Cerebellar Model Articulation Controller

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Cerebellar Model Articulation Controller
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Introduction

• The CMAC is a mathematical formalism developed to
  explain the characteristics of the cerebellum.
• The CMAC is type of local neural network.
• The CMAC is provided with the memory address
  algorithm.

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Fundamental Theorem

• A CMAC can be decomposed into three sub_mapping
• S M
• M A
• A P
• Where S input vector A the actual memory.
• M the conceptual memory used to encode S.
• P the output of the CMAC.

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The diagram of a CMAC
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• The S M mapping , called conceptual mapping.
• The M A , called random mapping.
• The A P computes a scale output by
  projecting the association cells determined by S
  M mapping on to a set of adjustable weights,
  w, such that

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An example of the conceptual mapping with two
inputs
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An example of the conceptual mapping with two
inputs
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example
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The weight updating method

• The error among the content of the
• association cells excited by the input
• vector.
• where is the learning rate A is the
  number of the activated neurons in the actual
  memoryxi is the activation state of actual
  memory cell i

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Improvement Fuzzy Decoding
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Improvement Fuzzy Decoding
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Improvement Fuzzy Decoding
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Improvement Fuzzy Decoding
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Improvement Fuzzy Decoding
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An example

• The comparison between a CMAC network and BP
  network.
• The learning rates of both the two network are
  0.5.
• The BP network contains 50 units in hidden layer.
• The CMAC network is divided into 20 segment

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• The batch Mean-Square-Error of a CMAC network and
  a BP network

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• The training pattern for the two kinds of neural
  networks

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• The output of the CMAC network at recall phase

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• The output of the BP network at recall phase