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2011
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There is the same winner-takes-all structure but learning rule is
modified so that weights to outputs neighbouring the winner (Ok)
are also modified using a ‘neighbourhood function’ F
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So F(i,k) decreases
(maximum is 1, minimum is 0) from 1 to 0 as the distance increases
between two neurons
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Biologically speaking, this could occur by physical spread of chemical
neurotransmitters or messengers
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So the perceptron learns to classify two groups of input patterns by
finding weights to establish a ‘decision boundary’ between them
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There is a set of training set of inputs with target outputs
values
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Present the input pattern and find the corresponding output values
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(tin –oin) is known as delta, it is the error made by output i for the
input pattern n
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The delta value could be positive or negative, if it’s positive,
connection weight increases, if it’s negative, connection weight
decreases
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After training, the network can be used to sort data
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There are anomalies because the
training data set will have different distribution to the data set being
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presented
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Another important about perceptrons is that the delta rule only
learns connection weights
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So in order to find the threshold value using
the delta rule, the threshold value can be changed by making it into
another connection weight
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e
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Perceptrons can have many output units forming a single layer
neural network
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What restrictions are there on the power of the perceptron as a
classification device, and how can such restrictions be overcome (5
marks)?
Perceptrons can perform linear discrimination but cannot solve
‘non-linearly’ separable problems, e
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the ‘exclusive OR’ problem
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In this case, the simple
delta rule has to be changed
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The neurons can use a continuous transfer function instead of the
threshold logic function
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If the output value is closer to the target
value then the change is good
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Discuss the biological plausibility of these learning algorithms (5
marks)
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Competitive learning- place cells may use this learning algorithm
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Training sets
may have distributions of data to actual sets of data, the linear
decision boundary generated by perceptrons would be too rigid
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Error-back propagation- very unlikely to be used in real life
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Unlike
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Hebbian learning which is based on one synapse and its presynaptic
and postsynaptic firing rates
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2
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The problem is that action signal is needed to be generated to
achieve a desired state from a given current state
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Then the brain needs to learn how to get to a
desired state from the current state, e
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like playing a stroke in
tennis, or trying to shoot hoops in basketball
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All the hidden values are unknown, so an
algorithm (e
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error-back propagation) is needed to find the values
in order to make accurate movements
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Forward models is used to train for predictions about the outcome
of an arbitrary signal
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The very first prediction would be inaccurate, but there is sensory
input (visual and proprioceptive) telling the brain where the arm
actually ended up
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This means the differences between the observed
and predicted effect is the delta used in error-back propagation to
train the model
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The inverse model is trained after the forward model becomes fully
trained
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When there is a desired state to be achieved, the difference
between the desired state and the predicted state is the error used
in error back-propagation for this part of the network
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Describe how convergent force fields generated from the spinal
cord could aid the control of limb movement (8 marks)
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The idea of convergence force fields originated with Bizzi et al
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He stimulated the spinal cord, either electrically or using
glutamate at different levels and different areas of the spinal cord
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This was expected
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They were called convergence force fields (CFF)
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In other words, if the leg was already at the
equilibrium position to start with, stimulation of lateral neuropil
region would produce no movement
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Micro-stimulation at different levels of spine produces CFFs with
different equilibrium positions
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This wiring is advantageous to the organism
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This was what Bizzi et al
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So if an animal wants their leg to go anywhere, you can move
it there from any position just by giving the right of relative
activation to different CFF generators, which all have equilibrium
positions around the edge of the work space
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This is the
equilibrium point control hypothesis
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of CFF generators
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While the equilibrium point
control hypothesis may be relevant for frogs, it might not be as
applicable to primates
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In
particular, fine movements of fingers and thumbs don’t seem to be
focused in this way
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Give an example of how the firing rates of many neurons, each
with broadly tuned responses to specific values of a behavioural
variable, can be combined to give an accurate estimate of that
variable (5 marks)
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A population vector is the
firing rate weighted vector sum of preferred firing directions of
neurons
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Basically each neuron has a preferred firing direction, and all the
neurons of different firing direction has different firing rates
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This is a
good way of averaging across all the noisy neurons to get a good
overall estimate of which direction the neurons are encoding
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g
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Reaching movement could be coded by population vector
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These
different neurons with different preferred reaching directions are all
fire at different rates, so just take the firing rate weighted vector
sum of preferred directions to get an estimate of which reaching
direction the neurons are encoding (Georgopoulos et al
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The
estimate is not exact but accuracy increase with number of neurons
to filter out noise
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Each place cell has a preferred location of firing,
which could be a vector, so a rat’s location is well predicted by firing
rate weighted vector average of preferred locations
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Also,
population vector is only actually the best optimal estimator when
the tuning is a cosine function
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Population vectors would work more efficiently for head direction,
as there is a possible coverage of all directions
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Make eye movement to retinal
position A, there is a bump of activity in all the neurons around A
centred on A
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Associative memory is being able to learn and remember
relationships between unrelated items
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E
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remember an event by linking the people, objects,
time and space together
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When a partial cue from the memory is presented, pattern
completion occurs and the whole episode is retrieved
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Describe how the hippocampus might act as an associative
memory system (6 marks), including how its anatomical structure
relates to this function (5 marks),
CA3 neurons in the hippocampus have recurrent connections to
other CA3 neurons
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This is a classic network of the hippocampus
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




CA3 neurons receive input from perforant pathway from the
entorhinal cortex, these are weak distal synapses
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o The inputs are small in number but very powerful- a
single DG synapse can make a cell fire; they are
detonator synapses
The other set of inputs from the perforant path of the
entorhinal cortex could be used for retrieval
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Then EC present partial cue and
causes retrieval of the pattern
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1995
A way to separate learning and retrieval by using neuromodulator
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Ach coming from medial septum
and it changes properties of neurons in CA3 to go between learning
and recall
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So during learning, there is a large flood of Ach to
suppress recurrent excitatory connections, enhance synaptic
plasticity and boost detonator synapses
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There are problems with this model: slow- neuromodulators will
take a few seconds to diffuse
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It is known that there is a lot of acetylcholine release from
the medial septum in rats when they are in a novel environment;
Ach modulates synaptic plasticity in the hippocampus; it is know
that it suppresses recurrent connections
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Perforant path synapses in the dentate gyrus undergo selforganisation to form new representations of input form
entorhinal cortex
2
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Excitatory recurrent connections in stratum radiatum (in
hippocampus) mediate auto-associative storage and recall
of these patterns
4
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5
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The
comparison of recall activity in region CA3 with direct input
to region CA1 regulates cholinergic modulation, allowing a
mismatch between recall and input to increase ACH, and a
match between recall and input to decrease Ach
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There is a network that an only store a limited number of patterns,
too many patterns means interference occur, spurious memories
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form
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In order of the hippocampus to do this, you need
very plastic synapses at a very fast learning rate- rapid ‘one-shot’
associative learning
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This is the price to pay for fast learning rate
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The slow system has no
problem with interference, can look at events over time and slowly
extract underlie structures, look at commonalities between events
and make them stronger
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This idea is based on Marr (1971)
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People argue
that during sleep, the hippocampus replays the event and
trains the neocortex to remember and associate the
different inputs (smell, sight etc
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o Is this transfer or training? Do memories truly leave
the hippocampus?
Timescale? One night or twenty years → graded retrograde
amnesia?
Generalisation / abstraction of meaning from multiple
events leads to semantic memory from episodic memory?

Hippocampus is an index (this index represents cross-modal biding)
or convergence zone for disparate neocortical sites which store the
memory content
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This is anatomical evidence why memory
transfer might be true
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The standard consolidation model (Squire and Alvarez 1995)


States that all declarative memories are treated in the same
way by the medial temporal lobe, this means semantic

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

memory of facts and episodic memory of events are the
same
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It binds together neocortical
memory traces
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Memory consolidation occurs when the hippocampal system
repeatedly reactivates representations in neocortex, leading
eventually to strong interconnections among cortical sites, which
can support memory independently of the hippocampal system
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So older memories are less susceptible to be
wiped away by hippocampal damage – as they are distributed more
widely so larger lesions needed to affect remote memories
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e
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However, true and detailed episodic memories always depend on
the hippocampus
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Eventually a memory can become
independent of the hippocampus but to remember it vividly, the
hippocampus is needed
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Discuss how the biophysical properties of a single neuron can
determine what type of function it performs (4 marks)
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A simple artificial neurons have a threshold logic function, the
network uses a simple integrate and fire model
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The ‘net input’ to the
neuron is calculated as the ‘weighted sum’ of input activations
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This is like calculating a dot product
of vectors
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Time of firing of neurons are especially useful in scale-invariant
recognition
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g
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Doesn’t matter if the person speaks softly or
loudly, the identity of the speaker can still be recognised
E
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scent, either weak or smell, still recognisable
Pattern of activity in input neurons is a vector, x
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To recognise input pattern of activity x as
similar to stored pattern x*, i
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x ≈ λx*
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Standard neural networks have to normalise inputs to do
scale-invariant recognition
o Normalisation could be achieved by feedback
inhibition
o But this still poses a problem as standard neural
networks are strength dependent rather than
pattern dependent
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This weak input is not
fundamental in deciding what the outcome is
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Linear pattern separation (perceptrons: weighted sum of
firing rates and threshold) are not suitable for scale invariant
recognition
Tuning to respond at a given absolute value (e
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head
direction and place cells, radial based functions) are not
suitable for scale-invariant recognition either
Tuning to respond to given relative values are suitable for
scale invariant recognition
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This model of
computation explains how one scheme of neuroarchitecture can be
used for very different sensory modalities and seemingly different
computations
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g
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When there is no input current, the sub-threshold cell potential
oscillation (solid line) never exceeds the firing threshold (horizontal
broken line)
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The pattern is coded by the timing of spikes relative to a subthreshold membrane potential oscillation
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e
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If there is a big input
current, then the shift of cell potential oscillation upwards will occur
relatively early in the oscillation wave
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So small inputs must fire
near the peak of the sub-threshold membrane potential oscillation
for it to be able to bring it to firing threshold
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Olfactory bulb, hippocampus have this oscillation so this might be
how information is coded in them
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The input
neurons are coded by the strength of a smell they’ve detected and
their inputs are one spike each, but the timing of that input is crucial
instead
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So neuron one fires early
in the oscillation wave because it has a large current and brings the
cell’s oscillation above firing threshold
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So all the neurons fire once per cycle at slightly differently points in
the cycle
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So all the input neurons’ spikes will arrive simultaneously
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at the output neuron, and that will make a big impact on the output
cell, especially if the cell does coincidence detection
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If there is a
different pattern, the conduction delays will not fit and the firing will
not summate
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Provides alternative to standard models of input values = activation
(firing rates) and processing using variable connection strengths
(more plausible due to existence of LTP and LTD)
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Adding scale invariant:
If the time advance (Ti) is proportional to the log of the input
current, log(xi), then the network will do scale-invariant recognition,
if the input current strength is doubled: log(2xi)= log(2) + log(xi)
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By doubling, the output neuron will respond
earlier by log(2)
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Consider the shape of the oscillatory curve, it is roughly sinusoidal so
it could produce something like a log coding of stimulus intensity
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So the shape of this membrane oscillation
curve over time means small increases in inputs are actually
magnified in giving a big time advance than big inputs
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Evaluation of model
The oscillation is 10 Hz, so that is 100 msec between each peak,
therefore time advance of different neurons have to be 10, 20 msec
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e
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However in myelinated axons,
transmission delays are much shorter than this, usually 1 or 2 msec
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In the hippocampus there are weird axons
from dentate gyrus granule cells going to CA3 pyramidal cells which
are not myelinated, so transmission may be slow
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However even if it is possible to
have different delays, there is no learning rule for setting delays or
means of changing them
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So a developmental setting might exist so
that important odours are hardwired and automatically detected,
but it is not particularly flexible like the standard model is, where
there is plenty of evidence that you can rapidly change the strength
of connections in synapses
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Discuss the neural representations that allow a mammal to
know where it is within its environment (8 marks)
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Place cells fire whenever a rat is in a given location (O’Keefe and
Dostrovsky 1971)
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They are mainly found in CA1 and CA3 of the hippocampus
proper, but have also been found in the subiculum and entorhinal
cortex
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However,
in narrow arm mazes, where the animal is running back and forth on
linear tracts, the place cells fire differently depending on the
direction of movement of the rat
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If all cues are removed, the place cells
might rotate slowly because the mouse doesn’t known the definitive
location anymore
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Hippocampal pyramidal cells are the final,
output layer of the device
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Sensory inputs  competitive learning  entorhinal cortex with
functions similar to place cells, but not as accurately tuned 
completive learning  place cells in the hippocampus (CA1 and
CA3)
O’Keefe and Burgess (1996) - Place cells also have cues from
boundary vector cells (BVCs)
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Sharper tuning of BVCs for shorter distances,
more broad tuning for longer distances
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Place
fields are modelled as the threshold sum of 2 or more BVC firing
fields
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Place cell firing in new environmental
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layouts can be predicted using BVCs
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2009)
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The
BVCs model is good at capturing sensory aspects, but it doesn’t take
learning into account
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Place field stability in a novel environment depends
on NMDA receptors in CA3 (Kentros et al
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2002)
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2002) and place cells distinguish locations with
experiences (Barry et al, 2006)
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Head direction cells: Ranck (1984) first discovered them in the dorsal
presubiculum
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The primary correlate is the
azimuthal orientation of the head in the horizontal plane
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(2005)
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Nearby gird cells have grids of similar
orientation and scale, but they are shifted to tile the environment
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What is the problem of “temporal credit assignment” in learning (3
marks)?
These problems occur in reinforced learning, a form of slightly
supervised learning
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The solution is to have an internal critic to assess performance and
guides actions
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The temporal difference learning is a slow ‘trial and error’ based
method, but it is biologically plausible
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Describe the neural mechanisms by which a mammal might learn
to find its way to a previously visited reward location, including

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how the temporal credit assignment problem would be solved (9
marks)
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g
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The first learning problem is how to act, i
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what to do to approach
the goal
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g
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So this means
place cells are the input and movement is the output
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The critic learns that location
at goal is good, which is easy because presence of immediate
reward
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The critic value (V) of
each state/input (u) is the expected future reward from that state
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δ(t) = v(t+1)-v(t)+r(t)
if δ(t)>0, action o(t) was good
But how to learn v? A simple learning rule creates a set of
connection weights (w) so that v(t) = w x u(t) and w → w + εS(t)δ(t),
i
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you can also use δ to learn weights for the critic!
Spatial example:
First encounters goal at location x: r=1, so increase weight to critic
from place cell at x
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Next time go to x from x’, v(t+1)-v(t)=1, so increase weight to critic
from place cell at x’
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Then nest time go to x’ from x’’, v(t+1) –v(t)=1, so increase weight to
critic from place cell at x’’, and so on
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There are sensory cells that project to the hippocampal place cells,
causing a particular output pattern in the place cells
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There are two sets of nucleus accumbens cells, left or
right, so one set of place cells may project to the left turn groups
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while the other set of place cells project to the right turn groups
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Also, head direction cells have modifiable connections to all of the
nucleus accumbens cells- this helps to decide whether the left or
right pool of neurons get more activation to make the animal move
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Recently active synapses which led to the ‘correct’
locomotor response are strengthened, so that any move which took
place in a particular locational and directional context, and resulted
in reinforcement, is ‘stamped in’ in a Thorndikian (1898, 1911)
manner
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Each of those connections had a decaying
memory of how often there had been Hebbian pre- and postsynaptic activity
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So under this scheme synapses which have been chronically or very
recently active are strengthened the most, while synapses with the
least cumulative activity are strengthened least
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e
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0term
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This type of model still requires trial error and it only learns when it
is at the goal
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Performance of simulations of the model
It learns stereotype trajectories rather than optimal trajectories
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Unfortunately the model doesn’t take into straight
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Place constant means the goal is always in the same place, place
random means the goal gets moved
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Evaluation

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Captures the idea of ‘response’ (body turn) learning in basal ganglia,
versus ‘place’ presentation in hippocampus
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The Brown and Sharp model performs complex ‘stimulus-response’
learning- takes into account place and direction and then make a
body turn of either left or right in order to get to the goal
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Solves the temporal credit assignment problem by using the
recency-weighted cumulative Hebbian value associated with each
connection
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There may be
something in the synapses that governs LTP which takes into
account decay
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But then it is impossible for one
synapse to know all the other synaptic activity of the other
synapses
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Title: Computational Neuroscience 2011 paper answers (UCL)
Description: Computational Science module for Neuroscience BSc at UCL I got 69 in the module and a first class degree in Neuroscience

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