Riemannian Graph Tokenizer for Structural Knowledge Transfer

Foundation models are at the forefront of artificial intelligence. A tokenizer, converting the raw input into discrete representations that the model can understand, plays an important role to the success of foundation models. Unlike the text tokenizer that is well studied in large language models, graph tokenizer is still at its early stage, facing the challenges of tackling the non-Euclidean structures and capturing the structural semantics. How to design a graph tokenizer for structural knowledge transfer? To this end, we propose a Riemannian Graph Tokenizer (RGT) that bridges the structural knowledge and quantized representations to support cross-domain structural knowledge transfer. The connection is established by Riemannian geometry. Specifically, we first define the geometric vocabulary (trees, cycles and sequences), which captures fundamental structural patterns and reflects the intrinsic geometry of graph. Second, we construct a Riemannian quantizer with Riemannian Straight-Through Estimator to tokenise graph structures across multiple domains into discrete tokens. To ensure consistency and transferability across diverse geometric spaces, RGT further incorporates a geometry-aligned decoder that projects manifoldspecific tokens into a unified tangent space. The theoretical analysis and geometric interpretations are provided to support the effectiveness of our proposed method. Extensive experiments across diverse datasets demonstrate that RGT significantly enhances structural knowledge transferability across graph domains. CCS Concepts • Computing methodologies → Knowledge representation and reasoning; • Theory of computation → Computational geometry.