I think to understand generalization, we need to look past the ideas of the spatial pooler and temporal memory algorithms as “spatial” and “temporal” processing components, and start viewing the layer like this:
Now we can talk about “feedforward” input coming across the proximal signal. This means input generally moving away from the senses. Distal input to a layer is a contextual signal. In the case of SMI, it might contain the location on an object associated with a sensory sensation coming feedforward. (Apical input might be used to play back memories without getting proximal stimulus at all, but that is another topic.) The layer processing unit does not know or care where these inputs originate.
In our SMI circuit example from the Columns Paper, the “input layer” learns how the sensor input associated with it typically moves across objects and predicts what the sensor will feel next based not upon the object being sensed, but the way in which the sensor interacts with the world. The “output layer” is doing temporal pooling and classification of objects that sensor column has felt in the past, and constantly associating the current stream of location/sensation data coming from the input layer with what objects fit that stream.
This is a spatial generalization happening over time as an agent interactively senses an object. This generalization is achieved by using the union properly of SDRs to narrow down all the object representation in the output layer as new sensation/locations are received from the input layer.
The “output layer” is temporal because it’s distal input comes from other neurons in the same layer (either within its own cortical column, or from neighboring columns). Remember if a layer’s context is other neurons in the same layer (or the same layer in neighboring columns), that makes the context temporal. In the case of our SMI circuit, some of the distal connections are to neurons within the same layer, and other are from neurons in the same layer in neighboring columns. You do not need this cross-column communication to do object classification, but it happens in the brain and it helps classify objects with fewer sensations.