Secrets of Neural Network Models

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Secrets of Neural Network Models
Note These slides have been provided online for
the convenience of students attending the 2003
Merck summer school, and for individuals who have
explicitly been given permission by Ken Norman.
Please do not distribute these slides to third
parties without permission from Ken (which is
easy to get just email Ken at knorman_at_princeton.e
du).

• Ken Norman
• Princeton University
• July 24, 2003

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• The Plan, and Acknowledgements
• The Plan
• I will teach you all of the the secrets of neural
  network models in 2.5 hours
• Lecture for the first half
• Hands-on workshop for the second half
• Acknowledgements
• Randy OReilly
• my lab Greg Detre, Ehren Newman, Adler Perotte,
  and Sean Polyn

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• The Big Question
• How does the gray glop in your head give rise to
  cognition?
• We know a lot about the brain, and we also know a
  lot about cognition
• The real challenge is to bridge between these two
  levels

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• Complexity and Levels of Analysis
• The brain is very complex billions of neurons,
  trillions of synapses, all changing every
  nanosecond
• Each neuron is a very complex entity unto itself
• We need to abstract away from this complexity!
• Is there some simpler, higher level for
  describing what the brain does during cognition?

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• We want to draw on neurobiology for ideas about
  how the brain performs a particular kind of task
• Our models should be consistent with what we know
  about how the brain performs the task
• But at the same time, we want to include only
  aspects of neurobiology that are essential for
  explaining task performance

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• Learning and Development
• Neural network models provide an explicit,
  mechanistic account of how the brain changes as a
  function of experience
• Goals of learning
• To acquire an internal representation (a model)
  of the world that allows you to predict what will
  happen next, and to make inferences about
  unseen aspects of the environment
• The system must be robust to noise/degradation/dam
  age
• Focus of workshop Use neural networks to
  explore how the brain meets these goals

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• Outline of Lecture
• What is a neural network?
• Principles of learning in neural networks
• Hebbian learning Simple learning rules that are
  very good at extracting the statistical structure
  of the environment (i.e., what things are there
  in the world, and how are they related to one
  another)
• Shortcomings of Hebbian learning Its good at
  acquiring coarse category structure (prototypes)
  but its less good at learning about atypical
  stimuli and arbitrary associations
• Error-driven learning Very powerful rules that
  allow networks to learn from their mistakes

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• Outline, Continued
• The problem of interference in neocortical
  networks, and how the hippocampus can help
  alleviate this problem
• Brief discussion of PFC and how networks can
  support active maintenance in the face of
  distracting information
• Background information for the hands-on portion
  of the workshop

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• Overall Philosophy
• The goal is to give you a good set of intuitions
  for how neural networks function
• I will simplify and gloss over lots of things.
• Please ask questions if you dont understand what
  Im saying...

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What is a neural network?

• Neurons measure how much input they receive from
  other neurons they fire (send a signal) if
  input exceeds a threshold value
• Input is a function of firing rate and connection
  strength
• Learning in neural networks involves adjusting
  connection strength

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What is a neural network?

• Key simplifications
• We reduce all of the complexity of neuronal
  firing to a single number, the activity of the
  neuron, that reflects how often the neuron is
  spiking
• We reduce all of the complexity of synaptic
  connections between neurons to a single number,
  the synaptic weight, that reflects how strong the
  connection is

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• Neurons are Detectors
• Each neuron is detecting some set of conditions
  (e.g., smoke detector). Representation is what
  is detected.

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Understanding Neural Components in Terms of the
Detector Model
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• Detector Model
• Neurons feed on each others outputs layers of
  ever more complicated detectors
• Things can get very complex in terms of content,
  but each neuron is still carrying out the basic
  detector function

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Two-layer Attractor Networks
Hidden Layer (Internal Representation)
Input/Output Layer

• Model of processing in neocortex
• Circles units (neurons) lines connections
  (synapses)
• Unit brightness activity line thickness
  synaptic weight
• Connections are symmetric

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Two-layer Attractor Networks
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Hidden Layer (Internal Representation)
Input/Output Layer

• Units within a layer compete to become active.
• Competition is enforced by inhibitory
  interneurons that sample the amount of activity
  in the layer and send back a proportional amount
  of inhibition
• Inhibitory interneurons prevent epilepsy in the
  network
• Inhibitory interneurons are not pictured in
  subsequent diagrams

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Two-layer Attractor Networks
I
Hidden Layer (Internal Representation)
Input/Output Layer

• These networks are capable of sustaining a stable
  pattern of activity on their own.
• Attractor a fancy word for stable pattern of
  activity
• Real networks are much larger than this, also gt 1
  unit is active in the hidden layer...

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• Properties of Two-Layer Attractor Networks
• I will show that these networks are capable of
  meeting the learning goals outlined
• Given partial information (e.g., seeing something
  that has wings and features), the networks can
  make a guess about other properties of that
  thing (e.g., it probably flies)
• Networks show graceful degradation

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Pattern Completion in two layer networks
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Pattern Completion in two layer networks
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Pattern Completion in two layer networks
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Pattern Completion in two layer networks
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Networks are Robust to Damage, Noise
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Networks are Robust to Damage, Noise
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Networks are Robust to Damage, Noise
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Networks are Robust to Damage, Noise
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Networks are Robust to Damage, Noise
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• Learning Overview
• Learning changing connection weights
• Learning rules How to adjust weights based on
  local information (presynaptic and postsynaptic
  activity) to produce appropriate network behavior
• Hebbian learning building a statistical model of
  the world, without an explicit teacher...
• Error-driven learning rules that detect
  undesirable states and change weights to
  eliminate these undesirable states...

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• Building a Statistical Model of the World
• The world is inhabited by things with relatively
  stable sets of features
• We want to wire detectors in our brains to detect
  these things. How can we do this?
• Answer Leverage correlation
• The features of a particular thing tend to appear
  together, and to disappear together a thing is
  nothing more than a correlated cluster of
  features
• Learning mechanisms that are sensitive to
  correlation will end up representing useful things

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• Hebbian Learning
• How does the brain learn about correlations?
• Donald Hebb proposed the following mechanism
• When the pre-synaptic neuron and post-synaptic
  neuron are active at the same time, strengthen
  the connection between them
• neurons that fire together, wire together

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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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• Hebbian Learning
• Proposed by Donald Hebb
• When the pre-synaptic (sending) neuron and
  post-synaptic (receiving) neuron are active at
  the same time, strengthen the connection between
  them
• neurons that fire together, wire together
• When two neurons are connected, and one is active
  but the other is not, reduce the connections
  between them
• neurons that fire apart, unwire

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Hebbian Learning
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Hebbian Learning
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Biology of Hebbian Learning NMDA-Mediated
Long-Term Potentiation
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• Biology of Hebbian Learning
• Long-Term Depression
• When the postsynaptic neuron is depolarized, but
  presynaptic activity is relatively weak, you get
  weakening of the synapse

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• What Does Hebbian Learning Do?
• Hebbian learning tunes units to represent
  correlated sets of input features.
• Here is why
• Say that a unit has 1,000 inputs
• In this case, turning on and off a single input
  feature wont have a big effect on the units
  activity
• In contrast, turning on and off a large cluster
  of 900 input features will have a big effect on
  the units activity

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Hebbian Learning
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Hebbian Learning
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Hebbian Learning

• Because small clusters of inputs do not reliably
  activate the receiving unit, the receiving unit
  does not learn much about these inputs

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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
Big clusters of inputs reliably activate the
receiving unit, so the network learns more about
big (vs. small) clusters (the gang effect).
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Hebbian Learning
Big clusters of inputs reliably activate the
receiving unit, so the network learns more about
big (vs. small) clusters (the gang effect).
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• What Does Hebbian Learning Do?
• Hebbian learning finds the thing in the world
  that most reliably activates the unit, and tunes
  the unit to like that thing even more!

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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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Hebbian Learning
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• What Does Hebbian Learning Do?
• Hebbian learning finds the thing in the world
  that most reliably activates the unit, and tunes
  the unit to like that thing even more!
• The outcome of Hebbian learning is a function of
  how well different inputs activate the unit, and
  how frequently they are presented

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• Self-Organizing Learning
• One detector can only represent one thing (i.e.,
  pattern of correlated features)
• Goal We want to present input patterns to the
  network and have different units in the network
  specialize for different things, such that each
  thing is represented by at least one unit
• Random weights (different initial receptive
  fields) and competition are important for
  achieving this goal
• What happens without competition ...

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No Competition
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No Competition
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No Competition
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No Competition
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No Competition
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No Competition
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Without competition, all units end up
representing the same gang of features other,
smaller correlations get ignored
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Competition is important
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Competition is important
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Competition is important
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Competition is important
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Competition is important
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Competition is important
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Competition is important
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Competition is important
When units have different initial receptive
fields and they compete to represent input
patterns, units end up representing different
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• Hebbian Learning Summary
• Hebbian learning finds the thing in the world
  that most reliably activates the unit, and tunes
  the unit to like that thing even more
• When
• There are multiple hidden units competing to
  represent input patterns
• Each hidden unit starts out with a distinct
  receptive field
• Then
• Hebbian learning will tune these units so that
  each thing in the world (i.e., each cluster of
  correlated features) is represented by at least
  one unit

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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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Problems with Penguins
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• Problems with Hebb, and Possible Solutions
• Self-organizing Hebbian learning is capable of
  discovering the high-level (coarse) categorical
  structure of the inputs
• However, it sometimes collapses across more
  subtle (but important) distinctions, and the
  learning rule does not have any provisions for
  fixing these errors once they happen

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• Problems with Hebb, and Possible Solutions
• In the penguin problem, if we want the network to
  remember that typical birds fly, but penguins
  dont, then penguins and typical birds need to
  have distinct (non-identical) hidden
  representations
• Hebbian learning assigns the same hidden unit to
  penguins and typical birds
• We need to supplement Hebbian learning with
  another learning rule that is sensitive to when
  the network makes an error (e.g., saying that
  penguins fly) and corrects the error by pulling
  apart the hidden representations of penguins vs.
  typical birds.

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• What is an error, exactly?
• One common way of conceptualizing error is in
  terms of predictions and outcomes
• If you give the network a partial version of a
  studied pattern, the network will make a
  prediction as to the missing features of that
  pattern (e.g., given something that has
  feathers, the network will guess that it
  probably flies)
• Later, you learn what the missing features are
  (the outcome). If the networks guess about the
  missing features is wrong, we want the network to
  be able to change its weights based on the
  difference between the prediction and the
  outcome.
• Today, I will present the GeneRec error-driven
  learning rule developed by Randy OReilly.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.
• Outcome phase
• Present the full pattern
• Let the network settle

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.
• Outcome phase
• Present the full pattern
• Let the network settle

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.
• Outcome phase
• Present the full pattern
• Let the network settle

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Error-Driven Learning

• Prediction phase
• Present a partial pattern
• The network makes a guess about the missing
  features.
• Outcome phase
• Present the full pattern
• Let the network settle

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Error-Driven Learning

• We now need to compare these two activity
  patterns and figure out which weights to change.

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• Motivating the Learning Rule
• The goal of error-driven learning is to discover
  an internal representation for the item that
  activates the correct answer.
• Basically, we want to find hidden units that are
  associated with the correct answer (in this case,
  waddles).
• The best way to do this is to examine how
  activity changes when waddles is clamped on
  during the outcome phase.
• Hidden units that are associated with waddles
  should show an increase in activity in the
  outcome (vs. prediction) phase.
• Hidden units that are not associated with
  waddles should show a decrease in activity in
  the outcome phase (because of increased
  competition from other units that are associated
  with waddle).

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• Motivating the Learning Rule
• Hidden units that are associated with waddle
  should show an increase in activity in the
  outcome (vs. prediction) phase.
• Hidden units that are not associated with
  waddle should show a decrease in activity in
  the outcome phase
• Here is the learning role
• If a hidden unit shows increased activity (i.e.,
  its associated with the correct answer),
  increase its weights to the input pattern
• If a hidden unit should decreased activity (i.e.,
  its not associated with the correct answer),
  reduce its weights to the input pattern

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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning

• Hebb and error have opposite effects on weights
  here!
• Error increases the extent to which penguin is
  linked to the right-hand unit, whereas Hebb
  reinforced penguins tendency to activate the
  left-hand unit

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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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Error-Driven Learning
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• Catastrophic Interference
• If you change the weights too strongly in
  response to penguin, then the network starts to
  behave like all birds waddle. New learning
  interferes with stored knowledge...
• The best way to avoid this problem is to make
  small weight changes, and to interleave penguin
  learning trials with typical bird trials
• The typical bird trials serve to remind the
  network to retain the association between
  wings/feathers/beak and flies...

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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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Interleaved Training
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• Gradual vs. One-Trial Learning
• Problem It appears that the solution to the
  catastrophic interference problem is to learn
  slowly.
• But we also need to be able to learn quickly!

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• Gradual vs. One-Trial Learning
• Put another way There appears to be a trade-off
  between learning rate and interference in the
  cortical network
• Our claim is that the brain avoids this trade-off
  by having two separate networks
• A slow-learning cortical network that gradually
  develops internal representations that support
  generalization, prediction, categorization, etc.
• A fast-learning hippocampal network that is
  specialized for rapid memorization (but does not
  support generalization, categorization, etc.)

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hippo- campus
CA3
CA1
Dentate Gyrus
Entorhinal Cortex input
Entorhinal Cortex output
neo- cortex
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• Interactions Between Hippo and Cortex
• According to the Complementary Learning Systems
  theory (McClelland et al., 1995), hippocampus
  rapidly memorizes patterns of cortical activity.
• The hippocampus manages to learn rapidly without
  suffering catastrophic interference because it
  has a built-in tendency to assign distinct,
  minimally overlapping representations to input
  patterns, even when they are very similar. Of
  course this hurts its ability to categorize.

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• Interactions Between Hippo and Cortex
• The theory states that, when you are asleep, the
  hippocampus plays back stored patterns in an
  interleaved fashion, thereby allowing cortex to
  weave new facts and experiences into existing
  knowledge structures.
• Even if something just happens once in the real
  world, hippocampus can keep re-playing it to
  cortex, interleaved with other events, until it
  sinks in...
• Detailed theory
• slow-wave sleep hippo playback to cortex
• REM sleep cortex randomly activates stored
  representations this strengthens pre-existing
  knowledge and protects it against interference

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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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Role of the Hippocampus
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• Error-Driven Learning Summary
• Error-driven learning algorithms are very
  powerful So long as the learning rate is small,
  and training patterns are presented in an
  interleaved fashion, algorithms like GeneRec can
  learn internal representations that support good
  pattern completion of missing features.
• Error-driven learning is not meant to be a
  replacement for Hebbian learning The two
  algorithms can co-exist!
• Hebbian learning actually improves the
  performance of GeneRec by ensuring that hidden
  units represent meaningful clusters of features

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• Error-Driven Learning Summary
• Theoretical issues to resolve with error-driven
  learning The algorithm requires that the network
  know whether you are in a prediction phase or
  an outcome phase, how does the network know
  this?
• For that matter, the whole phases idea is
  sketchy
• GeneRec based on prediction/outcome differences
  is not the only way to do error-driven
  learning...
• Backpropagation
• Learning by reconstruction
• Adaptive Resonance Theory (Grossberg Carpenter)

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• Learning by Reconstruction
• Instead of doing error-driven learning by
  comparing predictions and outcomes, you can also
  do error-driven learning as follows
• First, you clamp the correct, full pattern onto
  the network and let it settle.
• Then, you erase the input pattern and see whether
  the network can reconstruct the input pattern
  based on its internal representation
• The algorithm is basically the same, you are
  still comparing two phases...

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Learning by Reconstruction

• Clamp the to-be-learned pattern onto the input
  and let the network settle

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Learning by Reconstruction

• Clamp the to-be-learned pattern onto the input
  and let the network settle
• Next, wipe the input layer clean (but not the
  hidden layer) and let the network settle

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Learning by Reconstruction

• Clamp the to-be-learned pattern onto the input
  and let the network settle
• Next, wipe the input layer clean (but not the
  hidden layer) and let the network settle

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Learning by Reconstruction

• Clamp the to-be-learned pattern onto the input
  and let the network settle
• Next, wipe the input layer clean (but not the
  hidden layer) and let the network settle

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Learning by Reconstruction

• Clamp the to-be-learned pattern onto the input
  and let the network settle
• Next, wipe the input layer clean (but not the
  hidden layer) and let the network settle

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Learning by Reconstruction

• Compare hidden activity in the two phases and
  adjust weights accordingly (i.e., if activation
  was higher with the correct answer clamped,
  increase weights if activation was lower,
  decrease wts)

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Learning by Reconstruction

• Compare hidden activity in the two phases and
  adjust weights accordingly (i.e., if activation
  was higher with the correct answer clamped,
  increase weights if activation was lower,
  decrease wts)

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Adaptive Resonance Theory
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Adaptive Resonance Theory
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Adaptive Resonance Theory
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Adaptive Resonance Theory
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Adaptive Resonance Theory
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Adaptive Resonance Theory
MISMATCH!
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Adaptive Resonance Theory
MISMATCH!
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Adaptive Resonance Theory
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Adaptive Resonance Theory
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Spreading Activation vs. Active Maintenance

• Spreading activation is generally very useful...
  it lets us make predictions/inferences/etc.
• But sometimes you just want to hold on to a
  pattern of activation without letting activation
  spread (e.g., a phone number, or a persons
  name).
• How do we maintain specific patterns of activity
  in the face of distraction?

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Spreading Activation vs. Active Maintenance

• As you will see in the hands-on part of the
  workshop, the networks we have been discussing
  are not very robust to noise/distraction.
• Thus, there appears to be another tradeoff
• Networks that are good at generalization/predictio
  n are lousy at holding on to phone
  numbers/plans/ideas in the face of distraction

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Spreading Activation vs. Active Maintenance

• Solution We have evolved a network that is
  optimized for active maintenance Prefrontal
  cortex! This complements the rest of cortex,
  which is good at generalization but not so good
  at active maintenance.

• PFC uses isolated representations to prevent
  spread of activity...
• Evidence for isolated stripes in PFC

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Tripartite Functional Organization

• PC posterior perceptual motor cortex
• FC prefrontal cortex
• HC hippocampus and related structures

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Tripartite Functional Organization

• PC incremental learning about the structure of
  the environment
• FC active maintenance, cognitive control
• HC rapid memorization
• Roles are defined by functional tradeoffs

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Key Trade-offs

• Extracting what is generally true (across events)
  vs. memorizing specific events
• Inference (spreading activation) vs. robust
  active maintenance

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Hands-On Exercises

• The goal of the hands-on part of the workshop is
  to get a feel for the kinds of representations
  that are acquired by Hebbian vs. error-driven
  learning, and for network dynamics more generally.

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• Here is the network that we will be using

• Activity constraints Only 10 of hidden units
  can be strongly active at once in the input
  layer, only one unit per row
• Think of each row in the input as a feature
  dimension (e.g., shape) and the units in that row
  are mutually exclusive features along that
  dimension (square, circle, etc.)

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• This diagram illustrates the connectivity of the
  network

• Each hidden unit is connected to 50 of the input
  units there are also recurrent connections from
  each hidden unit to all of the other hidden units
• Weights are symmetric
• Initial weight values were set randomly

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• I trained up the network on the following 8
  patterns

Typical Bird Number 1
Typical Bird Number 2
Typical Fish Number 2
Typical Fish Number 1
Typical Bird Number 3
Atypical Bird (duck)
Atypical Fish (flying fish)
Typical Fish Number 3

• In each pattern, the bottom 16 rows encode
  prototypical features that tend to be shared
  across patterns within a category the top 8 rows
  encode item-specific features that are unique to
  each pattern.
• Each category has 3 typical items and one
  atypical item
• During training, the network studied typical
  patterns 90 of the time and it studied atypical
  patterns 10 of the time

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• To save time, the networks you will be using have
  been pre-trained on the 8 patterns (by presenting
  them repeatedly, in an interleaved fashion)
• For some of the simulations, you will be using a
  network that was trained with (purely) Hebbian
  learning

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• For other simulations, you will be using a
  network that was trained with a combination of
  error-driven (GeneRec) and Hebbian learning.
  Training of this network use a three-phase
  design
• First, there was a prediction (minus) phase
  where a partial pattern was presented
• Second, there was an outcome (plus) phase where
  the full version of the pattern was presented
• Finally, there was a nothing phase where the
  input pattern was erased (but not the hidden
  pattern)
• Error-driven learning occurred based on the
  difference in activity between the minus and plus
  patterns, and based on the differenced in
  activity between the plus and nothing patterns

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• When you get to the computer room, the simulation
  should already be open on the computer (some of
  you may have to double-up, I think there are
  slightly fewer computers than students) and there
  will be a handout on the desk explaining what to
  do
• You can proceed at your own pace
• I will be there to answer questions (about the
  lecture and about the computer exercises) and my
  two grad students Ehren Newman and Sean Polyn
  will also be there to answer questions.

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Your Helpers
Ehren Sean
me