# tf.nn.conv2d

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.13.1/tensorflow/python/ops/nn_ops.py#L2255-L2359) |

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

    tf.nn.conv2d(
        input,
        filters,
        strides,
        padding,
        data_format='NHWC',
        dilations=None,
        name=None
    )

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)>

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| ## Args ||
|---|---|
| `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. See [here](https://www.tensorflow.org/api_docs/python/tf/nn#notes_on_padding_2) for more information. 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 1. The dilation factor 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. If set to k \> 1, there will be k-1 skipped cells between each filter element on that dimension. The dimension order is determined by the value of `data_format`, see above for details. Dilations in the batch and depth dimensions if a 4-d tensor must be 1. |
| `name` | A name for the operation (optional). |

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| ## Returns ||
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| A `Tensor`. Has the same type as `input` and the same outer batch shape. ||

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