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REVIEW 5 major objections 4 minor 40 references

Language Models as Ontology Encoders

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read OnT embeds EL ontologies by tuning a pretrained language model in hyperbolic space, preserving logical structure and beating prior methods on axiom prediction and inference.

desk verdict OnT is an empirically strong ontology embedding method, but the logical-preservation claim outruns the proof. read the letter →

arxiv 2507.14334 v1 pith:BLTGWVNR submitted 2025-07-18 cs.AI

Hui Yang , Jiaoyan Chen , Yuan He , Yongsheng Gao , Ian Horrocks This is my paper · ORCID
classification cs.AI
keywords ontologyembeddingdescriptionlogicELhyperbolicspacepretrainedlanguagemodelaxiompredictioninferencePoincaréballrole
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes OnT, an ontology embedding method that tunes a pretrained language model inside a hyperbolic (Poincaré ball) space so that textual labels and Description Logic EL structure are encoded together. The authors argue that prior geometric methods ignore text, while language-model methods fail to preserve logical relationships such as subsumption transitivity and existential-restriction monotonicity. OnT verbalizes complex concepts, represents roles as rotation-and-scaling functions, and trains with hierarchy, role, and conjunction losses. On GALEN, Gene Ontology, and Uberon, it reports state-of-the-art results on both axiom prediction and axiom inference, along with transfer-learning success and a real SNOMED CT case. The reason to care is that ontology embeddings that keep logic in the vector space could support approximate reasoning and ontology completion in biomedicine and other structured domains.

What carries the argument

The load-bearing mechanism is a set of geometric-training losses in the Poincaré ball model of hyperbolic space: a hierarchy loss $\mathcal{L}_{\prec}$ that treats axioms $C \sqsubseteq D$ as a partial order (contrastive plus centripetal terms), a role loss $\mathcal{L}_r$ that identifies $x_{\exists r.D}$ with $f_r(x_D)$ through two opposite hierarchy losses, and a conjunction loss $\mathcal{L}_{\sqcap}$ that enforces $C \sqcap D \sqsubseteq C$ and $C \sqcap D \sqsubseteq D$. The role transformer $f_r(v) = k_r \odot (R(\Theta_r) \cdot v)$ is a rotation-scaling operation, and the axiom score $s(C \sqsubseteq D) = -(d_\kappa(x_C, x_D) + \lambda(\|x_D\|_\kappa - \|x_C\|_\kappa))$ combines hyperbolic distance with a norm-based penalty. These pieces together are what let the PLM embeddings carry both textual and formal-logical semantics.

What would settle it

Replace the compositional verbalizations with shuffled word sequences (same vocabulary, no grammatical relation) and rerun prediction and inference on GALEN, GO, and Uberon; if the metrics do not drop substantially, the specific semantics of the verbalization are not load-bearing for the reported gains.

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Extended reading notes

Core claim

The central claim is that a pretrained language model can act as an ontology encoder for EL when its outputs are placed in a Poincaré ball and trained with losses that mirror the logic. Complex concepts are first verbalized compositionally ($C \sqcap D$ becomes "$C$ and $D$"; $\exists r.C$ becomes "something that $V(r)$ some $V(C)$"), then embedded by the PLM; subsumption axioms $C \sqsubseteq D$ are treated as a partial order on hyperbolic points and learned with a hierarchical contrastive plus centripetal loss. Roles are embedded as hyperbolic transformations $f_r(v) = k_r \odot (R(\Theta_r) \cdot v)$, and two extra losses align $f_r(x_D)$ with $x_{\exists r.D}$ and enforce $C \sqcap D \sqsubseteq C$, $C \sqcap D \sqsubseteq D$. Proposition 1 shows that when $k_r = 1$, rotations leave hyperbolic distances and norms invariant, which makes the score for $\exists r.C \sqsubseteq \exists r.D$ equal to that for $C \sqsubseteq D$ and thereby captures the deductive pattern $A \sqsubseteq B \Rightarrow \exists r.A \sqsubseteq \exists r.B$. The paper reports consistent state-of-the-art performance in axiom prediction and inference on GALEN, GO, and Uberon, with up to a sevenfold improvement in Mean Rank over prior methods on GO prediction.

Load-bearing premise

The load-bearing premise is that the automatically generated English sentences for complex concepts—such as "something that is parent of some person"—preserve enough of the EL semantics that a pretrained language model can embed them faithfully; the paper does not test how sensitive results are to verbalization quality.

Editorial extensions

If this is right

  • Plausible new axioms, including inferred ones, can be ranked directly in vector space, supporting ontology completion and approximate reasoning without a separate classifier.
  • Unseen entities can be embedded from their textual descriptions alone, which is what enables the reported transfer-learning behaviour across GALEN, GO, and Uberon.
  • The rotation-based role model captures monotonicity of existential restrictions (if $A \sqsubseteq B$ then $\exists r.A \sqsubseteq \exists r.B$), a deductive pattern earlier LM-based embeddings lacked.
  • The method can flag missing and erroneous direct subsumptions during real ontology construction, as demonstrated on SNOMED CT.
  • Because OnT(w/o r) also outperforms most baselines, even the core hierarchy-plus-verbalization combination is a competitive option when role information is unavailable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not measure verbalization quality; if the English template were replaced by a semantically empty one, such as random word shuffles, with little change in results, that would suggest the PLM is mainly exploiting lexical overlap rather than compositional meaning.
  • The choice of hyperbolic space may matter more than the PLM size: the ablation shows large gains over Euclidean-style geometric baselines but modest differences among three sentence-transformer models.
  • The rotation-and-scaling role representation is untested on role inclusion axioms ($r \sqsubseteq s$) or role chains; extending the loss design to those patterns is a natural next step.
  • The reported GO prediction gains (about a sevenfold Mean Rank improvement) may depend on the evaluation protocol of ranking over all atomic concepts; direct comparison with other papers should be done carefully.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper introduces OnT, an approach to embedding EL ontologies that combines pretrained-language-model text representations with hyperbolic geometric constraints. Atomic concepts and roles are verbalized and encoded by a sentence transformer; complex concepts are embedded via compositional verbalization; roles are modeled as rotation-scaling transformations; and training uses a hierarchy loss together with role-alignment and conjunction losses. The method is evaluated on axiom prediction (held-out split) and axiom inference (entailed NF1 axioms) over GALEN, GO, and Uberon, reporting state-of-the-art results against geometric and text-based baselines, plus transfer-learning and SNOMED case studies.

Significance. If the empirical results hold, OnT is a useful engineering contribution: it combines textual semantics from PLMs with hyperbolic geometry for ontologies, and the released code and data should facilitate replication. The held-out prediction task is a clean evaluation of inductive ontology completion, and the reported gains, especially in mean rank, are substantial. However, the paper's central claim that OnT 'preserves logical relationships of EL' is not fully supported: Proposition 1 is an invariance statement about the role transformation, not a proof about the verbalized existential embeddings actually used in scoring, and the inference benchmark may be largely solvable from the norm-ordering term in the loss. The empirical comparisons would also be more convincing with error bars and validation of the re-implemented baselines.

major comments (5)
  1. [Section 4.3, Proposition 1, Eq. (4) and Eq. (6)] Proposition 1 only shows that the score s is invariant under the role transformation fr when kr=1. It does not relate fr(x_D) to the verbalization embedding x_{∃r.D}, which is the representation actually scored by Eq. (8) for existential concepts. The alignment loss in Eq. (6) is a pair of hierarchical losses with margins; it can be satisfied without exact equality between fr(x_D) and x_{∃r.D}, and kr is a learned parameter not constrained to 1. Consequently, the claimed preservation of the pattern A⊑B ⇒ ∃r.A⊑∃r.B is not guaranteed by the proof. Please either prove a bound under the actual training objective, report empirical distances between fr(x_D) and x_{∃r.D}, or reframe Proposition 1 as a design motivation rather than a preservation guarantee.
  2. [Section 4.3, Eq. (5) and Eq. (8); Section 5.3] The centripetal term in the hierarchy loss explicitly enforces ‖D‖κ < ‖C‖κ for every asserted subsumption C⊑D, and the scoring function in Eq. (8) contains the same norm-difference term. Along a chain C⊑D⊑E, transitivity follows from the norm ordering alone, so the strong inference results on entailed NF1 axioms may be largely driven by this term rather than by the role-alignment or conjunction losses. Table 3 is consistent with this concern: OnT(w/o r) is close to OnT on several inference metrics (e.g., GO H@100 39 vs 40, ANATOMY MR 499 vs 458). The authors should isolate the contribution of the role and conjunction losses to transitive inference, for example by ablating the norm-difference term in Eq. (8) or by measuring whether Eq. (6) actually brings fr(x_D) close to x_{∃r.D}.
  3. [Section 5.1] The experiments report no variance: each result appears to come from a single 80/10/10 split and a single run, with no error bars or significance tests. Given the large gains claimed in Table 2 (e.g., MR 1,121 vs 7,092 on GO), the absence of repeated-seed statistics makes it impossible to judge whether the state-of-the-art claim is robust. Please report means and standard deviations over multiple random splits and seeds, and ideally paired significance tests for the main comparisons.
  4. [Section 5.1] The geometric baselines (BoxEL, TransBox, ELBE, ELEM) were re-implemented rather than run from original code, and no validation against published numbers is provided. While the paper explains that dataset modifications require this, the re-implementations should be validated (e.g., by reproducing a previously reported score on a standard setting) and the re-implementation code should be clearly documented; otherwise the baselines may be unintentionally weaker than the original methods.
  5. [Section 4.1 and Section 6] All complex-concept embeddings are derived from the compositional verbalization templates V(C⊓D) = 'V(C) and V(D)' and V(∃r.C) = 'something that V(r) some V(C)', but the paper does not evaluate verbalization quality or sensitivity to alternative templates. The conclusion explicitly lists 'exploring the impact of verbalization quality' as future work, yet this is a load-bearing component of the method: any misrepresentation of the EL semantics in these strings propagates to all downstream scores. Please provide at least a qualitative evaluation of verbalization correctness or an ablation over template variants.
minor comments (4)
  1. [Table 3] In the ANATOMY column, the Box2EL row (0/1/7, 1, 11,801) is identical to the GO row, which is presumably a copy-paste error; please correct and re-verify all entries.
  2. [Section 5.3] The sentence 'incorporating role embeddings and losses for logical constraints allows OnT(w/o r) to achieve even better performance than both OnT and HiT' is contradictory; it should say 'omitting role embeddings' or similar.
  3. [Section 4.3] There are several typos, including 'on the other hand, in in Figure 2b' and 'where Dneg represents a randomly sampled concept' without specifying whether negatives are sampled from the ontology vocabulary or from all candidates; please clarify.
  4. [Section 5.3] The inference task evaluates only entailed NF1 axioms; the paper should justify this restriction and state whether the same conclusions would be expected for NF2–NF4 inferences, especially since those axiom types are present in the training data.

Circularity Check

2 steps flagged · score 4.0 of 10

Inference scores partly read out the fitted norm ordering, and Proposition 1 is a definitional identity that does not establish existential monotonicity.

  1. fitted input called prediction [Section 4.3 (Eq. 5, Eq. 8) and Section 5.1 (inference-task split)]
    "The centripetal loss is defined as: Lcentri(x C ≺ x D) = max(0, ∥x D∥κ − ∥x C∥κ + β) ... the score ... s(C ⊑ D) := −(dκ(x C, x D) + λ(∥x D∥κ − ∥x C∥κ)) ... For the inference task, we use the whole ontology as the training data, and all the inferred axioms of NF1 as the testing data."

    The centripetal loss trains every asserted subsumption C ⊑ D to make the parent norm smaller than the child norm, and the scoring function uses exactly the same norm difference λ(∥xD∥κ − ∥xC∥κ) as a positive confidence signal. Since the norm order is transitive, any entailed chain A ⊑ B ⊑ … ⊑ D inherits a positive score component for the unseen axiom A ⊑ D solely from the training constraints, so the inference score is in part a direct readout of the fitted norm ordering rather than an independent prediction. Moreover, because the test set is defined as all inferred NF1 axioms, the asserted NF1 axioms used as training data are themselves entailed and are not explicitly excluded, so part of the inference test set coincides with the training input by construction.

  2. other [Section 4.3, Proposition 1 and surrounding text]
    "We have the following proposition that allows us to control the difference between scores s(fr(xC) ≺ fr(xD)) and s(xC ≺ xD) using the scaling factor kr, and thus, capturing the deductive pattern A ⊑ B ⇒ ∃r.A ⊑ ∃r.B."

    When kr = 1, fr is a rotation and the score s depends only on hyperbolic distances and norms, both of which are rotation-invariant; the equality is therefore a definitional identity. The proposition never mentions x_{∃r.A} or x_{∃r.B}, the embeddings actually used by Eq. 8 for existential axioms; it only relates fr(xC) to fr(xD). The alignment loss Lr (Eq. 6) is two hierarchy losses with margins α, β and random negatives, so it can be minimized without making fr(xD) equal to x_{∃r.D}. Thus the claimed preservation of A ⊑ B ⇒ ∃r.A ⊑ ∃r.B is not derived from the proposition; it is an additional, unproved assumption of the loss. The first-principles result is essentially a tautology about rotation invariance plus an unsupported semantic leap.

full rationale

The prediction task is a clean held-out split: OnT trains on an 80% subset of axioms and ranks held-out candidates with Eq. 8, so the headline prediction numbers have independent content and are not circular. The inference task, however, is partly by construction: the centripetal component of L≺ (Eq. 5) directly enforces a norm ordering on asserted subsumptions, and Eq. 8 uses that same norm difference as a positive confidence term; the transitivity of the norm order then boosts entailed chains without any new evidence. In addition, Proposition 1 proves only rotation invariance of the score at kr = 1 and does not connect the role-transformed embedding fr(xD) to the verbalized existential embedding x_{∃r.D}; the existential monotonicity claim therefore rests on an unproved alignment assumption rather than on the proposition. These are real gaps, but they are not a full reduction of the central claim: the held-out prediction results, the ablations, and the comparisons against eight baselines still provide independent empirical support. Hence a moderate circularity score of 4 rather than a high one.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The method relies on a pretrained language model, which is a large external input, and introduces role-specific rotation and scaling functions, but these are parameterized transformations rather than new entities in the ontology. The main additional free parameters are the score weight and the role parameters; the principal assumptions are verbalization adequacy and alignment convergence.

free parameters (8)
  • score weight lambda = selected from {0, 0.1, ..., 1} on validation set
    In Eq. 8, lambda balances hyperbolic distance and relative depth; it is tuned on validation, so test results come after model selection.
  • contrastive margin alpha = 3.0
    Fixed from HiT defaults; affects the separation between positive and negative concept pairs in the contrastive loss.
  • centripetal margin beta = 0.5
    Fixed from HiT defaults; enforces the norm gap between child and parent concepts.
  • learning rate gamma = 1e-5
    Taken from HiT defaults; not tuned per ontology.
  • role scaling factor k_r = learned per role
    Role-specific scaling in Eq. 4; the Proposition 1 guarantee only holds for k_r = 1.
  • role rotation angles Theta_r = learned per role
    Role-specific rotation parameters in Eq. 4; applied as Euclidean rotations in the Poincare ball.
  • number of negative samples = 1
    Chosen in pre-test; affects the contrastive loss variance.
  • training epochs = 1
    Chosen after pre-test; short training may leave the role alignment loss far from convergence.
assumptions (5)
  • domain assumption Verbalization V(C) preserves enough of the EL semantics of C for a PLM to embed it usefully.
    Section 4.1 defines V(C) compositionally, but the paper does not evaluate verbalization quality and lists it as future work in the conclusion.
  • domain assumption The alignment loss L_r drives x_{∃r.D} close enough to f_r(x_D) for the rotation-invariance of the score to transfer to actual concept embeddings.
    Section 4.3 Eq. 6 trains this alignment, but with one epoch there is no guarantee the two embeddings coincide, so Proposition 1 applies only approximately.
  • standard math Rotation matrices in Eq. 4 act as valid hyperbolic isometries in the Poincare ball when k_r = 1.
    Section 3.2 and Proposition 1; rotations preserve Euclidean norms, hence hyperbolic distance and norm.
  • domain assumption The custom normalization of EL ontologies (introducing fresh atomic concepts) is logically faithful.
    Section 3.1; the authors reject existing normalizers, citing inconsistent axioms, but do not provide a formal verification of their own normalizer.
  • domain assumption Entailed axioms not present in the training ontology form a valid and meaningful inference test set.
    Section 5.1; this is the standard inference evaluation, but the centripetal loss directly encodes the norm ordering that underlies transitive subsumption.

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Cite this review

Pith. "Pith review of Language Models as Ontology Encoders." pith.science (2026). https://pith.science/paper/BLTGWVNR

@misc{pith2026250714334,
  author       = {Pith},
  title        = {Pith review of: Language Models as Ontology Encoders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BLTGWVNR}},
  note         = {Machine review of arXiv:2507.14334}
}
read the original abstract

OWL (Web Ontology Language) ontologies which are able to formally represent complex knowledge and support semantic reasoning have been widely adopted across various domains such as healthcare and bioinformatics. Recently, ontology embeddings have gained wide attention due to its potential to infer plausible new knowledge and approximate complex reasoning. However, existing methods face notable limitations: geometric model-based embeddings typically overlook valuable textual information, resulting in suboptimal performance, while the approaches that incorporate text, which are often based on language models, fail to preserve the logical structure. In this work, we propose a new ontology embedding method OnT, which tunes a Pretrained Language Model (PLM) via geometric modeling in a hyperbolic space for effectively incorporating textual labels and simultaneously preserving class hierarchies and other logical relationships of Description Logic EL. Extensive experiments on four real-world ontologies show that OnT consistently outperforms the baselines including the state-of-the-art across both tasks of prediction and inference of axioms. OnT also demonstrates strong potential in real-world applications, indicated by its robust transfer learning abilities and effectiveness in real cases of constructing a new ontology from SNOMED CT. Data and code are available at https://github.com/HuiYang1997/OnT.

Figures

Figures reproduced from arXiv: 2507.14334 by the authors.

Figure 1
Figure 1. Illustration of fr in a two-dimensional hyperbolic space. ontology O, denoted as V(C). For EL-ontologies, we generate these descriptions according to the following compositional rules: V(C⊓D) = “V(C) and V(D)”, V(∃r.C) = “ something that V(r) some V(C)”. For example, we will have V(Person ⊓ Student) = “person and student”, and V(∃isParentOf.Person) = “something that is parent of some person”. With the verbalization … view at source ↗
Figure 2
Figure 2. Illustration of impact of hierarchy Loss [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Transfer learning results of OnT and HiT with MiniLM-L12-v2. [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Case Study: Arrows C → D represent subsumption C ⊑ D with scores from Eq. 8. Each arrow shows three scores from three OnT models trained on GALEN/GO/ANATOMY ontologies, respectively. A higher score indicates a more likely subsumption. Blue/red highlights indicate the h…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.