Neural network feature map

A neural network feature map records a network's responses across positions in its input or an intermediate grid. In a convolutional neural network, one common convention calls each output neural network channel a feature map; several such maps are stacked to form the layer's output. State whether the phrase denotes one channel or the collection, since both usages occur.^[ref][ref]

For an own example, use the single-channel gridApply a two-by-two local averaging filter without padding and with convolution stride one. Its output map isA second filter subtracting each patch's left column from its right column givesFor example, its upper-left response is $(2+5)-(1+4)=2$. The two maps describe different local properties of the same input.

Stacking $A$ and $D$ gives an output with two neural network channels, each on a two-by-two grid: $2\times 2\times 2$ values in channel-height-width order. The channel index identifies which response rule was used; it is distinct from either spatial index. An activation function can then transform those values before another convolutional layer processes them.

The hand-chosen filters make the example interpretable, but learned maps need not correspond to a human-named object or property. Their entries are numerical responses determined jointly by the input, weights and preceding computation. A neural network feature map also need not have the same spatial dimensions as its input: patch size, convolution stride and padding affect the grid. Keeping the channel and spatial axes separate helps interpret both the computation and its dimensions.

A neural network channel indexes a component or response type at each position of a neural network's data grid. In a two-dimensional convolutional neural network, the channel axis is distinct from the two spatial axes. For example, an image represented with the RGB color model has red, green and blue input channels, while an intermediate neural network feature map can have many learned response channels.^[ref]

The arrangement of axes must be stated. In the documented convention $(N,C,H,W)$, $N$ counts examples, $C$ channels, $H$ rows and $W$ columns. Thus two three-channel images, each four pixels high and five pixels wide, have shape $(2,3,4,5)$ and containscalar entries. Changing the number of examples does not change the number of channels in each example.^[ref]

A dense convolutional layer can mix all input channels into each output channel. For the preceding input, use eight output channels, three-by-three filters, convolution stride one and no padding. The output shape iswith $96$ scalar entries. Its eight filters use $8(3)(3)(3)=216$ weights, plus eight biases if enabled, giving $224$ parameters. The leading example count does not multiply this parameter count: the same weights process each example.^[ref]

The eight output channels are not eight new primary colors. Their values are determined by learned combinations of the preceding channels and spatial neighborhoods. Individual channels can be useful for interpretation, but a channel's index does not by itself identify a human-named feature or make its response a probability.

A pointwise convolution makes the channel operation especially clear: at every spatial point it maps one channel vector to another using the same matrix of weights. By changing that matrix, it can reduce or increase the channel count while preserving the grid dimensions under unit-stride, unpadded conditions. Keeping channel, spatial and example axes separate prevents both shape errors and misleading interpretations.