What happens when previously active cells are all the cells in a column that bursts?

I assume the currently active cells will form a connection to one of those cells from the column that was bursting. Am I right?

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Yes, in vanilla TM, a single winner per minicolumn is chosen in the previous time step, and if a new segment needs to be grown in the current time step, it connects to just the winners.

Note that not all TM implementations follow this, though (for example, etaler which I mentioned on one of your earlier threads will grow connections randomly to active cells in the previous time step, not just the “winners”).

The vanilla TM algorithm will:

  • Only grow connections to previously active winner cells (not to ones which were not winners)
  • If a segment has “max new synapse count” active synapses when its post-synaptic cell becomes predicted active, then do not grow any additional synapses (to winners or otherwise)

@mrcslws explained the reasoning behind this here.