A second axis for the taxonomy#
Survey taxonomies usually answer “what problems does X solve?” Our revision adds the question reviewers actually ask: what kind of mathematical object is X in each paper? From the corpus tags, every paper was labeled with the role SE plays: objective, prior, metric, regularizer, feature, robustness.
Three readings fell out of the cross-tab (all counts machine-generated from the tag corpus, n=81):
- SE is consumed more than it is optimized. It appears as a metric in 59 papers and as a structural prior in 50, against 47 where it is the minimization objective itself. The field’s center of gravity has shifted from computing SE to using it.
- The distribution is direction-dependent in an interpretable way. In hierarchical clustering the objective role dominates (25 of 32) — there the encoding tree is the product. All 8 RL papers use SE as a prior shaping state/action abstractions, not as the thing being optimized.
- The regularizer role is strikingly rare (7 of 81). Adding an information term to a task loss is the standard way deep learning consumes such measures; its scarcity here is a direct consequence of SE’s differentiability gap — current differentiable formulations stop at shallow trees.
The LLM turn, organized by where the graph lives#
2025–26 produced the first real SE×LLM papers, and they slot into a clean three-way split by where in the LLM pipeline the graph is built:
- Over the outputs — SeSE (UAI'26 Oral): sample N answers, build an NLI semantic graph, and use the structural entropy of its optimal encoding tree as a hallucination-predicting uncertainty score. Provably generalizes semantic entropy.
- Over the internals — Lancet: locate hallucination-prone neurons, map their propagation pathways by minimizing SE over the activation-flow graph, intervene hierarchically.
- Over the input context — RagSEDE (WWW'26): an SE-maintained event knowledge base feeding a retrieval-augmented language model.
The open problem underneath all three: SE’s guarantees are stated for undirected graphs with degree-proportional stationary distributions, while every LLM-induced graph is directed, weighted, and heuristically sparsified. The bring-your-own-π generalization (π = attention mass) is the obvious unifying lever — and is sitting unclaimed.
Process note#
The revision went through an adversarial pass before push: an independent referee agent (16 findings, from a misdescribed protocol down to a dangling participle) and a claims auditor that recomputed every number in the diff against the tag corpus (14/14 verified). Two of the referee’s catches would have shipped: result numbers misaligned with their JSONs, and a section title that didn’t match its content.
The manuscript is now 36 pages, clean compile. Next post: what happened when the LLM-track reproduction actually ran.