Neural Network of the Cerebellum: Temporal Discrimination and the Timing of Responses

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Neural Network of the Cerebellum Temporal
Discrimination and the Timing of Responses
Michael D. MaukDean V. Buonomano
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The cerebellum is important for initiating
smooth, directed movements. Damage to the
cerebellum causes severe movement deficits,
including poor ability to time movements in
response to external stimuli or in directed
action. The speculation is that there must be a
distinct biological mechanism within the
cerebellum that encodes time differences between
sensory inputs.
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• Other models of the biological timing mechanism
  depend on delays between units, varying time
  constants, or other imposed design choices.
• The benefits of Mauks neural network model
• Temporal information about the stimulus is
  encoded in a subset of units activating the
  output unit.
• Emulating a conditioned stimulus/unconditioned
  stimulus response only takes one training phase
  to learn the temporal information before the
  testing phase
• Information for multiple different stimuli can
  be encoded. Multiple unconditioned stimuli over
  time can be coded for a single conditioned
  stimuli. Conditioned stimuli patterns can span
  multiple time steps and temporal information can
  still be retained.

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Some basic cerebellum anatomy

• Mauk uses theories of structure proposed by Marr
  and Albus in which
• Climbing Fibers outside input that contain
  error signals, modifies Purkinje cell synapses
• Mossy Fibers provide sensory stimulus
  information to the granule and golgi cells
• Granule cells encode the context in which
  movements take place
• Golgi cell provides negative feedback to
  granule cells to stabilize cell activity
• Purkinje cell provides the appropriate
  output, in this case a timed motor movement in
  response to a stimuli

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Some basic cerebellum anatomy
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Some basic cerebellum anatomy
Golgi Cell
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The model hypothesis The structure of
interactions between the granule cell layer and
the golgi cell layer allows population subsets of
the granule cell layer to represent physical and
temporal information about the stimulus. In
other words, a subset of granule cells will
encode not only a pattern of activations that
identify the unique input pattern (stimulus), but
also how much time has elapsed from the onset of
the input pattern. This is achieved by the mossy
fiber input layer seeding the feedback loop
between the granule cell layer and the golgi cell
layer.
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• How does this work?
• Input comes through the mossy fiber and activates
  a subset of granule cells.
• These granule cells activate a subset of golgi
  cells on the golgi cell layer.
• The activated golgi cells inhibit back to the
  granule cell layer in a negative feedback loop,
  but inhibit a different, overlapping subset of
  granule cells than were activated by the initial
  mossy fiber input.
• This negative feedback loop between layers
  creates a dynamic, nonperiodic population
  vector of granule cell activity representing the
  stimulus pattern, even if the mossy fiber input
  is periodic.
• Changing the weights on a particular granule cell
  subset that represents the correct time interval
  can represent that interval in purkinje cell
  activation levels.

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• Pyramidal regions depict the subset of granule
  or golgi cells which a cell on the other layer is
  able to contact. Within this subset of cells,
  the connections are uniformly distributed.
• White cells in the diagram depict post-synaptic
  cells that end up receiving input from the
  pre-synaptic cell in the other layer.

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• Specifics of the neural network
• 10,000 granule cells
• 900 golgi cells
• 500 mossy fiber inputs
• 1 purkinje cell output (graded activation)
• A single granule cell receives excitatory input
  from 3 mossy fiber inputs and inhibitory input
  from 3 golgi cells
• A single golgi cell receives excitatory input
  from 100 granule cells and 20 mossy fiber inputs
• The purkinje cell receives input from all the
  granule cells

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A clearer diagram
PC
Golgi Cell Layer
Granule Cell Layer
Mossy Fiber Input Layer
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Activation update mechanism
Integrate and fire cell types Vi Go the
voltage of each golgi cell Thri Go the
threshold voltage for the golgi cell i to fire Gi
Goleak current leak from golgi cell I Gi GoMF
mossy fiber to golgi cell synaptic current Gi
GoGr granule cell to golgi cell synaptic
current All inputs to the cell are summed
together into a single current, which saturates
at 1.0 and decays according to a set decay
constant
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Activation update mechanism cont.
This represents the synaptic current of a mossy
fiber to golgi cell I with respect to time. Sn
MF representation of a spike in a mossy
fiber Wgo MF synaptic weights for the mossy
fiber synapse at the golgi cell Synaptic
currents emulate instantaneous rise in voltage
and exponential decay in that voltage after
spiking. Granule cells are controlled by similar
equations, but they have additional inhibitory
versions of the equations from the golgi cells.
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• Specifics of the neural network cont.
• Initially all granule cells are connected to
  the single output Purkinje cell with the same
  weights
• When the first stimulus (conditioned stimulus
  emulation) is presented, the weights of the
  granule cells active within that window to the
  purkinje cell are decreased
• this simulates LTD produced by co-activation of
  the climbing fibers and parallel fibers to the
  purkinje cell
• The voltage of the purkinje cell is a
  weighted summed activity of all granule cells in
  the network with a time constant of 2.5 msec
• Mossy fiber activation patterns seed
  activation of different subsets of granule and
  golgi cells at each time step

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• Specifics of the neural network cont.
• In training trials
• at 200ms, unconditioned stimulus simulated by
  decreasing the strength of the all weights
  projecting from activated granule cells to the
  purkinje cell, like in the conditioned stimulus
• In testing trials
• the unconditioned stimulus is not simulated,
  but because the pattern of activation of granule
  cells is the same as in the training period (same
  initial mossy fiber activation pattern seed)
  there is a decrease in activation at the same
  time interval
• The model is capable of learning timing for
  multiple different stimulus patterns, and
  stimulus patterns over a series of time-steps

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Top line represents the of mossy fibers active
in each time bin. Initial increase in total
mossy fiber activation represents the conditioned
stimulus. The bottom line represents purkinje
cell activity in the testing phase. After
training an unconditioned stimulus at 200ms the
granule cell subset during that time step have
lower weights, dropping the purkinje cell voltage.
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The model is very sensitive to noise. Variance
in the mossy fibers used to signal the
conditioned stimulus, variance in the
pre-conditioned stimulus state of the model, and
variance in constants of units such as threshold
all have detrimental effects on the networks
ability to train the timing for the unconditioned
stimulus.
The network here is trained to respond to US at
125, 200, and 225ms. The injection of noise
eliminates its ability to predict the US after
enough has been injected into the model.
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• Additional weaknesses of the model
• The noise can be decreased by decreasing the
  influence of the mossy fibers on the golgi cells,
  but this also decreases its ability to retain
  temporal information.
• The model can discriminate temporal information
  for conditioned stimulus and unconditioned
  stimulus simulations, where the timing is
  absolute, but there is no mechanism for learning
  relative timing between sensory information
  patterns. The rhythm of a song, for example, is
  learned regardless of the tempo that the song is
  played at.