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# tf.nn.separable_conv2d

2-D convolution with separable filters.

Performs a depthwise convolution that acts separately on channels followed by a pointwise convolution that mixes channels. Note that this is separability between dimensions `[1, 2]` and `3`, not spatial separability between dimensions `1` and `2`.

In detail, with the default NHWC format,

``````output[b, i, j, k] = sum_{di, dj, q, r}
input[b, strides[1] * i + di, strides[2] * j + dj, q] *
depthwise_filter[di, dj, q, r] *
pointwise_filter[0, 0, q * channel_multiplier + r, k]
``````

`strides` controls the strides for the depthwise convolution only, since the pointwise convolution has implicit strides of `[1, 1, 1, 1]`. Must have `strides[0] = strides[3] = 1`. For the most common case of the same horizontal and vertical strides, `strides = [1, stride, stride, 1]`. If any value in `rate` is greater than 1, we perform atrous depthwise convolution, in which case all values in the `strides` tensor must be equal to 1.

`input` 4-D `Tensor` with shape according to `data_format`.
`depthwise_filter` 4-D `Tensor` with shape `[filter_height, filter_width, in_channels, channel_multiplier]`. Contains `in_channels` convolutional filters of depth 1.
`pointwise_filter` 4-D `Tensor` with shape `[1, 1, channel_multiplier * in_channels, out_channels]`. Pointwise filter to mix channels after `depthwise_filter` has convolved spatially.
`strides` 1-D of size 4. The strides for the depthwise convolution for each dimension of `input`.
`padding` A string, either `'VALID'` or `'SAME'`. The padding algorithm. See the "returns" section of `tf.nn.convolution` for details.
`rate` 1-D of size 2. The dilation rate in which we sample input values across the `height` and `width` dimensions in atrous convolution. If it is greater than 1, then all values of strides must be 1.
`name` A name for this operation (optional).
`data_format` The data format for input. Either "NHWC" (default) or "NCHW".
`dilations` Alias of rate.

A 4-D `Tensor` with shape according to 'data_format'. For example, with data_format="NHWC", shape is [batch, out_height, out_width, out_channels].

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