Moritz Lampert

Chester Tan, Moritz Lampert, Courtney Maynard et al.

Circuit localization is a mechanistic interpretability task whose goal is to identify a sparse subgraph of a transformer's computation graph sufficient to reproduce a particular behavior. Most established methods localize circuits independently for each model--task pair. We instead frame circuit localization as a graph machine learning problem in which the edges of a computation graph represent computational pathways, and graph neural networks (GNNs) model interactions among these pathways. We introduce Graph Circuit Learning (GCL), a supervised, amortized framework that trains a GNN across multiple model--task pairs and applies it to unseen cases. To provide sufficient data, we augment the InterpBench benchmark with additional cases derived from the TracrBench programs. Of the 14 evaluated GCL configurations, the highest scored a median edge AUROC of $0.902$ (interquartile interval $[0.861, 0.942]$) on the 16 original held-out InterpBench cases. This is close to the published InterpBench median of $0.910$ for EAP-IG while remaining below ACDC's $0.959$. Removing all message-passing edges reduces the median to $0.825$. We also adapt PGExplainer, a GNN explainability method, to circuit localization, obtaining a median edge AUROC of $0.858$ on the same cases. These preliminary results suggest that graph machine learning offers a natural and potentially powerful perspective on circuit localization, and we hope this perspective encourages closer exchange between the two communities.

Moritz Lampert, Ingo Scholtes

Many Graph Neural Networks (GNNs) add self-loops to a graph to include feature information about a node itself at each layer. However, if the GNN consists of more than one layer, this information can return to its origin via cycles in the graph topology. Intuition suggests that this "backflow" of information should be larger in graphs with self-loops compared to graphs without. In this work, we counter this intuition and show that for certain GNN architectures, the information a node gains from itself can be smaller in graphs with self-loops compared to the same graphs without. We adopt an analytical approach for the study of statistical graph ensembles with a given degree sequence and show that this phenomenon, which we call the self-loop paradox, can depend both on the number of GNN layers $k$ and whether $k$ is even or odd. We experimentally validate our theoretical findings in a synthetic node classification task and investigate its practical relevance in 23 real-world graphs.

Moritz Lampert, Christopher Blöcker, Ingo Scholtes

Dynamic link prediction is an important problem considered in many recent works that propose approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on continuous-time and discrete-time temporal graph datasets, typically using a traditional batch-oriented evaluation setup. However, as we show in this work, a batch-oriented evaluation is often unsuitable and can cause several issues. Grouping edges into fixed-sized batches regardless of their occurrence time leads to information loss or leakage, depending on the temporal granularity of the data. Furthermore, fixed-size batches create time windows with different durations, resulting in an inconsistent dynamic link prediction task. In this work, we empirically show how traditional batch-based evaluation leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data.