@inproceedings{yan-etal-2026-information,
title = "Information-Theoretic Limits of Positional Identifiability under Hybrid Graph Encodings",
author = "Yan, Zimo and
Xie, Zheng and
Liu, Chang and
Lv, Yiqin and
Duan, Runfan and
Wang, Yuan and
Zeng, Bingyao",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.734/",
pages = "15414--15434",
ISBN = "979-8-89176-462-0",
abstract = "Graph-based NLP and symbolic reasoning models often rely on positional encodings to distinguish tokens, entities, or reasoning states, but the identifiability provided by these encodings remains poorly understood. We analyze a hybrid graph encoding that combines anchor distances with quantized low-frequency spectral energy. Treating the encoding as a deterministic observation map gives an exact image-preimage identity for localization ambiguity and a one-sided information-theoretic converse: if the joint anchor, spectral, and quantization budget is too small, distinct nodes must share the same code, which also lower-bounds task-label ambiguity observable from that code. Experiments on random 3-regular graphs, CLUTRR relation graphs, and Universal Dependencies trees support the predicted scaling. Under matched normalized budgets, Hybrid is best or tied at 74 of 87 attained thresholds, while PE-only UD probes show improved recovery of syntactic-tree geometry. The results therefore position positional encoding as a pre-model, encoding-level necessary-condition diagnostic rather than an achievability guarantee or an end-to-end model claim."
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<abstract>Graph-based NLP and symbolic reasoning models often rely on positional encodings to distinguish tokens, entities, or reasoning states, but the identifiability provided by these encodings remains poorly understood. We analyze a hybrid graph encoding that combines anchor distances with quantized low-frequency spectral energy. Treating the encoding as a deterministic observation map gives an exact image-preimage identity for localization ambiguity and a one-sided information-theoretic converse: if the joint anchor, spectral, and quantization budget is too small, distinct nodes must share the same code, which also lower-bounds task-label ambiguity observable from that code. Experiments on random 3-regular graphs, CLUTRR relation graphs, and Universal Dependencies trees support the predicted scaling. Under matched normalized budgets, Hybrid is best or tied at 74 of 87 attained thresholds, while PE-only UD probes show improved recovery of syntactic-tree geometry. The results therefore position positional encoding as a pre-model, encoding-level necessary-condition diagnostic rather than an achievability guarantee or an end-to-end model claim.</abstract>
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%0 Conference Proceedings
%T Information-Theoretic Limits of Positional Identifiability under Hybrid Graph Encodings
%A Yan, Zimo
%A Xie, Zheng
%A Liu, Chang
%A Lv, Yiqin
%A Duan, Runfan
%A Wang, Yuan
%A Zeng, Bingyao
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F yan-etal-2026-information
%X Graph-based NLP and symbolic reasoning models often rely on positional encodings to distinguish tokens, entities, or reasoning states, but the identifiability provided by these encodings remains poorly understood. We analyze a hybrid graph encoding that combines anchor distances with quantized low-frequency spectral energy. Treating the encoding as a deterministic observation map gives an exact image-preimage identity for localization ambiguity and a one-sided information-theoretic converse: if the joint anchor, spectral, and quantization budget is too small, distinct nodes must share the same code, which also lower-bounds task-label ambiguity observable from that code. Experiments on random 3-regular graphs, CLUTRR relation graphs, and Universal Dependencies trees support the predicted scaling. Under matched normalized budgets, Hybrid is best or tied at 74 of 87 attained thresholds, while PE-only UD probes show improved recovery of syntactic-tree geometry. The results therefore position positional encoding as a pre-model, encoding-level necessary-condition diagnostic rather than an achievability guarantee or an end-to-end model claim.
%U https://aclanthology.org/2026.findings-emnlp.734/
%P 15414-15434
Markdown (Informal)
[Information-Theoretic Limits of Positional Identifiability under Hybrid Graph Encodings](https://aclanthology.org/2026.findings-emnlp.734/) (Yan et al., Findings 2026)
ACL