程序代写代做代考 Computational Neuroscience – 12 conditioning
Computational Neuroscience – 12 conditioning
Figure 1: This is a picture of one of Pavlov’s dogs, it has been stuffed and is preserved at
The Pavlov Museum. You can see where the salvia tube and container has been
implanted. [Picture from http://en.wikipedia.org/wiki/Ivan Pavlov]
Introduction
These notes are about the classical conditioning and the mesocortical dopaminergic pathway
which is believed to be responsible for the brain’s reward system.
Classical conditioning
Pavlov is the biggest fool I know; any policeman could tell you that much about a
dog. – George Bernard Shaw
In Pavlov’s famous experiment, conduction at the turn of the nineteenth and twentieth
centuries, a bell is rung a short time before a dog is fed; obviously feeding causes salivation in
the dog, but the curious thing is that after a while the dog salivates as soon as it hears the
bell. This experimental and the conclusion that were drawn from it were hugely controversial
at the time, opinions ranged from Shaw’s above, claiming that nothing interesting had been
measured or concluded. For its proponents, Pavlovian conditioning seemed to promise a new
scientific era of psychology and even promised the ‘the perfectibility of man’ and featured, for
example, in Aldous Huxley’s dystopian novel Brave New World and his utopian novel The
Island. As for Shaw:
If ‘A’ is drowning on one side of a pier and ‘B’ is equally drowning on the other,
and you have one lifebelt, to which of the two would you like to throw it? Which
would I save, Pavloff or Shaw? What is the good of Shaw? And what is the good
of Pavloff? Pavloff is a star which lights the world, shining above a vista hitherto
unexplored. Why should I hesitate with my lifebelt for one moment? – H.G. Wells
These days we describe the bell as an conditioned stimulus (CS), it produces salivation only
after training, the food is an unconditioned stimulus (US), it always produces response. In
other words, the US is the food since it already produces the reaction: salivation, whereas the
bell is the CS since it only produces the response after training, that is, after conditioning.
Classical, or Pavlovian, conditioning is also distinguished from instrumental or operant condi-
tioning in which the actions of animal determine the reinforcement; like Pavlovian conditioning,
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Computational Neuroscience – 12 conditioning
Figure 2: Changes in w. In each trial a stimulus is presented with probability 0.5; during the
first 150 trials the stimulus is accompanied by a reward of r = 1, after that by r = 0.
Plotted is the resulting Rescorla-Wagner changes in w as it learns the reward and
as the conditioning is extinguished. The learning rate is η = 0.05. This is roughly
based on a similar figure in [2].
operant conditioning has a controversial history, it is associated with another behaviourist, B.F.
Skinner, but away from the complex philosophical and political interpretations, both forms of
conditioning are now important neuroscientific tools.
Models of classical conditioning
The widely used Rescorla-Wagner model of classical conditioning works [1] like a perceptron;
based on the stimulus the animal anticipates a reward and adjusts its prediction according to
its accuracy. Hence, if x is a binary value representing the presence or absence of the stimulus,
r > 0 is the reward; a negative r would correspond to an aversive event, v is the predicted
reward and w the weight used by the animal to predict the reward:
v = wx (1)
The Rescorla-Wagner rule is then
w → w + ηδx (2)
where δ = r−v is the error in prediction and η is a learning rate. These dynamics are illustrated
in 2.
The Rescorla-Wagner rule generalizes to more than one stimulus-reward pair. Say xi is the
binary value representing the presence or absence of the ith stimulus and ri is the corresponding
reward, then the total reward is
r =
∑
i
xiri (3)
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Computational Neuroscience – 12 conditioning
and the predicted reward is
v =
∑
i
xiwi (4)
and the learning rule is
wi → wi + ηδxi (5)
where δ = r − v as before.
One significant victory for this proposal is that it explains blocking. Consider conditioning
a reward r on a stimulus s1 and then changing so that there are two stimuli used to predict r,
s1 and s2; now, when s2 is shown on its own to the animal it does not anticipate the reward.
Thus, for example, Pavlov’s dog might be shown a light just before it is fed and will soon
salivate when it sees the light; next a light is lit and a bell rung before feeding, now, if the
bell is rung on its own, the dog does not salivate; the light has blocked the bell. This is an
easy consequence of the Rescorla-Wagner rule since the w for the light already gives a correct
prediction of the target and so the w for the bell stays at zero as there is no error. Blocking is
not a consequence of other models of conditioning proposed at the same time. It has, however,
been observed in behavior. [3, 4].
Ventral tegmental area
The ventral tegmental area (VTA) is located immediately beside the substantia nigra (SN)
in the midbrain. In Wikipedia it says ‘[VTA] is important in cognition, motivation, orgasm,
drug addiction, intense emotions relating to love, and several psychiatric disorders.’ We are
interested in it here because it is believed to play an important role in the reward system.
The VTA has a large number of dopaminergic neurons, dopamine is a neuromodulator; the
level of dopamine alters the dynamics of synapses: different synapses have different dopamine
receptors and so their dynamics might be altered in different ways. Dopaminergic neurons
are not common, there are about 400,000 in the human brain, about half of these are in
the VTA and half of VTA neurons are dopaminergic. these dopaminergic neurons project to
diverse areas in the brain, see Fig. 3, including hippocampus, basal ganglia and the prefrontal
cortex. These projections transmit dopamine to these areas. Another peculiarity of VTA is
that contains a large number of gap junctions.
The idea here is that δ, the error, is calculated in dopaminergic VTA neurons and that
neuromodulation produces the Rescorla-Wagner rule. This is sketched out in Fig. 4. Evidence
for this can be seen in a famous experiment [5] in which the activity of dopaminergic cells was
recorded in monkeys during conditioning. Before condition the dopaminergic neurons fire at
an elevated rate when the reward is received, after conditioning they fire at a depressed rate if
the anticipated reward fails to appear after the stimulus, Fig. 5.
Another thing is apparent from Fig. 5: when the animal has been conditioned the dopamin-
ergic neurons fire at the stimulus, the activity shifts forward from reward to the stimulus that
predicts it. In a way this makes sense, the unanticipated event is the stimulus; this predicts the
reward but is itself a surprise. This is also obviously useful, it allows the credit for the reward
to be usefully associated with the event that predicts it. If there are a series of events one
predicting the other it allows the credit to filter forwards to the event that initiates the whole
sequence, this might have consequence for behavior. A mechanism for this shifting forward
is known, it is a sort of time-segmented Rescorla-Wagner called temporal difference learning
[6, 7].
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Computational Neuroscience – 12 conditioning
Figure 3: This shows the dopamine pathways from VTA and from SN; VTA has major projec-
tions to hippocampus, the nucleus accumbens in the basal ganlia and to the prefrontal
cortex. [Picture from http://en.wikipedia.org/wiki/Dopamine]
cortex
x1 x2
striatum
w1 w2
v
VTA
δdopamine r
Figure 4: A schematic of the VTA reward circuit. The conditioned stimulus is presented and
this is communicated via the cortex, neurons in the striatum adjust this to give the
input wixi and these are added producing the estimated reward. This inhibits a
dopaminergic neuron in VTA, this neuron also receives excitatory input correspond-
ing to the actual reward, this difference is δ and δ is effects dopamine modulation w1
and w2 effecting some version of the Rescorla-Wagner rule.
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Computational Neuroscience – 12 conditioning
Figure 5: Dopaminergic cell activity. In the top panel there has been no conditioning, this
means the predicted reward is zero and the dopaminergic neurons firing correspond-
ing to a positive error; the reward exceeded expectation. The bottom panel shows
what happens after conditioning if the reward is not received, since a reward is pre-
dicted this is a negative error and depresses firing. The middle panel shows that
the consequence of conditioning is to advance the dopamine firing forward in time.
[Figure taken from [5]].
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References
Figure 6: In A1 the change in strength of EPSPs is shown plotted against time, the synapse
with closed circles has been stimulated to induce long term potentiation, the one
with open circles is a control. In A2 the same thing is done, but with dopamine
receptors blocked during the stimulation. [Picture from [9] which in turn adapted it
from [10]]
The VTA and hippocampus
Back in Fig. 3 we saw that VTA also projects to the hippocampus; we have previously examined
memory in the hippocampus so it is interesting to speculate what the role of this projection is.
In [9] it is argued that there is a signal from VTA to hippocampal in which dopamine is used
to mark novel and salient stimuli, prompting their encoding in memory. In this model a new
stimulus is tested in CA1 or PRC to see if it is already stored in hippocampus, if it isn’t, this
is communicated to VTA where the local activity will test how novel, salient or surprising this
stimulus is, this is a role akin to, but slightly different from the role described above in classical
conditioning. If it is novel, activity in the dopaminergic neurons increased long term plastic
changes in hippocampus. Evidence for this is found in [10] where it is shown that blocking
dopamine receptors in hippocampus reduces learning.
References
[1] Rescorla RA and Wagner AR. (1972) A theory of Pavlovian conditioning: Variations in
the effectiveness of reinforcement and nonreinforcement, Classical Conditioning II, Black,
AH and Prokasy WF, Eds., 64–99. Appleton-Century-Crofts.
[2] Dayan P and Abbott FA. (2001) Theoretical neuroscience. MIT press (Cambridge, MA).
[3] Miller RR, Barnet RC and Grahame NJ. (1995) Assessment of the Rescorla-Wagner model.
Psychological bulletin 117: 363-86
[4] Azorlosa JL and Cicala GA. (1986) Blocking of conditioned suppression with 1 or 10
compound trials. Animal Learning and Behavior 14: 163–7.
[5] Schultz W, Dayan P and Montague PR. (1997) A neural substrate of prediction and
reward. Science 275: 1593–9.
[6] Sutton R (1988) Learning to predict by the methods of temporal differences. Machine
Learning 3: 9–44.
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References
[7] Sutton R and Barto S (1998). Reinforcement Learning. MIT Press (Cambridge, MA).
[8] Barto AG. (1995) Adaptive critics and the basal ganglia. Models of information processing
in the basal ganglia. Eds. Houk JC, Davis JL and Beiser DG. MIT press (Cambridge, MA).
[9] Lisman JE and Grace AA (2005) The hippocampal-VTA loop: controlling the entry of
information into long-term memory. Neuron 46: 703–13.
[10] Morris RG, Moser EI, Riedel G, Martin SJ, Sandin J, Day M and O’Carroll C (2003)
Elements of a neurobiological theory of the hippocampus: the role of activity-dependent
synaptic plasticity in memory. Philosophical Transactions of the Royal Society. 358: 773–
786.
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