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6th December (29
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g
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Associative chaining
a
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E
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this might apply to alphabet learning
2
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g
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We want to start the network off somehow and then make it produce sequence of
actions
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Recurrent connections: more complicated but also cause a series of connections

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

Static input leads to static output, but if there is feedback, dynamic output occurs
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g
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Jordan (1986)

6th December (29
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Elman (1990)
He was interested in the same thing, but have feedback from hidden layer of connections
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The hidden layer can feedback and it make a context for the next action, even though we
don’t have control over its activity
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Therefore this alters output, as input is altered
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Simple extension of feedforward architecture
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This doesn’t explain single trial learning
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Back-propagation algorithm is not biologically plausible due to the requirement of non-local
information from neurons (might be resolved by using more plausible algorithms e
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, reinforcement
learning)
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Normally used for static pattern completion, due to the symmetrical connections
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When learning symmetric weights (Hebbian rule for standard Hopfield network for static pattern
completion):

wji → wji + εSpiSpj

6th December (29
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‘Hebbian’ rule including increase for pre- then postsynaptic activation (plausible over short timescales, e
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< 100 ms):

This is not entirely biologically implausible, there is something called spike time independent plasticity
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If the presynaptic neuron’s activity is followed by activity in postsynaptic neurons, then the change in synapse is positive
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e
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So the
Hebbian rule is not as simple as having two neurons fire together, timing plays a large role
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the graph shows a sequence of actions
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11)
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Simple modification to the static pattern associator
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Can do fixed association of small number of elements in order, learning of stereotypical action
sequences, e
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‘central pattern generators’ (controlling muscle contractions in walking, swimming,
and heartbeat etc
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Providing neural “clocks” or “counters” (Amit 1988)

Shortcomings of Hopfield Serial Learning
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

Patterns must be uncorrelated
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Fundamental problems for chaining models (Lashley 1951)

What happens when there is a repeat? E
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spelling out ‘every’
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Also,
chains representing the spoken word, ‘cat’, ‘tack’ and ‘act’
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So different conflicting orders have to be learnt
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There is
a different representation of the same action occurring in different contexts
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The context-specific coding is not how the brain solves the problem
...
g
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A typical error is a transposition error,
i
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‘3, 4, 1, 2, 0’
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This
doesn’t fit well with association chaining model
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e
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Competitive queuing
A special mechanisms for the representation of time/serial position and for the serial selection of actions
(Grossberg 1978; Houghton, 1990)
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11)
Houghton thought that perception is parallel and the brain can process information in parallel, but action is
constrained to be serial
...
g
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There is competition between the two ideas, perception of tea and cake
are mirrored in neurons (grey) and they compete with each other
...
But then there is feedback inhibition from the tea neuron,
so the ‘tea’ neuron gets inhibited
...
But
then that receives inhibitory feedback neurons too and ‘tea’ neuron wins again and vice versa
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E
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cat, tact and act
...
e
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And these sounds are connected
by competitive filter, so the most active unit wins, and perform the
associated action, then the active unit is suppressed
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Dynamic control signal
Can learn to deal with repeats
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E
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spelling ‘every’
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And this could be done by associative chaining
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When the context signal is replayed the item units are reactivated in the order they
were perceived
...
g
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You can see a clear pattern of activation and deactivation
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It’s not that E will lead us back to N, in fact
whatever is stopping N firing (by some temporary noise or something), N is still going to be the most active
neuron, it is waiting to win the competition even more so now that it’s been missed out
...


6th December (29
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g
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Can manage different sequences of the same items
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Competitive filter fits well with more general requirement for action selection
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2002
Primates learn to draw shapes, each different line has a
different activity in the prefrontal cortex
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Even
before the primate starts to move, the different
representations of activity have an order, the first action is
the most active
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By adding feedback connections, sequences can be learned using standard supervised learning
algorithms
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Both these solutions implement a form of Associative Chaining
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A competitive filter allows only one action at a time
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Neurophysiological evidence exists for CQ in primate prefrontal cortex



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