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Transcript of 1 Complejidad Dia 7 Ecología Biologí a Psicologia Meteorología MacroEconomía Geofisica UBA,...
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1
Complejidad Dia 7
Ecología
Biología
Psicologia
Meteorología
MacroEconomíaGeofisica
UBA, Junio 19, 2012.
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“Learning as a collective“
• Chialvo and Bak, Neuroscience (1998)
• Bak and Chialvo, Phys. Rev. E (2001).
• Wakeling J. Physica A, 2003)
• Wakeling and Bak, Phys.Rev. E (2001).
Hoy:
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Learning is never smooth
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What Is the Problem?
The current emphasis is in …
• To understand how billions of neurons learn, remember and forget on a self-organized way.
• To find a relationship between neuronal long-term potentiation, (so called “LTP”) of synapses and memory.
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Biology is concerned with “Long-Term Potentiation”
If A and B succeed together to fire the neuron (often enough) synapse B will be reinforced
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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.
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What Is Wrong With the emphasis on “LTP”?
Nothing
but there is no evidence linking memory and LTP
and LTP is not the solution of how memory works
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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).
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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
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How It Works on a Simple Task
Connect one (or more) input neurons with a given output neuron.
Chialvo and Bak, Neuroscience (1999)
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A simple gizmo
a)left <->right
b)10% “blind”
c)10% “stroke”
d)40% “stroke”
Chialvo and Bak, Neuroscience (1999)
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How performance scales with “brain” size
More neurons -> faster learning.
It makes sense!The only model where
larger is better
Chialvo and Bak, Neuroscience (1999)
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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)
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Order-Disorder Transition
Learning time is optimized for > 1
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Order-Disorder Transition
At = 1 the network is critical
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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)
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If you make a mistake, next do something different
H. Ohta, Y.P. Gunji / Neural Networks 19 (2006) 1106–1119
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By “inhibiting” the past states
H. Ohta, Y.P. Gunji / Neural Networks 19 (2006) 1106–1119
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20H. Ohta, Y.P. Gunji / Neural Networks 19 (2006) 1106–1119
So you can learn new thing without deleting the old ones
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Solid‐State Atomic Switch
o“Mermistors”
nanoresistores con memoria
(o “electroquimica seca” o “electrolitos
solidos”)
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Tsuyoshi Hasegawa et al, Learning Abilities Achieved by a Single Solid‐State Atomic SwitchAdvanced Materials, 22, 1831-1834, 2010
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Tsuyoshi Hasegawa et al, Learning Abilities Achieved by a Single Solid‐State Atomic SwitchAdvanced Materials, 22, 1831-1834, 2010
Experimental result of a gradual increase in the current
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Memory is in the spatial configuration of the Ag cations.A collective memory…
nanogap
Ag2S
Electrodo Ag
Electrodo metal
Ag atomic bridge
Tsuyoshi Hasegawa et al, Learning Abilities Achieved by a Single Solid‐State Atomic SwitchAdvanced Materials, 22, 1831-1834, 2010
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a, Schematics of a Ag2S inorganic synapse and the signal transmission of a biological synapse. b,c, Change in the conductance of the inorganic synapse when the input pulses were applied with intervals of T=20 s (b) and 2 s (c).
Inorganic synapse showing STP and LTP, depending on input-pulse repetition time.
“Short-term plasticity and long-term potentiation mimicked in single inorganic synapses”
Takeo Ohno et al.
Nature Materials 10, 591–595 (2011)
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Emergent Criticality in Complex Turing B Type Atomic Switch Networks‐
“Emergent Criticality in Complex Turing B‐Type Atomic Switch Networks”Advanced Materials Stieg et al, 24, 286-293, 2011.
Fabrication scheme for complex, electronic networks
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Emergent Criticality in Complex Turing B Type Atomic Switch Networks‐
(a) Experimental I–V curve demonstrating hysteresis (b) Ultrasensitive IR image of a distributed device conductance. (c,e) Representative experimental network current response to a 2 V pulse showing switching between discrete, metastable conductance states. (d,f) Metastable states residence times for (d) single 10 ms pulse and (f) over 2.5 s during extended periods of pulsed stimulation.
“Emergent Criticality in Complex Turing B‐Type Atomic Switch Networks”Advanced Materials Stieg et al, 24, 286-293, 2011.
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Desafío:1) Modelar eficientemente la física del collectivo
de mermistores. Es decir: modelos numéricos eficientes de una red arbitraria de mermistores ( probable punto de partida: random fuse model)
2) Modelar aprendizaje en esa red: Es decir: Encontrar algoritmos de aprendizaje
auto-organizables implementables in silico.