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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 1 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 2 Requirements 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 Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 3 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 4 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 5 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 6 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 7 Brain Development J. Stiles Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 8 Exuberance and Pruning J. Stiles Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 9 Re-wiring studies: Input Matters M. Sur Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 10 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 11 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 12 S. Kelso Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 13 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 14 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 15 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 16 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 17 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 18 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 19 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 20 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 21 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 22 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 23 105 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 24 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 25 Why Make Mathematical or Computational Models? • • 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 26 Benefits 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 Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 27 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 28 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 29 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 30