# 1x1 Convolution

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.