Numenta VP of Research Subutai Ahmad delivered this presentation at the Centre for Theoretical Neuroscience, University of Waterloo on October 2, 2018.

1. University of Waterloo
October 2, 2018
Subutai Ahmad
sahmad@numenta.com
@SubutaiAhmad
Have We Missed Half of What the Neocortex Does?
A New Predictive Framework
Based on Cortical Grid Cells
Collaborators:
-Jeff Hawkins, Marcus Lewis,
Scott Purdy, Mirko Klukas

2. Standard Model of the Neocortex
Sensory array
Simple
features
Complex
features
ObjectsRegion 3
Region 2
Region 1

3. Vernon Mountcastle’s Big Idea
1) All areas of the neocortex look
the same because they perform
the same basic function.
2) What makes one region a visual
region and another an auditory
region is what it is connected to.
3) A small area of cortex, a 1mm2
“cortical column”, is the unit of
replication and implements the
common cortical algorithm.
Mountcastle, 1978

4. L2/3
L4
L6
L5
Input
Anatomy of a Cortical Column
1) Cortical columns are really complex!
The function of a cortical column must also be complex.
2) Local circuitry is remarkably consistent everywhere.
The function of a cortical column must be generic.
Simple
Output L2
L3a
L3b
L4
L6a
L6b
L6 ip
L6 mp
L6 bp
L5 tt
L5 cc
L5 cc-ns
L5: Calloway et. al, 2015
L6: Zhang and Deschenes, 1997
Binzegger et al., 2004
Nelson et al., 2013
Output, via thalamus
50%10%
Cortex
Thalamus
Output, direct
L5 CTC: Guillery, 1995
Constantinople and Bruno, 2013
Long range lateral connections
Realistic

5. What Does a Cortical Column Do?
The neocortex learns a model of the world
- Thousands of objects, how they appear on the sensors
- Relative location of features, invariant to sensor position
- Learned via movement of sensors
- Makes detailed predictions
- Models physical and abstract objects
Mountcastle corollary:
If the neocortex learns models of objects,
then each column learns models of objects

6. How can networks of neurons learn rich predictive
models of objects through movement?
Question:
The neocortex and cortical columns use “cortical grid
cells” and path integration to model an object’s
structure.
Proposal:
Talk Outline:
1) Properties of grid cells
2) Network model of cortical columns
3) Implications

7. Single Grid Cell
(Moser & Moser, 2013)

8. Grid Cell Module Contains Multiple Cells That Are Offset

9. Grid Cell Module Contains Multiple Cells That Are Offset

10. Multiple Modules At Different Scales and Orientations
Environment

11. Multiple Modules Can Represent Locations Uniquely
(Fiete et al, 2008; Sreenivasan and Fiete, 2011)

12. Path Integration
(Hafting et al, 2005;
McNaughton et al., 2006; Ocko et al., 2018)
- As animal moves, grid cells update their location
- This can happen in the dark, using efference copy of motion signals
- Path integration: regardless of path trajectory, the same location in
environment will activate a consistent grid code
- Imprecise, so sensory cues are used to “anchor” grid cells

13. Unique Location Spaces For Each Environment
- Each module randomly initialized in a new room, codes for each room will be unique
(e.g. 20 modules, 100 cells each = 10020 possible codes)
- Initial point implicitly defines a location space for each environment
- Modules update independently, so path integration still works
- Sensory cues can be used to anchor or re-activate the location space
(Rowland & Moser, 2014)

14. Summary: Grid Cells Represent the Structure of Environments
Entorhinal Cortex
Body in environments
Location
- Encoded by grid cells
- Unique to location in room AND room
- Location is updated by movement
A Room is:
- A set of locations that are connected
by movement (via path integration).
- Some locations have associated
features.

15. Proposal: Cortical Grid Cells Represent the Structure of Objects
Location
- Encoded by grid cells
- Unique to location in room AND room
- Location is updated by movement
A Room is:
- A set of locations that are connected
by movement (via path integration).
- Some locations have associated
features.
Entorhinal Cortex
Body in environments
Cortical Column
Sensor patch relative to objects
Location
- Encoded by grid-like cells
- Unique to location on object AND object
- Location is updated by movement
An Object is:
- A set of locations that are connected
by movement (via path integration).
- Some locations have associated
features.

16. Network Model (Single Cortical Column)
Grid cell modules
use movement to
update their location
Sensory predictions
(forward model)Predictions + sensation =>
sensory representation
- Sequence of discrete time steps
- Each time step consists of 4 stages
representing a movement followed by a
sensation
New sensation updates
location
(Lewis et al, submitted)

17. Updating Grid Cell Module Based On Motion
- Given a motion 𝒅 𝑡
, phase is shifted according to:
- Threshold activity to get a binary location representation
- Cells in each module represented by 2D phase Φ
- Activity at time t is a bump centered around a
phase Φ 𝑡
𝑖
- Each module has a different scale and orientation,
represented by a transform matrix:
𝑴𝑖 =
𝑠𝑖 cos 𝜃𝑖 − 𝑠𝑖 sin 𝜃𝑖
𝑠𝑖 sin 𝜃𝑖 𝑠𝑖 cos 𝜃𝑖
−1
Φ 𝑡,move
𝑖
= 𝜑 + 𝑴𝑖 𝒅 𝑡 mod 1.0 𝜑 ∈ Φ 𝑡−1
𝑖

18. Location Layer Forms Predictions in Sensory Layer
Sensory predictions
(forward model)

19. 5K to 30K excitatory synapses
- 10% proximal
- 90% distal
Distal dendrites are pattern detectors
- 8-15 co-active, co-located synapses
generate dendritic NMDA spikes
- sustained depolarization of soma but
does not typically generate AP
(Mel, 1992; Branco & Häusser, 2011; Schiller et al, 2000; Losonczy, 2006; Antic
et al, 2010; Major et al, 2013; Spruston, 2008; Milojkovic et al, 2005, etc.)
Active Dendrites in Pyramidal Neurons

20. Proximal synapses: Cause somatic spikes
Define classic receptive field of neuron
Distal synapses: Cause dendritic spikes
Put the cell into a depolarized, or “predictive” state
Depolarized neurons fire sooner, inhibiting nearby neurons.
A neuron can predict its activity in hundreds of unique contexts.
5K to 30K excitatory synapses
- 10% proximal
- 90% distal
Distal dendrites are pattern detectors
- 8-15 co-active, co-located synapses
generate dendritic NMDA spikes
- sustained depolarization of soma but
does not typically generate AP
HTM Neuron Model
Active Dendrites Predict a Neuron’s Inputs
(Poirazi et al., 2003)
(Hawkins & Ahmad, 2016)

21. Sensory Layer is a Sequence Memory Layer
- Neurons in a mini-column learn same FF receptive field.
- Distal dendritic segments form connections to cells in location layer.
- Active segments act as predictions and bias cells.
- With sensory input these cells fire first, and inhibit other cells within
mini-column.
(Hawkins & Ahmad, 2016; Hawkins et al, 2017)
No prediction
t=0
t=1
Sensory input
Predicted input
t=0
Predicted cells
inhibit neighbors
t=1
Sensory input
Sensory layer
Very specific sparse representation
that encodes the current sensory
input at the current location.
Dense representation that activates
the codes for this sensory input at
any location.

22. Multiple Simultaneous Locations Represents Uncertainty
- Sensory representation activates grid cell locations
- If this sensory representation is not unique, we activate
a union of grid cells in each module
- With sufficiently large modules, the union can represent
several locations without confusion
- Movement shifts all active grid cells
(Ahmad & Hawkins, 2016)
(Lewis et al, submitted)

23. Learning
- For a new object, we first activate a random
cell in each module and move to first feature
- Select random subset of active sensory cells for
this sensory input. Store location representation
on independent dendritic segment in sensory
cells.
- Store this sensory representation on an
independent dendritic segment in each active
location cell
- Move to next feature and repeat
- This process invokes a new unique location
space and sequentially stores specific location
representation with sensory cues, and specific
sensory code with locations.

24. An Example Recognition Walkthrough
Sense f1

25. An Example Recognition Walkthrough
Move to f2

26. An Example Recognition Walkthrough
Sense f2

27. An Example Recognition Walkthrough
Move to f1

28. Simulation: Network Convergence

29. Network Convergence Improves With Module Size
100 objects with 10 points each, pool of 10 unique features, 10 modules

30. Network Convergence Approaches Ideal Observer Model
100 objects with 10 points each, pool of 10 unique features, 10 modules

31. Capacity of Single Cortical Column
100 unique features

32. Single Cortical Column Model Of Sensorimotor Inference
- Objects are defined by the relative
locations of sensory features
- Objects are recognized through a
sequence of movements and sensations
- Grid cell code enables a powerful
predictive sensorimotor network
- Simulation results demonstrate
convergence and capacity

33. Sensorimotor Inference With Multiple Columns And Long-
Range Lateral Connections
- Each column has partial knowledge of object.
- Columns vote through long range lateral connections.
(Hawkins et al, 2017)

34. Convergence Is Much Faster With Multiple Columns

35. L2/3
L4
L6
Where Are Cortical Grid Cells?
L6 to L4:
Ahmed et al., 1994
Binzegger et al., 2004
Harris & Shepherd, 2015
L6 motor:
Harris & Shepherd, 2015
Nelson et al., 2013
Leinweber et al., 2017
Long-range lateral connections
Large pathway between L6 and L4
Strong motor projections into L6

36. L2/3
L4
L6
Object layer
Location layer
Sensory input layer
Grid cell
modules
Where Are Cortical Grid Cells?
L6 to L4:
Ahmed et al., 1994
Binzegger et al., 2004
Harris & Shepherd, 2015
L6 motor:
Harris & Shepherd, 2015
Nelson et al., 2013
Leinweber et al., 2017

37. 1) Border ownership cells:
Cells fire only if feature is present at object-centric location on object.
Detected even in primary sensory areas (V1 and V2).
(Zhou et al., 2000; Willford & von der Heydt, 2015)
2) Grid cell signatures in cortex:
Cortical areas in humans show grid cell like signatures (fMRI and single cell recordings)
Seen while subjects navigate conceptual object spaces and virtual environments.
(Doeller et al., 2010; Jacobs et al. 2013; Constantinescu et al., 2016; )
3) Sensorimotor prediction in sensory regions:
Cells predict their activity before a saccade.
Predictions during saccades are important for invariant object recognition.
(Duhamel et al., 1992; Nakamura and Colby, 2002; Li and DiCarlo, 2008)
4) Hippocampal functionality may have been conserved in neocortex:
(Jarvis et al., 2005; Luzatti, 2015)
Biological Evidence
37

38. Rethinking Hierarchy
L2/3
L4
L6

39. Rethinking Hierarchy: Thousand Brains Theory of Intelligence
Sense array
Objects
Objects
Objects
Sense array
Every column learns models of objects.
Each model is different depending on its inputs.
Cortical columns quickly resolve uncertainty through voting.
Neocortex contains thousands of massively parallel and distributed
independent modeling systems.

40. Experimentally Testable Predictions
40
1) Object coding:
Every sensory region will contain layers that are stable while sensing a familiar object.
The set of cells will be sparse but specific to object identity.
Ambiguous information will lead to denser activity in upper layers.
Each region will contain cells tuned to locations of features in the object’s reference frame.
(Zhou et al., 2000; Zheng & Kwon, 2018)
2) Cortical columns:
Cortical cols can learn complete object models
Complexity of objects tied to span of long-range lateral connections
Activity within stable layers will converge slower with long–range connections disabled
Subgranular layers of primary sensory regions (Layer 6) will be driven by motor signals
Grid-like cells in Layer 6a
(Nelson et al., 2013; Sutter et Shepherd, 2015; Lee et al, 2008; Leinweber et al, 2017)

41. L2/3
L4
L6
Summary
1. Cortical columns are much more
powerful than typically assumed.
2. Cortical columns model the
structure of objects using grid
cell mechanisms.
3. Multiple columns resolve
uncertainty through voting.
4. Thousands of cortical columns
vote through long-range
connections across regions and
sensory modalities.

42. Numenta Team
Jeff Hawkins Marcus Lewis
Contact: sahmad@numenta.com
@SubutaiAhmad
Scott Purdy
Mirko Klukas Luiz Scheinkman