(More) Biologically Plausible Learning

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(More) Biologically PlausibleLearning

• Psych 419/719
• March 13, 2001

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A Bit About Neurons
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There are a lot of them...

• It has been estimated that the brain has about
  1011 or so neurons
• Each neuron on average connects to about 1,000
  synapses
• So thats about 1014 connections

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Action Potentials

• At rest, the charge across a neurons membrane is
  slightly negative
• When a neuron is stimulated strongly enough, an
  action potential results.
• A wave of positive charge that propagates along
  the axon or dendrite
• Kind of like a cable
• Tend to be all-or-nothing. If stimulation is
  enough, you get a spike. Otherwise, nothing.

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Motion of Electrical Charge
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In Models Weve Considered..

• Some output a floating point value, say 0 to 1
• Can be thought of as the firing rate. Neurons
  fire at around 2-400 hz (give or take)
• Some stochastic networks weve considered either
  are on or off, probabilistically
• But are typically time-locked

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The Problem with Backprop

• In backprop, activity proceeds from one unit to
  another along weighted connections. Fine.
• But error proceeds backwards along those same
  connections.
• That doesnt seem to happen with real neurons...

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(Broadly) How the BrainIs Connected
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Different Layers Often WorkAt Different Levels
of Abstraction

• Area V1 codes things like line segments, local
  colors and such
• Have a small receptive field
• Higher areas (like IT) code for objects
• Much larger receptive field

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This Isnt How We (Typically) Do Things

• We allow excitatory and inhibitory connections to
  be intermixed
• Dont tend to constrain connectivity in this way
• We (generally) dont force our units to have
  restricted receptive fields. Hidden units tend to
  see the whole input

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Competitive Learning

• Here, we can force pools of units to compete with
  each other in a winner-take-all fashion
• Competition can be done explicitly, or through
  lateral inhibition

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The Idea...

• Each unit in a cluster gets input from same units
• A unit learns if and only if it wins the
  competition within its cluster
• Each units total input weight is the same

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Mathematically..

• c determines if unit i is on for pattern k
• n is the number of active units in pattern k

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What it Means

• Each winning units weight decays in proportion
  to g
• But gains some weight in proportion to g, and how
  many input are on.
• Shifts weight from inactive to active unit lines.
  Makes it more sensitive to what was going on in
  the input

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An Alternate Formulation

• If a unit always loses, something still happens
  to it.
• Strength of what happens for winner is higher
  than for loser

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What Happens

• Based on the statistics of the input, the network
  shifts its weights to respond selectively to
  common patterns
• Level of activity across units comes to reflect
  the structure of the input
• Has an inductive bias

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Inductive Biases

• Form a reduced representation - preform
  dimensionality reduction
• Identify abstract or relational features which
  predict other inputs (e.g., QU)
• A coarse code
• A sparse code - independent components
• Topological features in the structure of inputs

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Finding k Means
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Restricting Input
Instead of each unit receiving input from each
input unit, only from a set of organized input
units
The receptive field of each unit can overlap
with other ones, but not totally
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Local Excitation, Distal Inhibition

• We can arrange our lateral connections in space
  so that units near us are excited by us, and
  those further away are inhibited
• Can help preserve topology of inputs

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Space
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Ex Retinotopic Mapping

• The connections from the retina to visual area V1
  preserve the approximate topology of the retina
• How? Takes a lot of DNA to prescribe that
• Von Der Malsburgs solution combine inhibition
  and excitation in right spatial configuration

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The 1D Case
Either line preserves topology
Output Units
Inhibition and excitation depending on location
Input Units
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Phoneme Discrimination

• The phenomena Young Japanese infants (less than
  8 months) can distinguish the /r/ and /l/ phoneme
• They lose this ability as they get older
  phonemes are not contrastive in their language
• Lost discrimination seems resilient to experience

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A Theory...

• In a backprop net, exposures to training generate
  error if you make the wrong output. Thus, errors
  should get fixed over time.
• Doesnt seem to happen with such critical
  period effects like the /r/ - /l/ distinction
• With hebb learning, your output gets reinforced,
  even if its wrong.

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A Solution

• Generate stimuli that is so far outside of the
  normal range, that conditioned response cant
  happen
• Thus, conditioned response isnt reinforced
• And unlearning can occur.

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The /r/ - /l/ Intervention

• Based on a competitive map of phoneme space
  system learns to map similar sounds to the same
  representation.
• If you bombard the system with stimuli that are
  similar to what its seen, but different enough to
  force a new representation, these items can be
  discriminated
• As can the more similar ones

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The Experiment

• Expose subjects to exaggerated tokens of
  language. No feedback
• Adaptive case push the contrast so that they
  dont reinforce wrong results
• Non-Adaptive case used fixed contrasts
• Result Both improved perception
• Adaptive case more so than non-adaptive

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Upcoming...

• Next class
• Reinforcement learning. No required reading
• Hand in project proposals
• Homework 4 handed out
• Next Tuesday Steve Gotts guest lecture
• Next Thursday Anthony Cate guest lecture