding.
To describe what a convolution does, consider a 2d convolution, and pick some fixed batch
, z
, y
, x
coordinates in the output. Then (y,x)
is a position of a corner of the window within the base area (e.g. the upper left corner, depending on how you interpret the spatial dimensions). We now have a 2d window, taken from the base area, where each 2d point is associated to a 1d vector, so we get a 3d box. From the convolutional kernel, since we fixed the output coordinate z
, we also have a 3d box. The two boxes have the same dimensions, so we can take the sum of the elementwise products between the two boxes (similar to a dot product). That is the output value.
Note that if outputz
is e.g., 5, then each position of the window produces 5 values in the output into the z
dimension of the output. These values differ in what part of the convolutional kernel is used  there is a separate 3d box of values used for each outputz
coordinate. So you could think of it as 5 separate convolutions with a different filter for each of them.
Here is pseudocode for a 2d convolution with padding and striding:
for (b, oz, oy, ox) { // output coordinates value = 0; for (iz, ky, kx) { // kernel coordinates and input z iy = oy*stride_y + ky  pad_low_y; ix = ox*stride_x + kx  pad_low_x; if ((iy, ix) inside the base area considered without padding) { value += input(b, iz, iy, ix) * kernel(oz, iz, ky, kx); } } output(b, oz, oy, ox) = value; }
See also ComputationBuilder::ConvertElementType
.
Similar to an elementwise static_cast
in C++, performs an elementwise conversion operation from a data shape to a target shape. The dimensions must match, and the conversion is an elementwise one; e.g. s32
elements become f32
elements via an s32
tof32
conversion routine.
ConvertElementType(operand, new_element_type)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T with dims D 
new_element_type  PrimitiveType  type U 
The dimensions of the operand and the target shape must match. The source and destination element types must not be tuples.
A conversion such as T=s32
to U=f32
will perform a normalizing inttofloat conversion routine such as roundtonearesteven.
Note: The precise floattoint and visaversa conversions are currently unspecified, but may become additional arguments to the convert operation in the future. Not all possible conversions have been implemented for all targets.
let a: s32[3] = {0, 1, 2}; let b: f32[3] = convert(a, f32); then b == f32[3]{0.0, 1.0, 2.0}
See also ComputationBuilder::CrossReplicaSum
.
Computes a sum across replicas.
CrossReplicaSum(operand)
Arguments  Type  Semantics 

operand  ComputationDataHandle  Array to sum across replicas. 
The output shape is the same as the input shape. For example, if there are two replicas and the operand has the value (1.0, 2.5)
and (3.0, 5.25)
respectively on the two replicas, then the output value from this op will be (4.0, 7.75)
on both replicas.
Computing the result of CrossReplicaSum requires having one input from each replica, so if one replica executes a CrossReplicaSum node more times than another, then the former replica will wait forever. Since the replicas are all running the same program, there are not a lot of ways for that to happen, but it is possible when a while loop's condition depends on data from infeed and the data that is infed causes the while loop to iterate more times on one replica than another.
See also ComputationBuilder::CustomCall
.
Call a userprovided function within a computation.
CustomCall(target_name, args..., shape)
Arguments  Type  Semantics 

target_name  string  Name of the function. A call instruction will be emitted which targets this symbol name. 
args  sequence of N ComputationDataHandle s  N arguments of arbitrary type, which will be passed to the function. 
shape  Shape  Output shape of the function 
The function signature is the same, regardless of the arity or type of args:
extern "C" void target_name(void* out, void** in);
For example, if CustomCall is used as follows:
let x = f32[2] {1,2}; let y = f32[2x3] { {10, 20, 30}, {40, 50, 60}}; CustomCall("myfunc", {x, y}, f32[3x3])
Here is an example of an implementation of myfunc
:
extern "C" void myfunc(void* out, void** in) { float (&x)[2] = *static_cast<float(*)[2]>(in[0]); float (&y)[2][3] = *static_cast<float(*)[2][3]>(in[1]); EXPECT_EQ(1, x[0]); EXPECT_EQ(2, x[1]); EXPECT_EQ(10, y[0][0]); EXPECT_EQ(20, y[0][1]); EXPECT_EQ(30, y[0][2]); EXPECT_EQ(40, y[1][0]); EXPECT_EQ(50, y[1][1]); EXPECT_EQ(60, y[1][2]); float (&z)[3][3] = *static_cast<float(*)[3][3]>(out); z[0][0] = x[1] + y[1][0]; // ... }
The userprovided function must not have sideeffects and its execution must be idempotent.
Note: The opaque nature of the userprovided function restricts optimization opportunities for the compiler. Try to express your computation in terms of native XLA ops whenever possible; only use CustomCall as a last resort.
See also ComputationBuilder::Dot
.
Dot(lhs, rhs)
Arguments  Type  Semantics 

lhs  ComputationDataHandle  array of type T 
rhs  ComputationDataHandle  array of type T 
The exact semantics of this operation depend on the ranks of the operands:
Input  Output  Semantics 

vector [n] dot vector [n]  scalar  vector dot product 
matrix [m x k] dot vector [k]  vector [m]  matrixvector multiplication 
matrix [m x k] dot matrix [k x n]  matrix [m x n]  matrixmatrix multiplication 
The operation performs sum of products over the last dimension of lhs
and the onebeforelast dimension of rhs
. These are the "contracted" dimensions. The contracted dimensions of lhs
and rhs
must be of the same size. In practice, it can be used to perform dot products between vectors, vector/matrix multiplications or matrix/matrix multiplications.
See also ComputationBuilder::DotGeneral
.
DotGeneral(lhs, rhs, dimension_numbers)
Arguments  Type  Semantics 

lhs  ComputationDataHandle  array of type T 
rhs  ComputationDataHandle  array of type T 
dimension_numbers  DotDimensionNumbers  array of type T 
As Dot, but allows contracting and batch dimension numbers to be specified for both the 'lhs' and 'rhs'.
DotDimensionNumbers Fields  Type  Semantics 

'lhs_contracting_dimensions'  repeated int64  'lhs' contracting dimension numbers 
'rhs_contracting_dimensions'  repeated int64  'rhs' contracting dimension numbers 
'lhs_batch_dimensions'  repeated int64  'lhs' batch dimension numbers 
'rhs_batch_dimensions'  repeated int64  'rhs' batch dimension numbers 
DotGeneral performs the sum of products over contracting dimensions specified in 'dimension_numbers'.
Associated contracting dimension numbers from the 'lhs' and 'rhs' do not need to be the same, but must be listed in the same order in both 'lhs/rhs_contracting_dimensions' arrays and have the same dimension sizes. There must be exactly one contracting dimension on both 'lhs' and 'rhs'.
Example with contracting dimension numbers:
lhs = { {1.0, 2.0, 3.0}, {4.0, 5.0, 6.0} } rhs = { {1.0, 1.0, 1.0}, {2.0, 2.0, 2.0} } DotDimensionNumbers dnums; dnums.add_lhs_contracting_dimensions(1); dnums.add_rhs_contracting_dimensions(1); DotGeneral(lhs, rhs, dnums) > { {6.0, 12.0}, {15.0, 30.0} }
Associated batch dimension numbers from the 'lhs' and 'rhs' must have the same dimension number, must be listed in the same order in both arrays, must have the same dimension sizes, and must be ordered before contracting and noncontracting/nonbatch dimension numbers.
Example with batch dimension numbers (batch size 2, 2x2 matrices):
lhs = { { {1.0, 2.0}, {3.0, 4.0} }, { {5.0, 6.0}, {7.0, 8.0} } } rhs = { { {1.0, 0.0}, {0.0, 1.0} }, { {1.0, 0.0}, {0.0, 1.0} } } DotDimensionNumbers dnums; dnums.add_lhs_contracting_dimensions(2); dnums.add_rhs_contracting_dimensions(1); dnums.add_lhs_batch_dimensions(0); dnums.add_rhs_batch_dimensions(0); DotGeneral(lhs, rhs, dnums) > { { {1.0, 2.0}, {3.0, 4.0} }, { {5.0, 6.0}, {7.0, 8.0} } }
Input  Output  Semantics 

[b0, m, k] dot [b0, k, n]  [b0, m, n]  batch matmul 
[b0, b1, m, k] dot [b0, b1, k, n]  [b0, b1, m, n]  batch matmul 
It follows that the resulting dimension number starts with the batch dimension, then the 'lhs' noncontracting/nonbatch dimension, and finally the 'rhs' noncontracting/nonbatch dimension.
See also ComputationBuilder::DynamicSlice
.
DynamicSlice extracts a subarray from the input array at dynamic start_indices
. The size of the slice in each dimension is passed in size_indices
, which specify the end point of exclusive slice intervals in each dimension: [start, start + size). The shape of start_indices
must be rank == 1, with dimension size equal to the rank of operand
. Note: handling of outofbounds slice indices (generated by incorrect runtime calculation of 'start_indices') is currently implementationdefined.
DynamicSlice(operand, start_indices, size_indices)
Arguments  Type  Semantics 

operand  ComputationDataHandle  N dimensional array of type T 
start_indices  ComputationDataHandle  Rank 1 array of N integers containing the starting indices of the slice for each dimension. Value must be greater than or equal to zero. 
size_indices  ArraySlice<int64>  List of N integers containing the slice size for each dimension. Each value must be strictly greater than zero, and start + size must be less than or equal to the size of the dimension to avoid wrapping modulo dimension size. 
1dimensional example:
let a = {0.0, 1.0, 2.0, 3.0, 4.0} let s = {2} DynamicSlice(a, s, {2}) produces: {2.0, 3.0}
2dimensional example:
let b = { {0.0, 1.0, 2.0}, {3.0, 4.0, 5.0}, {6.0, 7.0, 8.0}, {9.0, 10.0, 11.0} } let s = {2, 1} DynamicSlice(b, s, {2, 2}) produces: { { 7.0, 8.0}, {10.0, 11.0} }
See also ComputationBuilder::DynamicUpdateSlice
.
DynamicUpdateSlice generates a result which is the value of the input array operand
, with a slice update
overwritten at start_indices
. The shape of update
determines the shape of the subarray of the result which is updated. The shape of start_indices
must be rank == 1, with dimension size equal to the rank of operand
. Note: handling of outofbounds slice indices (generated by incorrect runtime calculation of 'start_indices') is currently implementationdefined.
DynamicUpdateSlice(operand, update, start_indices)
Arguments  Type  Semantics 

operand  ComputationDataHandle  N dimensional array of type T 
update  ComputationDataHandle  N dimensional array of type T containing the slice update. Each dimension of update shape must be strictly greater than zero, and start + update must be less than operand size for each dimension to avoid generating outofbounds update indices. 
start_indices  ComputationDataHandle  Rank 1 array of N integers containing the starting indices of the slice for each dimension. Value must be greater than or equal to zero. 
1dimensional example:
let a = {0.0, 1.0, 2.0, 3.0, 4.0} let u = {5.0, 6.0} let s = {2} DynamicUpdateSlice(a, u, s) produces: {0.0, 1.0, 5.0, 6.0, 4.0}
2dimensional example:
let b = { {0.0, 1.0, 2.0}, {3.0, 4.0, 5.0}, {6.0, 7.0, 8.0}, {9.0, 10.0, 11.0} } let u = { {12.0, 13.0}, {14.0, 15.0}, {16.0, 17.0} } let s = {1, 1} DynamicUpdateSlice(b, u, s) produces: { {0.0, 1.0, 2.0}, {3.0, 12.0, 13.0}, {6.0, 14.0, 15.0}, {9.0, 16.0, 17.0} }
See also ComputationBuilder::Add
.
A set of elementwise binary arithmetic operations is supported.
Op(lhs, rhs)
Where Op
is one of Add
(addition), Sub
(subtraction), Mul
(multiplication), Div
(division), Rem
(remainder), Max
(maximum), Min
(minimum), LogicalAnd
(logical AND), or LogicalOr
(logical OR).
Arguments  Type  Semantics 

lhs  ComputationDataHandle  lefthandside operand: array of type T 
rhs  ComputationDataHandle  righthandside operand: array of type T 
The arguments' shapes have to be either similar or compatible. See the broadcasting documentation about what it means for shapes to be compatible. The result of an operation has a shape which is the result of broadcasting the two input arrays. In this variant, operations between arrays of different ranks are not supported, unless one of the operands is a scalar.
When Op
is Rem
, the sign of the result is taken from the dividend, and the absolute value of the result is always less than the divisor's absolute value.
An alternative variant with differentrank broadcasting support exists for these operations:
Op(lhs, rhs, broadcast_dimensions)
Where Op
is the same as above. This variant of the operation should be used for arithmetic operations between arrays of different ranks (such as adding a matrix to a vector).
The additional broadcast_dimensions
operand is a slice of integers used to expand the rank of the lowerrank operand up to the rank of the higherrank operand. broadcast_dimensions
maps the dimensions of the lowerrank shape to the dimensions of the higherrank shape. The unmapped dimensions of the expanded shape are filled with dimensions of size one. Degeneratedimension broadcasting then broadcasts the shapes along these degenerate dimensions to equalize the shapes of both operands. The semantics are described in detail on the broadcasting page.
See also ComputationBuilder::Eq
.
A set of standard elementwise binary comparison operations is supported. Note that standard IEEE 754 floatingpoint comparison semantics apply when comparing floatingpoint types.
Op(lhs, rhs)
Where Op
is one of Eq
(equalto), Ne
(not equalto), Ge
(greaterorequalthan), Gt
(greaterthan), Le
(lessorequalthan), Lt
(lessthan).
Arguments  Type  Semantics 

lhs  ComputationDataHandle  lefthandside operand: array of type T 
rhs  ComputationDataHandle  righthandside operand: array of type T 
The arguments' shapes have to be either similar or compatible. See the broadcasting documentation about what it means for shapes to be compatible. The result of an operation has a shape which is the result of broadcasting the two input arrays with the element type PRED
. In this variant, operations between arrays of different ranks are not supported, unless one of the operands is a scalar.
An alternative variant with differentrank broadcasting support exists for these operations:
Op(lhs, rhs, broadcast_dimensions)
Where Op
is the same as above. This variant of the operation should be used for comparison operations between arrays of different ranks (such as adding a matrix to a vector).
The additional broadcast_dimensions
operand is a slice of integers specifying the dimensions to use for broadcasting the operands. The semantics are described in detail on the broadcasting page.
ComputationBuilder supports these elementwise unary functions:
Abs(operand)
Elementwise abs x > x
.
Ceil(operand)
Elementwise ceil x > ⌈x⌉
.
Cos(operand)
Elementwise cosine x > cos(x)
.
Exp(operand)
Elementwise natural exponential x > e^x
.
Floor(operand)
Elementwise floor x > ⌊x⌋
.
IsFinite(operand)
Tests whether each element of operand
is finite, i.e., is not positive or negative infinity, and is not NaN
. Returns an array of PRED
values with the same shape as the input, where each element is true
if and only if the corresponding input element is finite.
Log(operand)
Elementwise natural logarithm x > ln(x)
.
LogicalNot(operand)
Elementwise logical not x > !(x)
.
Neg(operand)
Elementwise negation x > x
.
Sign(operand)
Elementwise sign operation x > sgn(x)
where
using the comparison operator of the element type of operand
.
Tanh(operand)
Elementwise hyperbolic tangent x > tanh(x)
.
Arguments  Type  Semantics 

operand  ComputationDataHandle  The operand to the function 
The function is applied to each element in the operand
array, resulting in an array with the same shape. It is allowed for operand
to be a scalar (rank 0).
The XLA gather operation stitches together several slices (each slice at a potentially different runtime offset) of an input tensor into an output tensor.
See also ComputationBuilder::Gather
. For a more intuitive description, see the "Informal Description" section below.
gather(operand, gather_indices, output_window_dims, elided_window_dims, window_bounds, gather_dims_to_operand_dims)
Arguments  Type  Semantics 

operand  ComputationDataHandle  The tensor we’re gathering from. 
gather_indices  ComputationDataHandle  Tensor containing the starting indices of the slices we're we're stitching together into the output tensor. 
index_vector_dim  int64  The dimension in gather_indices that contains the starting indices. 
output_window_dims  ArraySlice<int64>  The set of dimensions in the output shape that are window dimensions (defined below). Not all window dimensions may be present in the output shape. 
elided_window_dims  ArraySlice<int64>  The set of window dimensions that are not present in the output shape. window_bounds[i] must be 1 for all i in elided_window_dims . 
window_bounds  ArraySlice<int64> 
window_bounds[i] is the bounds for window dimension i . This includes both the window dimensions that are explicitly part of the output shape (via output_window_dims ) and the window dimensions that are elided (via elided_window_dims ). 
gather_dims_to_operand_dims  ArraySlice<int64>  A dimension map (the array is interpreted as mapping i to gather_dims_to_operand_dims[i] ) from the gather indices in gather_indices to the operand index space. It has to be onetoone and total. 
For every index Out
in the output tensor, we compute two things (more precisely described later):
An index into gather_indices.rank
 1
dimensions of gather_indices
, which gives us a starting index of a slice, operand slice, in the operand tensor. These gather_indices.rank
 1
dimensions are all the dimensions in gather_indices
except index_vector_dim
.
A window index that has the same rank as the operand. This index is composed of the values in Out
at dimensions output_window_dims
, embedded with zeroes according to elided_window_dims
.
The window index is the relative index of the element in operand slice that should be present in the output at index Out
.
The output is a tensor of rank output_window_dims.size
+ gather_indices.rank
 1
. Additionally, as a shorthand, we define output_gather_dims
of type ArraySlice<int64>
as the set of dimensions in the output shape but not in output_window_dims
, in ascending order. E.g. if the output tensor has rank 5
, output_window_dims
is {2
, 4
} then output_gather_dims
is {0
, 1
, 3
}
If index_vector_dim
is equal to gather_indices.rank
we implicitly consider gather_indices
to have a trailing 1
dimension (i.e. if gather_indices
was of shape [6,7]
and index_vector_dim
is 2
then we implicitly consider the shape of gather_indices
to be [6,7,1]
).
The bounds for the output tensor along dimension i
is computed as follows:
i
is present in output_gather_dims
(i.e. is equal to output_gather_dims[k]
for some k
) then we pick the corresponding dimension bounds out of gather_indices.shape
, skipping index_vector_dim
(i.e. pick gather_indices.shape.dims
[k
] if k
< index_vector_dim
and gather_indices.shape.dims
[k
+1
] otherwise).i
is present in output_window_dims
(i.e. equal to output_window_dims
[k
] for some k
) then we pick the corresponding bound out of window_bounds
after accounting for elided_window_dims
(i.e. we pick adjusted_window_bounds
[k
] where adjusted_window_bounds
is window_bounds
with the bounds at indices elided_window_dims
removed).The operand index In
corresponding to an output index Out
is computed as follows:
G
= { Out
[k
] for k
in output_gather_dims
}. Use G
to slice out vector S
such that S
[i
] = gather_indices
[Combine(G
, i
)] where Combine(A, b) inserts b at position index_vector_dim
into A. Note that this is well defined even if G
is empty  if G
is empty then S
= gather_indices
.S
_{in}, into operand
using S
by scattering S
using the gather_dims_to_operand_dims
map (S
_{in} is the starting indices for operand slice mentioned above). More precisely:S
_{in}[gather_dims_to_operand_dims
[k
]] = S
[k
] if k
< gather_dims_to_operand_dims.size
.S
_{in}[_
] = 0
otherwise.W
_{in} into operand
by scattering the indices at the output window dimensions in Out
according to the elided_window_dims
set (W
_{in} is the window index mentioned above). More precisely:W
_{in}[window_dims_to_operand_dims
(k
)] = Out
[k
] if k
< output_window_dims.size
(window_dims_to_operand_dims
is defined below).W
_{in}[_
] = 0
otherwise.In
is W
_{in} + S
_{in} where + is elementwise addition.window_dims_to_operand_dims
is the monotonic function with domain [0
, output_window_dims.size
) and range [0
, operand.rank
) \ elided_window_dims
. So if, e.g., output_window_dims.size
is 4
, operand.rank
is 6
and elided_window_dims
is {0
, 2
} then window_dims_to_operand_dims
is {0
→1
, 1
→3
, 2
→4
, 3
→5
}.
index_vector_dim
is set to gather_indices.rank
 1
in all of the examples that follow. More interesting values for index_vector_dim
does not change the operation fundamentally, but makes the visual representation more cumbersome.
To get an intuition on how all of the above fits together, let's look at an example that gathers 5 slices of shape [8,6]
from a [16,11]
tensor. The position of a slice into the [16,11]
tensor can be represented as an index vector of shape S64[2]
, so the set of 5 positions can be represented as a S64[5,2]
tensor.
The behavior of the gather operation can then be depicted as an index transformation that takes [G
,W
_{0},W
_{1}], an index in the output shape, and maps it to an element in the input tensor in the following way:
We first select an (X
,Y
) vector from the gather indices tensor using G
. The element in the output tensor at index [G
,W
_{0},W
_{1}] is then the element in the input tensor at index [X
+W
_{0},Y
+W
_{1}].
window_bounds
is [8,6]
, which decides the range of W_{0} and W_{1}, and this in turn decides the bounds of the slice.
This gather operation acts as a batch dynamic slice with G
as the batch dimension.
The gather indices may be multidimensional. For instance, a more general version of the example above using a "gather indices" tensor of shape [4,5,2]
would translate indices like this:
Again, this acts as a batch dynamic slice G
_{0} and G
_{1} as the batch dimensions. The window bounds are still [8,6]
.
The gather operation in XLA generalizes the informal semantics outlined above in the following ways:
We can configure which dimensions in the output shape are the window dimensions (dimensions containing W
_{0}, W
_{1} in the last example). The output gather dimensions (dimensions containing G
_{0}, G
_{1} in the last example) are defined to be the output dimensions that are not window dimensions.
The number of output window dimensions explicitly present in the output shape may be smaller than the input rank. These "missing" dimensions, which are listed explicitly as elided_window_dims
, must have a window bound of 1
. Since they have a window bound of 1
the only valid index for them is 0
and eliding them does not introduce ambiguity.
The slice extracted from the "Gather Indices" tensor ((X
, Y
) in the last example) may have fewer elements than the input tensor rank, and an explicit mapping dictates how the index should be expanded to have the same rank as the input.
As a final example, we use (2) and (3) to implement tf.gather_nd
:
G
_{0} and G
_{1} are used to slice out a starting index from the gather indices tensor as usual, except the starting index has only one element, X
. Similarly, there is only one output window index with the value W
_{0}. However, before being used as indices into the input tensor, these are expanded in accordance to "Gather Index Mapping" (gather_dims_to_operand_dims
in the formal description) and "Window Mapping" (window_dims_to_operand_dims
in the formal description) into [0
,W
_{0}] and [X
,0
] respectively, adding up to [X
,W
_{0}]. In other words, the output index [G
_{0},G
_{1},W
_{0}] maps to the input index [GatherIndices
[G
_{0},G
_{1},0
],X
] which gives us the semantics for tf.gather_nd
.
window_bounds
for this case is [1,11]
. Intuitively this means that every index X
in the gather indices tensor picks an entire row and the result is the concatenation of all these rows.
See also ComputationBuilder::GetTupleElement
.
Indexes into a tuple with a compiletimeconstant value.
The value must be a compiletimeconstant so that shape inference can determine the type of the resulting value.
This is analogous to std::get<int N>(t)
in C++. Conceptually:
let v: f32[10] = f32[10]{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; let s: s32 = 5; let t: (f32[10], s32) = tuple(v, s); let element_1: s32 = gettupleelement(t, 1); // Inferred shape matches s32.
See also tf.tuple
.
See also ComputationBuilder::Infeed
.
Infeed(shape)
Argument  Type  Semantics 

shape  Shape  Shape of the data read from the Infeed interface. The layout field of the shape must be set to match the layout of the data sent to the device; otherwise its behavior is undefined. 
Reads a single data item from the implicit Infeed streaming interface of the device, interpreting the data as the given shape and its layout, and returns a ComputationDataHandle
of the data. Multiple Infeed operations are allowed in a computation, but there must be a total order among the Infeed operations. For example, two Infeeds in the code below have a total order since there is a dependency between the while loops.
result1 = while (condition, init = init_value) { Infeed(shape) } result2 = while (condition, init = result1) { Infeed(shape) }
Nested tuple shapes are not supported. For an empty tuple shape, the Infeed operation is effectively a noop and proceeds without reading any data from the Infeed of the device.
Note: We plan to allow multiple Infeed operations without a total order, in which case the compiler will provide information about how the Infeed operations are serialized in the compiled program.
See also ComputationBuilder::Map
.
Map(operands..., computation)
Arguments  Type  Semantics 

operands  sequence of N ComputationDataHandle s  N arrays of types T_0..T_{N1} 
computation  Computation  computation of type T_0, T_1, ..., T_{N + M 1} > S with N parameters of type T and M of arbitrary type 
dimensions 
int64 array  array of map dimensions 
static_operands  sequence of M ComputationDataHandle s  M arrays of arbitrary type 
Applies a scalar function over the given operands
arrays, producing an array of the same dimensions where each element is the result of the mapped function applied to the corresponding elements in the input arrays with static_operands
given as additional input to computation
.
The mapped function is an arbitrary computation with the restriction that it has N inputs of scalar type T
and a single output with type S
. The output has the same dimensions as the operands except that the element type T is replaced with S.
For example: Map(op1, op2, op3, computation, par1)
maps elem_out < computation(elem1, elem2, elem3, par1)
at each (multidimensional) index in the input arrays to produce the output array.
See also ComputationBuilder::Pad
.
Pad(operand, padding_value, padding_config)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T

padding_value  ComputationDataHandle  scalar of type T to fill in the added padding 
padding_config  PaddingConfig  padding amount on both edges (low, high) and between the elements of each dimension 
Expands the given operand
array by padding around the array as well as between the elements of the array with the given padding_value
. padding_config
specifies the amount of edge padding and the interior padding for each dimension.
PaddingConfig
is a repeated field of PaddingConfigDimension
, which contains three fields for each dimension: edge_padding_low
, edge_padding_high
, and interior_padding
. edge_padding_low
and edge_padding_high
specify the amount of padding added at the lowend (next to index 0) and the highend (next to the highest index) of each dimension respectively. The amount of edge padding can be negative  the absolute value of negative padding indicates the number of elements to remove from the specified dimension. interior_padding
specifies the amount of padding added between any two elements in each dimension. Interior padding occurs logically before edge padding, so in the case of negative edge padding elements are removed from the interiorpadded operand. This operation is a noop if the edge padding pairs are all (0, 0) and the interior padding values are all 0. The figure below shows examples of different edge_padding
and interior_padding
values for a twodimensional array.
See also ComputationBuilder::Recv
.
Recv(shape, channel_handle)
Arguments  Type  Semantics 

shape  Shape  shape of the data to receive 
channel_handle  ChannelHandle  unique identifier for each send/recv pair 
Receives data of the given shape from a Send
instruction in another computation that shares the same channel handle. Returns a ComputationDataHandle for the received data.
The client API of Recv
operation represents synchronous communication. However, the instruction is internally decomposed into 2 HLO instructions (Recv
and RecvDone
) to enable asynchronous data transfers. See also HloInstruction::CreateRecv
and HloInstruction::CreateRecvDone
.
Recv(const Shape& shape, int64 channel_id)
Allocates resources required to receive data from a Send
instruction with the same channel_id. Returns a context for the allocated resources, which is used by a following RecvDone
instruction to wait for the completion of the data transfer. The context is a tuple of {receive buffer (shape), request identifier (U32)} and it can only be used by a RecvDone
instruction.
RecvDone(HloInstruction context)
Given a context created by a Recv
instruction, waits for the data transfer to complete and returns the received data.
See also ComputationBuilder::Reduce
.
Applies a reduction function to an array.
Reduce(operand, init_value, computation, dimensions)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T

init_value  ComputationDataHandle  scalar of type T

computation  Computation  computation of type T, T > T

dimensions 
int64 array  unordered array of dimensions to reduce 
Conceptually, this operation reduces one or more dimensions in the input array into scalars. The rank of the result array is rank(operand)  len(dimensions)
. init_value
is the initial value used for every reduction and may also be inserted anywhere during computation if the backend chooses to do so. So in most cases init_value
should be an identity of the reduction function (for example, 0 for addition).
The evaluation order of the reduction function is arbitrary and may be nondeterministic. Therefore, the reduction function should not be overly sensitive to reassociation.
Some reduction functions like addition are not strictly associative for floats. However, if the range of the data is limited, floatingpoint addition is close enough to being associative for most practical uses. It is possible to conceive of some completely nonassociative reductions, however, and these will produce incorrect or unpredictable results in XLA reductions.
As an example, when reducing across the one dimension in a 1D array with values [10, 11, 12, 13], with reduction function f
(this is computation
) then that could be computed as
f(10, f(11, f(12, f(init_value, 13)))
but there are also many other possibilities, e.g.
f(init_value, f(f(10, f(init_value, 11)), f(f(init_value, 12), f(13, init_value))))
The following is a rough pseudocode example of how reduction could be implemented, using summation as the reduction computation with an initial value of 0.
result_shape < remove all dims in dimensions from operand_shape # Iterate over all elements in result_shape. The number of r's here is equal # to the rank of the result for r0 in range(result_shape[0]), r1 in range(result_shape[1]), ...: # Initialize this result element result[r0, r1...] < 0 # Iterate over all the reduction dimensions for d0 in range(dimensions[0]), d1 in range(dimensions[1]), ...: # Increment the result element with the value of the operand's element. # The index of the operand's element is constructed from all ri's and di's # in the right order (by construction ri's and di's together index over the # whole operand shape). result[r0, r1...] += operand[ri... di]
Here's an example of reducing a 2D array (matrix). The shape has rank 2, dimension 0 of size 2 and dimension 1 of size 3:
Results of reducing dimensions 0 or 1 with an "add" function:
Note that both reduction results are 1D arrays. The diagram shows one as column and another as row just for visual convenience.
For a more complex example, here is a 3D array. Its rank is 3, dimension 0 of size 4, dimension 1 of size 2 and dimension 2 of size 3. For simplicity, the values 1 to 6 are replicated across dimension 0.
Similarly to the 2D example, we can reduce just one dimension. If we reduce dimension 0, for example, we get a rank2 array where all values across dimension 0 were folded into a scalar:
 4 8 12   16 20 24 
If we reduce dimension 2, we also get a rank2 array where all values across dimension 2 were folded into a scalar:
 6 15   6 15   6 15   6 15 
Note that the relative order between the remaining dimensions in the input is preserved in the output, but some dimensions may get assigned new numbers (since the rank changes).
We can also reduce multiple dimensions. Addreducing dimensions 0 and 1 produces the 1D array  20 28 36 
.
Reducing the 3D array over all its dimensions produces the scalar 84
.
See also ComputationBuilder::ReducePrecision
.
Models the effect of converting floatingpoint values to a lowerprecision format (such as IEEEFP16) and back to the original format. The number of exponent and mantissa bits in the lowerprecision format can be specified arbitrarily, although all bit sizes may not be supported on all hardware implementations.
ReducePrecision(operand, mantissa_bits, exponent_bits)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of floatingpoint type T . 
exponent_bits  int32  number of exponent bits in lowerprecision format 
mantissa_bits  int32  number of mantissa bits in lowerprecision format 
The result is an array of type T
. The input values are rounded to the nearest value representable with the given number of mantissa bits (using "ties to even" semantics), and any values that exceed the range specified by the number of exponent bits are clamped to positive or negative infinity. NaN
values are retained, although they may be converted to canonical NaN
values.
The lowerprecision format must have at least one exponent bit (in order to distinguish a zero value from an infinity, since both have a zero mantissa), and must have a nonnegative number of mantissa bits. The number of exponent or mantissa bits may exceed the corresponding value for type T
; the corresponding portion of the conversion is then simply a noop.
See also ComputationBuilder::ReduceWindow
.
Applies a reduction function to all elements in each window of the input multidimensional array, producing an output multidimensional array with the same number of elements as the number of valid positions of the window. A pooling layer can be expressed as a ReduceWindow
.
ReduceWindow(operand, init_value, computation, window_dimensions, window_strides, padding)
Arguments  Type  Semantics 

operand  ComputationDataHandle  N dimensional array containing elements of type T. This is the base area on which the window is placed. 
init_value  ComputationDataHandle  Starting value for the reduction. See Reduce for details. 
computation  Computation  Reduction function of type T, T > T , to apply to all elements in each window 
window_dimensions  ArraySlice<int64>  array of integers for window dimension values 
window_strides  ArraySlice<int64>  array of integers for window stride values 
padding  Padding  padding type for window (Padding\:\:kSame or Padding\:\:kValid) 
Below code and figure shows an example of using ReduceWindow
. Input is a matrix of size [4x6] and both window_dimensions and window_stride_dimensions are [2x3].
// Create a computation for the reduction (maximum). Computation max; { ComputationBuilder builder(client_, "max"); auto y = builder.Parameter(0, ShapeUtil::MakeShape(F32, {}), "y"); auto x = builder.Parameter(1, ShapeUtil::MakeShape(F32, {}), "x"); builder.Max(y, x); max = builder.Build().ConsumeValueOrDie(); } // Create a ReduceWindow computation with the max reduction computation. ComputationBuilder builder(client_, "reduce_window_2x3"); auto shape = ShapeUtil::MakeShape(F32, {4, 6}); auto input = builder.Parameter(0, shape, "input"); builder.ReduceWindow( input, *max, /*init_val=*/builder.ConstantLiteral(LiteralUtil::MinValue(F32)), /*window_dimensions=*/{2, 3}, /*window_stride_dimensions=*/{2, 3}, Padding::kValid);
Stride of 1 in a dimension specifies that the position of a window in the dimension is 1 element away from its adjacent window. In order to specify that no windows overlap with each other, window_stride_dimensions should be equal to window_dimensions. The figure below illustrates the use of two different stride values. Padding is applied to each dimension of the input and the calculations are the same as though the input came in with the dimensions it has after padding.
The evaluation order of the reduction function is arbitrary and may be nondeterministic. Therefore, the reduction function should not be overly sensitive to reassociation. See the discussion about associativity in the context of Reduce
for more details.
See also ComputationBuilder::Reshape
and the Collapse
operation.
Reshapes the dimensions of an array into a new configuration.
Reshape(operand, new_sizes)
Reshape(operand, dimensions, new_sizes)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T 
dimensions 
int64 vector  order in which dimensions are collapsed 
new_sizes 
int64 vector  vector of sizes of new dimensions 
Conceptually, reshape first flattens an array into a onedimensional vector of data values, and then refines this vector into a new shape. The input arguments are an arbitrary array of type T, a compiletimeconstant vector of dimension indices, and a compiletimeconstant vector of dimension sizes for the result. The values in the dimension
vector, if given, must be a permutation of all of T's dimensions; the default if not given is {0, ..., rank  1}
. The order of the dimensions in dimensions
is from slowestvarying dimension (most major) to fastestvarying dimension (most minor) in the loop nest which collapses the input array into a single dimension. The new_sizes
vector determines the size of the output array. The value at index 0 in new_sizes
is the size of dimension 0, the value at index 1 is the size of dimension 1, and so on. The product of the new_size
dimensions must equal the product of the operand's dimension sizes. When refining the collapsed array into the multidimensional array defined by new_sizes
, the dimensions in new_sizes
are ordered from slowest varying (most major) and to fastest varying (most minor).
For example, let v be an array of 24 elements:
let v = f32[4x2x3] { { {10, 11, 12}, {15, 16, 17}}, { {20, 21, 22}, {25, 26, 27}}, { {30, 31, 32}, {35, 36, 37}}, { {40, 41, 42}, {45, 46, 47}}}; Inorder collapse: let v012_24 = Reshape(v, {0,1,2}, {24}); then v012_24 == f32[24] {10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 45, 46, 47}; let v012_83 = Reshape(v, {0,1,2}, {8,3}); then v012_83 == f32[8x3] { {10, 11, 12}, {15, 16, 17}, {20, 21, 22}, {25, 26, 27}, {30, 31, 32}, {35, 36, 37}, {40, 41, 42}, {45, 46, 47}}; Outoforder collapse: let v021_24 = Reshape(v, {1,2,0}, {24}); then v012_24 == f32[24] {10, 20, 30, 40, 11, 21, 31, 41, 12, 22, 32, 42, 15, 25, 35, 45, 16, 26, 36, 46, 17, 27, 37, 47}; let v021_83 = Reshape(v, {1,2,0}, {8,3}); then v021_83 == f32[8x3] { {10, 20, 30}, {40, 11, 21}, {31, 41, 12}, {22, 32, 42}, {15, 25, 35}, {45, 16, 26}, {36, 46, 17}, {27, 37, 47}}; let v021_262 = Reshape(v, {1,2,0}, {2,6,2}); then v021_262 == f32[2x6x2] { { {10, 20}, {30, 40}, {11, 21}, {31, 41}, {12, 22}, {32, 42}}, { {15, 25}, {35, 45}, {16, 26}, {36, 46}, {17, 27}, {37, 47}}};
As a special case, reshape can transform a singleelement array to a scalar and vice versa. For example,
Reshape(f32[1x1] { {5}}, {0,1}, {}) == 5; Reshape(5, {}, {1,1}) == f32[1x1] { {5}};
See also ComputationBuilder::Rev
.
Rev(operand, dimensions)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T 
dimensions  ArraySlice<int64>  dimensions to reverse 
Reverses the order of elements in the operand
array along the specified dimensions
, generating an output array of the same shape. Each element of the operand array at a multidimensional index is stored into the output array at a transformed index. The multidimensional index is transformed by reversing the index in each dimension to be reversed (i.e., if a dimension of size N is one of the reversing dimensions, its index i is transformed into N  1  i).
One use for the Rev
operation is to reverse the convolution weight array along the two window dimensions during the gradient computation in neural networks.
See also ComputationBuilder::RngNormal
.
Constructs an output of a given shape with random numbers generated following
mu
and sigma
, and RngNormal(mean, sigma, shape)
Arguments  Type  Semantics 

mu  ComputationDataHandle  Scalar of type F32 specifying mean of generated numbers 
sigma  ComputationDataHandle  Scalar of type F32 specifying standard deviation of generated numbers 
shape  Shape  Output shape of type F32 
See also ComputationBuilder::RngUniform
.
Constructs an output of a given shape with random numbers generated following
RngUniform(a, b, shape)
Arguments  Type  Semantics 

a  ComputationDataHandle  Scalar of type T specifying lower limit of interval 
b  ComputationDataHandle  Scalar of type T specifying upper limit of interval 
shape  Shape  Output shape of type T 
See also ComputationBuilder::Select
.
Constructs an output array from elements of two input arrays, based on the values of a predicate array.
Select(pred, on_true, on_false)
Arguments  Type  Semantics 

pred  ComputationDataHandle  array of type PRED 
on_true  ComputationDataHandle  array of type T 
on_false  ComputationDataHandle  array of type T 
The arrays on_true
and on_false
must have the same shape. This is also the shape of the output array. The array pred
must have the same dimensionality as on_true
and on_false
, with the PRED
element type.
For each element P
of pred
, the corresponding element of the output array is taken from on_true
if the value of P
is true
, and from on_false
if the value of P
is false
. As a restricted form of broadcasting , pred
can be a scalar of type PRED
. In this case, the output array is taken wholly from on_true
if pred
is true
, and from on_false
if pred
is false
.
Example with nonscalar pred
:
let pred: PRED[4] = {true, false, false, true}; let v1: s32[4] = {1, 2, 3, 4}; let v2: s32[4] = {100, 200, 300, 400}; ==> Select(pred, v1, v2) = s32[4]{1, 200, 300, 4};
Example with scalar pred
:
let pred: PRED = true; let v1: s32[4] = {1, 2, 3, 4}; let v2: s32[4] = {100, 200, 300, 400}; ==> Select(pred, v1, v2) = s32[4]{1, 2, 3, 4};
Selections between tuples are supported. Tuples are considered to be scalar types for this purpose. If on_true
and on_false
are tuples (which must have the same shape!) then pred
has to be a scalar of type PRED
.
See also ComputationBuilder::SelectAndScatter
.
This operation can be considered as a composite operation that first computes ReduceWindow
on the operand
array to select an element from each window, and then scatters the source
array to the indices of the selected elements to construct an output array with the same shape as the operand array. The binary select
function is used to select an element from each window by applying it across each window, and it is called with the property that the first parameter's index vector is lexicographically less than the second parameter's index vector. The select
function returns true
if the first parameter is selected and returns false
if the second parameter is selected, and the function must hold transitivity (i.e., if select(a, b)
and select(b, c)
are true
, then select(a, c)
is also true
) so that the selected element does not depend on the order of the elements traversed for a given window.
The function scatter
is applied at each selected index in the output array. It takes two scalar parameters:
source
that applies to the selected indexIt combines the two parameters and returns a scalar value that's used to update the value at the selected index in the output array. Initially, all indices of the output array are set to init_value
.
The output array has the same shape as the operand
array and the source
array must have the same shape as the result of applying a ReduceWindow
operation on the operand
array. SelectAndScatter
can be used to backpropagate the gradient values for a pooling layer in a neural network.
SelectAndScatter(operand, select, window_dimensions, window_strides, padding, source, init_value, scatter)
Arguments  Type  Semantics 

operand  ComputationDataHandle  array of type T over which the windows slide 
select  Computation  binary computation of type T, T > PRED , to apply to all elements in each window; returns true if the first parameter is selected and returns false if the second parameter is selected 
window_dimensions  ArraySlice<int64>  array of integers for window dimension values 
window_strides  ArraySlice<int64>  array of integers for window stride values 
padding  Padding  padding type for window (Padding\:\:kSame or Padding\:\:kValid) 
source  ComputationDataHandle  array of type T with the values to scatter 
init_value  ComputationDataHandle  scalar value of type T for the initial value of the output array 
scatter  Computation  binary computation of type T, T > T , to apply each scatter source element with its destination element 
The figure below shows examples of using SelectAndScatter
, with the select
function computing the maximal value among its parameters. Note that when the windows overlap, as in the figure (2) below, an index of the operand
array may be selected multiple times by different windows. In the figure, the element of value 9 is selected by both of the top windows (blue and red) and the binary addition scatter
function produces the output element of value 8 (2 + 6).
The evaluation order of the scatter
function is arbitrary and may be nondeterministic. Therefore, the scatter
function should not be overly sensitive to reassociation. See the discussion about associativity in the context of Reduce
for more details.
See also ComputationBuilder::Send
.
Send(operand, channel_handle)
Arguments  Type  Semantics 

operand  ComputationDataHandle  data to send (array of type T) 
channel_handle  ChannelHandle  unique identifier for each send/recv pair 
Sends the given operand data to a Recv
instruction in another computation that shares the same channel handle. Does not return any data.
Similar to the Recv
operation, the client API of Send
operation represents synchronous communication, and is internally decomposed into 2 HLO instructions (Send
and SendDone
) to enable asynchronous data transfers. See also HloInstruction::CreateSend
and HloInstruction::CreateSendDone
.
Send(HloInstruction operand, int64 channel_id)
Initiates an asynchronous transfer of the operand to the resources allocated by the Recv
instruction with the same channel id. Returns a context, which is used by a following SendDone
instruction to wait for the completion of the data transfer. The context is a tuple of {operand (shape), request identifier (U32)} and it can only be used by a SendDone
instruction.
SendDone(HloInstruction context)
Given a context created by a Send
instruction, waits for the data transfer to complete. The instruction does not return any data.
Scheduling of channel instructions
The execution order of the 4 instructions for each channel (Recv
, RecvDone
, Send
, SendDone
) is as below.
Recv
happens before Send
Send
happens before RecvDone
Recv
happens before RecvDone
Send
happens before SendDone
When the backend compilers generate a linear schedule for each computation that communicates via channel instructions, there must not be cycles across the computations. For example, below schedules lead to deadlocks.
See also ComputationBuilder::Slice
.
Slicing extracts a subarray from the input array. The subarray is of the same rank as the input and contains the values inside a bounding box within the input array where the dimensions and indices of the bounding box are given as arguments to the slice operation.
Slice(operand, start_indices, limit_indices)
Arguments  Type  Semantics 

operand  ComputationDataHandle  N dimensional array of type T 
start_indices  ArraySlice<int64>  List of N integers containing the starting indices of the slice for each dimension. Values must be greater than or equal to zero. 
limit_indices  ArraySlice<int64>  List of N integers containing the ending indices (exclusive) for the slice for each dimension. Each value must be strictly greater than the respective start_indices value for the dimension and less than or equal to the size of the dimension. 
1dimensional example:
let a = {0.0, 1.0, 2.0, 3.0, 4.0} Slice(a, {2}, {4}) produces: {2.0, 3.0}
2dimensional example:
let b = { {0.0, 1.0, 2.0}, {3.0, 4.0, 5.0}, {6.0, 7.0, 8.0}, {9.0, 10.0, 11.0} } Slice(b, {2, 1}, {4, 3}) produces: { { 7.0, 8.0}, {10.0, 11.0} }
See also ComputationBuilder::Sort
.
Sorts the elements in the operand.
Sort(operand)
Arguments  Type  Semantics 

operand  ComputationDataHandle  The operand to sort 
See also the tf.reshape
operation.
Transpose(operand)
Arguments  Type  Semantics 

operand  ComputationDataHandle  The operand to transpose. 
permutation  ArraySlice<int64>  How to permute the dimensions. 
Permutes the operand dimensions with the given permutation, so ∀ i . 0 ≤ i < rank ⇒ input_dimensions[permutation[i]] = output_dimensions[i]
.
This is the same as Reshape(operand, permutation, Permute(permutation, operand.shape.dimensions)).
See also ComputationBuilder::Tuple
.
A tuple containing a variable number of data handles, each of which has its own shape.
This is analogous to std::tuple
in C++. Conceptually:
let v: f32[10] = f32[10]{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; let s: s32 = 5; let t: (f32[10], s32) = tuple(v, s);
Tuples can be deconstructed (accessed) via the GetTupleElement
operation.
See also ComputationBuilder::While
.
While(condition, body, init)
Arguments  Type  Semantics 

condition  Computation  Computation of type T > PRED which defines the termination condition of the loop. 
body  Computation  Computation of type T > T which defines the body of the loop. 
init  T  Initial value for the parameter of condition and body . 
Sequentially executes the body
until the condition
fails. This is similar to a typical while loop in many other languages except for the differences and restrictions listed below.
While
node returns a value of type T
, which is the result from the last execution of the body
.T
is statically determined and must be the same across all iterations.While
nodes are not allowed to be nested. (This restriction may be lifted in the future on some targets.)The T parameters of the computations are initialized with the init
value in the first iteration and are automatically updated to the new result from body
in each subsequent iteration.
One main use case of the While
node is to implement the repeated execution of training in neural networks. Simplified pseudocode is shown below with a graph that represents the computation. The code can be found in while_test.cc
. The type T
in this example is a Tuple
consisting of an int32
for the iteration count and a vector[10]
for the accumulator. For 1000 iterations, the loop keeps adding a constant vector to the accumulator.
// Pseudocode for the computation. init = {0, zero_vector[10]} // Tuple of int32 and float[10]. result = init; while (result(0) < 1000) { iteration = result(0) + 1; new_vector = result(1) + constant_vector[10]; result = {iteration, new_vector}; }
© 2018 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/performance/xla/operation_semantics