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Neural Networks: Part 2 Sensory Motor Integration

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Neural Networks: Part 2 Sensory Motor Integration I. Sensory-motor (S-M) Coordination Problem II. Physiological Foundations III. S-M Computation: Tensor Theory (optional) – PowerPoint PPT presentation

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Title: Neural Networks: Part 2 Sensory Motor Integration


1
Neural Networks Part 2Sensory Motor
Integration
  • I. Sensory-motor (S-M) Coordination Problem
  • II. Physiological Foundations
  • III. S-M Computation Tensor Theory (optional)

2
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3
I. Sensory-motor Coordination Problem
4
  • Problem to be solved
  • Given the representation of the target object in
    visual space, specify the arm position in motor
    space whether the tip of the arm touches the
    object.
  • (?,?) ?? f(?,?)

5
  • Correspondence Between Sensory Space and Motor
    Space

6
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7
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8
  • Projection of Sensory onto Motor Space
  • Non-orthogonal nature of the representations

9
II. Physiological Foundations
10
  • Superior Colliculus (SC)
  • (deformed topographic map of visual field)

11
  • Cerebellum
  • (translate topo map of SC into motor coordinate)

12
Sensory-Motor Integration
13
  • Cerebella Network

14
III. S-M Computation Tensor Theory (optional)
  • S-M Computation Matrix Computation?
  • B FA
  • where
  • B (?,?)
  • F (fik), 2x2 matrix
  • A (?,?)
  • No, it turns out to perform tensor computation
    instead.
  • Note Both types of computation (matrix and
    tensor) can be
  • represented as neural networks.

15
  • Matrix multiplication in Cerebellum??

16
  • S-M Transformation General Case
  • (Question)
  • How about the S-M transformation from a sensory
    space of n dimensions to a motor space of m
    dimensions where n and m are different and both
    greater than 2?
  • (Answer) Tensor Hypothesis
  • The transformation can be represented by a
    covariant metric tensor
  • (Pellionisz Llinas, 1985)

17
  • What Is Tensor?
  • A tensor is a set of numbers specifying relations
    that exist between two representations of the
    same object using different, possibly
    non-orthogonal over-complete, coordinate
    systems.

18
  • Example of Hyper-dimensional Sensory Coordinate
    System

19
  • Eye Muscle Activities as Sensory Inputs
  • Note the non-orthogonal (over-complete, i.e.,
    non-unique) nature of the motor system

20
  • Arm Muscle Activities as Motor Outputs

21
Transformation of Visual cortex activities into
arm muscle activities
22
  • Cerebella Network

23
  • Neural Circuit An Example

24
  • Summary
  • Tensor Theory (Hypothesis)
  • 1. A sensory input is represented by a covariant
    vector, a motor output by a contravariant vector,
    and the transformation between them by a
    covariant metric tensor.
  • 2. In the brain the metric tensor is implemented
    by a matrix in a neuronal network.
  • (Pellionisz Llinas, 1985)

25
  • Tensor Equation for S-M Integration
  • en gnkik (n1,,N k1,,M)
  • I (i1, i2, , iM) Representation in sensory
    space
  • E (e1, e2, , eN) Representations in motor
    space
  • G (gnk) Tensor that relates I to E
  • Q What is the object that the above tensorial
    system purports to represent?

26
  • Tensor Calculation in the Cerebellum
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