Here I want to discuss a problem in which the main goal is to find a set of dendrites to optimally cover a data set of high-dimensional SDRs.

“high” means something like tens of thousands or more bits instead of hundreds or a couple thousands as the input pattern series are sized in HTM.

Why? because

- the search space in HTM-like tools is performance capped by the size/complexity of input.
- the eager strategy on tapping on immediate available potential patterns within a SDR might not be optimal.

What does “optimal” means? There are two types of metrics to consider, one is the individual dendrite level and the other one is global, population-of dendrites level.

- a dendrite’s
**sharpness**- it is considered to be “sharp” when its all synapse inputs are either active or inactive. And “confused” when only some of its synapses are active. We can call it “consistency” - the dendrite is optimized for a clear micro-pattern (or feature) in the large SDR. - at population level we have
**completeness**or coverage criteria - a complete coverage is when all 1 bits within an any given input SDR are covered by signalling dendrites. Which means “no bits left unaccounted” in input SDRs - also at population level we have two
**minimalist**criteria,- at dataset level to have a minimum and sufficient number of dendrites necessary to cover any input SDR in the dataset.
- minimize redundancy on any individual SDR which means again have as few as possible active dendrites.

As you see the optimising for all three criteria above could be a tricky problem.

This seems related to the tiling problem in which dendrite is a tile. The differences are:

- we can pick any “shape” for a “tile”,
- there is no limited number of tiles BUT we want to find those particular shapes that allow for a minimum number of tiles.
- the are many “spaces” to be covered - each input SDR On bits form a different space.

Further motivation:

Biological intelligence manages to somehow not only figure out a way to “recognize” a “large” pattern but to also home in to a minimum set of micro-patterns that are necessary and sufficient (== representative) for the larger pattern.

The highly praised “few shot learning” animals are allegedly capable of might involve more than just quickly adding/removing some synapses as in “here-s a paper then voila I understood (e.g.) Newtonian gravity”. It takes time to dig into finding the significant correlations needed to represent then understand any given problem or spatio-temporal context.

There are reasons to believe the high number of (mini)columns are needed not only *to record and recognize* all patterns we encounter, but also for *large scale data mining* needed discover a minimalist set of relevant ones.