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. 1.(blah blah) Complex vs. Complicated (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?

Is Learning & Memory 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 complex … we can seat and wait forever…But if happen to be complex … we can seat and wait 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 Potentiation 1. 1.Rapid stimulation of neurons depolarizes them Their NMDA receptors open, Ca 2+ ions flows into the cell and bind to calmodulin This activates calcium-calmodulin-dependent kinase II (CaMKII) CaMKII phosphorylates AMPA receptors making them more permeable to the inflow of Na + ions (i.e., increasing the neuron’ sensitivity to future stimulation The number of AMPA receptors at the synapse also increases 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 on neuron with largest W*(k*,j*) fires… 3) If firing leads to success: Do nothing  Do nothing otherwise otherwise   decrease W* by  That 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=2 m 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.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- phenomena. 2.Intuition tell us that learning in brains must be a collective process. Theory is needed here. 3.As an exercise we showed an alternative toy model of self- organized learning (not based on LTP) which is biologically plausible.