Graph Dynamics : Learning and Representation by Andre

Graphs are often used in artificial intelligence as means for symbolic knowledge representation. A graph is nothing more than a collection of symbols connected to each other in some fashion. For example, in computer vision a graph with five nodes and some edges can represent a table – where nodes correspond to particular shape descriptors for legs and a top, and edges to particular spatial relations. As a framework for representation, graphs invite us to simplify and view the world as objects of pure structure whose properties are fixed in time, while the phenomena they are supposed to model are actually often changing. A node alone cannot represent a table leg, for example, because a table leg is not one structure (it can have many different shapes, colors, or it can be seen in many different settings, lighting conditions, etc.) Theories of knowledge representation have in general concentrated on the stability of symbols – on the fact that people often use properties that remain unchanged across different contexts to represent an object (in vision, these properties are called invariants). However, on closer inspection, objects are variable as well as stable. How are we to understand such problems? How is that assembling a large collection of changing components into a system results in something that is an altogether stable collection of parts? The work here presents one approach that we came to encompass by the phrase “graph dynamics”. Roughly speaking, dynamical systems are systems with states that evolve over time according to some lawful “motion”. In graph dynamics, states are graphical structures, corresponding to different hypothesis for representation, and motion is the correction or repair of an antecedent structure. The adapted structure is an end product on a path of test and repair. In this way, a graph is not an exact record of the environment but a malleable construct that is gradually tightened to fit the form it is to reproduce.