Florian Seiffarth

Florian Seiffarth

Message-passing neural networks (MPNNs) are a powerful framework for learning representations of graph-structured domains. However, weights in MPNNs act on features only, limiting their ability to capture structural patterns. We introduce a novel structure-aware weight sharing principle that explicitly incorporates information inherent to the graph structure. Weights are indexed directly by user-chosen graph invariants, i.e., functions preserved under node permutations, enabling systematic reuse across structurally equivalent subgraphs. We present ShareGNNs, which instantiate this principle within a simple encoder-decoder architecture, resulting in an MPNN with learnable adjacency and transformer-like connectivity. We show that their expressivity is at least as strong as the discriminative power of the chosen invariants, providing explicit control over the model complexity. Experiments on synthetic and real-world data, as well as subgraph counting tasks, demonstrate consistent improvements over standard MPNNs, competitive expressivity beyond the 1-WL test, and scalability to large datasets.

Florian Seiffarth

A common problem of classical neural network architectures is that additional information or expert knowledge cannot be naturally integrated into the learning process. To overcome this limitation, we propose a two-step approach consisting of (1) generating rule functions from knowledge and (2) using these rules to define rule based layers -- a new type of dynamic neural network layer. The focus of this work is on the second step, i.e., rule based layers that are designed to dynamically arrange learnable parameters in the weight matrices and bias vectors depending on the input samples. Indeed, we prove that our approach generalizes classical feed-forward layers such as fully connected and convolutional layers by choosing appropriate rules. As a concrete application we present rule based graph neural networks (RuleGNNs) that overcome some limitations of ordinary graph neural networks. Our experiments show that the predictive performance of RuleGNNs is comparable to state-of-the-art graph classifiers using simple rules based on Weisfeiler-Leman labeling and pattern counting. Moreover, we introduce new synthetic benchmark graph datasets to show how to integrate expert knowledge into RuleGNNs making them more powerful than ordinary graph neural networks.

Florian Seiffarth, Tamas Horvath, Stefan Wrobel

Several concept learning problems can be regarded as special cases of half-space separation in abstract closure systems over finite ground sets. For the typical scenario that the closure system is implicitly given via a closure operator, we show that the half-space separation problem is NP-complete. As a first approach to overcome this negative result, we relax the problem to maximal closed set separation, give a generic greedy algorithm solving this problem with a linear number of closure operator calls, and show that this bound is sharp. For a second direction, we consider Kakutani closure systems and prove that they are algorithmically characterized by the greedy algorithm. As a first special case of the general problem setting, we consider Kakutani closure systems over graphs and give a sufficient condition for this kind of closure systems in terms of forbidden graph minors. For a second special case, we then focus on closure systems over finite lattices, give an improved adaptation of the generic greedy algorithm, and present an application concerning subsumption lattices.