A hyperstring is a special kind of distributed representation. It
allows for transparallel processing, that is, it enables a search for
regularity
in up to 2
^{N} strings as if only one string of length
N were concerned. See
Hyperstring proofs
for the formal definition of hyperstrings; here, this concept is illustrated.
In the next figure, the 15 strings at the top are gathered in
a
distributed representation on 9 vertices. Every path from vertex 1 to
vertex
9 represents one of the 15 strings, by way of the edge labels in such a
path.
For instance, the path along vertices 1, 2, 4, 5, and 9, represents the
string
ayfw.
This distributed representation is a hyperstring, which, in graph-theoretical terms, is a
simple semi-Hamiltonian
directed acyclic graph with two crucial properties:
- It contains one and only one Hamilton path, that is, one
and only
one path that visits every vertex;
- The set of substrings represented by all paths between one
pair of vertices and the set of substrings represented by all paths
between another pair of
vertices are either
completely disjunct or completely identical -- never something in
between.
For instance, as indicated in red in the figure above, the set of strings represented by all paths from
vertex
1 to vertex 4 is identical to the set of strings represented by all paths from vertex 5 to vertex 8.
Because of these properties, the hyperstring can be conceived of as
one
string in which each substring stands for such a set of all paths
between
two vertices. Any identity relationship between substrings in one of
the
15 strings corresponds to an identity relationship between substrings
in
this single string. Inversely, any identity relationship between
substrings
in this single string corresponds, in one go, to identity relationships
between
substrings in many of the 15 strings. This implies that a search for
regularity
in this single string suffices to get all regularities in all
15
strings.
The foregoing finds application in the computation of minimal codes of
strings (see
PISA),
which requires a hierarchically recursive search for regularities. For
instance,
in the next figure, the string at the top can be encoded into 9 different
symmetries.
To compute a minimal code of the string at the top, the arguments of
all
these 9 symmetries have to be recoded in turn. At first glance, it seems
necessary
to encode each of the 9 symmetry arguments separately. However, the
9 symmetry
arguments can be gathered in a distributed representation which, by nature,
forms
a hyperstring (see
Hyperstring
proofs). This implies that
all 9 symmetry arguments can be recoded in a transparallel fashion, that is, as if only one symmetry argument
were
concerned.
For a full account of transparallel processing by hyperstrings, see
Proceedings
of the National
Academy of Sciences USA 2004
For a demo on its position with respect to other forms of processing, see
Smart processing
For a demo on its potential relevance in cognitive (neuro)science, see
Cognitive architecture
For an extensive discussion on these issues, see
Cognitive Processing 2012
For a natural example of transparallel processing without hyperstrings, see
Pencil selection