SYDE 556/750: Simulating Neurobiological Systems

Accompanying Readings: Chapter 1

Terry Stewart

Overall Goal

• Building simulated brains
• Why?
  • To figure out how brains work
  • To apply this knowledge to building systems

Administration

• Course website: http://compneuro.uwaterloo.ca/research/syde-750.html
• Contact information
  • Terry Stewart: tcstewar@uwaterloo.ca
  • Course times: 11:00-12:30 DWE 3519
  • Office hours: 2 hours after each lecture

Coursework

• Four assignments (60%)

  • 20%, 20%, 10%, 10%
  • Two weeks for each assignment, except last one (one week)
  • Everyone writes their own code, generates their own graphs, writes their own answers
    • But it helps to get together to discuss things

• Final project

  • Make a novel model of some neural system
  • For 556 students, this can be just an extension of something seen in class
  • For 750 students, this must be more of a research project
  • ideas

Schedule

My Background

• Undergrad: Systems (Waterloo)
  • option in Cognitive Science
• Masters of Philosophy in Computer Science and AI (Sussex)
  • experimental psychology on robots
• PhD in Cognitive Science (Carleton)
  • philosophy of computational modelling

Research Theme

• How does the mind work?
• Most complex and most interesting system humanity has ever studied
  • Why study anything else?
• How should we go about studying it?
  • What techniques/tools?
  • How do we know if we're making progress?
  • How do we deal with the complexity?

Standard Approach

• Psychology
  • Measure people's performance in lots of situations
  • Describe processes that might explain observations
  • Example: memory

• Problems
  • Hard to get quantitative predictions
  • Compare to Aristotelian gravity
    • "All bodies move toward their natural place"

Cognitive Modelling

• Let's build it
  • Specify theory in enough detail that this is possible
  • Tends to get complex, so need computer simulation
• Do for psychology what Newton did for physics
  • Note that Newton got lucky that gravity turned out to be analytically tractable
  • If he had a computer, he wouldn't have had to invent calculus

Cognitive Models

• Lots of different models
  • e.g. Conditioning (Rescorla-Wagner model)

Cognitive Architectures

• Don't want to make a whole new model for each situation
  • Hard to generalize
  • Lots of parameters
  • Can fit anything
• Identify basic components used across tasks
  • Adds constraints
  • Imposes a high-level organizational theory

ACT-R

• Most widely used cognitive architecture
  • http://act-r.psy.cmu.edu/
  • Remembering lists
  • Driving a car
  • Dialing a phone
  • Mental arithmetic
  • Parsing a sentence
  • Military training
  • etc etc
• Each components has equations
  • Memory activation: $A_i = ln( \sum t_j^{-d})+\beta_i$
  • Including timing
  • Recall time: $T = F e^{-fA_i}$

Problems

• Disconnected from neuroscience
  • Trying to map components of the model to brain areas
  • When a component is active, maybe neurons in that area are more active?
• No "bridging laws"
  • Like having rules of chemistry that never mention that it's all built out of atoms and electrons
• No constraints on the equations
  • Just anything that can be written down
  • Many possibilities; hard to figure out what matches human data best
• Maybe that's okay
  • Do we understand the brain enough to make this connection and constrain theories?
  • When understanding a word processor, do we worry about transistors?

The Brain

• 2 kg (2% of body weight)
• 20 Watts (25% of power consumption)
• Area: 4 sheets of paper
• Neurons: 100 billion (150,000 per $mm^2$)

Brain structures

• Lots of visually obvious structure
• Lots of greek and latin names to remember
  • frontal cortex, thalamus, amygdala, hypothalamus, substantia nigra, etc etc

A Neuron

Neurons in the brain

• 100 billion
• 100's or 1000's of visually distinct types
• Axon length: from $10^{-4}$ to $5$ m
• Each neuron: 500-200,000 inputs and outputs
  • 72km of axons
• Communication: 100's of different neurotransmitters

Neuron communication: Synapses

What it really looks like

What it really really looks like

Considering the brain

• lesion studies
• what are the effects of damaging different parts of the brain?
  • occipital cortex: blindness (call it visual cortex)
  • inferior frontal gyrus: can't speak (Broca's area)
  • posterior superior temporal gyrus: can't understand speech (Wernicke's area)
  • fusiform gyrus: can't recognize faces (and other complex objects)
  • prefrontal cortex: moral judgement???
  • aperceptive visual agnosia
  • etc, etc, etc

fMRI

• Functional Magnetic Resonance Imaging
• Measure blood oxygenation levels in the brain
  • show the difference between two tasks
  • averaged over ~100 trials
• Measured while performing tasks
  • ~4 second between scans
  • some attempts at going faster, but blood vessels don't change much faster than this
• Shows where energy is being used in the brain
  • equivalent to figuring out how a CPU works by measuring temperature
  • a bit more fine-grained than lesion studies
• Neurosynth

EEG

• Electrical activity at the scalp
• High time resolution
• Large-scale communication between areas

Single cell recording

Local Field Potential

• Place electrodes into the brain, record from it
  • not necessarily right at a neuron
• Multielectrode recordings
• Post-processing: "Spike sorting"

Rat place cells

Calcium Imaging

• In a fish embryo

Calcium imaging

• In a stalking fish

Optogenetics

What do we know?

• lots of details
  • Data: "The proportion of type A neurons in area X is Y"
  • Conclusion: "Therefore, the proportion of type A neurons in area X is Y".

• hard to get a big picture

  • over-generalizing from data

• "data-rich and theory-poor"

  • need some way to connect these details
  • need a unifying theory

Levels of description

Computational Neuroscience

• what I cannot create, I do not understand
• build a computer simulation
  • do to neuroscience what Newton did to physics
  • too complex to be analytically tractable, so use computer simulation
• Can we use this to connect the levels?

Single neuron simulation

• Hodgkin & Huxley, 1952

Single neuron simulation

• Hodgkin & Huxley, 1952

Single neuron simulation

Millions of neurons

Billions of neurons

• Simplify the neuron model
  • $C {dV \over dt} = I - {V \over R}$

The controversy

• what level of detail for the neurons? how should they be connected?
• IBM SyNAPSE project
  • billions of neurons, but very simple models
  • randomly connected
  • 2009: "Cat"-scale brain (1 billion neurons)
    • 2012: "Human"-scale brain (100 billion neurons)
  • Called a "hoax and PR stunt" by:
• Blue Brain
  • much more detailed neurons
  • randomly connected
• how much detail is enough?
  • how could we know?

• The real test: connecting to behaviour
  • How can we build models that actually do something?
  • How should we connect realistic neurons so they work together?

The Neural Engineering Framework

• Our attempt
  • probably wrong, but got to start somewhere
• Three principles
  • Representation
  • Transformation
  • Dynamics
• Building behaviour out of detailed low-level components

Representation

• How do neurons represent information?
• What is the mapping between a value to be stored and the activity of a group of neurons?
• What sorts of values can be stored?
• Examples:
  • Line detection in retina
  • Place cells
• Claim: every group of neurons should be thought of as representing something
  • each neuron has some preferred value
  • neurons fire more strongly the closer the value is to that preferred value
  • values are vectors

Transformation

• Connections compute functions on those vectors
• Activity of one group of neurons causes another group to fire
  • One group may represent $x$, connected to annother group representing $y$
  • Whatever firing pattern we get in $y$ due to $x$ is a function $y = f(x)$
• Can find what class of functions are well approximated this way
• Puts limits on the algorithms we can implement with neurons

Dynamics

• Recurrent connections (feedback)
• Turns out to allow us to compute functions of this form:
  • ${dx \over dt} = f(x, u)$
  • where $x$ is what the neurons represent, and $u$ is the input neurons
• Great for implementing all of control theory
• Also memory! (${dx \over dt} = u$)

Examples

• This approach gives us a neural compiler
• Given an algorithm, you can solve for the connections between neurons that will approximate that algorithm
  • Works for a wide variety of neuron models
  • Number of neurons affects accuracy
  • Neuron properties influence timing

Vision: character recognition

Simple reactions: Braitenburg vehicle

Problem solving: Tower of Hanoi

Spaun: digit recognition

Spaun: copy drawing

Spaun: addition by counting

Spaun: pattern completion

Benefits

• No one else can do this
• New ways to test theories (neurological constraints)
• Suggests different types of algorithms
• Potential medical applications
• New ways of understanding the mind and who we are

Homework

• Get the textbook
  • Eliasmith and Anderson (2003). Neural Engineering: Representation, Computation and Dynamics in Neurobiological Systems. MIT Press.
• Read chapter 1