Transcript brain - FIAS

CogSci 260:
The Self-organizing Brian
Spring Quarter 2004
Prof. Jochen Triesch
Natural Computation Group
Dept. of Cognitive Science
University of California, San Diego
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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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)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Requirements
1. Paper Presentation: 20% of grade
•
present some papers or book chapter in class
2. Project: 70% of grade
•
•
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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
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come to class and actively participate
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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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 should
look 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.
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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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?
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Development: 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)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Using, Re-using, Timing
Eve gene in fruit fly:
• switched on 10 different times during development
• different promoters are used in different tissues to switch it on
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
small differences in timing of gene expression during
development can lead to very different body plans
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Brain Development
J. Stiles
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Exuberance and Pruning
J. Stiles
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Re-wiring studies: Input Matters
M. Sur
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Self-Organization or not
heat exchange
expansion of a gas
diffusion of ink drop
H. Haken
Typically, macroscopic structure vanishes:
thermodynamics: entropy (disorder) always increases,
no self-organization
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Benard 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
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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S. Kelso
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Other 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
H. Haken
Other:
• reaction-diffusion
• laser
•…
chemical reactions
“cloud streets”
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Biological Systems
“boids”
anchovie school
Formation of fish schools and bird flocks:
• local interactions sufficient for emergence of global order
• separation, cohesion, alignment
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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S. Camazine
Nests building in fish:
• each individual is attracted to build nest close to that of others
• defends his nest from others
Tilapia mossambica
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
male blugill
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S. Camazine
Other self-organized biological systems:
• social insects (ants, termites, bees, …)
• fire fly synchronization
• slime mold
• formation of animal coat patterns
• sea shell patterns
•…
marble cone shell
(conus marmoreus)
porphyry olive shell
(Olivia porphyria)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
termite mound
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Different “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”)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Structure at many Spatial Scales
figure from Churchland
and Sejnowski (1992)
nervous systems span a range of spatial scales; at every scale there
is interesting structure that we would like to understand
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Anatomical Structure and Efficient
Communication 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)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Laughlin & Sejnowski, 2003
volume of white matter scales approx.
as the 4/3 power of gray matter volume:
explained by fixed bandwidth of
long-distance communication per
unit area of cortex
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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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
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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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)
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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105
growing up
108
1010
107
109
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
1012
1011
1013 time/s
neuroevolution
103
106
human life
101
Infant habituation
10-1
object recog.
action potential
10-3
104
1 day = 8.6×104 s,
1 year = 3.2×107 s
infant walks
102
learn skill
plan chess move
1
percept. learning
simple motor act
10-2
LTP, LTD
membrane constant
Dynamics across Temporal Scales
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The 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
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Why Make Mathematical or
Computational Models?
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helps understand the
brain at the level of
detail required for rebuilding it (neural
prosthesis, AI)
Some examples:
1.
2.
3.
4.
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
Hippocampus chip
Vision for the blind
Silicon Retina
Cochlea Implants
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Benefits of Computational Models
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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
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Issues with Computational Models
(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 aspects
2. too complex: analysis may become unpractical
“Make everything as simple as possible, but not simpler.”
Albert Einstein
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Models of a Neuron
Structure, structure, structure!
Is it necessary to model the
detailed spatial structure?
It depends…
Is it necessary to model the
detailed 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
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
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Classes of Neuron Models
b: cont. activation vs. spiking
a: compartmental vs. point model
a:
highest realism,
most difficult
to simulate
lowest realism,
most easy
to simulate
b:
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch
our focus will
mostly be here
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