A common approach to create more expressive GNNs is to change the message passing function of MPNNs. If a GNN is more expressive than MPNNs by adapting the message passing function, we call this non-standard message passing . Examples of this are message passing variants that operate on subgraphs [Frasca et al., 2022, Bevilacqua

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers).

Nevertheless, we show that under certain minimal and realistic distributional settings, it is possible to obtain a (1+ null)-approximation with a nearly linear running time and poly (k/null) + O ( k log n) columns. Namely, we show that if the input matrix A has the form A = B + E, where B is an arbitrary rank-k matrix, and E is a matrix with i.i.d.

Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from

Figure 1 illustrates model predictions across every Number Game concept in [33].Figure 6: Model predictions across every Number Game concept in [33] (Figure 1). For the number game, every model has its outputs transformed by a learned Platt transform. Logical concept models do not use Platt transforms. We fit these parameters using Adam with a learning rate of 0.001. For the number game we do 10-fold cross validation to calculate holdout predictions.