SpaceToBatch¶

Versioned name: SpaceToBatch-2

Category: Data movement

Short description: The SpaceToBatch operation divides “spatial” dimensions [1, ..., N - 1] of the data input into a grid of blocks of shape block_shape, and interleaves these blocks with the batch dimension (0) such that in the output, the spatial dimensions [1, ..., N - 1] correspond to the position within the grid, and the batch dimension combines both the position within a spatial block and the original batch position. Prior to division into blocks, the spatial dimensions of the input are optionally zero padded according to pads_begin and pads_end.

Detailed description:

The operation is equivalent to the following transformation of the input tensor data of shape [batch, D_1, D_2 ... D_{N - 1}] and block_shape, pads_begin, pads_end of shapes [N] to Y output tensor.

Zero-pad the start and end of dimensions \([D_0, \dots, D_{N - 1}]\) of the input according to pads_begin and pads_end:

\[x = [batch + P_0, D_1 + P_1, D_2 + P_2, \dots, D_{N - 1} + P_{N - 1}]\]

\[x' = reshape(x, [batch, \frac{D_1 + P_1}{B_1}, B_1, \frac{D_2 + P_2}{B_2}, B_2, \dots, \frac{D_{N - 1} + P_{N - 1}}{B_{N - 1}}, B_{N - 1}])\]

\[x'' = transpose(x', [2, 4, \dots, (N - 1) + (N - 1), 0, 1, 3, \dots, N + (N - 1)])\]

\[y = reshape(x'', [batch \times B_1 \times \dots \times B_{N - 1}, \frac{D_1 + P_1}{B_1}, \frac{D_2 + P_2}{B_2}, \dots, \frac{D_{N - 1} + P_{N - 1}}{B_{N - 1}}]\]

where

\(P_i\) = pads_begin[i] + pads_end[i]
\(B_i\) = block_shape[i]
\(P_0\) for batch dimension is expected to be 0 (no-padding)
\(B_0\) for batch is ignored

Attributes

No attributes available.

Inputs

1: data - input N-D tensor [batch, D_1, D_2 ... D_{N - 1}] of T1 type with rank >= 2. Required.
2: block_shape - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be >= 1. block_shape[0] is expected to be 1. Required.
3: pads_begin - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be non-negative. pads_begin specifies the padding for the beginning along each axis of data input . It is required that block_shape[i] divides data_shape[i] + pads_begin[i] + pads_end[i]. pads_begin[0] is expected to be 0. Required.
4: pads_end - input 1-D tensor of T2 type with shape [N] that is equal to the size of data input shape. All values must be non-negative. pads_end specifies the padding for the ending along each axis of data input. It is required that block_shape[i] divides data_shape[i] + pads_begin[i] + pads_end[i]. pads_end[0] is expected to be 0. Required.

Outputs

1: N-D tensor with shape [batch * block_shape[0] * block_shape[1] * ... * block_shape[N - 1], (D_1 + pads_begin[1] + pads_end[1]) / block_shape[1], (D_2 + pads_begin[2] + pads_end[2]) / block_shape[2], ..., (D_{N -1} + pads_begin[N - 1] + pads_end[N - 1]) / block_shape[N - 1] of the same type as data input.

Types

T1: any supported type.
T2: any supported integer type.

Example

 <layer type="SpaceToBatch" ...>
     <input>
         <port id="0">       < !-- data -->
             <dim>2</dim>    < !-- batch -->
             <dim>6</dim>    < !-- spatial dimension 1 -->
             <dim>10</dim>   < !-- spatial dimension 2 -->
             <dim>3</dim>    < !-- spatial dimension 3 -->
             <dim>3</dim>    < !-- spatial dimension 4 -->
         </port>
         <port id="1">       < !-- block_shape value: [1, 2, 4, 3, 1] -->
             <dim>5</dim>
         </port>
         <port id="2">       < !-- pads_begin value: [0, 0, 1, 0, 0] -->
             <dim>5</dim>
         </port>
         <port id="3">       < !-- pads_end value: [0, 0, 1, 0, 0] -->
             <dim>5</dim>
         </port>
     </input>
     <output>
         <port id="3">
             <dim>48</dim>   < !-- data.shape[0] * block_shape.shape[0] * block_shape.shape[1] *... * block_shape.shape[4] -->
             <dim>3</dim>    < !-- (data.shape[1] + pads_begin[1] + pads_end[1]) / block_shape.shape[1]  -->
             <dim>3</dim>    < !-- (data.shape[2] + pads_begin[2] + pads_end[2]) / block_shape.shape[2] -->
             <dim>1</dim>    < !-- (data.shape[3] + pads_begin[3] + pads_end[3]) / block_shape.shape[3] -->
             <dim>3</dim>    < !-- (data.shape[4] + pads_begin[4] + pads_end[4]) / block_shape.shape[4] -->
         </port>
     </output>
 </layer>