On the sixth day of Creation...

1. ורבופרו And replenish the earth and subdue it, and have dominion over the fish of the sea and over birds in the sky and reptilians on land On the sixth day of Creation...

2. after some clarification... granulate and multiply And replenish the… GENESIS I, 28

3. granulate AND MULTIPLY ?!? We took it to mean, to insert granule cell layers into our cortex and then, to see if it leads to multiplication...

4. GRANULATE, I …. take the medial wall of the premammalian cortex and insert the fascia dentata, with its granule cells, at the input end note that the granule cells have become (excitatory) interneurons

5. Multiply, I ? NO! H human the new structure remains stable and unique across mammalian species opossum H

6. GRANULATE, II We took it seriously, and went on, trying to insert granule cell layers into our cortex. Not quite in the same way as for the medial wall... • now, the dorsal cortex. It acquires fine topography... • ...and it laminates

7.  granulating the dorsal wall, leads to the mammalianisocortex the brand new `neocortex’ has laminated, i.e. inserted a granular layer IV in between two pyramidal cells layers. what does this other granulation buy us? Layer IV granules are now (excitatory) interneurons

8. Isocortical lamination • emerges together with fine topographic mapping • does not apply to the non topographic olfactory system • is underdeveloped in caetaceans It might be a computational solution to the need to relay precise information about both ‘where’and ‘what’sensory stimuli are.

9. the model src recurrent collaterals patch of cortex input station feedforward connections sff input activity spatial focus detailed pattern R

10. The activation of units in the previous station is the product of a spatial ‘focus’, say, a Gaussian of radius R(which presumably would be picked up by optical imaging, or by multi-unit recording) and a detailed unit-by-unit pattern of activity (which would require single unit recording to be revealed). p patterns of activity (e.g. 2-12) are established at the beginning, drawn at random from a given distribution, and used repeatedly in one simulation. The activation of units in the cortical patch is compared with the activations resulting from the application of each input pattern at each spatial focus, to decode the pattern and focus x of the current activation. This allows measuring as well as both population measures, reflecting activity in the whole patch

11. Both recurrent and feedforward weights are modified according to a simple ‘Hebbian’ associative rule, over the course of several training epochs. Each training epoch involves presenting, in random order, each input pattern at each activation focus. The map is thus pre-wired at a coarse, statistical level, and self-organized at a finer scale. After a training epoch, noisy versions, again of each pattern at each activation focus, are presented for testing, with no weight change. The full information about position and identity cannot be decoded from the activation in the patch, because the activation in the input is noisy (in practice, e.g. 40% of the input units follow the prescribed pattern, and 60% are randomly activated with the same distribution) If R << Src, it is rather intuitive to predict how much information can be relayed by feedforward projections of spread Sff:

12. Iident is small initially • grows with learning • no difference between layers Results for p=4

13. Ipos is less affected by learning • decreases with more diffuse feedforward connections • again, no difference between layers

14. These data, plotted as Ipos vs. Iident, demonstrate the what/where conflict as a boundary • using more patterns merely shifts the same boundary upwards

15. Differentiating a granular layer (IV) in which units receive focused FF connections, also more restricted RC connections, and follow a specific dynamics • may nail down the focus of activation within the cortical map (preserving detailed positional information) • without interfering with the retrieval of the identity of the specific activation pattern (achieved mainly by the collaterals of the pyramidal layers)

16. the model src recurrent collaterals patch of cortex input station feedforward connections sff input activity spatial focus detailed pattern R

17. Indeed it happens! Laminated cortex can relay more combined what and where information than if it were not laminated • The advantage is somewhat more evident for larger p • it is small, but should scale up in a network of realistic size

18. Dependence on the size of the cue: the effect of learning...

19. …the advantage is there whatever the size of the cue

20. but what do I do to layer IV ? 1) restrict its collaterals 2) focus its afferents 3) sustain its dynamics (but suppress it in training)

21. The granular layer may nail down the focus of activation within the cortical map (preserving detailed positional information) without interfering with attractor-mediated retrieval of the identity of the specific activation pattern (achieved mainly by the collaterals of the pyramidal layers)

22. A differentiation between supra- and infra-granular layers may be usefully coupled to their different extrinsic connectivity, if: • the supragranular layers preserve both positional and identity information, and trasmit it onward for further analysis • the infragranular layers relay backwards and downwards identity information freshly squeezed from the attractors, without bothering to replicate positional information

23. and what do I do to layer V ? 4) remove its afferents from layer IV V III IV

24. Lamination+directional connectivity make each layer convey a better mix of information, beyond the capability of any unlaminated patch, whatever its Sff • they also slow down learning, though, so the advantage would be greater if more learning epochs had been allowed (here they are set to 3)

26. Oops! I forgot the timing.. ..this account is roughly independent of dynamics (a detailed analysis of relative timings, e.g. of the different inputs to the deep layers) the only “dynamical” element introduced is firing frequency adaptation, which is however used in a time-independent fashion we shall discuss more time-related uses of adaptation over the next two days, in generating transitions along continuous and among discrete attractors.

27. A functional hypothesis A common mode of operation of the primordial sensory neocortex of mammals may have been autoassociative attractor dynamics. Attractors may be formed by self-organizing weight changes on FF and RC connections, and may dominate the dynamics of both SG and IG layers, although the former can be kept in tighter positional register by layer IV. Thanksto Hamish Meffin, with whom I discussed such ideas, with divergent conclusions (see his Ph.D. Thesis, U. of Sidney)

28. 2 suggestions • Understanding specific mammalian mechanisms of information representation and retrieval may require quantitative (information theoretical) analyses at the level of populations of individual neurones • Only notions of sufficient abstraction and generality as to apply to each sensory cortex can help explain the appearance, in evolution, of this universal neocortical microchip.

29. YES ! Multiply, II ? cat but why ? hedgehog monkey We are busy trying to understand it. Maybe next time...