A structured organization of information is typically required by symbolic processing. On the other hand, most connectionist models assume that data are organized according to relatively poor structures, like arrays or sequences. The framework described in this paper is an attempt to unify adaptive models like artificial neural nets and belief nets for the problem of processing structured information. In particular, relations between data variables are expressed by directed acyclic graphs, where both numerical and categorical values coexist. The general framework proposed in this paper can be regarded as an extension of both recurrent neural networks and hidden Markov models to the case of acyclic graphs. In particular we study the supervised learning problem as the problem of learning transductions from an input structured space to an output structured space, where transductions are assumed to admit a recursive hidden statespace representation. We introduce a graphical formalism for r...

While neural networks are very successfully applied to the processing of fixedlength vectors and variable-length sequences, the current state of the art does not allow the efficient processing of structured objects of arbitrary shape (like logical terms, trees or graphs). We present a connectionist architecture together with a novel supervised learning scheme which is capable of solving inductive inference tasks on complex symbolic structures of arbitrary size. The most general structures that can be handled are labeled directed acyclic graphs . The major difference of our approach compared to others is that the structure-representations are exclusively tuned for the intended inference task. Our method is applied to tasks consisting in the classification of logical terms. These range from the detection of a certain subterm to the satisfaction of a specific unification pattern. Compared to previously known approaches we got superior results on that domain.

This paper is a study on LRAAM-based (Labeling Recursive Auto-Associative Memory) classification of symbolic recursive structures encoding terms. The results reported here have been obtained by combining an LRAAM network with an analog perceptron. The approach used was to interleave the development of representations (unsupervised learning of the LRAAM) with the learning of the classification task. In this way, the representations are optimized with respect to the classification task. The intended applications of the approach described in this paper are hybrid (symbolic/connectionist) systems, where the connectionist part has to solve logic-oriented inductive learning tasks similar to the termclassification problems used in our experiments. These problems range from the detection of a specific subterm to the satisfaction of a specific unification pattern, and they can get a very satisfactory solution by our approach. 1

While neural networks are widely applied as powerful tools for inductive learning of mappings in domains of fixed-length feature vectors, there are still expressed principled doubts whether the domain can be enlarged to structured objects of arbitrary shape (like trees or graphs). We present a connectionist architecture together with a novel supervised learning scheme which is capable of solving inductive inference tasks on complex symbolic structures of arbitrary size. Labeled directed acyclic graphs are the most general structures that can be handled. The processing in this architecture is driven by the inherent recursive nature of the given structures. Our approach can be viewed as a generalization of the well-known discrete-time, continuous-space recurrent neural networks and their corresponding training procedures. We give first results from experiments with inductive learning tasks consisting in the classification of logical terms. These range from the detection of a certain su...