Nature requires Nurture

Initial wiring is genetically controlled
 Sperry

Experiment
But environmental input critical in early
development

Occular dominance columns

Hubel and Wiesel experiment
Critical Periods in Development
There are critical periods in development
(pre and post-natal) where stimulation is
essential for fine tuning of brain
connections.
 Other examples of columns

 Orientation
columns
Pre-Natal Tuning: Internally
generated tuning signals

But in the womb, what provides the feedback to establish which
neural circuits are the right ones to strengthen?

Not a problem for motor circuits - the infant moves its limbs to refine the
feedback and control networks.
 But there is no vision in the womb.



--Systematic moving patterns of activity are spontaneously generated prenatally in the retina.
A predictable pattern, changing over time, provides excellent training data for
tuning the connections between visual maps.
The pre-natal development of the auditory system

Research indicates that infants, immediately after birth, preferentially
recognize the sounds of their native language over others. The
assumption is that similar activity-dependent tuning mechanisms work
with speech signals perceived in the womb.
Post-natal environmental tuning

The pre-natal tuning of neural connections using
simulated activity can work quite well –
a
newborn colt or calf is essentially functional at birth.


This is necessary because the herd is always on the move.
For many animals, including people, experience is
absolutely necessary for normal development (as in
the kitten experiment).

For a similar reason, if a human child has one weak eye, the
doctor will sometimes place a patch over the stronger one,
forcing the weaker eye to gain experience.
Adult Plasticity and Regeneration
The brain has an amazing ability to reorganize itself
through new pathways and connections rapidly.
• Through Practice:
• London cab drivers, motor regions for the skilled
• After damage or injury
• Undamaged neurons make new connections and take
over functionality or establish new functions
• But requires stimulation
• Stimulation standard technique for stroke victim
rehabilitation
When nerve stimulation changes, as with amputation, the brain
reorganizes. In one theory, signals from a finger and thumb of an
uninjured person travel independantly to separate regions in the brain's
thalamus (left). After amputation, however, neurons that formerly
responded to signals from the finger respond to signals from the thumb
(right).
Summary

Both genetic factors and activity dependent
factors play a role in developing the brain
architecture and circuitry.
 There
are critical developmental periods where
nurture is essential, but there is also a great ability for
the adult brain to regenerate.


Next: What computational models satisfy some
of the biological constraints.
Question: What is the relevance of development
and learning in language and thought?
Connectionist
Models: Basics
Srini Narayanan
CS182/CogSci110/Ling109
Spring 2008
Neural networks abstract from
the details of real neurons
Conductivity delays are neglected
 An output signal is either discrete (e.g.,
0 or 1) or it is a real-valued number
(e.g., between 0 and 1)
 Net input is calculated as the weighted
spatial sum of the input signals
 Net input is transformed into an output
signal via a simple function (e.g., a
threshold function)

The McCullough-Pitts Neuron
yj
wij
xi
f
yi
ti : target
xi = ∑j wij yj
yi = f(xi – qi)
Threshold
yj: output from unit j
Wij: weight on connection from j to i
xi: weighted sum of input to unit i
Neural nets: Mapping from neuron
Nervous System
Computational Abstraction
Neuron
Node
Dendrites
Input link and propagation
Cell Body
Axon
Combination function,
threshold, activation function
Output link
Spike rate
Output
Synaptic strength
Connection strength/weight
Simple Threshold Linear Unit
Simple Neuron Model
1
Simple Neuron Model
1
1
1
1
Simple Neuron Model
1
1
1
1
1
Simple Neuron Model
0
1
1
1
Simple Neuron Model
0
1
1
1
0
Abstract Neuron
output y
y {1 if net > 0
0 otherwise
n
net   wiii
i 0
w0
I0 = 1
w1
i1
w2
i2
wn
...
input i
in
Computing with Abstract Neurons

McCollough-Pitts Neurons were initially used to
model
 pattern classification
 size = small AND shape = round AND color = green AND
location = on_tree => unripe
 linking classified patterns to behavior
 size = large OR motion = approaching => move_away
 size = small AND direction = above => move_above

McCollough-Pitts Neurons can compute logical
functions.
 AND,
NOT, OR
Computing logical functions: the OR
function
i1
i2
b=1
w01
w02
w0b
x0
f
y0
i1
i2
y0
0
0
0
0
1
1
1
0
1
1
1
1
• Assume a binary threshold activation function.
• What should you set w01, w02 and w0b to be so that
you can get the right answers for y0?
Many answers would work
y = f (w01i1 + w02i2 + w0bb)
i2
recall the threshold function
the separation happens when
w01i1 + w02i2 + w0bb = 0
i1
move things around and you get
i2 = - (w01/w02)i1 - (w0bb/w02)
Decision Hyperplane




The two classes are therefore separated by the
`decision' line which is defined by putting the
activation equal to the threshold.
It turns out that it is possible to generalise this
result to TLUs with n inputs.
In 3-D the two classes are separated by a
decision-plane.
In n-D this becomes a decision-hyperplane.
Linearly separable patterns
Linearly Separable Patterns
PERCEPTRON is an architecture which can
solve this type of decision boundary problem.
An "on" response in the output node
represents one class, and an "off" response
represents the other.
The XOR function
i1
i2
y
0
0
0
1
0
1
1
1
0
1
1
0
The Input Pattern Space
The Decision planes
Multiple Layers
y
0.5
1
-1
0.5
1.5
1
1
1
I1
1
I2
Multiple Layers
y
0.5
1
-1
0.5
1.5
1
1
1
1
I1
I2
0
1
Multiple Layers
y
0.5
1
-1
0.5
1.5
1
1
1
1
I1
I2
1
1
Types of abstract neuron
parameters
•
The form of the combination function - e.g. linear,
sigma-pi, cubic.
• The activation-output relation - linear, hard-limiter, or
sigmoidal.
• The nature of the signals used to communicate
between nodes - analogue or boolean.
• The dynamics of the node - deterministic or
stochastic.
• Spatio temporal information encoding:
•
Pulse coding and Spiking Neurons
Types of Activation functions
The Sigmoid Function
y=a
x=neti
The Sigmoid Function
Output=1
y=a
Output=0
x=neti
The Sigmoid Function
Output=1
Sensitivity to input
y=a
Output=0
x=neti
Changing the exponent k(neti)
K >1
K<1
Radial Basis Function
f ( x)  e
 ax 2
Stochastic units

Replace the binary threshold units by binary
stochastic units that make biased random
decisions.
 The
“temperature” controls the amount of
noise
p( si 1)

1 e
1
  s j wij
j
T
temperature
Spiking Neurons and Pulse coding

Rate coding (ex. Sigmoid units)
 Spatial summation of input
 Output is the average number
of spikes in some time
window (normalized between 0 and 1).

Pulse coding (More realistic)
 Look at each individual spike (the time it is generated)
 Can take into account refractory period
 EXAMPLE: Integrate and fire neurons
 EXAMPLE: Time to first spike (Thorpe 1996).
 Adds power to the basic neuron by adding temporal
information
Triangle Nodes:
Encoding relational information with abstract neurons
The triangle node (aka 2/3 node) is a
useful function that activates its outputs (3)
if any (2) of its 3 inputs are active
 Such a node will be useful for lots of
representations.

Triangle nodes and
McCullough-Pitts Neurons?
Relation
Object
Value
A
B
C
Networks of Triangle nodes:
example sentence “They all rose”
triangle nodes:
when two of the
abstract neurons
fire, the third also
fires
model of
spreading
activation
Basic Ideas behind connectionist
models





Parallel activation streams.
Top down and bottom up activation combine to
determine the best matching structure.
Triangle nodes bind features of objects to values
Mutual inhibition and competition between
structures
Mental connections are active neural
connections
5 levels of Neural Theory of
Language
Pyscholinguistic
experiments
Spatial
Relation
Motor
Control
Metaphor Grammar
Cognition and Language
abstraction
Computation
Structured Connectionism
Neural Net
Triangle Nodes
SHRUTI
Computational Neurobiology
Biology
Neural
Development
Quiz
Midterm
Finals