Jochen Triesch, UC San Diego, triesch 1 Prof. Jochen Triesch Natural Computation Group Dept. of Cognitive Science University of.

Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 1

Prof. Jochen Triesch

Natural Computation GroupDept. of Cognitive Science

University of California, San Diego

CogSci 260:CogSci 260:The Self-organizing BrianThe Self-organizing Brian

Spring Quarter 2004


Topics by Week:• Introduction (today): self-organization and the brain• Reaction-Diffusion Systems, Pattern Formation, CAs• Neurodynamics 1: non-linear systems, chaos, decisions• Neurodynamics 2: memory, pattern formation• Networks: random graphs, small world networks, scale free

graphs, preferential attachment (Christof Teuscher)• Models based on Information theory: entropy, mutual information,

info max, independent component analysis, sparse coding • Synaptic and Intrinsic Plasticity, Map Formation: Hebbian

learning, intrinsic learning, self-organized map formation• Learning through Reinforcement: exploration/exploitation,

temporal difference learning, actor critic architectures, application to modeling cognitive development

• Synchronization, Binding, Self-organized Information Flow, cue integration

• Final Project Presentations (week 10)


RequirementsRequirements

1. Paper Presentation: 20% of grade• present some papers or book chapter in class

2. Project: 70% of grade• conduct modeling project and write 6 page report or• write 10 page review paper• can work in teams of 2

3. Class Participation: 10% of grade• come to class and actively participate


Self-Organization: structure for free?Self-Organization: structure for free?Gedankenexperiment: How can you build a house?

Solution A:Use a bunch of bricks, get a blue-print of how the house shouldlook like. Put the bricks where they belong.

Solution B: Use fancier bricks with little legs and sensors and a certain program.Bricks will sense each other and arrange each other in the right pattern, leaving just the right holes for windows and doors, etc.


Solution C: Use an even fancier brick with little legs, sensors, a program, and the ability to grow a copy of itself. You start with just a single brick but after some time you find an entire house at the scene.

Solution D: Now consider bricks that, in addition, can change their own properties, that can become different things (a piece of a water pipe, a roof tile, etc.). Could you, with the right program, get a full house like this?

Discussion: What are the advantages/disadvantages of different solutions?Why is practically all of today’s engineering working like Solution A?


Development: Some NumbersDevelopment: Some Numbers

The numbers (genome): • 30,000-40,000 genes in human genome• 3 × 109 base pairs (2 bits each)• 95% - 99% overlap with chimpanzee genome• chimpanzee genome closer to ours than to that of gorilla

The numbers (brain): • ~1010 neurons• ~1014 synapses

Genome cannot contain an explicit description of the structure of the adult brain.“The genome is not a blueprint for constructing a body,

it is a recipe for baking a body.” (Matt Ridley)


Using, Re-using, TimingUsing, Re-using, Timing

small differences in timing of gene expression duringdevelopment can lead to very different body plans

Hox genes (early 1980s):• tell fly where to grow its wings• tell mouse where to grow ribs

Hoxc8 gene:• controls transition from neck to thorax in development of vertebral column• small changes in promoter can delay expression of Hoxc8 gene• chicken: longer neck with more vertebrae than mouse• python: Hoxc8 expressed right away → python consists of one long thorax

Eve gene in fruit fly: • switched on 10 different times during development• different promoters are used in different tissues to switch it on


Brain DevelopmentBrain Development

J. Stiles


Exuberance and PruningExuberance and Pruning

J. Stiles


Re-wiring studies: Input MattersRe-wiring studies: Input Matters

M. Sur


Self-Organization or notSelf-Organization or not

Typically, macroscopic structure vanishes:thermodynamics: entropy (disorder) always increases,

no self-organization

heat exchange

expansion of a gas

diffusion of ink drop

H. Haken


Benard SystemBenard System

temperature gradient:conduction, convection.

Convection:colder fluid on top more dense: wants to sink down

Viscosity:sinking volume drags down neighboring volumes

H. Haken


S. Kelso


Other Physcial/Chemical SystemsOther Physcial/Chemical Systems

Formation of sand dunes:• wind blows sand through air• sand somewhat more likely to be deposited behind little ripple• ripple can get bigger and bigger (positive feedback)• different ripples (dunes) compete for finite amount of sand in system

“cloud streets”chemical reactions

Other:• reaction-diffusion• laser• …

H. H

aken


Biological SystemsBiological Systems

Formation of fish schools and bird flocks:• local interactions sufficient for emergence of global order• separation, cohesion, alignment

anch

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“boi

ds”


Nests building in fish:• each individual is attracted to build nest close to that of others• defends his nest from others

Tilapia mossambica male blugill

S. C

amaz

ine


Other self-organized biological systems:• social insects (ants, termites, bees, …)• fire fly synchronization• slime mold• formation of animal coat patterns• sea shell patterns• …

termite moundporphyry olive shell(Olivia porphyria)

marble cone shell(conus marmoreus)

S. C

amaz

ine


Different “Perspectives” on the BrainDifferent “Perspectives” on the Brain

Perspective A: The brain is a computation device. It finds solutions to certain computational problems. Sometimes these solutions are only approximate. (“top-down view”)

Perspective B: The brain is a complex dynamical system with many non-linearly interacting parts. The behavior emerging from these interactions is often difficult to predict (“bottom-up view”)


Structure at many Spatial ScalesStructure at many Spatial Scales

nervous systems span a range of spatial scales; at every scale thereis interesting structure that we would like to understand

figure from Churchlandand Sejnowski (1992)


Anatomical Structure and Efficient Anatomical Structure and Efficient Communication in BrainsCommunication in Brains

Ramon y Cajal: “We realized that all of the various conformations of the neuron and its various

components are simply morphological adaptations governed by laws of conservation for time, space, and material.”

Wiring Patterns: brains should optimize their wiring patterns

• Nematode worm Caenorhabditis elegans: 302 neurons in 11 ganglia, layout minimizes total wiring length (exhaustive search)


volume of white matter scales approx.as the 4/3 power of gray matter volume:explained by fixed bandwidth oflong-distance communication perunit area of cortex

Lau

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van Essen, 1990s

Cortex:• global: layout of cortical areas minimizes total

lengths of axons to connect them• local: much higher probability of

connectedness for nearby neurons


Speed savings in gray matter:• 60% of gray matter are axons and dendrites• optimal balance between transmission speed and component density:

• bigger axons take up more space and push neurons apart• bigger axons also transmit signals faster (cable properties)

Communication Bandwidth:• assume 1010 neurons, each 100 bit/s → 1 terabit/s, comparable to total world

backbone capacity of the Internet• But: not all neurons highly active at the same time!

Energy Efficiency:• brain makes up 20% of your total energy expenditure• for infants even 60%• sparse codes are energy efficient; “Economy of spikes” (Barlow)


Dynamics across Temporal ScalesDynamics across Temporal Scales

time/s 10-3 10-1 101 103 105 107 109 1013

1 10-2 102 104 106 108 1010

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1 day = 8.6×104 s,1 year = 3.2×107 s

1011

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The Brain as a Computing DeviceThe Brain as a Computing Device

Brain very differently organized from today’s main stream computers:

• 1011 neurons, parallel processing• individual neurons slow (and noisy)• 104 connections each, every other neuron only a “few synapses away”: immense connectivity• enough “wire” in the brain to go to the moon and back• learning takes place when neurons and synapses change properties, memory and processing not as nicely separated


Why Make Mathematical or Why Make Mathematical or Computational Models?Computational Models?

• helps understand the brain at the level of detail required for re-building it (neural prosthesis, AI)

• Some examples:1. Hippocampus chip2. Vision for the blind3. Silicon Retina4. Cochlea Implants


Benefits of Computational ModelsBenefits of Computational Models

• help understand brain at level of detail required for re-building it

• help come up with new explanations for cognitive phenomena

• can help tie explanations of cognitive phenomena to the biological mechanisms

• can bridge gaps between vastly different spatial and temporal scales

• forces explicitness about any assumptions• such explicitness helps uncover flaws in other less

formal theories• allows to make precise predictions that can be tested

and falsified


Issues with Computational ModelsIssues with Computational Models(or any formal theories in the sciences)(or any formal theories in the sciences)

• it is easy to account for just any one set of data• it is even easier to account for no data• sometimes, it is almost impossible to account for all

available data• what is the right level of abstraction?

1. too simple: may lose essential aspects2. too complex: analysis may become unpractical

“Make everything as simple as possible, but not simpler.”Albert Einstein


Models of a NeuronModels of a Neuron

Structure, structure, structure!

Is it necessary to model the detailed spatial structure?It depends…

Is it necessary to model thedetailed temporal structure?It depends…

Is it necessary to explicitly model the various conductances and transmitter systems?It depends… A: cortical pyramidal cell; B: Purkinje cell

of cerebellum; C: stellate cell of cerebral cortex


Classes of Neuron ModelsClasses of Neuron Models

a: compartmental vs. point model

b: c

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acti

vati

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s. s

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ng

highest realism,most difficult

to simulate

lowest realism,most easyto simulate

our focus willmostly be here

a:

b:

Jochen Triesch, UC San Diego, triesch 1 Prof. Jochen Triesch Natural Computation Group Dept. of Cognitive Science University of.

Documents

uc san diego

san diego cogsci

numbers genome

human genome

synapses genome

fancier bricks

intrinsic learning

pattern formation networks