Representation in populations of neurons

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Representation in populations of neurons
Biomedical engineering Group School of Electrical
Engineering Sharif University of Technology

• Representing Scalar Magnitudes

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World Description and prediction

• Noticing Events
• Velocity / Position
• Acceleration / Force
• Force / Charge
• Measuring
• m/s, m m/s2, N N, C
• Finding Relationship
• Vdx/dt Fma

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Predicting changes in environment.
Representing the current physical properties of
the target
Representing where the target would be
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Measurements / Prediction
Theories
Prediction
Measurements
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Representing by Neurons.

• Physical Properties are broken down into two
  parts
• A scalar magnitude
• A unit
• The relations hold regardless of which units are
  chosen
• How scalar magnitudes are encoded into neural
  activities?

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Scalar to Vectors
?
Representation
Scalar Value
Representation
Scalar Value
Representation
Scalar Value
Representation
Scalar Value
Representation
Scalar Value
Representation
Scalar Value
Representation
Scalar Value
Vector
Representation
Scalar Value
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REPRESENTING SCALAR MAGNITUDES

• Engineered representation
• Biological representation

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Engineered representation

• Similarities between natural and engineered
  systems (e.g. Computer)
• The combined resources of many simple encoders
• Both Real physical systems
• Both encode all physical magnitudes into some
  common language

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Ex Voice Encoding
vibrations in a medium
compression waves
Transducer Microphone
time dependent voltage
A/D
Signal Conditioning
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Flash Converter
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3-Bit Flash Converter
A
B
C
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Truth Table
precision
C1 C2 C3 C4 C5 C6 C7 A B C
1 1 1 1 1 1 1 0 0 0
1 1 1 1 1 1 0 0 0 1
1 1 1 1 1 0 0 0 1 0
1 1 1 1 0 0 0 0 1 1
1 1 1 0 0 0 0 1 0 0
1 1 0 0 0 0 0 1 0 1
1 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 1 1 1
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Characterizing Representation

• Range of input (ex 0 to 5.12 V)
• Number of bits to represent (ex 8)

a8 a7 a6 a5 a4 a3 a2 a1
Decoder
Encoder
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Terms

• ?i is the integer that has the value of an on
  bit at bit number i
• It embodies a rule for estimating the original
  value of x
• They are called the decoding weights
• X can be found by a linear combination of the
  relevant encoded coefficients and decoding
  weights (despite the highly nonlinear encoding
  process) ?P1
• P1 Neural representations are defined by the
  combination of nonlinear encoding and weighted
  linear decoding

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Biological representation

• The population of encoders is comprised of
  neurons rather than Gates/transistors
• Individual neurons respond selectively to various
  stimuli
• To understand the encoding procedure

dendritic input
current changes in the neurons soma
neuron spike trains
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Neuron Response Functions
The human cortical regular spiking cells.
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Neurons tuning curve.

• The relation between the relevant physical
  magnitude and the neurons firing rate
• Two processes
• An extremely complex process that includes all
  processing of input signals and spikes up to the
  soma
• generation of voltage spikes given this soma
  current (well-characterized by neuroscientists)
• Soma Current results from combining two
  distinguishable currents.
• bias or background current that is the result
  of intrinsic processes in the neuron, and/or
  constant input current from the rest of the
  nervous system.
• The driving current of the soma that drives the
  neurons behavior from its background state

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