Convolution

Convolution  // A batched convolution operation

Description¶

Long description

Inputs¶

Name	Element Type	Shape
`image_batch`	Any	`(N, C_in, d_1, ..., d_n)`
`filters`	Same as `image_batch`	`(N, C_in, df_1, ..., df_n)`

Attributes¶

Name	Type	Notes
`window_movement_strides`	`Strides[n]`	How far to slide the window along each axis at each step
`window_dilation_strides`	`Strides[n]`	Per-axis dilation to apply to the filters
`padding_below`	`Shape[n]`	How many padding elements to add below the 0-coordinate on each axis
`padding_above`	`Shape[n]`	How many padding elements to add above the max-coordinate on each axis
`image_dilation_strides`	`Strides[n]`	Per-axis dilation to apply to the image batch

Outputs¶

Name	Element Type	Shape
`features_out`	Same as `image_batch`	`(N, C_in, d_1 - df_1 + 1, ..., d_n - df_n + 1)`

It must be the case that after dilation and padding are applied, the filter fits within the image.

Mathematical Definition¶

Padding¶

Let \(p\) (the padding below) and \(q\) (the padding above) be a sequence of \(n\) integers, and \(T\) be a tensor of shape \((d_1,\dots,d_n)\), such that for all \(i\), \(p_i + d_i + q_i \ge 0\). Then \(\mathit{Pad}[p,q](T)\) is the tensor of shape \((p_1 + d_1 + q_1,\dots,p_n + d_n + q_n)\) such that

\[\begin{split}\mathit{Pad}[p,q](T)_{i_1,\dots,i_n} \triangleq \begin{cases} T_{i_1 - p_1,\dots,i_n - p_n} &\mbox{if for all }j, i_j \ge p_j\mbox{ and }i_j < p_j + d_j \\ 0 &\mbox{otherwise.} \end{cases}\end{split}\]

Dilation¶

Let \(l\) (the dilation strides) be a sequence of \(n\) positive integers, and \(T\) be a tensor of shape \((d_1,\dots,d_n)\). Then \(\mathit{Dilate}[l](T)\) is the tensor of shape \((d'_1,\dots,d'_n)\) where \(d'_i = \mathit{max}(0,l_i(d_i - 1) + 1)\) such that

\[\begin{split}\mathit{Dilate}[l](T)_{i_1,\dots,i_n} \triangleq \begin{cases} T_{i_1/l_1,\dots,i_n/l_n} &\mbox{if for all }j, i_j\mbox{ is a multiple of }l_j \\ 0 &\mbox{otherwise.} \end{cases}\end{split}\]

Striding¶

Let \(s\) (the strides) be a sequence of \(n\) positive integers, and \(T\) be a tensor of shape \((d_1,\dots,d_n)\). Then \(\mathit{Stride}[s](T)\) is the tensor of shape \((d'_1,\dots,d'_n)\) where \(d'_i = \left\lceil \frac{d_i}{s_i} \right\rceil\) such that

\[\mathit{Stride}[s](T)_{i_1,\dots,i_n} \triangleq T_{s_1i_1,\dots,s_ni_n}\]

\(s\) is the how far, not the unit of farness.

Convolution¶

Padded, Dilated, Strided Convolution¶

\[\mathit{PDSConv}[g,p,q,l,s](T_\mathit{image},T_\mathit{filter} \triangleq \mathit{Stride}[s](\mathit{Conv}(\mathit{Pad}[p,q](\mathit{Dilate}[g](T_\mathit{batch})),\mathit{Dilate}[l](T_\mathit{filter})))\]

Batched, Padded, Dilated, Strided Convolution¶

C++ Interface¶

class Convolution : public ngraph::op::Op¶

Batched convolution operation, with optional window dilation and stride.

Public Functions

const std::string &description() const¶

Get the string name for the type of the node, such as Add or Multiply. The class name, must not contain spaces as it is used for codegen.

Return: A const reference to the node’s type name

Convolution()¶: Constructs a batched convolution operation.

Convolution(const Output<Node> &data_batch, const Output<Node> &filters, const Strides &window_movement_strides, const Strides &window_dilation_strides, const CoordinateDiff &padding_below, const CoordinateDiff &padding_above, const Strides &data_dilation_strides, const PadType &pad_type = PadType::EXPLICIT)¶

Constructs a batched convolution operation.