On Bubbles and Drifts: Continuous attractor networks and their relation to working memory, path integration, population decoding, attention, and motor functions

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On Bubbles and DriftsContinuous attractor
networks and their relation to working memory,
path integration, population decoding, attention,
and motor functions

• Thomas Trappenberg
• Dalhousie University, Canada

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CANNs can implement motor functions
Stringer, Rolls, Trappenberg, de Araujo,
Self-organizing continuous attractor networks
and motor functions Neural Networks 16 (2003).
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My plans for this talk

• Basic CANN model
• Idiothetic CANN updates (path-integtration)
• CANN motor functions
• Limits on NMDA stabilization

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Once upon a time ... (my CANN shortlist)

• Wilson Cowan (1973)
• Grossberg (1973)
• Amari (1977)
• Sampolinsky Hansel (1996)
• Zhang (1997)
• Stringer et al (2002)

Wilshaw van der Malsburg (1976)
Droulez Berthos (1988)
Redish, Touretzky, Skaggs, etc
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Basic CANN Its just a Hopfield net
Recurrent architecture
Synaptic weights
Nodes can be scrambled!
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In mathematical terms
Updating network states (network dynamics)
Gain function
Weight kernel
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Network can form bubbles of persistent activity
(in Oxford English activity packets)
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Space is represented with activity packets in the
hippocampal system
From Samsonovich McNaughton Path integration
and cognitive mapping in a continuous attractor
neural J. Neurosci. 17 (1997)
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Various gain functions are used
End states
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Superior colliculus intergrates exogenous and
endogenous inputs
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Superior Colliculus is a CANN
Trappenberg, Dorris, Klein Munoz, A model of
saccade initiation based on the competitive
integration of exogenous and endogenous inputs
J. Cog. Neuro. 13 (2001)
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Weights describe the effective interaction in
Superior Colliculus
Trappenberg, Dorris, Klein Munoz, A model of
saccade initiation based on the competitive
integration of exogenous and endogenous inputs
J. Cog. Neuro. 13 (2001)
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There are phase transitions in the
weight-parameter space
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CANNs can be trained with Hebb
Hebb
Training pattern
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Normalization is important to have convergent
method

• Random initial states
• Weight normalization

w(x,y)
w(x,50)
x
x
y
Training time
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Gradient-decent learning is also possible (Kechen
Zhang)
Gradient decent with regularization Hebb
weight decay
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CANNs have a continuum of point attractors
Point attractors and basin of attraction
Line of point attractors
Can be mixed Rolls, Stringer, Trappenberg A
unified model of spatial and episodic
memory Proceedings B of the Royal Society
2691087-1093 (2002)
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CANNs work with spiking neurons
Xiao-Jing Wang, Trends in Neurosci. 24 (2001)
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Shutting-off works also in rate model
Node
Time
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CANN (integrators) are stiff
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and can drift and jump
Trappenberg, Dynamic cooperation and competition
in a network of spiking neurons ICONIP'98
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Neuroscience applications of CANNs

• Persistent activity (memory) and winner-takes-all
  (competition)
• Cortical network (e.g. Wilson Cowan,
  Sampolinsky, Grossberg)
• Working memory (e.g. Compte, Wang, Brunel, Amit
  (?), etc)
• Oculomotor programming (e.g. Kopecz Schoener,
  Trappenberg et al.)
• Attention (e.g. Sompolinsky, Olshausen, Salinas
  Abbott (?), etc)
• Population decoding (e.g. Wu et al, Pouget,
  Zhang, Deneve, etc )
• SOM (e.g. Wilshaw van der Malsburg)
• Place and head direction cells (e.g. Zhang,
  Redish, Touretzky,
• Samsonovitch, McNaughton, Skaggs, Stringer et
  al.)
• Motor control (Stringer et al.)

b a s i c C A N N
P I
Path-integration
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Modified CANN solves path-integration
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CANNs can implement motor functions
Stringer, Rolls, Trappenberg, de Araujo,
Self-organizing continuous attractor networks
and motor functions Neural Networks 16 (2003).
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... learning motor sequences (e.g. speaking a
work)
Experiment 1
Movement selector cells motor
cells state cells
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from noisy examples
Experiment 2
state cells learning from noisy examples
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and reaching from different initial states
Experiment 3
Stringer, Rolls, Trappenberg, de
Araujo, Self-organizing continuous attractor
networks and motor function Neural Networks 16
(2003).
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Drift is caused by asymmetries
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CANN can support multiple packets
Stringer, Rolls Trappenberg, Self-organising
continuous attractor networks with multiple
Activity packets, and the representation of
space Neural Networks 17 (2004)
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How many activity packets can be stable?
Trappenberg, Why is our working memory capacity
so large? Neural Information Processing-Letters
and Reviews, Vol. 1 (2003)
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Stabilization can be too strong
Trappenberg Standage, Multi-packet regions in
stabilized continuous attractor networks,
submitted to CNS04
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Conclusion

• CANN are widespread in neuroscience models
  (brain)
• Short term memory, feature selectivity (WTA)
• Path-integration is an elegant mechanisms to
  generate dynamic sequences (self-organized)

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With thanks to

• Cognitive Neuroscience, Oxford Univ.
• Edmund Rolls
• Simon Stringer
• Ivan Araujo
• Psychology, Dalhousie Univ.
• Ray Klein
• Physiology, Queens Univ.
• Doug Munoz
• Mike Dorris
• Computer Science, Dalhousie
• Dominic Standage

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CANN can discover dimensionality
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CANN with adaptive input strength explains
express saccades
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CANN are great for population decoding (fast
pattern matching implementation)
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John Lismans hippocampus
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The model equations
Continuous dynamic (leaky integrator)
activity of node i firing rate synaptic
efficacy matrix global inhibition visual
input time constant scaling factor
connections per node slope threshold
NMDA-style stabilization
Hebbian learning