Bridging Input Feature Spaces Towards Graph Foundation Models

TL;DR

This paper introduces ALL-IN, a method that enables graph models to transfer across datasets with different input features by projecting features into a shared space and using covariance-based representations.

Contribution

ALL-IN provides a theoretically grounded approach for input feature space alignment, allowing transferability of graph models without retraining or architecture modifications.

Findings

ALL-IN achieves strong performance on unseen datasets with new input features.

The method produces invariant node representations under feature permutations and orthogonal transformations.

Empirical results demonstrate effective transferability across diverse graph tasks.

Abstract

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.