7.2.3. Transformation Operators on Graphs

(lsh/libgraph/gtransform.lsh)

7.2.3.0. (new GTrans)

[CLASS] (lsh/libgraph/gtransform.lsh)

A transformer is the object which embodies the rules used for creating a new graph from one or two graphs using g-transform or g-compose . Class GTrans is the base class for all transformers.

Method check is used for selecting links in the initial graph(s) for which structures will be created between two nodes of the destination graph.
Method vcost and fcost compute the cost of these structures without actually building them. Method vcost (Viterbi's cost) computes the cost of the best path. Method fcost (Forward's cost) computes the logadded cost of all paths.
Method build build a structure in the resulting graph on the basis of the information provided by the corresponding links in the parent graphs. This involves computing cost, label and data.
Method bprop is used during training to update the gradient with respect to the cost of the initial graph. The implentation of this method requires that the transformer remembers the association between the structures created by build and the initial links. This memory is cleaned by method reset .

The base class GTrans accepts all links of the product graph. The cost in the link of the product graph will be the sum of the costs of the corresponding links in both graphs. The label and data component are copied from the second and first graph respectively.

See: (==> gtrans check link1 link2 )
See: (==> gtrans vcost link1 link2 )
See: (==> gtrans fcost link1 link2 )
See: (==> gtrans build ngraph nnodefrom nnodeto link1 link2 )
See: (==> gtrans remember rememberp )
See: (==> gtrans reset)
See: (==> gtrans bprop)

7.2.3.1. (==> gtrans check link1 link2)

[MSG] (lsh/libgraph/gtransform.lsh)

Tells g-transform or g-compose if they must create a structure in the new graph corresponding to the given links of the parent graphs. A structure may be as simple as a single link or as complex as a subgraph.

In the case of g-transform , arguments link1 and link2 are equal and identify a link of the initial graph. This function returns t if a new structure corresponding to this link must be created in the new graph
In the case of g-compose , argument link1 and link2 identify two links in the two initial graph. This function returns t if a new structure corresponding to these links must be created in the new graph

7.2.3.2. (==> gtrans vcost link1 link2)

[MSG] (lsh/libgraph/gtransform.lsh)

Given two links link1 and link2 in two graphs, this method returns a floating point number indicating the cost of the best path in the structure corresponding to links link1 and link2 .

The default function just adds the costs of both links.

7.2.3.3. (==> gtrans fcost link1 link2)

[MSG] (lsh/libgraph/gtransform.lsh)

Given two links link1 and link2 in two graphs, this method returns a floating point number indicating the loadadded cost of all paths in the structure corresponding to links link1 and link2 .

The default function just calls vcost .

7.2.3.4. (==> gtrans build ngraph nnodefrom nnodeto link1 link2)

[MSG] (lsh/libgraph/gtransform.lsh)

Given to links link1 and link2 in two graphs (for which method check indicates that we should build something in the resulting graph), method build creates a new structure between nodes nnodefrom and nnodeto in graph ngraph . This task involves computing cost, label and data for the new links.

The default function just builds a single new link whose label comes from link2 and whose data slot comes from link1 .

7.2.3.5. (==> gtrans bprop)

[MSG] (lsh/libgraph/gtransform.lsh)

Propagates the gradients of the links of the destination graph into the the corresponding links of the initial graph. The resulting gradients are accumulated into the fields dcost of the corresponding links.

If running the transformer involves parametric operations (e.g. running a network), the gradients are also propagated along these operations and finally accumulated into the parameter vector.

To achieve this task (optional), the transformer must remember all structures build since its creation.

7.2.3.6. (==> gtrans remember rememberp)

[MSG] (lsh/libgraph/gtransform.lsh)

Sets or resets memoryless mode. Argument rememberp is a boolean specifying if it is useful to remember the result of the next calls to the method build of the transformer.

7.2.3.7. (==> gtrans reset)

[MSG] (lsh/libgraph/gtransform.lsh)

Resets the data remembered by the transformer for a possible call of method bprop .

7.2.3.8. (g-copy graph ngraph nstart nend)

(lsh/libgraph/gtransform.lsh)

Copies graph graph between nodes nstart and nend of a new graph ngraph . This function only considers the nodes and links that we can reach from both the starting node and the end node. The other nodes and link are not copied.

WARNING: This function merely copies the data pointers. The corresponding data are not copied into the new pool. You can change these data pointer within a new pass.

7.2.3.9. (g-transform graph trans)

(lsh/libgraph/gtransform.lsh)

Transforms graph graph according to transformer trans . The resulting graph is bu1ild by calling method build of the transformer for all links in the initial graph for which method check returns true.

This function ideally should only builds the nodes and the links which are reachable from both the startnode and the endnode. Yet function g-tranform may build extra nodes and links if the final graph has cycle(s) or if the transformer method build builds unecessary nodes.

See: (new GTrans)

7.2.3.10. (g-compose graph1 graph2 trans)

(lsh/libgraph/gtransform.lsh)

Composes graphs graph1 and graph2 according to transformer trans . The resulting graph is build by calling method build of the transformer between all nodes of the product graph for which method check returns true.

This function ideally should only builds the nodes and the links which are reachable from both the startnode and the endnode. Yet function g-compose may build extra nodes and links if the final graph has cycle(s) or if the transformer method build builds unecessary nodes.

See: (new GTrans)