Morphogenetic “neuron flocking”:
Dynamic self-organization of neural activity into mental shapes René Doursat, http://doursat.iscpif.fr Complex Systems Institute, Paris Ile-de-France / Ecole Polytechnique, Paris / CNRS Gif-sur-Yvette, France THE CASE FOR “MENTAL SHAPES (IMAGERY)” FROM THE COGNITIVE PERSPECTIVE “Abstract” representations should not mandate “symbolic”
Example 1: cognitive linguistics, iconic grammar
→ “analogic” formats preserving the underlying combinatorial complexity are critical!
→ Proposal: semantics is a spatio-temporal affair (not nodes in a parse tree)
in
→ Proposal: graphs representing the same object class are structurally similar and can be matched with each other
IN
traditional logical atomism (set theory): “things” are individuated symbols and “relations” are links connecting these symbols the bird
Example 2: graph representations in vision
TR
(1) (a) the cat in the house
TR
(b) the bird in the garden
by contrast, in the “Gestaltist” or “mereological” conception, things and relations constitute analogic wholes: relations are not taken for granted but emerge together with the objects through segmentation and transformation
TR
(e) the chair in the corner
LM TR
(f) the water in the vase
TR
Institut fuer Neuroinformatik, Bochum
LM
TR LM
(h) the foot in the stirrup
Bienenstock & Doursat (1994)
LM
(g) the crack in the vase
LM metonymy: vase = surface of vase
⇒
TR
(i) ?the finger in the ring
Petitot & Doursat (2011) Cognitive Morphodynamics. Peter-Lang.
TR metonymy: flowers = stems
LM
(d) the bird in the tree
prototype
LM TR
(c) the flowers in the vase
the cage
LM
adapted from Herskovits (1986)
LM
THE CASE FOR “MENTAL SHAPES (PATTERNS) ” FROM THE COMPLEX SYSTEMS PERSPECTIVE The Tower of Complex Systems in Nature
The Tower of Complex Systems in the Brain
Brain anatomy: from neurons to brain, via neural development
Mind function: from neurons to mind, via self-organizing objects made of correlated activity
. . .
NetLogo “Fur”
From cells to patterns and structure, via development
The Tower of Complex Systems in Cognition “John gives a book to Mary”
. . .
⇒
“Mary is the owner of the book”
after Bienenstock (1995, 1996)
BlueColumn
ctivator
synfire chains dynamics (stability, chaos, regimes, bifurcations)
nhibitor IR/regular A/sync activity
EXC
Markram (2006)
Abeles, Bienenstock, Diesmann (1982, 1995, 1999) ex: Freeman (1994) polychronous groups morphodynamics bumps, blobs
INH
Vogels & Abbott (2006) Ramón y Cajal 1900
Petitot, Doursat (1997, 2005)
. . .
Izhikevich (2006)
McCulloch & Pitts Hodgkin & Huxley integrate & fire oscillatory, Izhikevich
. . .
ex: Amari (1975)
Hebb STDP LTP/LTD
THE CASE FOR “MENTAL SHAPES (CORRELATIONS) ” FROM THE NEURAL CODE PERSPECTIVE MORPHOGENETIC “NEURON-FLOCKING”
The Brain as a Pattern Formation Machine
Compositionality from Temporal Correlations
Temporal binding is the “glue” of shape-based composition
Reminder: the importance of temporal coding more than mean rates → temporal correlations among spikes high activity rate
phase space view: complex spatiotemporal pattern = mental shape
high activity rate
rate coding
(dynamic)
Mary
emergence? structure? (long-term) persistence? learning? storage? compositionality? properties?
G
book
O
give
John
R
language, perception, cognition are a game of building blocks
John
high activity rate
G
O
give
book
R
low activity rate
Mary
mental representations are internally structured
low activity rate low activity rate
physical space view: mega-MEA raster plot = activity of 106-108 neurons
temporal coding
G
zero-delays: synchrony
after von der Malsburg (1981) and Abeles (1982)
O
give
elementary components assemble dynamically via temporal binding
ball
R
(1 and 2 more in sync than 1 and 3)
nonzero delays: rhythms
(4, 5 and 6 correlated through delays)
after Bienenstock (1995)
after Shastri & Ajjanagadde (1993)
EXAMPLE: A Neural Dynamics Model of Pattern Storage and Retrieval – Temporally Coding Coordinates by Phases, and Shapes by Waves Wave-based pattern retrieval and matching Lattices of coupled oscillators (zero delays)
group synchronization traveling waves 2D wave shapes shape metric deformation
+ Ii
i ← j coupling features
isotropic proportional to the u signal difference
positive connection weight kij possible transmission delay τij
wave propagation chain growth pattern storage and retrieval
o
only in spiking domain u < 0
o
here zero delays τij = 0
i
kij ,τij
coupling term
input term
Lattice of coupled oscillators – traveling waves Random propagation z = −0.346, I = 0 k = 0.04
Circular wave generation z = −0.29, k = 0.10, I = −0.44 (point stimulus
)
j
kij ,τij
Synfire braids (transitive delays)
τ= 0
τ= 5
Synfire chains (uniform delays)
Lattice of coupled oscillators
τ = 15
τ= 5
Planar & mixed wave generation z = −0.29, k = 0.10, I = −0.44 (bar stimulus
shape storage and retrieval 2D wave-matching
)
τ = 10
Lattice of coupled oscillators – 2D wave shapes
Lattice of coupled oscillators – shape metric deformation ex: no deformation: planar & orthogonal waves
coding coordinates with phases y coordinates
STPy
virtual phase space
o o
uniform weights on PX and PY orthogonal full-bar stimuli
uniform weight distribution:
k = 0.09
PY
ex: irregular deformation
heterogeneous waves o o
ex: “shear stress” and “laminar flow” deformation
similar to buoys floating on water
PX
Lattice of coupled oscillators – shape metric deformation
x coordinates
vert./laminar + horiz./vert. wave o o
STPx gradient weight landscape:
k ∈ [0.09, 0.20]
Y-gradient of weights on PY or PX orthogonal full-bar stimuli
random weight distribution (bumps & dips) on PX and PY orthogonal full-bar stimuli
various weight combinations
