Its All Graph To Me: Foundational Topology Models with Contrastive Learning on Multiple Domains

Representations and embeddings of graph data have been essential in many domains of research. The principle benefit of learning such representations is that the pre-trained model can be fine-tuned on smaller datasets where data or labels are scarse. Existing models, however, are domain specific; for example a model trained on molecular graphs is fine-tuned on other molecular graphs. This means that in many application cases the choice of pre-trained model can be arbitrary, and novel domains may lack an appropriate pre-trained model. This is of particular issue where data is scarse, precluding traditional supervised methods. In this work we use adversarial contrastive learning to present a \method, a model pre-trained on many graph domains. We train the model only on topologies but include node labels in evaluation. We evaluate the efficacy of its learnt representations on various downstream tasks. Against baseline models pre-trained on single domains, as well as un-trained models and non-transferred models, we show that performance is equal or better using our single model. This includes when node labels are used in evaluation, where performance is consistently superior to single-domain or non-pre-trained models.

Hierarchical GNNs for Large Graph Generation

Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and synthetic datasets among others. While GNN (Graph Neural Network) models have been applied in these domains their high in-memory costs restrict them to small graphs. Conversely less costly rule-based methods struggle to reproduce complex structures. We propose HIGGS (Hierarchical Generation of Graphs) as a model-agnostic framework of producing large graphs with realistic local structures. HIGGS uses GNN models with conditional generation capabilities to sample graphs in hierarchies of resolution. As a result HIGGS has the capacity to extend the scale of generated graphs from a given GNN model by quadratic order. As a demonstration we implement HIGGS using DiGress, a recent graph-diffusion model, including a novel edge-predictive-diffusion variant edge-DiGress. We use this implementation to generate categorically attributed graphs with tens of thousands of nodes. These HIGGS generated graphs are far larger than any previously produced using GNNs. Despite this jump in scale we demonstrate that the graphs produced by HIGGS are, on the local scale, more realistic than those from the rule-based model BTER.

$β^{4}$-IRT: A New $β^{3}$-IRT with Enhanced Discrimination Estimation

Item response theory aims to estimate respondent's latent skills from their responses in tests composed of items with different levels of difficulty. Several models of item response theory have been proposed for different types of tasks, such as binary or probabilistic responses, response time, multiple responses, among others. In this paper, we propose a new version of $\beta^3$-IRT, called $\beta^{4}$-IRT, which uses the gradient descent method to estimate the model parameters. In $\beta^3$-IRT, abilities and difficulties are bounded, thus we employ link functions in order to turn $\beta^{4}$-IRT into an unconstrained gradient descent process. The original $\beta^3$-IRT had a symmetry problem, meaning that, if an item was initialised with a discrimination value with the wrong sign, e.g. negative when the actual discrimination should be positive, the fitting process could be unable to recover the correct discrimination and difficulty values for the item. In order to tackle this limitation, we modelled the discrimination parameter as the product of two new parameters, one corresponding to the sign and the second associated to the magnitude. We also proposed sensible priors for all parameters. We performed experiments to compare $\beta^{4}$-IRT and $\beta^3$-IRT regarding parameter recovery and our new version outperformed the original $\beta^3$-IRT. Finally, we made $\beta^{4}$-IRT publicly available as a Python package, along with the implementation of $\beta^3$-IRT used in our experiments.