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A convolutional neural network uses local connections and weight sharing across input positions. Each learned filter detects the same local feature at multiple positions; successive activation functions and layers combine those features. Shared filters impose translation equivariance away from boundary and sampling effects, while a pooling layer can reduce spatial size.

For a standard dense-channel two-dimensional convolution with a $k_h$ by $k_w$ kernel, $C_{\mathrm{in}}$ input channels and $C_{\mathrm{out}}$ output channels, the parameter count including one bias per output channel isIt is independent of the image's spatial dimensions. For example, a three-by-three convolution from three channels to sixteen channels has $3\cdot 3\cdot 3\cdot 16+16=448$ parameters. Grouped or depthwise convolutions use different connectivity and therefore different counts.

Inception is a family of convolutional neural network architectures built around modules with parallel processing branches. An early module combines several convolution sizes and a pooling layer, then joins their outputs along the channel dimension. Pointwise convolution can reduce channel counts before more expensive spatial operations.^[ref]

For a stipulated shape example, let every branch produce a $28\times 28$ grid, with output channel counts $64$, $128$, $32$ and $32$. Joining channels gives a $28\times 28\times 256$ output becauseThe equal spatial grid sizes are an assumption ensured by the branch design. Channel joining does not add corresponding values into one channel; it retains the distinct branch outputs as separate channels of the combined neural network feature map.

A cost example explains the reduction branch. Ignoring biases, a dense three-by-three convolutional layer from $192$ input channels to $128$ output channels hasweights. Reducing first from $192$ to $32$ channels with a one-by-one pointwise convolution, then applying the three-by-three layer, usesweights. This own example isolates channel dimensions; it is not a reported layer configuration or a claim that the two computations represent identical functions.

The original paper presents this design in the GoogLeNet network and evaluates image classification and detection. Later Rethinking the Inception Architecture for Computer Vision by Christian Szegedy and others develops additional factorization and training choices. The family name therefore does not identify one immutable list of layers or one universal performance result.^[ref][ref]