The dimensionality used to discuss convolutional layers in CNNs is based on the dimensionality of the input without considering channels.
- 1D CNNs might process raw audio sources (mono or stereo), text sequences, IR spectrometry from a single sample point
- 2D CNNs can process photographic images (regardless of colour/depth etc information), audio spectrograms, grid-based board games
- 3D CNNs can process voxels from Minecraft, image sequences from videos etc
It is often possible to perform signal processing that changes dimensions of signal sources. Whether that adds "channels" or adds a dimension can be a matter of convenience to fit a particular approach. In terms of defining a n-dimensional array, then the addition of channels is just another dimension. In terms of considering signal processing performed in CNNs, we care about the distinction between channels and the rest of the space that the signal exists in.
One way to decide whether something is considered a channel or a CNN layer dimension is whether there is an ordering or metric that consistently separates measurements over that dimension. If a metric such as space, time or frequency applies, then that dimension can be considered part of the "core" dimensionality that defines the problem, whilst a more arbitrary set of features (e.g. each entry in the vector embedding of a word) is more channel-like.
As standard CNN design involves summing over all input channels to create each output feature/channel, which is mathematically the same as increasing the convolution dimension (when the kernel size in that dimension matches to the number of channels), then in practice the convolution operation implemented in a CNN layer of a particular dimensionality can be one dimension size higher. E.g. a layer class labelled "Conv1D" will perform a 2D convolution operation, with the added dimension size matching exactly to the number of input channels. However, conceptually it makes sense to view this as a sum of lower-dimension convolutions, because of the need to exactly match the dimension size. This extra dimension is seen as a convenience for calculation, and not part of the definition.