"reducing sequences"

Fujii, Hokusai: theculturetrip.com

Reducing Sequences

  In this article, we'll discuss the entropy reduction of a sequence
  by representing it as a binary tree which is multi-dimensional.
  In computer programming there are standard methods of representing
  the elements of a sequences with a binary tree whose elements are
  the nodes.  The multi-dimensional tree [1] is the progressive expansion
  of sequences from a vector of elements, to a binary tree of nodes,
  and into forest of multiple overlapping of binary trees.

  In the context of building neural networks, a sequence is an ordered
  list of elements.  It's a time ordered, Markov process which is
  embedded in a type of binary tree called a trie.  You can visualize
  a trie as a two dimensional lattice or trellis.  A three dimensional
  trie is an overlay of a pair of two dimensional tries.

  Propagating or traversing the 3-D tree is equivalent to propagating
  each of the pairs of binary trees.  The order of looping on 2-D trees
  is 2 whereas the order on a 3-D tree is 1.  In practice, in computer
  programs we only propagate over 2-D trees instead of multi-dimensional

  The philosophy, or the vocabulary of the metaworld, for content and
  form are, respectively, parts and rules.  The nodes at the vertices
  of trees are the parts of the forest, and the rules are the links in
  the tree of a rewriting system. [2]  With respect to the programming
  language Lisp, the content and form are the variables and functions.
  The neural network is a dynamic system in which the content and form
  of the trees are represented by neurons and their connections.  The
  computer simulation of this network is a recurrent temporally ordered
  Markov process.  In using the Markov model for simulating neural nets
  you would, by trail and error, compute the probabilities for the
  state transitions.  In the binary tree formulation you would use
  the structure or form of the connections between the nodes.  By
  trail and error you would try to geometrically build the connections
  between the neurons.

  This is as simple as I can get it so far.  If you have any ideas,
  whether from a philosophical, mathematical or programming view,  and
  want to collaborate on this, please contact me at:
  glenn @ neuralmachines . com.


  [1] Multidimensional Trees, William Baldwin and George Strawn, 1991

  [2] Pattern Recognition, Satosi Watanabe, 1985, p. 385



Zen Gardens -
Breaty to a Machine

Structure of the Machine -
Dimensionality Reduction
Using Prefix Trees

Multi-dimensional Sequences

Reducing Sequences