Positional encoding has become a standard component in graph learning, especially for graph Transformers and other models that must distinguish structurally similar nodes, yet its fundamental identifiability remains poorly understood. In this work, we study node localization under a hybrid positional encoding that combines anchor-distance profiles with quantized low-frequency spectral features. We cast localization as an observation-map problem whose difficulty is controlled by the number of distinct codes induced by the encoding and establish an information-theoretic converse identifying an impossibility regime jointly governed by the anchor number, spectral dimension, and quantization level. Experiments further support this picture: on random $3$-regular graphs, the empirical crossover is well organized by the predicted scaling, while on two real-world DDI graphs identifiability is strongly graph-dependent, with DrugBank remaining highly redundant under the tested encodings and the Decagon-derived graph becoming nearly injective under sufficiently rich spectral information. Overall, these results suggest that positional encoding should be understood not merely as a heuristic architectural component, but as a graph-dependent structural resolution mechanism.

翻译：位置编码已成为图学习中的标准组件，尤其适用于图Transformer及其他需区分结构相似节点的模型，但其基础的可辨识性仍缺乏深入理解。本文研究混合位置编码下的节点定位问题，该编码结合锚点距离分布与量化低频谱特征。我们将节点定位建模为观测映射问题，其难度取决于编码所生成的唯一码数量，并建立信息论逆推定理，识别出由锚点数量、谱维数与量化水平共同控制的不可行区域。实验进一步支撑该结论：在随机$3$-正则图中，经验交叉点与预测标度关系高度吻合；而在两个真实DDI图中，可辨识性显著依赖于图结构，DrugBank图在测试编码下保持高度冗余，而源自Decagon的图在充足谱信息下趋近单射。总体而言，本研究结果表明位置编码应被理解为一种依赖于图的结构解析机制，而非仅为启发式的架构组件。