Why don't Graph Transformers attend to the same token?

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.

Global self-attention drives modern graph transformers, yet the softmax at its core imposes a structural constraint rarely examined directly: every attention row is non-negative and sums to one, so each per-head output is a mass-conserving convex combination of value vectors. A node can never "attend to nothing." We argue this conservation constraint is a single root cause behind three pathologies usually studied in isolation: the collapse of node representations with depth (over-smoothing), a low-rank bottleneck on per-head outputs, and brittle optimization in deep stacks. Drawing on how sigmoid gating removes analogous attention sinks in language models, we introduce SigGate-GT, a graph transformer that applies a learned, per-head, input-conditioned sigmoid gate to the attention output inside the GraphGPS framework. The gate is a smooth, per-dimension "volume control" that can drive head outputs toward zero, relaxing the constraint without abandoning attention's probabilistic interpretation. Analytically and through synthetic experiments, we show the gate strictly increases the stable rank of per-head outputs, and connect this rank gain to all three manifestations. On five molecular and long-range benchmarks, SigGate-GT matches the prior best on ZINC (0.059 MAE), records the strongest result among the graph-transformer baselines we evaluate on ogbg-molhiv (82.47% ROC-AUC), and is competitive on ogbg-molpcba and the Long-Range Graph Benchmark, with statistically significant gains over GraphGPS on all five datasets (p < 0.05). Mechanism analyses confirm the diagnosis: gating slows over-smoothing (a 30% mean relative gain in representation diversity across 4-16 layers), keeps attention entropy from collapsing, and stabilizes training across a 10x learning-rate range, at about 1% parameter overhead on OGB and under 3% wall-clock cost.

Transformers commonly exhibit an attention sink: disproportionately high attention to the first position. We study this behavior in GPT-2-style models with learned query biases and absolute positional embeddings. Combining structural analysis with causal interventions, validated across natural-language, mathematical, and code inputs, we find that the sink arises from the interaction among (i) a learned query bias, (ii) the first-layer MLP transformation of the positional encoding, and (iii) structure in the key projection. Crucially, each component we identify is individually dispensable: architectures omitting each of them robustly exhibit sinks. This indicates that attention sinks may arise through distinct circuits across architectures. These findings inform mitigation of sinks, and motivate broader investigation into why sinks emerge.