DiGRAF: Diffeomorphic Graph-Adaptive Activation Function

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.

Zero-shot Logical Query Reasoning on any Knowledge Graph

Complex logical query answering (CLQA) in knowledge graphs (KGs) goes beyond simple KG completion and aims at answering compositional queries comprised of multiple projections and logical operations. Existing CLQA methods that learn parameters bound to certain entity or relation vocabularies can only be applied to the graph they are trained on which requires substantial training time before being deployed on a new graph. Here we present UltraQuery, an inductive reasoning model that can zero-shot answer logical queries on any KG. The core idea of UltraQuery is to derive both projections and logical operations as vocabulary-independent functions which generalize to new entities and relations in any KG. With the projection operation initialized from a pre-trained inductive KG reasoning model, UltraQuery can solve CLQA on any KG even if it is only finetuned on a single dataset. Experimenting on 23 datasets, UltraQuery in the zero-shot inference mode shows competitive or better query answering performance than best available baselines and sets a new state of the art on 14 of them.

GraphMETRO: Mitigating Complex Distribution Shifts in GNNs via Mixture of Aligned Experts

Graph Neural Networks' (GNNs) ability to generalize across complex distributions is crucial for real-world applications. However, prior research has primarily focused on specific types of distribution shifts, such as larger graph size, or inferred shifts from constructed data environments, which is highly limited when confronted with multiple and nuanced distribution shifts. For instance, in a social graph, a user node might experience increased interactions and content alterations, while other user nodes encounter distinct shifts. Neglecting such complexities significantly impedes generalization. To address it, we present GraphMETRO, a novel framework that enhances GNN generalization under complex distribution shifts in both node and graph-level tasks. Our approach employs a mixture-of-experts (MoE) architecture with a gating model and expert models aligned in a shared representation space. The gating model identifies key mixture components governing distribution shifts, while each expert generates invariant representations w.r.t. a mixture component. Finally, GraphMETRO aggregates representations from multiple experts to generate the final invariant representation. Our experiments on synthetic and realworld datasets demonstrate GraphMETRO's superiority and interpretability. To highlight, GraphMETRO achieves state-of-the-art performances on four real-world datasets from GOOD benchmark, outperforming the best baselines on WebKB and Twitch datasets by 67% and 4.2%, respectively.

MIST: Defending Against Membership Inference Attacks Through Membership-Invariant Subspace Training

In Member Inference (MI) attacks, the adversary try to determine whether an instance is used to train a machine learning (ML) model. MI attacks are a major privacy concern when using private data to train ML models. Most MI attacks in the literature take advantage of the fact that ML models are trained to fit the training data well, and thus have very low loss on training instances. Most defenses against MI attacks therefore try to make the model fit the training data less well. Doing so, however, generally results in lower accuracy. We observe that training instances have different degrees of vulnerability to MI attacks. Most instances will have low loss even when not included in training. For these instances, the model can fit them well without concerns of MI attacks. An effective defense only needs to (possibly implicitly) identify instances that are vulnerable to MI attacks and avoids overfitting them. A major challenge is how to achieve such an effect in an efficient training process. Leveraging two distinct recent advancements in representation learning: counterfactually-invariant representations and subspace learning methods, we introduce a novel Membership-Invariant Subspace Training (MIST) method to defend against MI attacks. MIST avoids overfitting the vulnerable instances without significant impact on other instances. We have conducted extensive experimental studies, comparing MIST with various other state-of-the-art (SOTA) MI defenses against several SOTA MI attacks. We find that MIST outperforms other defenses while resulting in minimal reduction in testing accuracy.

Efficient Subgraph GNNs by Learning Effective Selection Policies

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 then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. 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. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

An OOD Multi-Task Perspective for Link Prediction with New Relation Types and Nodes

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 OOD 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 an OOD link prediction method using the theoretical concept of double exchangeability (for nodes & relation types), in contrast to the (single) exchangeability (only for nodes) used to design Graph Neural Networks (GNNs). In this work we further extend the double exchangeability concept to multi-task double exchangeability, 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 entirely new relation types in test, without access to additional information, yielding significant performance improvements over existing methods.

MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning

A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE) dynamical system with different unknown ODE parameters, and demand accurate forecasts even under out-of-support initial conditions and out-of-support ODE parameters. In this work we propose a solution for such tasks, which we define as a meta-learning procedure for causal structure discovery (including invariant risk minimization). Using three different OOD tasks, we empirically observe that the proposed approach significantly outperforms existing state-of-the-art PIML and deep learning methods.

Causal Lifting and Link Prediction

Current state-of-the-art causal models for link prediction assume an underlying set of inherent node factors -- an innate characteristic defined at the node's birth -- that governs the causal evolution of links in the graph. In some causal tasks, however, link formation is path-dependent, i.e., the outcome of link interventions depends on existing links. For instance, in the customer-product graph of an online retailer, the effect of an 85-inch TV ad (treatment) likely depends on whether the costumer already has an 85-inch TV. Unfortunately, existing causal methods are impractical in these scenarios. The cascading functional dependencies between links (due to path dependence) are either unidentifiable or require an impractical number of control variables. In order to remedy this shortcoming, this work develops the first causal model capable of dealing with path dependencies in link prediction. It introduces the concept of causal lifting, an invariance in causal models that, when satisfied, allows the identification of causal link prediction queries using limited interventional data. On the estimation side, we show how structural pairwise embeddings -- a type of symmetry-based joint representation of node pairs in a graph -- exhibit lower bias and correctly represent the causal structure of the task, as opposed to existing node embedding methods, e.g., GNNs and matrix factorization. Finally, we validate our theoretical findings on four datasets under three different scenarios for causal link prediction tasks: knowledge base completion, covariance matrix estimation and consumer-product recommendations.

Double Permutation Equivariance for Knowledge Graph Completion

This work provides a formalization of Knowledge Graphs (KGs) as a new class of graphs that we denote doubly exchangeable attributed graphs, where node and pairwise (joint 2-node) representations must be equivariant to permutations of both node ids and edge (& node) attributes (relations & node features). Double-permutation equivariant KG representations open a new research direction in KGs. We show that this equivariance imposes a structural representation of relations that allows neural networks to perform complex logical reasoning tasks in KGs. Finally, we introduce a general blueprint for such equivariant representations and test a simple GNN-based double-permutation equivariant neural architecture that achieve 100% Hits@10 test accuracy in both the WN18RRv1 and NELL995v1 inductive KG completion tasks, and can accurately perform logical reasoning tasks that no existing methods can perform, to the best of our knowledge.

Bias Challenges in Counterfactual Data Augmentation

Deep learning models tend not to be out-of-distribution robust primarily due to their reliance on spurious features to solve the task. Counterfactual data augmentations provide a general way of (approximately) achieving representations that are counterfactual-invariant to spurious features, a requirement for out-of-distribution (OOD) robustness. In this work, we show that counterfactual data augmentations may not achieve the desired counterfactual-invariance if the augmentation is performed by a context-guessing machine, an abstract machine that guesses the most-likely context of a given input. We theoretically analyze the invariance imposed by such counterfactual data augmentations and describe an exemplar NLP task where counterfactual data augmentation by a context-guessing machine does not lead to robust OOD classifiers.