Lost in Tokenization: Fundamental Trade-offs in Graph Tokenization for Transformers
Authors: Maya Bechler-Speicher, Gilad Yehudai, Gil Harari, Clayton Sanford, Amir Globerson, Joan Bruna
Abstract
Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this work, we show that this choice is a fundamental component of transformer expressivity. We examine three tokenizations that serve as building blocks for many existing graph tokenizations: spectral, random-walk, and adjacency tokenizations. We prove that different tokenizations induce distinct depth regimes: the same graph computation may be realizable by a shallow transformer under one tokenization, while requiring substantially larger depth under another. For example, we prove that random-walk tokenization is lossy for any walk length, making it impossible in general to recover the graph from it, and that while spectral tokenization is lossless, it is ill-conditioned for local tasks. We further show that although both random-walk and spectral tokenizations are derived from adjacency information, it is impossible for a limited-depth transformer to convert between tokenization families in general. In particular, we establish lower bounds and impossibility results showing that unfavorable tokenizations may preclude the efficient recovery of more suitable structural representations. Finally, we complement our theory with controlled experiments on synthetic and real-world tasks, validating the predicted separations and showing that different tasks favor different structural views, and combining complementary tokenizations allows the transformer to leverage distinct signals from each representation.
The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph tasks. As a widely recognized paradigm, Graph-Tokenizing LLMs (GTokenLLMs) compress complex graph data into graph tokens and treat them as prefix tokens for querying LLMs, leading many to believe that LLMs can understand graphs more effectively and efficiently. In this paper, we challenge this belief: \textit{Do GTokenLLMs fully understand graph tokens in the natural-language embedding space?} Motivated by this question, we formalize a unified framework for GTokenLLMs and propose an evaluation pipeline, \textbf{GTEval}, to assess graph-token understanding via instruction transformations at the format and content levels. We conduct extensive experiments on 6 representative GTokenLLMs with GTEval. The primary findings are as follows: (1) Existing GTokenLLMs do not fully understand graph tokens. They exhibit over-sensitivity or over-insensitivity to instruction changes, and rely heavily on text for reasoning; (2) Although graph tokens preserve task-relevant graph information and receive attention across LLM layers, their utilization varies across models and instruction variants; (3) Additional instruction tuning can improve performance on the original and seen instructions, but it does not fully address the challenge of graph-token understanding, calling for further improvement.
We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined Wave-Induced Rotary Encodings (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.
Graph Language Models (GLMs) have become a promising direction for adapting Large Language Models (LLMs) to graph learning tasks. By transforming graph topology and node information into graph tokens, GLMs allow LLMs to jointly process structured graph inputs and textual instructions. Yet, it remains unclear how LLMs internally interpret these graph tokens and whether graph tokens act as meaningful carriers of graph structure. In this work, we analyze how LLMs process graph information through graph-token behavior in representative GLM architectures. Findings. We find that the internal saliency of graph tokens in GLMs is not equivalent to graph information utilization. Graph sink tokens consistently emerge as activation-level outliers: they can be identified by massive activation values along a small set of hidden-state dimensions and are biased toward early graph-token positions. However, this activation-level saliency does not imply that these tokens are the main carriers of graph information. Unlike classical attention sinks in language and vision-language models, graph sink tokens do not necessarily attract the largest attention weights from query tokens. Through pruning, repositioning, and swapping interventions, we show that graph sink tokens are not the most important semantic or structural tokens for downstream prediction. Implications. Together, these results suggest that after current GLMs map graph structure into the LLM token space, the resulting graph-token representations do not naturally form a fully usable topology-aware internal representation; instead, they exhibit a decoupling between activation-level saliency and graph-semantic utility. This decoupling points to limitations in existing graph-token construction, placement, and alignment mechanisms.