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Computes a 2-D convolution given input and 4-D filters tensors.

The input tensor may have rank 4 or higher, where shape dimensions [:-3] are considered batch dimensions (batch_shape).

Given an input tensor of shape batch_shape + [in_height, in_width, in_channels] and a filter / kernel tensor of shape [filter_height, filter_width, in_channels, out_channels], this op performs the following:

  1. Flattens the filter to a 2-D matrix with shape [filter_height * filter_width * in_channels, output_channels].
  2. Extracts image patches from the input tensor to form a virtual tensor of shape [batch, out_height, out_width, filter_height * filter_width * in_channels].
  3. For each patch, right-multiplies the filter matrix and the image patch vector.

In detail, with the default NHWC format,

output[b, i, j, k] =
    sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
                    filter[di, dj, q, k]

Must have strides[0] = strides[3] = 1. For the most common case of the same horizontal and vertical strides, strides = [1, stride, stride, 1].

Usage Example:

x_in = np.array([[
  [[2], [1], [2], [0], [1]],
  [[1], [3], [2], [2], [3]],
  [[1], [1], [3], [3], [0]],
  [[2], [2], [0], [1], [1]],
  [[0], [0], [3], [1], [2]], ]])
kernel_in = np.array([
 [ [[2, 0.1]], [[3, 0.2]] ],
 [ [[0, 0.3]],[[1, 0.4]] ], ])
x = tf.constant(x_in, dtype=tf.float32)
kernel = tf.constant(kernel_in, dtype=tf.float32)
tf.nn.conv2d(x, kernel, strides=[1, 1, 1, 1], padding='VALID')
<tf.Tensor: shape=(1, 4, 4, 2), dtype=float32, numpy=..., dtype=float32)>

input A Tensor. Must be one of the following types: half, bfloat16, float32, float64. A Tensor of rank at least 4. The dimension order is interpreted according to the value of data_format; with the all-but-inner-3 dimensions acting as batch dimensions. See below for details.
filters A Tensor. Must have the same type as input. A 4-D tensor of shape [filter_height, filter_width, in_channels, out_channels]
strides An int or list of ints that has length 1, 2 or 4. The stride of the sliding window for each dimension of input. If a single value is given it is replicated in the H and W dimension. By default the N and C dimensions are set to 1. The dimension order is determined by the value of data_format, see below for details.
padding Either the string "SAME" or "VALID" indicating the type of padding algorithm to use, or a list indicating the explicit paddings at the start and end of each dimension. When explicit padding is used and data_format is "NHWC", this should be in the form [[0, 0], [pad_top, pad_bottom], [pad_left, pad_right], [0, 0]]. When explicit padding used and data_format is "NCHW", this should be in the form [[0, 0], [0, 0], [pad_top, pad_bottom], [pad_left, pad_right]].
data_format An optional string from: "NHWC", "NCHW". Defaults to "NHWC". Specify the data format of the input and output data. With the default format "NHWC", the data is stored in the order of: batch_shape + [height, width, channels]. Alternatively, the format could be "NCHW", the data storage order of: batch_shape + [channels, height, width].
dilations An int or list of ints that has length 1, 2 or 4, defaults to