# Neural Networks: Part 2 Sensory Motor Integration - PowerPoint PPT Presentation

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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
• 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?
• 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