Specific Research Projects  Simulation of Learning  on Small Graphs


We investigate learning mechanisms and learning strategies in networks. The main interest is the evolutionary development of these mechanisms, i.e., the adaptation to particular requirements of the environment as part of an evolutionary process (sometimes called evolutionary learning) and the emergence of individual learning mechanisms during such an evolutionary process. Learning and memorizing are two major prerequisites of any thinking process, as they set the basis (mental states and mental content) on which thinking operations act. Furthermore, the reaction to a stimulus as a result of previous experiences (which is simulated in our models) can even be considered as an elementary and rudimentary thinking process itself.


The results should give insight into learning processes in general, in particular into the emergence of modularity in the occurring dynamics. The model also allows the investigation of learning strategies (splitting the task, learning of easier tasks first, etc.).  A better understanding of the emergence of individual learning during an evolutionary process should reveal interdependencies between various skills, abilities and requirements (e.g., the relevance of a short term memory, a “penalty”-system, a Hebb-like rule for changing the synaptic weights, or features of the environment which gives individual learning an evolutionary advantage).

Approach, methodology, and findings
We make computer simulations of learning mechanisms in networks with the following characteristic features: we use small graphs (with usually less than 10-20 internal vertices), and we use a non-monotonic transfer function (for large input activities the output activity of a vertex may decrease beyond a maximal value). Evolutionary learning is simulated by random changes in the network and the selection of the one with the best performance according to a predefined optimal reaction. Individual learning involves a dynamical mechanism to change the synaptic weights in a network. With respect to evolutionary learning we find the characteristic features of punctuated equilibrium (long periods of almost no changes are interrupted by short periods of rapid changes), signs of modularity with respect to the different tasks, and a non-monotonic measure for the complexity of the learning process (which may be related to pragmatic measures of information). It turns out that neural networks are very good in rule extraction, although the exact rules according to which the network works may not always be easily recognizable.

Relevance and connection to other Parmenides projects
The modeling of systems which may have common features with certain parts of the brain and which may reveal general dynamical aspects of learning processes is one of the central activities of the Parmenides foundation. In particular, the emergence of “process modules” and their realization in networks can be of relevance for the general modularity hypotheses in thinking processes. Furthermore, certain stimuli, which we intend to use in imaging experiments, can be tested and developed (with suitable changes) in these simulations.