Do real circuits store memories at the theoretical capacity?
In plain words
Theory predicts how many patterns a network of neurons can store, and that at maximum storage most synapses should be switched off. Testing whether real circuits run at this limit means matching measured synapse statistics to the theory.
Precise statement
For a sign-constrained perceptron with $N$ excitatory inputs storing random associations with margin $\kappa$, Gardner theory gives the capacity and the weight distribution at capacity (a delta peak of silent synapses plus a truncated Gaussian); for cerebellar Purkinje cells this predicted a silent-synapse fraction above one half, consistent with data (Brunel and co-workers, 2004). Determine whether measured synaptic weight distributions in cortical circuits match capacity-optimal predictions for their measured coding level and noise.
What would settle it
Connectomic and electrophysiological measurement of synaptic weight distributions in a cortical circuit compared with the Gardner prediction at its measured coding level.