Download - Learning, Memory and Criticality
Dante R. Chialvo
Learning, Memory and Criticality
“Most of our entire life is devoted to learn. Although its importance in medicine is tremendous, the field don’t quite have yet an understanding of what is the essence of brain learning. We have the intuition that brain learning must be a collective process (in the strong sense) for which there is not yet theory. Main stream efforts runs in a direction we argue will not leads to the solution. In this “motivational” talk we illustrate briefly the main point.”
1. (blah blah) Complex vs. Complicated .
2. (numerics) Toy model of learning -> is critical.
Why We Do What We Do?
1. Brains self-organize to survive predators escaping, moving.2. Immune systems self-organize to survive predators(when is
inside and escaping is useless).3. Societies self-organize to survive predators (when the
individual response is useless) .4. …. More.
All these systems are complex dynamical systems, with very large number of nonlinear degrees of freedom, curiously share a property: memory… would it be possible to learn something
relevant about memory studying societies, brains etc?..
Brains found useful to be the way they are
many linear pieces + a central supervisor + blueprint = “whole”
Example: a tv set
many nonlinear pieces + coupling + injected energy = “emergent properties”
Example: society
Complex system
Complicated system
Complicated or Complex?Complicated or Complex?
Is Learning & Memory Is Learning & Memory a Complex or a Complicated Problem?a Complex or a Complicated Problem?
•If learning & memory is just complicated, then somebody will eventually figure out the whole problem.
•But if happen to be But if happen to be complex complex … we can seat and wait … we can seat and wait forever… forever…
Note that: Current experiments explore isolated details (i.e. one neuron, few synapses… etc.)
What Is the Problem?
The current emphasis is …
• To understand how billions of neurons learn, remember and forget on a self-organized way.
I Don’t Know the Solution! The problem belong to biology but the solution
to physics.
• To find a relationship between hippocampal long-term potentiation, (“LTP”) of synapses and memory.
Steps of Long-term PotentiationSteps of Long-term Potentiation1. Rapid stimulation of neurons depolarizes them.2. Their NMDA receptors open, Ca2+ ions flows into
the cell and bind to calmodulin.3. This activates calcium-calmodulin-dependent
kinase II (CaMKII).4. CaMKII phosphorylates AMPA receptors making
them more permeable to the inflow of Na+ ions (i.e., increasing the neuron’ sensitivity to future stimulation.
5. The number of AMPA receptors at the synapse also increases.
6. Increased gene expression (i.e., protein synthesis - perhaps of AMPA receptors) and additional synapses form.
Biology is concerned with “Long-Term Potentiation”
If A and B succeed together to fire the neuron (often enough) synapse B will be reinforced
What Is Wrong With “LTP”?
First of all:There is no evidence* linking memory LTP
Furthermore:• It is a process purely local (lacking any global coupling).• It implies a positive feedback (“addictive”).• It needs multiple trials (“rehearsal”).
Finally: Network components are not constant, neurons are
replaced (even in adults).
*(non-circumstantial)
How difficult would be for a neuronal network to learn
The idea was not to invent another “learning algorithm” but to play with the simplest, still biologically realistic, one.
• Chialvo and Bak, Neuroscience (1999)
• Bak and Chialvo, Phys. Rev. E (2001).
• Wakeling J. Physica A, 2003)
• Wakeling and Bak, Phys.Rev. E (2001).
Self-organized Learning: Toy Model
1) Neuron “I*” fires
2) Neuron “j*” with largest W*(j*,I*) fires
and son onneuron with largest W*(k*,j*) fires…
3) If firing leads to success: Do nothingDo nothing
otherwiseotherwise decrease W* by
That is allThat is all
• Bak and Chialvo. Phys. Rev. E (2001).
• Chialvo and Bak, Neuroscience (1999)
• Wakeling J. Physica A, 2003)
How It Works on a Simple Task
Connect one (or more) input neurons with a given output neuron.
Chialvo and Bak, Neuroscience (1999)
A simple gizmo
a)left <->right
b)10% “blind”
c)10% “stroke”
d)40% “stroke”
Chialvo and Bak, Neuroscience (1999)
How It Scales With Brain Size
More neurons -> faster learning.
It makes sense!The only model where larger is better
Chialvo and Bak, Neuroscience (1999)
How It Scales With Problem Size (on the Parity Problem)
• A) Mean error vs Time for various problem’ sizes (i.e., N=2m bit strings)
• B) Rescaled Mean error (with k=1.4)
Chialvo and Bak, Neuroscience (1999)
Order-Disorder Transition
Learning time is optimized for > 1
Order-Disorder Transition
At = 1 the network is critical!
Synaptic landscape remains rough• Elimination of the least-
fit connections• Activity propagates
through the best-fit ones• At all times the synaptic
landscape is rough
Fast re-learning
Chialvo and Bak, Neuroscience (1999)
Summing up:
1.1. We discusses why we don’t share the main-stream idea that We discusses why we don’t share the main-stream idea that learning in the brain is based on LTP. Probably LTP is an epi-learning in the brain is based on LTP. Probably LTP is an epi-phenomena. phenomena.
2.2. Intuition tell us that learning in brains must be a collective Intuition tell us that learning in brains must be a collective process. Theory is needed here.process. Theory is needed here.
3.3. As an exerciseAs an exercise we showed an alternative toy model of self- we showed an alternative toy model of self-organized learning (not based on LTP) which is biologically organized learning (not based on LTP) which is biologically plausible.plausible.