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Neural Fields, a Cognitive Approach
Attention, Decision & Plasticity
Nicolas P. Rougier
Inria - Institute of Neurodegenerative Diseases - Bordeaux, France
Computational Neuroscience Course - Nice, April 1st
, 2019
Introduction
Mnemosyne Project
Major cognitive and behavioral functions emerge from adaptive sensorimotor loops
involving the external world, the body and the brain. We study, model and implement
such loops and their interactions toward a fully autonomous behavior. With such a
systemic approach, we mean that such complex systems can only be truly
apprehended as a whole and in natural behavioral situation.
What is cognition ?
What are the questions ?
• What are the main forms of cognition ?
• What are the minimal mechanisms ?
• What is/are the right biological levels ?
• How do we identify a satisfactory answer ?
• What is the role of the observer ?
Many definitions, many forms, many species
4
The case of Caenorhabditis elegans
Sensory motor behavior
Q. Wen, M.D. Po, E. Hulme, S. Chen, X. Liu, S. Wai Kwok, M. Gershow, A. M. Leifer, V. Butler, C. Fang-Yen, T. Kawano, W.R.
Schafer, G. Whitesides, M. Wyart, D.B. Chklovskii, M. Zhen, A.D.T. Samueln, Proprioceptive Coupling within Motor
Neurons Drives C. elegans Forward Locomotion. Neuron, 2012.
Plasticity, learning and memory
H. Sasakura and I. Mori, Behavioral plasticity, learning, and memory in C. elegans, Current Opinion in Neurobiology,
2013.
Decision making
T.A. Jarrell, Y. Wang, A.E. Bloniarz, C.A. Brittin, M. Xu, J.N. Thomson, D.G. Albertson, D.H. Hall, S.W. Emmons, The
Connectome of a Decision-Making Neural Network, Science, 2012.
5
What really matters for cognition ?
Some figures
• C.Elegans → 302 neurons
• Mouse → 71,000,000 neurons
• Rat → 200,000,000 neurons
• Macaque → 6,376,000,000 neurons
• Human → 86,000,000,000 neurons
The human brain in numbers [...], S. Herculano-Houzel,
Frontier in Human Neuroscience, 2009
6
What really matters for cognition ?
Specific structures ?
• Neocortex
• Basal Ganglia
• Amygdala
• Frontal cortex
Specific architecture ?
• Connectivity
• Density
• Modularity
• Self-organisation
Specific abilities ?
• To recognize self/others
• To imitate
• To use tools
• To communicate
7
Theoretical frameworks
Biological framework
→ Anatomical facts
→ Physiological recordings
→ Experimental data
Cognitive framework
→ Subsumption architecture
→ Embodied cognition
→ Affordances, emotions, etc.
Computational framework
→ Computational paradigm
→ Plasticity & learning
→ Evaluation of models
Philosophical framework
→ Strong AI / Weak AI
→ Emergence
→ Theories of mind
8
Where do we start ?
What is/are the right biological level(s) of description ?
• Molecule ? → neurotransmitters
• Organelle ? → axons, dendrites, synapses
• Cell ? → neurons, glial cells
• Tissue ? → brain lobes & structures
• Organ ? → brain
Neural fields, between cells and tissue
→ Complex Dynamic
→ Large population
→ Fast simulation
9
Spatio-temporal framework
Continuous space
... stable patterns of neuronal activation ultimately steer the periphery into
dynamical states, from which behavior emerges, without any need to ever ab-
stract from the space-time contiguous processes that embody cognition.
G.Schöner (2008)
Continuous time
The first challenge is that sensori-motor systems evolve continuously in real
time, but cognition can jump from one state to another, that is, from one
thought to another
Spencer et al. (2009)
10
Computational Framework
A unit is a set of arbitrary values that can vary along time under the influence of other
units and learning.
• Distributed
→ No supervisor nor executive
• Asynchronous
→ No central clock
• Numerical
→ No symbols
• Adaptive
→ No a priori knowledge
Group Group
Unit
Link
Layer
Link
Value
Value
Value
We want to make sure that emerging properties are those of the model and not those
of the software running the model (see dana.loria.fr).
11
Neural Fields
Equation
Let u(x,t) be the membrane potential at position x and time t, f a transfer function and
w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by:
τ
time constant
·
∂u(x, t)
∂t
= −u(x, t)
leak term
+
∫ +∞
−∞
w(x, y) · f(u(y, t))
lateral interactions
dy + I(x)
input
+ h
resting potential
Velocity
Unless specified otherwise, we’ll generally consider infinite speed, i.e. instantaneous
transmission of information.
12
Neural Fields
Function
The activity of a neural field can be interpreted from a functional point of view.
Filter Decision Tracking Memory
Measure
Using a specific set of parameters, the activity of a neural field can also be interpreted
as a measure of the input.
Input = 0.25 Input = 0.50 Input = 0.75 Input = 1.00
13
Attention
Visual

Attention
On ne voit que ce que l’on regarde
Everyone knows what attention is. It is the possession by the mind, in clear and vivid
form, of one out of what seem several simultaneously possible objects or trains of
thought. Focalization, concentration, of consciousness are of its essence. It implies
withdrawal from some things in order to deal effectively with others, and is a
condition which has a real opposite in the confused, dazed, scatterbrained state
which in French is called distraction, and Zerstreutheit in German.
W. James, (1890)
15
How much blind are you ?
16
The grand illusion of seeing...
• Images on retina are formed
upside-down
• There is a blind spot on the retina
where optic nerves passes
throught it
• Retina receptors are not uniformly
distributed over the surface of the
retina
• Eye is always moving even when
fixing a point (micro-tremors)
17
The many visual pathways
The dorsal pathway
• Where or How pathway
• Motion and object locations
The ventral pathway
• What pathway
• Form and object representation
The frontal pathway
• Executive control
• Organization of behavior
• Visual Awareness 32 cortical areas, 10 hierarchical levels
18
Visual exploration
19
Attention
Clinical Description (Sohlberg & Mateer, 1989)
Focused to respond discretely to a specific stimuli.
Sustained to maintain a consistent behavioral response
Selective to maintain attention in the face of distractors
Alternating to shift focus of attention
Divided to respond simultaneously to multiple tasks
Cognitive Description
Motor movements preparation, priming, etc.
Sensory auditory, visual, proprioception, etc.
Overt motor response (explicit)
Covert cognitive response (implicit)
Top-down goal driven, bias, etc.
Bottom-Up stimulus driven, pop-out, etc.
20
Visual Attention
Spotlight metaphor
Attention is the capacity to select a relevant region of the sensory space
• Topological region of the sensory space → spatial attention
• Featural region of the sensory space → feature oriented attention
• Object as such → object oriented attention
21
Parallel Search
Search for ’X’
22
Parallel Search
Search for ’X’
23
Parallel Search
Search for ’X’
24
Sequential Search
Search for ’X’
25
A computational approach
Theories of Visual Attention
→ Saliency Maps (Itti & Koch, 2001)
Saliency map is a topographically arranged map that represents visual saliency of
a corresponding visual scene.
• Inhibition Of Return (IOR, Posner, 1980)
IOR operates to decrease the likelihood that a previsously inspected item in the
visual scene will be reinspected.
• Premotor Theory of Attention (Rizzolati, 1987)
Attention may derive from weaker activation of same fronto-parietal circuits.
26
Saliency maps
Image Saliency map
27
Saliency maps
• Simple model of visual tracking
• Robustness to noise, distractors and
saliency
• Dynamic & reactive behavior
Saliency
Input
Focus
Competition
28
A computational approach
Theories of Visual Attention
• Saliency Maps (Itti & Koch, 2001)
Saliency map is a topographically arranged map that represents visual saliency of
a corresponding visual scene.
→ Inhibition Of Return (IOR, Posner, 1980)
IOR operates to decrease the likelihood that a previsously inspected item in the
visual scene will be reinspected.
• Premotor Theory of Attention (Rizzolati, 1987)
Attention may derive from weaker activation of same fronto-parietal circuits.
29
Inhibition of Return
Fixation frame
Uncued Cued
Cue
Time
0 100 200 300 400 500
Cue Target SOA (ms)
350
375
400
425
Reactiontime(ms)
Cued
Uncued
30
Inhibition of Return
• Dynamic Working memory
• Biased competition
• Sequential behavior
Saliency
Memory
Update
Input
Focus
Memorization
Bias/Gating
Competition
31
A computational approach
Theories of Visual Attention
• Saliency Maps (Itti & Koch, 2001)
Saliency map is a topographically arranged map that represents visual saliency of
a corresponding visual scene.
• Inhibition Of Return (IOR, Posner, 1980)
IOR operates to decrease the likelihood that a previsously inspected item in the
visual scene will be reinspected.
→ Premotor Theory of Attention (Rizzolati, 1987)
Attention may derive from weaker activation of same fronto-parietal circuits.
32
Making saccades
Occular saccades lead to drastic changes in visual perception.
33
Visual anticipation
Spatial reference
• Independent of eye movements
• Eye-centered
Action in perception
• To anticipate the consequences of
own actions
• To update working memory
accordingly
Bias/Gating
Saliency
Memory
Anticipation
Update
Saccade
Bias
Focus
Prediction
Input
Competition
Memorization
34
A model of covert and overt attention
Search task
The camera is placed in front of a
visual scene and is able to pan and
tilt. The task can be either to look for a
specific orientation or colour or to
look for a conjunction of such features.
Visual Scene
Camera position
Visual Field
Camera image
35
A model of covert and overt attention
Memorized
locations
Working
memory Anticipation
Saliency Focus
Switch
Current
memory
Prediction
Gating
Competition
Update Prepared
saccade
Spatial
inhibition
Spatial processing
Orientation
filters
Color filters
Feature maps
Spatial bias
Perceived
features
Target
Feature processing
Motor commands
SwitchMove
Feature based
attention
Spatial
attention
36
A model of covert and overt attention
Time
• Feature based attention facilitates processing of relevant features
• Spatial based attention facilitates processing of relevant region
• Working memory prevents to explore already seen location
• Model exhibits both overt and covert attention using same substrate
37
Towards the organization of visual behavior
A bottom-up sequential exploratory behavior has emerged based on distributed &
numeric computation but...
From an automated behavior...
• Visual attention can be spatialy or featurally biased
• Most salient stimulus are likely to be attended
• How to circumvent this automated behavior ?
...to a motivated one
• To consider saccadic behavior as a motivated exploration
• To make hypothesis about the world make saccades to try to confirm them
38
Decision
Decision

Making
How a decision is made ?
Equation
Let u(x,t) be the membrane potential at position x and time t, f a transfer function and
w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by:
τ
time constant
·
∂u(x, t)
∂t
= −u(x, t)
leak term
+
∫ +∞
−∞
w(x, y) · f(u(y, t))
lateral interactions
dy + I(x)
input
+ h
resting potential
No decision Noisy decision
40
A degenerated neural field



˙x = α × (1 − x) + (x − y) × (1 − x), x > 0
˙y = α × (1 − y) + (y − x) × (1 − y), y > 0
0.0 0.2 0.4 0.6 0.8 1.0
x position
0.0
0.2
0.4
0.6
0.8
1.0
yposition
250 trajectories of a dual particle system (x,y)
41
Superior Colliculus
42
Superior colliculus
Superficial layers
I (SZ) II (SGS) III (SO)
Intermediate layers
IV (SGI) V (SAI)
Deep layers
VI (SGP) VII (SAP)
Brainstem
Retina
LGN
Visual
Associative
Motor/Sensory
Basal ganglia
• I (SZ): stratum zonale
• II(SGS): stratum griseum superficiale
• III (SO): stratum opticum
• IV (SGI): stratum griseum intermediale
• V (SAI): stratum album intermediale
• VI (SGP): stratum griseum profundum
• VII (SAP): stratum album profundum
43
Superior colliculus
How are saccades encoded
• Population coding ? sum ? average ?
• What level of precision ?
• What does the receptive fields look like ?
• What is the influence of lesions ?
How decision is made ?
• What if two stimuli are presented ?
• What are the preferred stimuli ?
What is the dynamic ?
• What is the influence of stimulus size, magnitude or position ?
• What is the influence of distractors ?
44
Many computational models
Logarithmic projection
• (Optican 1995)
• (Lefèvre 1998)
• (Trappenberg 2001)
• (Nakahara, 2006)
• (Marino, 2008)
• ...
Homogeneous computation
• (Droulez & Berthoz, 1991)
• (Arai et al., 1994)
• (Gancarz & Grossberg, 1999)
• (Trappenberg, 2001)
• (Schneider & Erlhager, 2002)
• (Nakahara et al., 2006)
• (Marino 2012)
• ....
45
Logarithmic projection
5°
10°
20°
40°
80°
-90°
-45°
0°
45°
90°
2°
5°
10°
20° 40° 80°
-90°
-45°
0°
45°
90°
46
A minimal model
47
Receptive fields
0 5 10 15 20 25
Target eccentricity (◦
)
0
400Hz
500Hz
Dischargerateratio
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 1.00
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.24
48
Influence of stimuli size
0 500 1000 1500 2000 2500
Time from stimulus onset (ms)
0
400 Hz
500Hz
DischargeRate(Hz)
Saccade Trigger Treshold
Relative magnitude
0.50
0.75
1.00
1.50
2.50
3.00
5.00
0 1 2 3 4 5 6
Stimulus Relative Magnitude
0
200
400
600
800
1000
1200
1400
1600
Responsetime(msec)
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 1.00
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 1.00
49
Influence of stimuli magnitude
0 500 1000 1500 2000 2500
Time from stimulus onset (ms)
0
400 Hz
500Hz
DischargeRate(Hz)
Saccade Trigger Treshold
Size
0.50
0.75
1.00
1.25
1.50
2.00
2.50
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Stimulus Size (°)
0
200
400
600
800
1000
1200
1400
1600
Responsetime(msec)
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 1.00
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 4.98 0.00 1.00
50
Influence of stimuli eccentricity
0 500 1000 1500 2000 2500
Time from stimulus onset (ms)
0
400 Hz
500Hz
DischargeRate(Hz)
Saccade Trigger Treshold
Eccentricity
1.0◦
1.5◦
2.0◦
3.0◦
4.0◦
5.0◦
10.0◦
15.0◦
0 5 10 15 20
Stimulus Eccentricity (°)
0
200
400
600
800
1000
1200
1400
1600
Responsetime(msec)
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 1.00
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.59
51
Decision
20 30 40 50 60 70 80
Relative distance between targets [°]
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
Normalizedyposition
A
B
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.55
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.61
52
Dynamics
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.60
0°
10°
20°
40°
80°
-90°
-60°
-30°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 1.00 0.00 0.61
Azimuth [°]
50
0
50
Time [ms]
0
50
100
150
200
250
Dischargerate[Hz]
0
100
200
300
400
500
Azimuth [°]
50
0
50
Time [ms]
0
50
100
150
200
250
Dischargerate[Hz]
0
100
200
300
400
500
53
Encoding precision
2°
5°
10°
20°
40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20°
40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 0.02
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 0.08
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 0.20
2°
5°
10°
20° 40° 80°
-90°
-60°
-30°
0°
30°
60°
90°
0.00 0.28
54
Conclusion
Major cognitive and behavioral functions emerge from such sensorimotor loops
involving the external world, the body and the brain. We study, model
Embodiment constrains decision
The very shape of the retina provide an implicit computation that influence the final
decision on where to saccade.
55
Plasticity
Cortical

Plasticity
The Somatosensory System
Donald O. Hebb
• Neurons that fire together wire together
Hubel and Wiesel
• Simple and complex cells (1959)
• Ocular dominance columns (1962)
• Critical period, no plasticity after that period (1963-1965)
Merzenich, Kaas and Rasmusson
• Cortical organization of the primary somatosensory cortex (1981)
• Reorganization of the adult primary somatosensory cortex (1983)
57
The Somatosensory System
58
Plasticity in the Somatosensory System
Area 3b
Topographic organization of somatosensory
cortical area 3b of owl monkeys after dorsal
column transection.
A. Normal somatotopy of the hand representation
B. Complete dorsal column section at cervical
levels deprives the hand representation of all
activating inputs
C. Over the course of weeks, the influence of the
spared inputs expands
59
Plasticity in the Somatosensory System
• When, where and how organization occurs in the first place ?
• How representations can be both stable and plastic ?
• How to cope with cortical and/or sensory lesions ?
• Do current computational models give a fair account on cortical plasticity ?
• Are there other mechanisms or structures involved ?
• What is actually represented through cortical activity ?
• What is the role ot the motor-sensory loop ?
60
Self-Organizing maps
Self-organization...
• Simple 2D topology
• Unsupervised learning
• Density driven
but...
• Decreasing neighborhood & learning rate
• Frozen terminal state
• Winner-takes-all algorithm
61
Neural Gas
Efficient VQ...
• Density driven
• Unsupervised learning
• No dead units
but...
• A posteriori topology
• Decreasing learning rate
• Frozen terminal state
• Winner-takes-all algorithm
62
Dynamic Self-Organizing maps
To what extent it is possible to have both stable and dynamic representations ?
Dynamic
The model must dynamically adapts itself to the data.
Stability
Model representations must be stable if the input is stable.
Topology
Two physically neighborhood cells mut have similar representations.
63
Dynamic Self-Organizing maps
DSOM is a neural map equipped with a structure (a hypercube or hexagonal lattice)
and each neuron i is assigned a fixed position pi in Rq where q is the dimension of
the lattice (usually 1 or 2). The learning process is an iterative process where vectors
v ∈ Ω are sequentially presented to the map with respect to the probability density
function f. For each presented vector v, a winner s ∈ N is determined and all codes
wi from the codebook W are shifted towards v according to
∆wi = ε∥v − wi∥Ω hη(i, s, v) (v − wi)
64
Dynamic Self-Organizing maps
Learning rate is modulated
using the closeness of the
winner to the data.
hη(i, s, v) = e
− 1
η2
∥pi−ps∥2
∥v−ws∥2
Ω
65
Dynamic Self-Organizing maps
66
Dynamic Self-Organizing maps
67
Dynamic Self-Organizing maps
Dynamic...
• Simple 2D topology
• Unsupervised learning
• No decreasing parameters
but...
• Winner-takes-all algorithm
• Elasticity tuning
68
Neurophysiological evidence
Laminar organization
• Six horizontal layers
Columnar organization
• minicolumns
• maxicolumns
Topographic organization
• retinotopy
• somatotopy
• sonototopy
69
Dynamic Neural Fields
Equation
Let u(x,t) be the membrane potential at position x and time t, f a transfer function and
w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by:
τ
time constant
·
∂u(x, t)
∂t
= −u(x, t)
leak term
+
∫ +∞
−∞
w(x − y) · f(u(y, t))
lateral interactions
dy + I(x)
input
+ h
resting potential
Matching property
Input = 0.25 Input = 0.50 Input = 0.75 Input = 1.00
70
Dynamic Neural Fields
Dynamic gain modulation
Dynamic gain enforces competition and can further modulate learning.
A
Slice
0.49 0.81
0
1
Discargerate
Slice detail
Trigger threshold
B
Slice
0.53 0.77
0
1
Discargerate
Trigger threshold
Slice detail
C
Slice
0.55 0.75
0
1
Discargerate
Trigger threshold
Slice detail
0.00 1.25 0.00 1.25 0.00 1.25
71
Dynamic Neural Fields
Competition
Let u(x,t) be the membrane potential at position x and time t, f a transfer function and
w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by:
τ
time constant
·
∂u(x, t)
∂t
= −u(x, t)
leak term
+
∫ +∞
−∞
wl(x, y) · f(u(y, t))
lateral interactions
dy + I(x)
input
+ h
resting potential
Learning
Learning occurs at every time step.
τ
time constant
·
∂wf(x, t)
∂t
= γ
learning rate
(
s(z, t) − wf(x, t)
)
thalamo-cortical
∫ +∞
−∞
we(x, y)
excitatory lateral
f(u(y, t))dy
Using wl(x, y) = we(x, y) − wi(x, y) = Ke exp
(
−d2
2σ2
e
)
− Ki exp
(
−d2
2σ2
i
)
72
Computational model of area 3b
Skin model
0.2 mm5 mm40 mm
A B C
Non Toric Toric
73
Computational model of area 3b
• Neural field promotes competition
• Lateral connections are fixed and
dynamic
• Feed-forwards connections are plastic
• Learning shapes receptive fields
Cortical Layer
Neuron
wf
Input Layer
Stimulus
Receptor
we(x)
wi(x)
74
Computational model of area 3b
• Model has been trained on 50000
random samples
• Learning occurs at every time step
• Thalamo-cortical connections have
been shaped
• Receptive fields covers uniformly the
skin patch
• Topology is enforced everywhere
75
Computational model of area 3b
Temporal evolution of a receptive field
The shaping of receptive fields occurs through an early expansion stage followed by a
shrinking and a specialization stage.
76
Cortical lesion
• 25% of neurons are killed
• 3 types of lesion
• Reorganization in three phases
• Silence
• Expansion
• Shrinkage
• Expansion to non-represented
skin areas.
• Partial recovery
77
Cortical lesion
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
A
Reference (REF)
(Mean:0.00%, STE: 0.6)
# Cells
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
B
Cortical Lesion (CL)
(Mean:20.07%, STE: 2.9)
# Cells
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
C
Center Cortical Lesion (CCL)
(Mean:19.86%, STE: 3.1)
# Cells
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
D
Boundary Cortical Lesion (BCL)
(Mean:19.90%, STE: 2.9)
# Cells
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
REFsize: 0.024 mm2
0 1
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
CLsize: 0.027 mm2
0 1
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
CCLsize: 0.046 mm2
0 1
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
BCLsize: 0.016 mm2
0 1
78
Sensory deprivation
• 25% of receptors are silenced
• 3 types of lesion
• Reorganization in three phases
• Silence
• Expansion
• Shrinkage
• Migration of receptive fields
• Full recovery
79
Sensory lesion
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
B
Skin Lesion (SL)
(Mean:20.84%, STE: 3.9)
# Cells
-50% 0 +50%
0
20
40
60
80
100
120
140
160
180
200
C
Center Skin Lesion (CSL)
(Mean:20.79%, STE: 3.0)
# Cells
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
REFsize: 0.024 mm2
0 1
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0(mm) SLsize: 0.016 mm2
0 1
0.0 0.2 0.4 0.6 0.8 1.0
(mm)
0.0
0.2
0.4
0.6
0.8
1.0
(mm)
CSLsize: 0.022 mm2
0 1
80
Structure of Receptive Fields...
Stimulus
Surface
200 microns
shift
Random dot pattern
Receptive Field
Surface
2.0 mm
5 mm
B
C
40 mm
A
81
Structure of Receptive Fields...
82
Influence of attention...
5 10 30
Excitatory area (mm2)
5
10
30
Inhibitoryarea(mm2
n = 1024
83
Some questions received (hypothetical) answers
✓ When, where and how organization occurs in the first place ?
✓ How representations can be both stable and plastic ?
✓ How to cope with cortical and/or sensory lesions ?
✓ Do current computational models give a fair account on cortical plasticity ?
□ Are there other mechanisms or structures involved ?
□ What is actually represented through cortical activity ?
□ What is the role ot the motor-sensory loop ?
84
Conclusion
Conclusion
Neural fields
• Powerful modeling tool
• Strong mathematical framework
• Experimental evidences
Cognition
• Still many questions to be addressed
• Embodiment and emergence are key concepts
• Mathematical analysis unlikely
Mathematical solutions do not characterize functional blocks
Filter Decision Tracking Memory
85
Is there something like an objective behavior ?
Curious (visual tracking) ?
Saliency
Input
Focus
C
om
petition
Camera
We can connect the model to a pan-tilt camera
such that it follows a given stimulus
Shy (visual avoidance) ?
Saliency
Input
Focus
C
om
petition
Camera
We can connect the model to a pan-tilt camera
such that it looks away from a given stimulus
The actual behavior of the model depends on the links to its body. Ultimately, the
modeler is the one who decide on the behavior.
86
What is a model ?
Supposons qu’un être (ou une situation) extérieur(e) X présente un comportement énigmatique, et
que nous nous posions à son sujet une (ou plusieurs) question(s). Pour répondre à cette question,
on va s’efforcer de modéliser X, c’est-à-dire, on va construire un objet (réel ou abstrait) M, considéré
comme l’image, l’analogue de X : M sera dit le modèle de X.
R. Thom, Modélisation et scientificité, 1978
Question (Q')
Question (Q)
Being (X)
Analogy
Model (M)
Answer (A')
Answer (A)
To an observer B, an object A* is a model of an object A to the extent that B can use A* to answer
questions that interest him about A.
M. Minsky, Matter, Mind and Models, 1965
87
Evaluation of models
The standard model (theory)
provides a direct access to the question
MODEL OBSERVER
88
Evaluation of models
The standard model (theory)
provides a direct access to the question
The computational model
objective mathematical properties
subjective functional interpretations
Brain
MODEL OBSERVER
Brain
88
Evaluation of models
The standard model (theory)
provides a direct access to the question
The computational model
objective mathematical properties
subjective functional interpretations
The embodied model
behavior through embodiment
quantifiable performances
Brain
Body
MODEL OBSERVER
Brain
Body
88
Evaluation of models
The standard model (theory)
provides a direct access to the question
The computational model
objective mathematical properties
subjective functional interpretations
The embodied model
behavior through embodiment
quantifiable performances
The cognitive model
observation through interaction
interpretation may depends on our own behavior
Brain
Body
SENSORY/MOTOR
World
MODEL
OBSERVATION
INTERACTION
OBSERVER
Brain
Body
SENSORY/MOTOR
World
88
All code available on github or my homepage
• http://www.labri.fr/perso/nrougier/
• https://github.com/rougier
If not, mail to nicolas.rougier@inria.fr
89
Conclusion

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Neural fields, a cognitive approach

  • 1. Neural Fields, a Cognitive Approach Attention, Decision & Plasticity Nicolas P. Rougier Inria - Institute of Neurodegenerative Diseases - Bordeaux, France Computational Neuroscience Course - Nice, April 1st , 2019
  • 3. Mnemosyne Project Major cognitive and behavioral functions emerge from adaptive sensorimotor loops involving the external world, the body and the brain. We study, model and implement such loops and their interactions toward a fully autonomous behavior. With such a systemic approach, we mean that such complex systems can only be truly apprehended as a whole and in natural behavioral situation.
  • 4. What is cognition ? What are the questions ? • What are the main forms of cognition ? • What are the minimal mechanisms ? • What is/are the right biological levels ? • How do we identify a satisfactory answer ? • What is the role of the observer ?
  • 5. Many definitions, many forms, many species 4
  • 6. The case of Caenorhabditis elegans Sensory motor behavior Q. Wen, M.D. Po, E. Hulme, S. Chen, X. Liu, S. Wai Kwok, M. Gershow, A. M. Leifer, V. Butler, C. Fang-Yen, T. Kawano, W.R. Schafer, G. Whitesides, M. Wyart, D.B. Chklovskii, M. Zhen, A.D.T. Samueln, Proprioceptive Coupling within Motor Neurons Drives C. elegans Forward Locomotion. Neuron, 2012. Plasticity, learning and memory H. Sasakura and I. Mori, Behavioral plasticity, learning, and memory in C. elegans, Current Opinion in Neurobiology, 2013. Decision making T.A. Jarrell, Y. Wang, A.E. Bloniarz, C.A. Brittin, M. Xu, J.N. Thomson, D.G. Albertson, D.H. Hall, S.W. Emmons, The Connectome of a Decision-Making Neural Network, Science, 2012. 5
  • 7. What really matters for cognition ? Some figures • C.Elegans → 302 neurons • Mouse → 71,000,000 neurons • Rat → 200,000,000 neurons • Macaque → 6,376,000,000 neurons • Human → 86,000,000,000 neurons The human brain in numbers [...], S. Herculano-Houzel, Frontier in Human Neuroscience, 2009 6
  • 8. What really matters for cognition ? Specific structures ? • Neocortex • Basal Ganglia • Amygdala • Frontal cortex Specific architecture ? • Connectivity • Density • Modularity • Self-organisation Specific abilities ? • To recognize self/others • To imitate • To use tools • To communicate 7
  • 9. Theoretical frameworks Biological framework → Anatomical facts → Physiological recordings → Experimental data Cognitive framework → Subsumption architecture → Embodied cognition → Affordances, emotions, etc. Computational framework → Computational paradigm → Plasticity & learning → Evaluation of models Philosophical framework → Strong AI / Weak AI → Emergence → Theories of mind 8
  • 10. Where do we start ? What is/are the right biological level(s) of description ? • Molecule ? → neurotransmitters • Organelle ? → axons, dendrites, synapses • Cell ? → neurons, glial cells • Tissue ? → brain lobes & structures • Organ ? → brain Neural fields, between cells and tissue → Complex Dynamic → Large population → Fast simulation 9
  • 11. Spatio-temporal framework Continuous space ... stable patterns of neuronal activation ultimately steer the periphery into dynamical states, from which behavior emerges, without any need to ever ab- stract from the space-time contiguous processes that embody cognition. G.Schöner (2008) Continuous time The first challenge is that sensori-motor systems evolve continuously in real time, but cognition can jump from one state to another, that is, from one thought to another Spencer et al. (2009) 10
  • 12. Computational Framework A unit is a set of arbitrary values that can vary along time under the influence of other units and learning. • Distributed → No supervisor nor executive • Asynchronous → No central clock • Numerical → No symbols • Adaptive → No a priori knowledge Group Group Unit Link Layer Link Value Value Value We want to make sure that emerging properties are those of the model and not those of the software running the model (see dana.loria.fr). 11
  • 13. Neural Fields Equation Let u(x,t) be the membrane potential at position x and time t, f a transfer function and w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by: τ time constant · ∂u(x, t) ∂t = −u(x, t) leak term + ∫ +∞ −∞ w(x, y) · f(u(y, t)) lateral interactions dy + I(x) input + h resting potential Velocity Unless specified otherwise, we’ll generally consider infinite speed, i.e. instantaneous transmission of information. 12
  • 14. Neural Fields Function The activity of a neural field can be interpreted from a functional point of view. Filter Decision Tracking Memory Measure Using a specific set of parameters, the activity of a neural field can also be interpreted as a measure of the input. Input = 0.25 Input = 0.50 Input = 0.75 Input = 1.00 13
  • 17. On ne voit que ce que l’on regarde Everyone knows what attention is. It is the possession by the mind, in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought. Focalization, concentration, of consciousness are of its essence. It implies withdrawal from some things in order to deal effectively with others, and is a condition which has a real opposite in the confused, dazed, scatterbrained state which in French is called distraction, and Zerstreutheit in German. W. James, (1890) 15
  • 18. How much blind are you ? 16
  • 19. The grand illusion of seeing... • Images on retina are formed upside-down • There is a blind spot on the retina where optic nerves passes throught it • Retina receptors are not uniformly distributed over the surface of the retina • Eye is always moving even when fixing a point (micro-tremors) 17
  • 20. The many visual pathways The dorsal pathway • Where or How pathway • Motion and object locations The ventral pathway • What pathway • Form and object representation The frontal pathway • Executive control • Organization of behavior • Visual Awareness 32 cortical areas, 10 hierarchical levels 18
  • 22. Attention Clinical Description (Sohlberg & Mateer, 1989) Focused to respond discretely to a specific stimuli. Sustained to maintain a consistent behavioral response Selective to maintain attention in the face of distractors Alternating to shift focus of attention Divided to respond simultaneously to multiple tasks Cognitive Description Motor movements preparation, priming, etc. Sensory auditory, visual, proprioception, etc. Overt motor response (explicit) Covert cognitive response (implicit) Top-down goal driven, bias, etc. Bottom-Up stimulus driven, pop-out, etc. 20
  • 23. Visual Attention Spotlight metaphor Attention is the capacity to select a relevant region of the sensory space • Topological region of the sensory space → spatial attention • Featural region of the sensory space → feature oriented attention • Object as such → object oriented attention 21
  • 28. A computational approach Theories of Visual Attention → Saliency Maps (Itti & Koch, 2001) Saliency map is a topographically arranged map that represents visual saliency of a corresponding visual scene. • Inhibition Of Return (IOR, Posner, 1980) IOR operates to decrease the likelihood that a previsously inspected item in the visual scene will be reinspected. • Premotor Theory of Attention (Rizzolati, 1987) Attention may derive from weaker activation of same fronto-parietal circuits. 26
  • 30. Saliency maps • Simple model of visual tracking • Robustness to noise, distractors and saliency • Dynamic & reactive behavior Saliency Input Focus Competition 28
  • 31. A computational approach Theories of Visual Attention • Saliency Maps (Itti & Koch, 2001) Saliency map is a topographically arranged map that represents visual saliency of a corresponding visual scene. → Inhibition Of Return (IOR, Posner, 1980) IOR operates to decrease the likelihood that a previsously inspected item in the visual scene will be reinspected. • Premotor Theory of Attention (Rizzolati, 1987) Attention may derive from weaker activation of same fronto-parietal circuits. 29
  • 32. Inhibition of Return Fixation frame Uncued Cued Cue Time 0 100 200 300 400 500 Cue Target SOA (ms) 350 375 400 425 Reactiontime(ms) Cued Uncued 30
  • 33. Inhibition of Return • Dynamic Working memory • Biased competition • Sequential behavior Saliency Memory Update Input Focus Memorization Bias/Gating Competition 31
  • 34. A computational approach Theories of Visual Attention • Saliency Maps (Itti & Koch, 2001) Saliency map is a topographically arranged map that represents visual saliency of a corresponding visual scene. • Inhibition Of Return (IOR, Posner, 1980) IOR operates to decrease the likelihood that a previsously inspected item in the visual scene will be reinspected. → Premotor Theory of Attention (Rizzolati, 1987) Attention may derive from weaker activation of same fronto-parietal circuits. 32
  • 35. Making saccades Occular saccades lead to drastic changes in visual perception. 33
  • 36. Visual anticipation Spatial reference • Independent of eye movements • Eye-centered Action in perception • To anticipate the consequences of own actions • To update working memory accordingly Bias/Gating Saliency Memory Anticipation Update Saccade Bias Focus Prediction Input Competition Memorization 34
  • 37. A model of covert and overt attention Search task The camera is placed in front of a visual scene and is able to pan and tilt. The task can be either to look for a specific orientation or colour or to look for a conjunction of such features. Visual Scene Camera position Visual Field Camera image 35
  • 38. A model of covert and overt attention Memorized locations Working memory Anticipation Saliency Focus Switch Current memory Prediction Gating Competition Update Prepared saccade Spatial inhibition Spatial processing Orientation filters Color filters Feature maps Spatial bias Perceived features Target Feature processing Motor commands SwitchMove Feature based attention Spatial attention 36
  • 39. A model of covert and overt attention Time • Feature based attention facilitates processing of relevant features • Spatial based attention facilitates processing of relevant region • Working memory prevents to explore already seen location • Model exhibits both overt and covert attention using same substrate 37
  • 40. Towards the organization of visual behavior A bottom-up sequential exploratory behavior has emerged based on distributed & numeric computation but... From an automated behavior... • Visual attention can be spatialy or featurally biased • Most salient stimulus are likely to be attended • How to circumvent this automated behavior ? ...to a motivated one • To consider saccadic behavior as a motivated exploration • To make hypothesis about the world make saccades to try to confirm them 38
  • 43. How a decision is made ? Equation Let u(x,t) be the membrane potential at position x and time t, f a transfer function and w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by: τ time constant · ∂u(x, t) ∂t = −u(x, t) leak term + ∫ +∞ −∞ w(x, y) · f(u(y, t)) lateral interactions dy + I(x) input + h resting potential No decision Noisy decision 40
  • 44. A degenerated neural field    ˙x = α × (1 − x) + (x − y) × (1 − x), x > 0 ˙y = α × (1 − y) + (y − x) × (1 − y), y > 0 0.0 0.2 0.4 0.6 0.8 1.0 x position 0.0 0.2 0.4 0.6 0.8 1.0 yposition 250 trajectories of a dual particle system (x,y) 41
  • 46. Superior colliculus Superficial layers I (SZ) II (SGS) III (SO) Intermediate layers IV (SGI) V (SAI) Deep layers VI (SGP) VII (SAP) Brainstem Retina LGN Visual Associative Motor/Sensory Basal ganglia • I (SZ): stratum zonale • II(SGS): stratum griseum superficiale • III (SO): stratum opticum • IV (SGI): stratum griseum intermediale • V (SAI): stratum album intermediale • VI (SGP): stratum griseum profundum • VII (SAP): stratum album profundum 43
  • 47. Superior colliculus How are saccades encoded • Population coding ? sum ? average ? • What level of precision ? • What does the receptive fields look like ? • What is the influence of lesions ? How decision is made ? • What if two stimuli are presented ? • What are the preferred stimuli ? What is the dynamic ? • What is the influence of stimulus size, magnitude or position ? • What is the influence of distractors ? 44
  • 48. Many computational models Logarithmic projection • (Optican 1995) • (Lefèvre 1998) • (Trappenberg 2001) • (Nakahara, 2006) • (Marino, 2008) • ... Homogeneous computation • (Droulez & Berthoz, 1991) • (Arai et al., 1994) • (Gancarz & Grossberg, 1999) • (Trappenberg, 2001) • (Schneider & Erlhager, 2002) • (Nakahara et al., 2006) • (Marino 2012) • .... 45
  • 51. Receptive fields 0 5 10 15 20 25 Target eccentricity (◦ ) 0 400Hz 500Hz Dischargerateratio 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 1.00 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.24 48
  • 52. Influence of stimuli size 0 500 1000 1500 2000 2500 Time from stimulus onset (ms) 0 400 Hz 500Hz DischargeRate(Hz) Saccade Trigger Treshold Relative magnitude 0.50 0.75 1.00 1.50 2.50 3.00 5.00 0 1 2 3 4 5 6 Stimulus Relative Magnitude 0 200 400 600 800 1000 1200 1400 1600 Responsetime(msec) 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 1.00 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 1.00 49
  • 53. Influence of stimuli magnitude 0 500 1000 1500 2000 2500 Time from stimulus onset (ms) 0 400 Hz 500Hz DischargeRate(Hz) Saccade Trigger Treshold Size 0.50 0.75 1.00 1.25 1.50 2.00 2.50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Stimulus Size (°) 0 200 400 600 800 1000 1200 1400 1600 Responsetime(msec) 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 1.00 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 4.98 0.00 1.00 50
  • 54. Influence of stimuli eccentricity 0 500 1000 1500 2000 2500 Time from stimulus onset (ms) 0 400 Hz 500Hz DischargeRate(Hz) Saccade Trigger Treshold Eccentricity 1.0◦ 1.5◦ 2.0◦ 3.0◦ 4.0◦ 5.0◦ 10.0◦ 15.0◦ 0 5 10 15 20 Stimulus Eccentricity (°) 0 200 400 600 800 1000 1200 1400 1600 Responsetime(msec) 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 1.00 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.59 51
  • 55. Decision 20 30 40 50 60 70 80 Relative distance between targets [°] 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 Normalizedyposition A B 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.55 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.61 52
  • 56. Dynamics 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.60 0° 10° 20° 40° 80° -90° -60° -30° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 1.00 0.00 0.61 Azimuth [°] 50 0 50 Time [ms] 0 50 100 150 200 250 Dischargerate[Hz] 0 100 200 300 400 500 Azimuth [°] 50 0 50 Time [ms] 0 50 100 150 200 250 Dischargerate[Hz] 0 100 200 300 400 500 53
  • 57. Encoding precision 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 0.02 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 0.08 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 0.20 2° 5° 10° 20° 40° 80° -90° -60° -30° 0° 30° 60° 90° 0.00 0.28 54
  • 58. Conclusion Major cognitive and behavioral functions emerge from such sensorimotor loops involving the external world, the body and the brain. We study, model Embodiment constrains decision The very shape of the retina provide an implicit computation that influence the final decision on where to saccade. 55
  • 61. The Somatosensory System Donald O. Hebb • Neurons that fire together wire together Hubel and Wiesel • Simple and complex cells (1959) • Ocular dominance columns (1962) • Critical period, no plasticity after that period (1963-1965) Merzenich, Kaas and Rasmusson • Cortical organization of the primary somatosensory cortex (1981) • Reorganization of the adult primary somatosensory cortex (1983) 57
  • 63. Plasticity in the Somatosensory System Area 3b Topographic organization of somatosensory cortical area 3b of owl monkeys after dorsal column transection. A. Normal somatotopy of the hand representation B. Complete dorsal column section at cervical levels deprives the hand representation of all activating inputs C. Over the course of weeks, the influence of the spared inputs expands 59
  • 64. Plasticity in the Somatosensory System • When, where and how organization occurs in the first place ? • How representations can be both stable and plastic ? • How to cope with cortical and/or sensory lesions ? • Do current computational models give a fair account on cortical plasticity ? • Are there other mechanisms or structures involved ? • What is actually represented through cortical activity ? • What is the role ot the motor-sensory loop ? 60
  • 65. Self-Organizing maps Self-organization... • Simple 2D topology • Unsupervised learning • Density driven but... • Decreasing neighborhood & learning rate • Frozen terminal state • Winner-takes-all algorithm 61
  • 66. Neural Gas Efficient VQ... • Density driven • Unsupervised learning • No dead units but... • A posteriori topology • Decreasing learning rate • Frozen terminal state • Winner-takes-all algorithm 62
  • 67. Dynamic Self-Organizing maps To what extent it is possible to have both stable and dynamic representations ? Dynamic The model must dynamically adapts itself to the data. Stability Model representations must be stable if the input is stable. Topology Two physically neighborhood cells mut have similar representations. 63
  • 68. Dynamic Self-Organizing maps DSOM is a neural map equipped with a structure (a hypercube or hexagonal lattice) and each neuron i is assigned a fixed position pi in Rq where q is the dimension of the lattice (usually 1 or 2). The learning process is an iterative process where vectors v ∈ Ω are sequentially presented to the map with respect to the probability density function f. For each presented vector v, a winner s ∈ N is determined and all codes wi from the codebook W are shifted towards v according to ∆wi = ε∥v − wi∥Ω hη(i, s, v) (v − wi) 64
  • 69. Dynamic Self-Organizing maps Learning rate is modulated using the closeness of the winner to the data. hη(i, s, v) = e − 1 η2 ∥pi−ps∥2 ∥v−ws∥2 Ω 65
  • 72. Dynamic Self-Organizing maps Dynamic... • Simple 2D topology • Unsupervised learning • No decreasing parameters but... • Winner-takes-all algorithm • Elasticity tuning 68
  • 73. Neurophysiological evidence Laminar organization • Six horizontal layers Columnar organization • minicolumns • maxicolumns Topographic organization • retinotopy • somatotopy • sonototopy 69
  • 74. Dynamic Neural Fields Equation Let u(x,t) be the membrane potential at position x and time t, f a transfer function and w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by: τ time constant · ∂u(x, t) ∂t = −u(x, t) leak term + ∫ +∞ −∞ w(x − y) · f(u(y, t)) lateral interactions dy + I(x) input + h resting potential Matching property Input = 0.25 Input = 0.50 Input = 0.75 Input = 1.00 70
  • 75. Dynamic Neural Fields Dynamic gain modulation Dynamic gain enforces competition and can further modulate learning. A Slice 0.49 0.81 0 1 Discargerate Slice detail Trigger threshold B Slice 0.53 0.77 0 1 Discargerate Trigger threshold Slice detail C Slice 0.55 0.75 0 1 Discargerate Trigger threshold Slice detail 0.00 1.25 0.00 1.25 0.00 1.25 71
  • 76. Dynamic Neural Fields Competition Let u(x,t) be the membrane potential at position x and time t, f a transfer function and w a kernel of lateral interaction. The temporal evolution of u(x,t) is given by: τ time constant · ∂u(x, t) ∂t = −u(x, t) leak term + ∫ +∞ −∞ wl(x, y) · f(u(y, t)) lateral interactions dy + I(x) input + h resting potential Learning Learning occurs at every time step. τ time constant · ∂wf(x, t) ∂t = γ learning rate ( s(z, t) − wf(x, t) ) thalamo-cortical ∫ +∞ −∞ we(x, y) excitatory lateral f(u(y, t))dy Using wl(x, y) = we(x, y) − wi(x, y) = Ke exp ( −d2 2σ2 e ) − Ki exp ( −d2 2σ2 i ) 72
  • 77. Computational model of area 3b Skin model 0.2 mm5 mm40 mm A B C Non Toric Toric 73
  • 78. Computational model of area 3b • Neural field promotes competition • Lateral connections are fixed and dynamic • Feed-forwards connections are plastic • Learning shapes receptive fields Cortical Layer Neuron wf Input Layer Stimulus Receptor we(x) wi(x) 74
  • 79. Computational model of area 3b • Model has been trained on 50000 random samples • Learning occurs at every time step • Thalamo-cortical connections have been shaped • Receptive fields covers uniformly the skin patch • Topology is enforced everywhere 75
  • 80. Computational model of area 3b Temporal evolution of a receptive field The shaping of receptive fields occurs through an early expansion stage followed by a shrinking and a specialization stage. 76
  • 81. Cortical lesion • 25% of neurons are killed • 3 types of lesion • Reorganization in three phases • Silence • Expansion • Shrinkage • Expansion to non-represented skin areas. • Partial recovery 77
  • 82. Cortical lesion -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 A Reference (REF) (Mean:0.00%, STE: 0.6) # Cells -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 B Cortical Lesion (CL) (Mean:20.07%, STE: 2.9) # Cells -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 C Center Cortical Lesion (CCL) (Mean:19.86%, STE: 3.1) # Cells -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 D Boundary Cortical Lesion (BCL) (Mean:19.90%, STE: 2.9) # Cells 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) REFsize: 0.024 mm2 0 1 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) CLsize: 0.027 mm2 0 1 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) CCLsize: 0.046 mm2 0 1 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) BCLsize: 0.016 mm2 0 1 78
  • 83. Sensory deprivation • 25% of receptors are silenced • 3 types of lesion • Reorganization in three phases • Silence • Expansion • Shrinkage • Migration of receptive fields • Full recovery 79
  • 84. Sensory lesion -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 B Skin Lesion (SL) (Mean:20.84%, STE: 3.9) # Cells -50% 0 +50% 0 20 40 60 80 100 120 140 160 180 200 C Center Skin Lesion (CSL) (Mean:20.79%, STE: 3.0) # Cells 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) REFsize: 0.024 mm2 0 1 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0(mm) SLsize: 0.016 mm2 0 1 0.0 0.2 0.4 0.6 0.8 1.0 (mm) 0.0 0.2 0.4 0.6 0.8 1.0 (mm) CSLsize: 0.022 mm2 0 1 80
  • 85. Structure of Receptive Fields... Stimulus Surface 200 microns shift Random dot pattern Receptive Field Surface 2.0 mm 5 mm B C 40 mm A 81
  • 86. Structure of Receptive Fields... 82
  • 87. Influence of attention... 5 10 30 Excitatory area (mm2) 5 10 30 Inhibitoryarea(mm2 n = 1024 83
  • 88. Some questions received (hypothetical) answers ✓ When, where and how organization occurs in the first place ? ✓ How representations can be both stable and plastic ? ✓ How to cope with cortical and/or sensory lesions ? ✓ Do current computational models give a fair account on cortical plasticity ? □ Are there other mechanisms or structures involved ? □ What is actually represented through cortical activity ? □ What is the role ot the motor-sensory loop ? 84
  • 90. Conclusion Neural fields • Powerful modeling tool • Strong mathematical framework • Experimental evidences Cognition • Still many questions to be addressed • Embodiment and emergence are key concepts • Mathematical analysis unlikely Mathematical solutions do not characterize functional blocks Filter Decision Tracking Memory 85
  • 91. Is there something like an objective behavior ? Curious (visual tracking) ? Saliency Input Focus C om petition Camera We can connect the model to a pan-tilt camera such that it follows a given stimulus Shy (visual avoidance) ? Saliency Input Focus C om petition Camera We can connect the model to a pan-tilt camera such that it looks away from a given stimulus The actual behavior of the model depends on the links to its body. Ultimately, the modeler is the one who decide on the behavior. 86
  • 92. What is a model ? Supposons qu’un être (ou une situation) extérieur(e) X présente un comportement énigmatique, et que nous nous posions à son sujet une (ou plusieurs) question(s). Pour répondre à cette question, on va s’efforcer de modéliser X, c’est-à-dire, on va construire un objet (réel ou abstrait) M, considéré comme l’image, l’analogue de X : M sera dit le modèle de X. R. Thom, Modélisation et scientificité, 1978 Question (Q') Question (Q) Being (X) Analogy Model (M) Answer (A') Answer (A) To an observer B, an object A* is a model of an object A to the extent that B can use A* to answer questions that interest him about A. M. Minsky, Matter, Mind and Models, 1965 87
  • 93. Evaluation of models The standard model (theory) provides a direct access to the question MODEL OBSERVER 88
  • 94. Evaluation of models The standard model (theory) provides a direct access to the question The computational model objective mathematical properties subjective functional interpretations Brain MODEL OBSERVER Brain 88
  • 95. Evaluation of models The standard model (theory) provides a direct access to the question The computational model objective mathematical properties subjective functional interpretations The embodied model behavior through embodiment quantifiable performances Brain Body MODEL OBSERVER Brain Body 88
  • 96. Evaluation of models The standard model (theory) provides a direct access to the question The computational model objective mathematical properties subjective functional interpretations The embodied model behavior through embodiment quantifiable performances The cognitive model observation through interaction interpretation may depends on our own behavior Brain Body SENSORY/MOTOR World MODEL OBSERVATION INTERACTION OBSERVER Brain Body SENSORY/MOTOR World 88
  • 97. All code available on github or my homepage • http://www.labri.fr/perso/nrougier/ • https://github.com/rougier If not, mail to nicolas.rougier@inria.fr 89