These are slides on a workshop Subutai Ahmad hosted on March 5, 2018 at the Computational and Systems Neuroscience Meeting (Cosyne) 2018. About: This workshop on long-range cortical circuits is focused on our peer-reviewed paper, “A Theory of How Columns in the Neocortex Enable Learning the Structure of the World.” Subutai discussed the inference mechanism introduced in the paper, our theory of location information, and how long-range connections allow columns to integrate inputs over space to perform object recognition.

1. Cortical circuits: functions and
models of long-range connections
March 5, 2018
Subutai Ahmad
sahmad@numenta.com
Could A Model Of Predictive Voting
Explain Many Long-Range Connections?
Co-authors:
-Jeff Hawkins, Marcus Lewis, Scott Purdy

2. Feedforward Models Do Not Account For Most Connections
Inputs project to multiple levels at once.
Multiple long-range lateral connections within each level (layers 2/3, 5, 6).
Significant feedback connections – they also skip levels.
Sense
Simple features
Complex features
ObjectsRegion 3
Region 2
Region 1
Sensor array
Reality
(Markov et al., 2017), (Stettler et al., 2002), (Schnepel et al., 2015)
Classic feedforward model

3. Feedforward Models Do Not Account For Most Connections
Sense
Simple features
Complex features
Objects
Classic feedforward model
Sensor array Sensor array
vision touch
Region 3
Region 2
Region 1
Reality
Inputs project to multiple levels at once.
Multiple long-range lateral connections within each level (layers 2/3, 5, 6).
Significant feedback connections – they also skip levels.
Long range reciprocal connections between multiple modalities
(Markov et al., 2017), (Stettler et al., 2002), (Schnepel et al., 2015), (Suter & Shepherd, 2015), (Leinweber et al., 2017)

4. L2
L3a
L3b
L4
L6a
L6b
L6 ip
L6 mp
L6 bp
L5 tt
L5 cc
L5 cc-ns
L2/3
L4
L6
L5
Input
The Cortical Column
1) Cortical columns are complex
2) The function of a cortical column must also be complex.
3) The function of a cortical column must be universal
L5: Calloway et. al, 2015
L6: Zhang and Deschenes, 1997
Binzegger et al., 2004
Simple
Output, via thalamus
50%10%
Cortex
Thalamus
Output, direct
L5 CTC: Guillery, 1995
Constantinople and Bruno, 2013
Output

5. Observation:
The neocortex is constantly predicting its inputs.
“the most important and also the most neglected problem of
cerebral physiology” (Lashley, 1951)
How can networks of pyramidal neurons learn predictive
models of the world?
Research question:

6. 1) How can neurons learn predictive models of extrinsic temporal sequences?
3) Implications
- Hierarchy revisited
- Properties and experimentally testable predictions
- Pyramidal neuron uses active dendrites for prediction
- A single layer network model for complex predictions
- Works on real world applications
- Extension of sequence memory model
- Learns predictive models of objects using motion based context signal
- Predictive voting for disambiguation via long-range connections
“Why Neurons Have Thousands of Synapses, a Theory of Sequence Memory in the Neocortex”
Hawkins and Ahmad, Frontiers in Neural Circuits, 2016/03/30
“A Theory of How Columns in the Neocortex Learn the Structure of the World”
Hawkins, Ahmad, and Cui, Frontiers in Neural Circuits, 2017/10/25
2) How can neurons learn predictive models of sensorimotor sequences?

7. 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
Pyramidal Neuron
(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.)
Prediction Starts In The Neuron

8. Proximal synapses: Cause somatic spikes
Define classic receptive field of neuron
Distal synapses: Cause dendritic spikes and provide context for cell
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
Prediction Starts In The Neuron
Pyramidal Neuron
(Poirazi et al., 2003)
(Hawkins & Ahmad, 2016)

9. A Single Layer Network Model For Sequence Memory
- Neurons in a mini-column learn same FF receptive field.
- Active dendritic segments form connections to nearby cells.
- Depolarized cells fire first, and inhibit other cells within mini-column.
No prediction Predicted input
t=0
t=1
Predicted cells inhibit
neighbors
Next prediction t=2
t=0
t=1

10. Synaptic changes localized to dendritic segments:
(Losonczy et al., 2008)
1. If a cell was correctly predicted, positively reinforce the dendritic
segment that caused the prediction.
2. If a cell was incorrectly predicted, slightly negatively reinforce the
corresponding dendritic segment.
3. If no cell was predicted in a mini-column, reinforce the dendritic
segment that best matched the previous input.
Continuous Branch Specific Learning

11. Works Well On Complex Real World Temporal Sequences
- Can learn non-Markovian sequences
- Accuracy is comparable to state of the art ML techniques (LSTM, ARIMA, etc.)
- Continuous unsupervised learning - adapts to changes far better than other techniques
- Top benchmark score in detecting anomalies and unusual behavior
- Extremely fault tolerant (tolerant to 40% noise and faults)
- Multiple open source implementations (some commercial)
“Continuous online sequence learning with an unsupervised neural network model”
Cui, Ahmad and Hawkins, Neural Computation, 2016
“Unsupervised real-time anomaly detection for streaming data”
Ahmad, Lavin, Purdy and Zuha, Neurocomputing, 2017
2015-04-20
Monday
2015-04-21
Tuesday
2015-04-22
Wednesday
2015-04-23
Thursday
2015-04-24
Friday
2015-04-25
Saturday
2015-04-26
Sunday
0 k
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PassengerCountin30minwindow
A
B C
Shift
AR
IM
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3000LSTM
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D
?
NYC Taxi Demand Machine Temperature Sensor Data

12. 1) How can neurons learn predictive models of extrinsic temporal sequences?
3) Implications
- Hierarchy revisited
- Properties and experimentally testable predictions
- Pyramidal neuron uses active dendrites for prediction
- A single layer network model for complex predictions
- Works on real world applications
- Extension of sequence memory model
- Learns predictive models of objects using motion based context signal
- Predictive voting for disambiguation via long-range connections
2) How can neurons learn predictive models of sensorimotor sequences?

13. How Could a Layer of Neurons Learn a Predictive Model of
Sensorimotor Sequences?
Sequence memory
Sensorimotor sequences
SensorMotor-related context
By adding motor-related context, can a cellular layer predict
its input as the sensor moves?

14. Sensorimotor sequences
SensorMotor-related context
Hypothesis:
- We need to provide an “allocentric location”, updated through movement
Proposal:
- Cortical columns use grid cell like modules, applied to objects instead of
environments, to compute allocentric location
(Lewis & Hawkins, Cosyne poster, 2018)
What Is The Correct Motor Related Context?

15. Two Layer Model of Sensorimotor Inference
Feature @ location
Object
Sparse code for object identity
Stable over movement
- Activity in object layer starts out dense and gets progressively
sparser as more evidence is received.
Sensor
Feature
Allocentric
Location
Seq Mem
Changes with each movement
Predicts next sensory feature
Lateral connections on active
dendrites vote and bias cells
towards recent hypotheses

16. Object
Feature @ Location
Allocentric
location
Column 1 Column 2 Column 3
Sensor
feature
Sensorimotor Inference With Multiple Columns And Long-
Range Lateral Connections
- Each column has partial knowledge of object.
- Long range lateral connections in object layer allow columns to vote.
- Inference is much faster with multiple columns.
- Very similar to optimal context integration model (Iyer & Mihalas, 2017)

17. FeatureFeatureFeatureLocationLocationLocation
Output
Input
Objects Recognized By Integrating Inputs Over Time

18. FeatureLocationFeatureLocationFeatureLocation
Column 1 Column 2 Column 3
Output
Input
Recognition is Faster with Multiple Columns

19. Yale-CMU-Berkeley (YCB) Object Benchmark (Calli et al, 2017)
- 80 objects designed for robotics grasping tasks
- Includes high-resolution 3D CAD files
YCB Object Benchmark
We created a virtual hand using the Unity game engine
Curvature based sensor on each fingertip
4096 neurons per layer per column
98.7% recall accuracy (77/78 uniquely classified)
Convergence time depends on object, sequence of
sensations, number of fingers.
Simulation using YCB Object Benchmark

20. Pairwise confusion between objects after 1 touch
Convergence 1 finger 1 touch

21. Pairwise confusion between objects after 2 touches
Convergence 1 finger 2 touches

22. Pairwise confusion between objects after 6 touches
Convergence 1 finger 6 touches

23. Pairwise confusion between objects after 10 touches
Convergence 1 finger 10 touches

24. Convergence Is Faster With Long-Range Connections

25. 1) How can neurons learn predictive models of extrinsic temporal sequences?
3) Implications
- Hierarchy revisited
- Properties and experimentally testable predictions
- Pyramidal neuron uses active dendrites for prediction
- A single layer network model for complex predictions
- Works on real world applications
- Extension of sequence memory model
- Learns predictive models of objects using motion based context signal
- Predictive voting for disambiguation via long-range connections
2) How can neurons learn predictive models of sensorimotor sequences?

26. Hierarchy Revisited
Sensor array Sensor array
vision touch
Proposed

27. Hierarchy Revisited
Every column learns complete predictive models of all the objects it can.
Columns operate at different scales, with different sensory inputs.
Massively distributed parallel system.
Non-hierarchical connections allow columns to predict, vote and
disambiguate shared elements.
Sensor array
Objects
Objects
Objects
Sensor array
vision touch
Proposed

28. 1) Impact of NMDA spikes:
Dendritic NMDA spikes cause cells to fire faster than they would otherwise.
Fast local inhibitory networks (e.g. minicolumns) inhibit cells that don’t fire early.
Sparser activations during a predictable sensory stream, denser when surprised.
(Vinje & Gallant, 2002; Smith et al, 2013; Wilmes et al, 2016)
2) Branch specific plasticity:
Strong LTP in dendritic branch when NMDA spike followed by back action potential (bAP).
Weak LTP (without NMDA spike) if synapse cluster becomes active followed by a bAP.
Weak LTD when an NMDA spike is not followed by an action potential/bAP.
(Holthoff et al, 2004; Losonczy et al, 2008; Yang et al, 2014; Cichon & Gang, 2015)
3) Object modeling in cortical columns:
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.
Cortical cols can learn complete objects (complexity tied to long-range lateral connections).
Ambiguous information will lead to denser activity in upper layers.
Activity within these layers will converge slower with long–range connections disabled.
Each region will contain cells tuned to locations of features in the object’s reference frame.
(Zhou et al, 2000; Zheng & Kwon, 2018)
Properties And Experimentally Testable Predictions
28

29. - Layer of pyramidal neurons can form predictive models of sequences
- Active dendrites and dendritic spikes provide context for predictions
- Cortical columns are much more powerful than simple filters
- Each column attempts to build models of objects within its input space
- The cortex is composed of hundreds of thousands of parallel predictive models
- Uncertainty is resolved by voting across the hierarchy and across modalities
29
Summary