Transcript Connectionism

Summer 2011
Monday, 8/1
As you’re working on your paper
• Make sure to state your thesis and the
structure of your argument in the very first
paragraph.
• Help the reader (me!) by including signposts
of where you are in the argument.
• Ask yourself what the point of each paragraph
is and how it contributes to your argument.
• Give reasons for your claims! Don’t make
unsupported assertions.
Neural Networks
• The brain can be thought of as a highly complex, non-linear
and parallel computer whose structural constituents are
neurons. There are billions of neurons in the brain.
• The computational properties of neurons are the reason why
we’re interested in neurons more than in any other, nonneuronal cells in the brain.
Neural Networks
• Consider a simple recognition task, e.g. matching
an image with a stored photograph.
• To perform the task, a computer must compare
the image with thousands of stored photographs.
• At the end of all the comparisons, the computer
may output the photograph that best matches
the image.
• If the photograph database is as large as the one
in our memory, this may take several hours.
• But our brain can do this instantly!
Neural Networks
• A silicon chip can perform a computation in
nanoseconds (10 to the power of -9 seconds).
• But neuronal computations are done in
miliseconds, which are 6 orders slower!
• Yet it seems that our computational capability
(processing speed) is enormously greater than
that of the typical computer.
• How is this possible?
Neural Networks
• The answer seems to lie in the massively
parallel structure of the brain, which includes
trillions of interconnections between neurons.
Artificial Neural Networks
• Inspired by the organization of the brain.
• Like the brain, are composed of many simple
processors linked in parallel.
• In the brain, the simple processors are neurons
and the connections are axons and synapses.
• In connectionist theory, the simple processing
elements (much simpler than neurons) are called
units and the connections are numerically
weighted links between these units.
• Each unit takes inputs from a small group of
neighbouring units and passes outputs to a small
group of neighbors.
NETtalk
• An artificial neural network that can be
trained to pronounce English words.
• Consists of about 300 units (neurons)
arranged in three layers: an input layer, which
reads the words, an output layer, which
generates speech sounds, or phonemes, and a
middle, ''hidden layer,'' which mediates
between the other two.
• The units are joined to one another with
18,000 synapses, adjustable connections
whose strengths can be turned up or down.
NETtalk
• At first volume controls are set at random and
NetTalk is a structureless, homogenized tabula
rasa. Provided with a list of words, it babbles
incomprehensibly. But some of its guesses are
better than others, and they are reinforced by
adjusting the strengths of the synapses
according to a set of learning rules.
• After a half day of training, the pronunications
become clearer and clearer until NetTalk can
recognize some 1,000 words. In a week, it can
learn 20,000.
NETtalk
• NetTalk is not provided with any rules for how
different letters are pronounced under different
circumstances.
(It has been argued that ''ghiti'' could be
pronounced ''fish'' - ''gh'' from ''enough'' and ''ti''
from ''nation.'')
• But once the system has evolved, it acts as
though it knows the rules. They become implicitly
coded in the network of connections, though noone has any idea where the rules are located or
what they look like. (On the surface, there’s just
“numerical spaghetti”)
Back-Propagation
• The network begins with a set of randomly selected
connection weights.
• It is then exposed to a large number of input patterns.
• For each input pattern, some (initially incorrect)
output is produced.
• An automatic supervisory system monitors the
output, compares it to the target output, and
calculates small adjustments to the connection
weights.
• This is repeated until (often) the network solves the
problem and yields the desired input-output profile.
Distributed Representation
• A connectionist system’s knowledge base does
not consist in a body of declarative statements
written out in a formal notation.
• Rather, it inheres in the set of connection weights
and the unit architecture.
• The information active during the processing of a
specific input may be equated with the transient
activation patterns of the hidden units.
• An item of information has a distributed
representation if it is expressed by the
simultaneous activity of a number of units.
Superpositional Coding
• Partially overlapping use of distributed
resources, where the overlap is
informationally significant.
• For example, the activation pattern for a black
panther may share some of the substructure
of the activation pattern for a cat.
• The public language words “cat” and
“panther” display no such overlap.
“Free” Generalizations
• A benefit of connectionist architecture.
• Generalizations occur because a new input
pattern, if it resembles the old one in some
aspects, yields a response that’s rooted in that
partial overlap.
Graceful Degradation
• Another benefit of connectionist architecture.
• The ability of the system to produce sensible
responses given some systematic damage.
• Such damage tolerance is possible in virtue of
the use of distributed, superpositional storage
schemes.
• This is similar to what goes on in our brains.
Compare: Messing with wiring in a computer.
Sub-symbolic representation
• Physical symbol systems displayed semantic
transparency: familiar words and ideas were
rendered as simple inner symbols.
• Connectionist approaches introduce greater
distance between daily talk and the contents
manipulated by the computational system.
• The contentful elements in a subsymbolic
program do not reflect our ways of thinking
about the task domain.
• The structure that’s represented by a large
pattern of unit activity may be too rich and subtle
to be captured in everyday language.
Post-training Analysis
How do we figure out what knowledge and
strategies the network is actually using to
solve the problems in its task domain?
1. Artificial lesions.
2. Statistical Analysis, e.g. PCA, cluster
analysis.
Recurrent Neural Networks
• “Second generation” neural networks.
• Geared towards producing patterns that are
extended in time (e.g. commands to produce a
running motion) and to recognizing temporally
extended patterns (e.g. facial motions).
• Includes a feedback-loop that “recycles” some
aspects of the networks activity at time t1 along
with the new inputs arriving at t2.
• The traces that are preserved act as short-term
memory, enabling the network to generate new
responses that depend both on current input and
on the previous activity of the network.
Dynamical Connectionism
• “Third generation” connectionism.
• Puts even greater stress on dynamic and time
involving properties.
• Introduces more neurobiologically realistic
features, including special purpose units, more
complex connectivity, computationally salient
time delays in processing, deliberate use of
noise, etc.