Fully inductive knowledge graph models can be trained on multiple domains and subsequently perform zero-shot knowledge graph completion (KGC) in new unseen domains. This is an important capability towards the goal of having foundation models for knowledge graphs. In this work, we introduce a more expressive and capable fully inductive model, dubbed TRIX, which not only yields strictly more expressive triplet embeddings (head entity, relation, tail entity) compared to state-of-the-art methods, but also introduces a new capability: directly handling both entity and relation prediction tasks in inductive settings. Empirically, we show that TRIX outperforms the state-of-the-art fully inductive models in zero-shot entity and relation predictions in new domains, and outperforms large-context LLMs in out-of-domain predictions. The source code is available at https://github.com/yuchengz99/TRIX.

Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be surprisingly effective, achieving performance comparable to end-to-end training counterparts, across various tasks and datasets. Specifically, we show that by replacing learnable weights with random weights, GNNs can retain strong predictive power, while significantly reducing training time by up to 6$\times$ and memory usage by up to 3$\times$. Moreover, the random weights combined with our construction yield random graph propagation operators, which we show to reduce the problem of feature rank collapse in GNNs. These understandings and empirical results highlight random weights as a lightweight and efficient alternative, offering a compelling perspective on the design and training of GNN architectures.

In this paper, we propose a novel activation function tailored specifically for graph data in Graph Neural Networks (GNNs). Motivated by the need for graph-adaptive and flexible activation functions, we introduce DiGRAF, leveraging Continuous Piecewise-Affine Based (CPAB) transformations, which we augment with an additional GNN to learn a graph-adaptive diffeomorphic activation function in an end-to-end manner. In addition to its graph-adaptivity and flexibility, DiGRAF also possesses properties that are widely recognized as desirable for activation functions, such as differentiability, boundness within the domain and computational efficiency. We conduct an extensive set of experiments across diverse datasets and tasks, demonstrating a consistent and superior performance of DiGRAF compared to traditional and graph-specific activation functions, highlighting its effectiveness as an activation function for GNNs.

In recent years, significant efforts have been made to refine the design of Graph Neural Network (GNN) layers, aiming to overcome diverse challenges, such as limited expressive power and oversmoothing. Despite their widespread adoption, the incorporation of off-the-shelf normalization layers like BatchNorm or InstanceNorm within a GNN architecture may not effectively capture the unique characteristics of graph-structured data, potentially reducing the expressive power of the overall architecture. Moreover, existing graph-specific normalization layers often struggle to offer substantial and consistent benefits. In this paper, we propose GRANOLA, a novel graph-adaptive normalization layer. Unlike existing normalization layers, GRANOLA normalizes node features by adapting to the specific characteristics of the graph, particularly by generating expressive representations of its neighborhood structure, obtained by leveraging the propagation of Random Node Features (RNF) in the graph. We present theoretical results that support our design choices. Our extensive empirical evaluation of various graph benchmarks underscores the superior performance of GRANOLA over existing normalization techniques. Furthermore, GRANOLA emerges as the top-performing method among all baselines within the same time complexity of Message Passing Neural Networks (MPNNs).

In the realm of Graph Neural Networks (GNNs), two exciting research directions have recently emerged: Subgraph GNNs and Graph Transformers. In this paper, we propose an architecture that integrates both approaches, dubbed Subgraphormer, which combines the enhanced expressive power, message-passing mechanisms, and aggregation schemes from Subgraph GNNs with attention and positional encodings, arguably the most important components in Graph Transformers. Our method is based on an intriguing new connection we reveal between Subgraph GNNs and product graphs, suggesting that Subgraph GNNs can be formulated as Message Passing Neural Networks (MPNNs) operating on a product of the graph with itself. We use this formulation to design our architecture: first, we devise an attention mechanism based on the connectivity of the product graph. Following this, we propose a novel and efficient positional encoding scheme for Subgraph GNNs, which we derive as a positional encoding for the product graph. Our experimental results demonstrate significant performance improvements over both Subgraph GNNs and Graph Transformers on a wide range of datasets.

The task of inductive link prediction in (discrete) attributed multigraphs infers missing attributed links (relations) between nodes in new test multigraphs. Traditional relational learning methods face the challenge of limited generalization to test multigraphs containing both novel nodes and novel relation types not seen in training. Recently, under the only assumption that all relation types share the same structural predictive patterns (single task), Gao et al. (2023) proposed a link prediction method using the theoretical concept of double equivariance (equivariance for nodes & relation types), in contrast to the (single) equivariance (only for nodes) used to design Graph Neural Networks (GNNs). In this work we further extend the double equivariance concept to multi-task double equivariance, where we define link prediction in attributed multigraphs that can have distinct and potentially conflicting predictive patterns for different sets of relation types (multiple tasks). Our empirical results on real-world datasets demonstrate that our approach can effectively generalize to test graphs with multi-task structures without access to additional information.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. In essence, a Subgraph GNN first transforms an input graph into a bag of subgraphs, obtained according to a predefined generation policy. For instance, each subgraph might be generated by deleting exactly one node in the original graph, or, more generally, by marking exactly one node in the original graph, while leaving the connectivity unaltered (Papp & Wattenhofer, 2022). Then, it applies an equivariant architecture to process the bag of subgraphs, and aggregates the representations to obtain graphor node-level predictions. The popularity of Subgraph GNNs can be attributed not only to their increased expressive power compared to MPNNs but also to their remarkable empirical performance, exemplified by their success on the ZINC molecular dataset (Frasca et al., 2022; Zhang et al., 2023). Unfortunately, Subgraph GNNs are hampered by their computational cost, since they perform message-passing operations on all subgraphs within the bag.

Spearman's work started a revolution that gave us, among other things, matrix and tensor factorizations, Principal Component Analysis (PCA), and Independent Component Analysis (ICA). Simultaneously, The Abilities of Man also warned us about interpreting the factors of subject i as innate rather than acquired abilities. For instance, regarding Woolley and Fischer's observation that "boys are enormously superior [to girls] at [... ] spatial relations" (i.e., in how objects relate in space) [76], Spearman warns that "evidence of this difference being really innate [rather than acquired] is still dubious". Today, we can describe Spearman's warning as being about two competing causal hypotheses that describe link formation between young children and their abilities. A path-dependent hypothesis where past links influence future links [46] and an innate factors hypothesis where link formation is just a manifestation of latent innate factors [75]. In Woolley and Fischer's experiments, both hypotheses are able to describe the data: Either boys are innately better than girls at spatial reasoning (innate factors hypothesis), or boys in 1914 just happened to have had more playtime with spatial tasks than girls, with each task further improving Work partially done at Purdue University and Intel Labs.

Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. We ensure invariance in the next-step prediction across such inputs, by employing a self-supervised objective derived by our observation, formalised in a causal graph. We prove that the resulting method, which we call Hint-ReLIC, improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3$\times$ improvements on the OOD test data.