A 1x1 convolution or a network in network is an architectural technique used in some convolutional neural networks.

The technique was first described in the paper Network In Network.

A 1x1 convolution is a convolutional layer where the filter is of dimension \(1 \times 1\).

The filter takes in a tensor of dimension \(n_h \times n_w \times n_c\), over the \(n_c\) values in the third dimension and outputting a \(n_h \times n_w\) matrix. Subsequently, an activation function (like ReLU) is applied to the output matrix.

If we have \(p\) \(1 \times 1\) filters, then the output of the layer is a tensor of dimension \(n_h \times n_w \times p\). This is useful if the number of channels \(n_c\) in the previous layer of the network has grown too large and needs to be altered to \(p\) channels.

The \(1 \times 1\) convolution technique was featured in paper introducing the Inception network architecture, titled Going Deeper With Convolutions.