If you think of the dendrite festooned with synapses - it is an input device to sample the local environment. A given dendrite can only reach about 250 µm away, or a circle of 500 µm in diameter reach for a given mini-column. Remember that these mini-columns are pitched about 30 µm apart so a dendrite can reach about 8 mini-columns away in any direction, or about 225 mini-columns total.
The lateral connections allow for a distant winning cell (beyond the reach of the dendrites) to add input/excitement. These are sideways branching projections of the output axons from a cell. I tend to focus on the topology of L2/3 as this is the pattern matching & intermap signalling layer; deeper layer lateral connections have a somewhat longer reach.
Do keep in mind that EVERY mini-column has these lateral connections shooting out in random directions and they are all working at the same time. They are all about the same length and they influence a population of distant cells in a rough circle around the cell body. I am not sure of the count but let’s start with 10 or so as a working number.
What I see at the most important feature is that this allows coverage of an area larger than any one column could cover by itself with voting - each sees a pattern but the two cells working other signal that they are seeing a part of a larger pattern.
See this picture:
Each little circle is an individule mini-column with about 100 cell bodies. The larger black circle is the dendrite reach of the center mini-column. The black beam in this picture is the long-distance lateral connection between the two center minicolumns so that the two minicolumn “receptive fields” connected by this link covers the space with very little overlap and very little area missed.
I made this diagram to show the correspondence between the biology and this idealized diagram.
There are other features/advantages:
Important point: In HTM we have binary signal that fire or does not, and the temporal memory is a rigid sequential operation. Real nerve firing is binary AND rate oriented to add an analog dimension; there are weak and strong signal and they can build over time.
Ideally - this lateral signal should push a cell that is on the edge of firing into firing and learning its inputs. In this way, a mini-column will help other mini-columns to learn a new pattern.
These connections should also allow three or more cells that are sensing a weak and noisy signal to “egg each other on” and agree that they do know this pattern and fire.
One other important bit: These lateral connections are the input to fire the inhibitory interneurons. The inhibitory interneurons should act to suppress other mini-columns that are not as sure of themselves because they have a weaker match to the input; this acts as a filter to pick weak signals out of the noise.
The signal weighting is very important - it should not force firing nor should it be so weak it is irrelevant. The balance between these lateral connections and the inhibitory interneurons is an important parameter and I suspect that models will have to tune this to get the best performance.
I hope this helps.