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Computes sums of N-D convolutions (actually cross-correlation).

This also supports either output striding via the optional strides parameter or atrous convolution (also known as convolution with holes or dilated convolution, based on the French word "trous" meaning holes in English) via the optional dilations parameter. Currently, however, output striding is not supported for atrous convolutions.

Specifically, in the case that data_format does not start with "NC", given a rank (N+2) input Tensor of shape

[num_batches, input_spatial_shape[0], ..., input_spatial_shape[N-1], num_input_channels],

a rank (N+2) filters Tensor of shape

[spatial_filter_shape[0], ..., spatial_filter_shape[N-1], num_input_channels, num_output_channels],

an optional dilations tensor of shape N specifying the filter upsampling/input downsampling rate, and an optional list of N strides (defaulting [1]*N), this computes for each N-D spatial output position (x[0], ..., x[N-1]):

  output[b, x[0], ..., x[N-1], k] =
      sum_{z[0], ..., z[N-1], q}
          filter[z[0], ..., z[N-1], q, k] *
                       x[0]*strides[0] + dilation_rate[0]*z[0],
                       x[N-1]*strides[N-1] + dilation_rate[N-1]*z[N-1],

where b is the index into the batch, k is the output channel number, q is the input channel number, and z is the N-D spatial offset within the filter. Here, padded_input is obtained by zero padding the input using an effective spatial filter shape of (spatial_filter_shape-1) * dilation_rate + 1 and output striding strides as described in the comment here.

In the case that data_format does start with "NC", the input and output (but not the filters) are simply transposed as follows:

convolution(input, data_format, **kwargs) = tf.transpose(convolution(tf.transpose(input, [0] + range(2,N+2) + [1]), **kwargs), [0, N+1] + range(1, N+1))

It is required that 1 <= N <= 3.

input An (N+2)-D Tensor of type T, of shape [batch_size] + input_spatial_shape + [in_channels] if data_format does not start with "NC" (default), or [batch_size, in_channels] + input_spatial_shape if data_format starts with "NC".
filters An (N+2)-D Tensor with the same type as input and shape spatial_filter_shape + [in_channels, out_channels].
padding A string, either "VALID" or "SAME". The padding algorithm.
strides Optional. Sequence of N ints >= 1. Specifies the output stride. Defaults to [1]*N. If any value of strides is > 1, then all values of dilation_rate must be 1.
dilations Optional. Sequence of N ints >= 1. Specifies the filter upsampling/input downsampling rate. In the literature, the same parameter is sometimes called input stride or dilation. The effective filter size used for the convolution will be spatial_filter_shape + (spatial_filter_shape - 1) * (rate - 1), obtained by inserting (dilation_rate[i]-1) zeros between consecutive elements of the original filter in each spatial dimension i. If any value of dilation_rate is > 1, then all values of strides must be 1.
name Optional name for the returned tensor.
data_format A string or None. Specifies whether the channel dimension of the input and output is the last dimension (default, or if data_format does not start with "NC"), or the second dimension (if data_format starts with "NC"). For N=1, the valid values are "NWC" (default) and "NCW". For N=2, the valid values are "NHWC" (default) and "NCHW". For N=3, the valid values are "NDHWC" (default) and "NCDHW".
filters Alias of filter.
dilations Alias of dilation_rate.

A Tensor with the same type as input of shape

[batch_size] + output_spatial_shape + [out_channels]

if data_format is None or does not start with "NC", or

[batch_size, out_channels] + output_spatial_shape

if data_format starts with "NC", where output_spatial_shape depends on the value of padding.

If padding == "SAME": output_spatial_shape[i] = ceil(input_spatial_shape[i] / strides[i])

If padding == "VALID": output_spatial_shape[i] = ceil((input_spatial_shape[i] - (spatial_filter_shape[i]-1) * dilation_rate[i]) / strides[i]).

ValueError If input/output depth does not match filters shape, if padding is other than "VALID" or "SAME", or if data_format is invalid.