Geometric Constraints for Small Language Models to Understand and Expand Scientific Taxonomies
Authors: Liri Fang
Dongqi Fu
Jiawei Han
Jingrui He
Vetle I Torvik
Venue: ICLR 2026 Poster (2026)
Keywords: Small LM
Hyperbolic Deep Learning
Taxonomy Structure
Primary area: learning on graphs and other geometries & topologies

Abstract: Recent findings reveal that token embeddings of Large Language Models (LLMs) exhibit strong hyperbolicity. This insight motivates leveraging LLMs for scientific taxonomy tasks, where maintaining and expanding hierarchical knowledge structures is critical. Although potential, generally-trained LLMs face challenges in directly handling domain-specific taxonomies, including computational cost and hallucination. Meanwhile, Small Language Models (SLMs) provide a more economical alternative if empowered with proper knowledge transfer. In this work, we introduce SS-Mono (Structure-Semantic Monotonization), a novel pipeline that combines local taxonomy augmentation from LLMs, self-supervised fine-tuning of SLMs with geometric constraints, and LLM calibration. Our approach enables efficient and accurate taxonomy expansion across root, leaf, and intermediate nodes. Extensive experiments on both leaf and non-leaf expansion benchmarks demonstrate that a fine-tuned SLM (e.g., DistilBERT-base-110M) consistently outperforms frozen LLMs (e.g., GPT-4o, Gemma-2-9B) and domain-specific baselines. These findings highlight the promise of lightweight yet effective models for structured knowledge enrichment in scientific domains.

Published as a conference paper at ICLR 2026
GEOMETRIC CONSTRAINTS FOR SMALL LANGUAGE MODELS TO UNDERSTAND AND EXPAND SCIENTIFIC TAXONOMIES
Liri Fang Dongqi F Han Jingrui He Vetle I. Torvik
University of Illinois tibana-Champaign' Meta AI* (lirif2, hanj, jingrui, vtorvik @illinoii.....e.eeeeeiiiiiiiiiii e.duu, donggi.fu@mta..com http://ggttaa.ccoiiirteeee
ABSTRACT
Recent findings reveal that token embeddings of Large Language Models (LLMs) exhibit strong hyperbolicity. This insight motivates leveraging LLMs for scien- tific taxonomy tasks, where maintaining and expanding hierarchical knowledge structures critical. Although potential, generally-triined LLMS face challenges in directly handling domain-specific taxonomies, including computational cost and hallucination. Meanwhile, Small Language Models (SLMs) provide more eco- nomical alternative if empowered with proper knowledge transfer. this work, we introduce SS-MoNO (Structure-Semantee Monotonization), a novel pipeline that combines local taxonomy augmentation from LLMs, self-supervised fine-tuning of SLMs with geometric constraints, and LLM calibration. Our approach enables efficient and accurate taxonomy expansion across root, leaf, and intermediate nodes. Extensive experiments on both Ieaf and non-leaf expansion benchmarks demonstrate that a fine-tuned SLM (c.g.. DistilBERT-base (0ase-110M)) consistently outperforms frozen LLMs (e.g., GPT-4,, Gemma- (eemma-2-9B) and domain-specific base- lines. These findings highlight the promise of lightweight yet effective models for structured knowledge enrichment in scientific domains.
INTRODUCTION
Recently, researchers discovered that token embeddings of Large Language Models (LLMs) can exhibit a high degree of hyperbolicity, which implies a latent hyperbolic structure in the embedding space (Patil et al. 2025 Yang et al. 2025). Building on this insight, fine-tuning LLMs in hyperbolic space could yield strong performance gains in an efficient manner (Yang et al. 2025). Similarly, this phenomenon is also verified, some extent, that the embedding matrices of LLMs show the semantic structures, e.g., directions of antonym pairs (Kozlowski et al. 2025). Above evidence suggests that LLMSs have the potential to be powerful tool for solving the scientific taxonomy related tasks, like knowledge understanding and enrichment.
Scientific taxonomy, as a specific kind of text-attributed graph, in addition to the textual concept attached to each node, has more rigorous and hierarchical structure than normal undirected graphs, i.e., which can be represented within an explicit hierarchy such trees or directed acyclic graphs for the hypernym and hyponym, e.g., Glycoproteins + Proteins + Ribosomal Proteins - Peptide Elongation Factors, shown in Figure [ the real world, scientific taxonomy now serving many applications, such as knowledge organization and question answering (Shen & Han 2022).
According the above discussion, the hyperbolic space discovery LLM'' embedding space indicates the direction that LLM can solve the scientific taxonomy tasks. However, scientific taxonomy, as a type of controlled vocabulary, is always domain-specific, and LLMs' pre-training is usually executed on large-scale general corpus. This disagreement means that highly likely LLMs can not be directly used for scientific taxonomies like prompting or in-context learning, but often call for the post-training self-supervised fine-tuning process. Based the recent studies (He) jet al. 2024), LLMs are not always affordable, especially when involved with fine-tuning, and under "suitable operations' small language models (SLMs) can be sufficiently powerful and economical

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Prompt:
Plaase generate the desoription the relationship and definition of the following target terms.
Target terms protein, peptide elongation factors
pi parent
Relationship: protein is the parent of peptide elongetion factors. plyooruteiis the parent of protein. inttonneeeenennn pestettinnn cos.rreeettttttte Here'ss a description the relationship and definhions for target
Node pl: porent of
provided structurp:
Quary mode (e.g..
Parent mode p (e-g,, protein)
Ribosomal proteins]
Glycoproteins (Parent of Protein)
plycopratcins are protoins that
Child node c (e.g. paptide
Proteiin of Glycoproteins, Parent Peptide Elongation Factors)
elongation factors)
Closest
Furthest
Proteins are large, complex molecules made up of
Node di child of
sibling
sibling node w
Peptide Elongstion Factors (Child Proteins) Peptide Elongation Factors are specific proteins that
Node of chilld
Relationship:
Glycoproteins Proteins: Glycoprateims specialied
farm proteins characteriee... ...
Proteins + Peptido Elongation Factors: Proteins encompass
description (ta., concept) of each node taconomyy
makecules, includin...
Augmented dlsccr ciptiinnon of each edge by LLM
Overall, this structure Ilustrates how
Figure 1: Scientific Taxonomy with LLM Augmentation (Edge-Level).
for many application scenarios and pave the way for the future of agentic Al (Belcak et al. (025). Then, we need to ask, for the specific scientific taxonomy domain, are we able to first provide LLMM-toSSI.M solution?
In the era of big data, new concepts continuously emerge, posing significant challenges for maintaining structured knowledge systems. Taxonomy expansion aims to insert the newly emerged concepts to the existing taxonomy appropriately instead of constructing a whole new taxonomy from scratch (Tiang eet al.) 2023 Zeng et al. 20246 Xu et al. 2025). In this paper, we consider more general and challenging taxonomy expansion problem, such that the query concept can be inserted everywhere in the existing taxonomy, including the root, leaf, and anywhere in between. As shown in Figure 3 the insertion in between realized by the Query-Positions Matching process: taking every existing edge as the candidate position (candidate answer) to a query, the query will rank all of them based on a scoring function, and select the highest rank to break its old edge and add two new edges. More details are also visualized in Figure in Appendix L.
To begin with, we first verify that LLMS have great potential (and larger model performs better) but are not capable of directly understanding (or through simple prompting) the entire domain- specific taxonomy and making the correct expansion for the following reasoning and cases: (1) Long Context Limit: tested LLMSs
incapable of taking entire existing text-attributed graph input; (2) Hallucination: tested L.LMs are prone to imagine non-existing edges in the existing taxonomy for query insert; (3) No Answer: tested LLMs fail to generate available answer for the taxonomy expansion; (4) Partial Answer: tested LLMs only generate part of correct answer. The real-world failed cases and statistics are shown in Section 4.3 and Figure
Based on the above preliminary testing, we propose the design principle that: on the one hand, we need to 'borrow knowledge' from LLMs SLMs; on the other hand, the 'borrowing' process should avoid computational cost as much as possible. Motivated by this, we propose the method named MS-MONO relying on (1) local taxonomy augmentation by an LLM,, (2) fine-tuning of an SLM with geometric constraints, and (3) LLM calibration. The above pipeline strictly follows the existing hierarchical topology structure, considers the context of the raw textual attribute, adheres to augmentation by LLMs, and verifies the calibration of LLMs. We name this pipeline Structure- Semantic Monotonization. Empirically, the entire training process of SS MONO is self-supervised. With leaf and non-leaf taxonomy expansion benchmark, a fine-tuned tiny LM like DistilBERT- base- 1 10M leads the comprehensive outperformance over frozen general LLMs (like Gemma-2- 9B Mesnard et al. 2024) and GPT-4o mini (Hurst al. ) and domain-specifie baselines.
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2 PRELIMINARY
We define a taxonomy T= (V, , E) as directed acyclic graph (i.e., DAG), where each node e E V represents unique concept, and a directed edge (p,c) E E represents relation pointing from the parent node p to the child node c. Furthermore, each concept (i.e., node v E V) has a textual description, such that The corresponding feature matrix of the input taxonomy graph T (including the query node q) is denoted as H E kVul where is the feature dimension, and we use H, E R² to denote the input feature vector of node v. The detailed process of obtaining H from fine-tuning language models can be found in Appendix
obtain the embedding features of each concept through language models.
3 PROPOSED SS-MONO
In this section, start to introduce the proposed framework SS-MONO, whose core technique is named structure-semantic monotonization. Here, we first introduce the overview and then use three subsections illustrate the implementation details systematically.
3.1 OVERVIEW OF STRUCTURE-SEMET
MONOTONIZATION
Based on the existing taxonomy T = (V, the core of SS-MONO is to explore and integrate the structural information and contextual semantics of concepts to seek the best candidate position to insert the new concept. To achieve this matching. SS-MONO relies on the proposed structure- semantic monotonization via two encoder modules: structure-dominated encoder introduced in Section 3 2 and context-dominated encoder introduced in Section
First, the structure-dominnteed encoder tries verify whether the query node posits in the correct position bounded by the positions of its ground-truth hypernym (i.e., parent node) and ground-truth hyponym (i.e., child node). other words, their relationship should be monotomic along the taxonomy structure. To verify this, the structure- dominated encoder adapts the hyperbolic representation learning project their contextualized embedding into a hyperbolic space so that their hyperbolic embeddings obey the monotonic relationship along the taxonomy, i.e., the transitivity in the hyperbolic space. With this kind of hyperbolic embedding, we can try to compute the corresponding ranking score to rank the candidate positions for matching the query concept.
structure-dominated
However, the contextual semantics certain taxonomy are limited compared with the large language models. Therefore, we propose the second module, context-dominated encoder. Intuitively, this encoder tests whether the semantic meaning around a candidate position shares the similarity with the query node. To obtain the semantic meaning of candidate position, frozen LLM is first prompted to give the textual explanation. Then the context- context-dominated dominated encoder samples ancestors, descendants, and siblings along the hierarchy from that candidate position, encodes the text (augmented and raw node textual attribute) into representation vectors, and computes the matching score between the candidate position and the query.
To make these two encoder modules well-trained, we finally introduce self-supervised optimization, i.e., using the existing taxonomy guide the learning process without human labeling costs.
3.2 DOMMNNATEE ENCODER
Since taxonomy organizes concepts in the explicit hierarchy, this hierarchical structure restricts the concepts to follow particular order from parent to child. Accordingly, the appropriate candidate position (p, e) for a query q to insert should satisfy the transitivity of hierarchical relations between position (p, c) and query q, i.e., <pg
To this end, SS-MONO preserves the hierarchical relation among concepts (e.g., query and candidate positions) together with their contextualized embedding H by adapting (1) hyperbolic encoding (Tif) rea et al. 2019) to project H into hierarchy hhesarehy-peseeveed metric space and (2) nested entailment cones (Ganea et al. 20188) regulate the projection to obey the hierarchical transitivity in the hyperbolic space. In the tollowing two subsections, we first introduce the hyperbolic embedding method and then explain why the transitivity is preserved.
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Hyperbolic Encoding Given the contextualized embedding H R R/Vual in order preserve their hierarchical relationships, the first step is to project H into a hyperbolic space, because the hyperbolic space fits the tree-like structure more for providing more space for lower level entries than Euclidean space (Tifrea et al. 2019) Chami et al. 2020)..
Poincaré ball, model of hyperbolic space. To be specific, the space is defined as ID = {ir E IRd; ||=||| < 1), with the Riemannian metric Jh X2g2, where X2 == |
Mathematically,
gB I, and || is the Euclidean norm. Then, based on (Ganea et al., 2018b), two necessary transformation operations between this Poincaré ball and Euclidean space, map from transformer embeddings (Euclidean space) to hyperbolic space or vice versa.
Therefore, in SS-MONO, we can project the contextualized embedding H to the Poincaré ball space by a linear map and exponential map at the origin point For each node p. let 2p = w H. E ToD*, where Hp E I and W E hgx Then, H. = expo(zp). where expa(-) is the exponential map function with detailed computations illustrated in Appendix C
Nested Entailment Cones
To regulate the transitivity of hyperbolic embeddings, nested entailment cones (Ganea et al. 2018a) are adapted in SS-MONO.
Claim 3.1. Given two hierarchical relationships (p, qp and (g, c), the angle between p and g should be smaller than the half aperture of the parent cone ()(2), and the angle between and e should be smaller than the half aperture of the query cone 6 ()(())
By introducing cone @ of a point u with the width function (uu) that satisfies the transitivity of partial order in an embedding space (as described in Appendix (D), the ultimate goal is to ensure that SS-MONS regularizes hierarchical relation in the taxonomy obeying the angle E(u, v) s é(u) for pair < (i.e., e is the child of u). To avoid the singularity at the origin and ensure the aperture é(u) well-defined, we restrict cone apices
WD ((0,s) s) (i.e., ||u]] E).
Therefore, we design the energy score E(u, v) based on cone modeling. Accordingly, the objective of cone loss is defined as a max-margin loss to enforce E(u, v) for positive examples (i.e.. ground -ruth matched query and position) and E(u, v) > for negative ones.
Elu,v) == max (0, E(u, v) <(u))
(1)
The corresponding loss function is defined as follows.
Loone (u, v) = Elu, v) E 0,06 ((..)) max (0, 7 13-F((u(-) F((((),
(2)
where N(u, v) is sampling distribution that returns negative pair (u(-)xu(-) different from (u,z). Here, negative pairs refer to (-() is not the ancestor of u(-), >> 0 is the margin.
The structure loss Latuuture is the summation of Leone on p and q and on q and for a given candidate position (p, c) and query node
Lamucure Loone H H Loone HH H
where H Hy, H is the hyperbolic embedding of parent node p. query node q and child node c, and the label generation is discussed in Section 3.4
3.3
ENCODER
Compared with LLMs, the semantics information in certain taxonomy is not that rich. It is common to see only node has textual attributes but not edges (Bordea et al., 2016 Lipscomb] (2000] Jurgens Pilehvar 2016), and the construction of the existing taxonomy is often hand-crafted with explicit knowledge to follow.
To provide enough context information, we first introduce frozen LLM and prompt it with our designed template (details are in Appendix MM), such that can output the explanation of a candidate position (p. c) about why directed edge connected the hypemny and hyponym in the existing taxonomy T, as the example of ("Protein", "Peptide Elongation Factors") shown in the left of Figure
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For further collecting the contextualized semantics of (p,c) from the given taxonomy T. three kinds of relationships need to be considered for query q, ie.. its ancestors, descendants, and siblings. For example, the candidate position ("Protein". "Peptide Elongation Factors") is the appropriate position to insert query "Ribosomal proteins". Then after inserting. "Protein" becomes the parent of "Ribosomal proteins", "Peptide Elongation Factors" becomes the child of "Ribosomal proteins". other children of "Protein" become siblings of "Ribosomal proteins".
Next, we introduce the different aspects of context embedding manners respectively.
LLM Guidance Encoding First, we have the augmented description of LLM towards candidate position (p, c). In order to force SS-MoNO to fit the LLM's knowledge an efficient way, this LLM is frozen, i.e., no fine-tuning is involved. Then, the representation vector of the augmented description, REIM, is obtained.
RELM = SAM (e, HLLM]
where HILM = PLM(LLM((..)) is embedding vector. LLM stands for a frozen Large Language Model, e.g., Gemma (Mesnard et al., 2024) Llama (Touvron et al. 2023) and LLM c) is the PLM stands for a
augmented description of the candidate position (p,c) as shown Figure
frozen rreative small language model to get the embedding vector of text, which is a more affordable way to get the hidden representation vectors of text, like DistiBBERT (Sanh et al. 2011)).
Moreover, in Eq. 4 SAM stands for the self-attention mechanism (Vaswani al. 2017), vector E R is randomized vector as the initial placeholder, its output after the self-attention mechanism serves the relational vector RLLM-
Ancestor Context Encoding This encoding method is proposed project the contextualized embedding H. E R² of q together with its ancestors into a semantic relational representation vector R₂ as follows.
R. SAM (e, Hp", Hy.
(5)
where R. means the semantic relational encoding with ancestors. Representation vector H, is obtained through fine-tuned SLM over the given textual attribute of node q. The details of the computation are shown in Appendix L.3 and the same manner applies other text-attributed nodes in the existing taxonomy graph.
Eq. is an instance containing 3-hop ancestors, given p' is the parent of p, and p" is the parent of p'. Note that, in DAG-based taxonomy, node may have multiple parents. If so, multiple parents will be selected and concatenated.
Descendant Context Encoding Similar to the ancestor context encoding, the descendant context encoding is defined as follows.
R SAM [e, H., He, H Ho"]
(6)
where R, is the semantic relational encoding with descendants. Eq. 6 an instance containing 3-hop descendants, given c" is the child of c'. and c' is the child c.
Sibling Context Encoding For sibling context encoding, the token list formation is different from Eq.5land Eq Because the taxonomy can be quite wide, i.e., a parent node can have various child nodes, which means the query can have multiple siblings when considering one candidate position. Beyond that, the meaning across the siblings can diverge and be dependent on the depth of the taxonomy. To this end, we borrow the philosophy from (Wang et al. (022) first sample the most similar sibling and the worst similar sibling w in terms of the contextualized embedding H based on language models.
argmax Co H,), w argmin, veChild(p)) CosSim(H,, H.)
(7)
where is the parent node, Child(p) is the set of all child nodes of p besides in the existing taxonomy T, and CosSim denotes the cosine similarity.
Note that different from ancestor, descendant, and sibling context encodings, only in Eq the SL.M is frozen.
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Then, the sibling semanties encoding can be expressed as follows.
R = SAM (e, Hy, Hg. Hyl
(8)
Finally, with RLLM. Rig, Rid, R.,, we can then sample training samples and design context-dominet loss function.
To be specific, when targeting candidate position samples, a positive position sample means the parent p. child and siblings and are all ground truth for the query q- Then, the straightforward idea is that a negative position sample means that any entry from p. c, b, and w is not true towards To make positive samples obtain a higher context-based matching score F(-) and the negative samples take lower score, we design the following loss function.
First, the context-based query-position matching score F-) is expressed as follows.
F(Hg: RLLM. R,,, R R = W2(ReLUU Reoeet + b1) + b2)
where W,, 22. b,, and b2 are weight matrices obtained from trainable parameters, and Reoncat H RIIM; R., Ra; R.] means concatenation of Hg. RIIM. R., R2, and R., Then, the context- based loss function is designed as follows.
Leontent
log ((H,; RLIM, Ra, Rd, R₂)) (1 y) log(1 F(H,, RLLM: Ra, Rd, R.)) (10)
where y the label for candidate position, y 1 means positive position sample such that each entry from (p, b, w) is ground truth towards and y = O means negative position sample that anyone from (p. c, b, w) is not the ground truth.
Hard Training Samples Within negative position sample, besides the scenario that every compo- nent is not true, the harder samples exist. For example, we can sample a candidate position (p, é), where p is the ground-truth parent for q. but è is not the ground-truth child for g. Similarly, we can also sample incorrect p. 6, ú. Therefore, we further split Eq. 9 and Eq. into series of fine-grained computations for hard negative samples.
Just take (p.c) and (p, é) as example, the fine-grained version of Eq. targeting positive and negative descendants, Faeses is expressed as follows.
Fdese (Ra)) (ReU (R.) + ba) + b4)
(11)
where W3. W4, by and by are matrices of trainable parameters. Then, the corresponding context- based loss function i0 specialized below.
Ccontert_ _eac ly log (Faese (Ra) + +1 - y) log(1 Fdeee (Ra))
(12)
where y = 1 means the child position is the ground truth child to insert g, and y 0 otherwise.
Follow the same way, we can design ancestor score Fane (ane(Ra) with ancestor loss Coontext_ and sibling score Fst (R.) with sibling loss Lcontert_stt- Note that in Lcontext y iff two selected siblings are both ground truth.
3.4 SELF-SUPERVISED OPTIMIZATION
To save human labeling efforts in the training SS-MONO, we introduce self-supervised learning manner. The idea is straightforward. We first remove an existing concept from the existing taxonomy, then sample corresponding positive and negative samples to train SS-MONO, and test if SS-MONO could replace the removal correctly. Next, we introduce how the training samples are prepared and the entire loss function to train SS-MONO.
Positive and Negative Sampling. In the existing taxonomy. we select an existing transitive relation (p, q, c). which means p is the parent q, and & is the parent c. Then, starting from p. we sample the best and least similar sibling for and get b and Now, we have positive sample (p. b, w). For the negative sample, we randomly replace any component in (p, c, b, w) with the rest nodes the existing taxonomy. With the positive and negative samples, we trace the corresponding ancestors and descendants to compute the matching scores stated above. With those scores, we model the seeking of the best candidate position classification problem with the following loss function.

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Loss Function. Below is the total loss function for training SS-MONO, which combines the individual loss based on structure and (fine- (ine-grained) context information, a prructure-semante monotonization manner, as discussed above.
Littol &Lsstrcture + 3ooontent + pL desc + Xooontent ann + & sib
(13)
where o, B. u4, X, and are hyperparameters to control the weights of individual loss functions.
4 EXPERIMENTS
4.1 DATASETS, BASELINES, AND METRICS
We prepared three public datasets, i.e., SemEval-Food, MeSH, and WordNet- Verb, as shown in Table [ SemEval- -Fod is the taxonomy for the food domain, which is released by SemEval-2016 Task 13 (Bordea et al. 2016). MeSH contains the subgraph the Medical Subject Headings (MeSH) in the biomedical domain, published by NLM annually (Lipscomb) 2000). WordNet- Verb is the verb taxonomy containing the description of each verb, which is published as SemEval 2016 Task 14 (Jurgens& & Pilehvar 2016).
We consider the leaf expansion and non-leaf ex- pansion capabilities together. Therefore, we in-
Table I: Dataset statistics, |N [1) D. L). L%, and |Q| denote number of nodes, edges, depth, leaf nodes, leaf ratio, and query concepts.
clude the corresponding SOTA baselines: Bilin-
Model (Sutskever et al. (2009), Neural Tensor
Network (Socher et al. 2003).. TaxoExpan (Shen
al. 2020p. ARBORIST (Manzoor et al. 2020).
Dataset
[8]
[L]
L%
[Q]
TMN Zhang et al., ).21). QEN (Wang et al.
Semeval-Food
1,486
1,533
8
1,184
79.7%
148
2022). TaxBox (Xue et al.] 2004). more detailed
McSH
9,710
10,498
6,613
68. 18.1%
819
WordNettVVorb
13,936
13,407
12
10,581
75.9%
1,000
introduction of baselines is placed in Appendix E
L.MMs (>1B) retrieve and rank candidate edges as LLM baselines, including DeepScek-RR R1-8 (DeepSek-AAl al. 2025), Llama-3.1-88 (Touvron
Furthermore, we explore the ability of several
ctt al. 2023). Gemma-2-9B (Mesnard et al.] 2024). and GPT-4o mini (Hurst et al., 2024). The implementation details of LLM basclines are provided in Appendix F We prepared 15 metrics to comprehensively evaluate the performance of all baseline methods, covering recall, precision, mean, etc. The details of the illustration are in Appendix G The generation and verification process of the augmented edge description by LLMs is given in Appendix Mo demonstrate the trustworthiness of augmentation.
4.2 EFFECTIVENESS OF SS-MONO
Table reports the comprehensive performance of all baselines on the SemEval-Food, WordNet- Verb, and MeSH datasets. SS-MONO (w/o AD) denotes the proposed model without LLM augmented description for every candidate position, and SS-MONO denotes the full proposed model. To be
specific. LLM baselines like DeepSeck-BB RI-8B (DeepSeck-AI et al. 2025) or GPT-4o mini (Hurst et al. 2024) directly infer to rank the top 10 positions (Detailed implementation is in Appendix F the analysis of the cardinality of candidate pool as the input of LLMs can be found in Appendix [.1]. Consequently, if the ground truth edges do not appear among the top 10 candidates, we cannot compute rank- metrics such as MR and MRR. The symbol - in Table denotes cases where metric results are unavailable. TaxoBox (Xue al. 2024 does not report MR and R @ 10 for both leaf and non-leaf nodes, nor does it provide results for the MeSH dataset. Since TaxoBox does not publicly release its implementation scripts, we mark its performance as
In general. as shown in Table 2 SS-MONO (w/ AD) achieves competitive performance compared with baselines, and SS-MONO achieves the best performance overall comparisons in each dataset. The corresponding visualization case study is placed in Appendix H For cross-dataset comparisons of an individual algorithm, MRR (Mean Reciprocal Rank) and R@ (Recall@k) are more appropriate indicators, as they are scale-invariat and reflect relative ranking quality independent of taxonomy size. MR is absolute value grows naturally with larger and deeper taxonomies and cannot be directly compared across datasets with divergent scales. Also, in Table it can be observed that including LLM Augmented Descriptions (AD) does not always enhance intermediate (non-leafe expansion, a detailed analysis is placed in Appendix Moreover, also prepared the performance of Fine-Tuned
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Table Performance comparison on three taxonomy expansion benchmarks. Bold colors indicate 3 per column (best=red, second=blue, third-green). SS-MONO is our full model; SS- -MMN (w/o AD) disables LLM augmentation.
SemiEvul- Food
Method
Total
Leaf
Nan-lcaf
MRR
R@01 1
R4
P0:10
MR.
MR.
MRR
DecyS:ck-R1-88
0.016
0.033
0.003
0.005
0.033
0.006
0.007
0.031
0.006
Genna 2
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0.000
GIP mimi
0016
0055
0858
003
0,23
0,02
0.000
0.103
Bilinor
0.143
01014
0.110
0120
0.9
0103
209.00
0.005
0.394
2416.1
D0K
01000
NTN
65541
0.04
0.423
2568.6
0.000
698
0.207
01411
0.001
D0K3
01134
0.455
2519.36
0,000
Non-L.M
ARRORIST
700179
0.179
0003
0.013
0.88
0027
0.22
0018
260.35
0.380
0.195
2467.65
00005
0.000
TMN
$59.81
0.221
0.077
0.113
0.160
0.074
0.966
0.332
179.40 49
0.482
0.356
2451.15
0.007
0.000
QEN
397.75
0.315
0.071
0.164
0.228
0.149
0.000
0.948
275.07
0.367
0.276
1250.36
0.099
0.033
Tastlox
0.389
0.204
0.918
0.628
MONG (wri AD)
315.79
0.430
0.283
0.358
0.071
0,090
705.47
0,998
S5-MoND
239.17
0.400
0.186
0.209
0.325
0.302
0.126
0.088
143.94
0.705
0.645
756
0.147
0.059
WorlNet-Yabb
Vyge
Method
Total
Leaf
Nan-baf
MB
MRRI
R
RP.
PAI1
PRST
PGR 10
MR.
MRR
BAV10 F
MR
MRR
Ree 10
DeepSerk-R1-B
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Gemna-2.0B
0.000
0.000
0.000
0.000
0.000
0.000
0.000
CiPI-lo mini
0001
0.011
0101
0001
0.000
0.000
0.000
0.002
Bilinex
1961.30
0.174
0.02
0.52
0,895
0.188
0,016
0.014
358.55
0.247
0,140
5451.59
I.059
0.044
NTN
1568.62
0.251
0.050
0.124
0.171
0.075
0.037
0.026
819.93
0.413
0.309
4659.76
0.067
0.013
TuueEspa
2023,85
0.231
0.000
0.025
0.392
S701
0.007
Non-IIM
ARBORIST
1499.40
0.235
0.996
0.49
0.023
0.033
0.315
4309.64
0.086
TMN
1580U17
0.291
0.066
0.154
0.297
0.99
0
0031
751.15
0.439
0,542
002307
01121
0.882
QEN
1802 40
0.340
0
0.186
0.249
0.124
0.057
0.038
1055.87
0.495
0.407
4909.49
0.166
0.093
TuxBox
1286.00
0.330
0.105
0.212
0,262
0,179
0,072
0.845
0.481
0.185
MUND (wrl
2579.85
0.044
0.31
1746.12
0.999
1626.53
106
0.103
0.511
4351.11
0,055
McSHI
Type
Method
Total
Leaf
leaf
MR
MRR 1
R4917
R405
R3110
P011
PG51
10
MR
MRK
MR
MKR
10
DeepSeek RI SB
0.003
0.005
0.008
0.006
0,002
0.002
0.013
0.005
LLM
LIame- 2B
2:4B
01001
0.006
0.001
0.006
0.001
0.000
0.005
0.000
0.010
01002
GPT
0.000
0.003
0.000
0,000
0.001
0,000
Bilinear
955.25
0.275
0.038
0.115
0.173
D006
0,052
0.399
485002
0.395
0.284
2064.7
11192
0.100
NTN
702.33
0,329
01064
0.167
02227
0.143
0,075
01051
408.17
0,542
0.654
135475
01159
0.07
TopoPopen
6764. V)
0.173
0.044
0.885
0.123
0053
0.033
0.088
466.25
0.434
0.310
20957 05
0.031
0.000
Non LLM
ARBORIST
80081
0.533
0.434
1413.45
0.202
0.175
TMN
0.410
01081
0,197
0.137
0135
401.20
0.555
0.180
QEN
$3083
0.421
0.01
0.198
0.284
0.188
0.091
0.056
$11.93
0.54
573.01
0.932
08187
TucBus
Dun
SS. MOND (woa
MOND
354
0.405
0.046
0.175
0.267
0.173
0.112
0.623
0.033
0.058
602.1
0.475
0.363
$45.99
0.365
0.39
0.166
LLM for the taxonomy expansion task in Appendix N This experiment further confirms that (1) our geometric deep learning objective is easily compatible with thf-the-shelff LLM checkpoints, i.e., only minimal modifications are needed to plug in an LLM encoder, and training remains computationally lightweight. (2) Fine-tuning LLMs is not always outperforming, the way we designed to "borrow" knowledge from LLMs to SLMs is effective and competitive.
4.3 CALIBRATION BY LLMS
Given a query g. SS-MONO will rank all the existing edges in the taxonomy and select the highest one to insert. Therefore, when SS-MONO outputs the ranking list, we insert this ranking list to a promoted LIM (a template example is given in Appendix D) and ask LLM to rerank it to the best of their knowledge.
For example, in the testing set of SemEval- Foodd we have 148 queries to be inserted into the existing taxonomy, and the existing taxonomy has 7,313 candidate positions. In other words, for each one of 148, SS-MONO provides a ranking list 7,313 entries, and Llama3. 1-BB (Touvron et al. 2023) reranks them. Due to the long context limit of LLMs, we need to truncate the ranking list and ask Llama to only rerank the truncated list and leave the rest remaining. We use k to denote the length of the truncated ranking list, e.g., k = 10, 50, 100, 200. Then, we evaluate the rerank (calibrated) ranking list and report the comparison in Table
8

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Published as a conference paper at ICLR 2026
Table Performance comparison of SS-MONO variants with LLM calibration on SemEval-Food SS-MONO-k denotes reranking the top-k candidates using LLMs. Bold indicates the best score.
Mathod
Total
Leaf
Non-Ical
Ang. Rank
MR
MRR
RG11
B:85
R4619
P4110
MRR
MRR
RG:10
MR.
MRR.
R410
MoNO
315.79
0.430
0.285
0.338
0.071
228.18
0.690
0.642
768.47
0.098
4.786
SS-MONO
239:17
0.299
756.74
S5 MoNN-100
240.07
0.398
0.158
0.338
0.332
0.291
0.067
139.70
0.721
0.677
758.65
0.144
0.057
5,011
S5-Moxn-50
15
0.480
0.201
0.334
0.373
0.426
0.078
198
0.736
0.679
754.52
0.201
0.132
2.145
MoNo-100
SS Moxo 200
238.06
0.417
0.190
0.318
0.341
0.399
0.072
137.99
0.728
0.664
753.05
0.171
0.086
2,929
D Output without reranked list
0 Output with hallucinated edges
Output with shorter list
Avg. ReRanked Length
Hallucinated Edge Ratio
0.6
100
Perventage (%)
0.4
50
0.2
90
0
50
100
200
10
50
100
200
Reranked Candidates
Reranned Candidates
(a) Key trends.
(b) Failure-type percentages.
Figure 2: Statistics of failed cases in LLM calibration under different reranked candidate sizes. (a) Key trends: hallucinated edge ratio (red solid line) vs. average reranked list length (blue dash line). (b) Distribution across failure types, denoted by blue bar, red bar, and brown bar.
During the calibration, also observe considerable amount of failed cases of LLM's output, such as (1) demonstrated LLMs could not rerank the given ranking list but generate the rerank idea or python code; (2) demonstrated LLMs generate some existing edges in the given ranking list, i.e. hallucination; (3) demonstrated LLMs are sometimes lazy to generate the full ranking list as the given. The statistics are shown Figure [] and concrete examples
Appendix [K] Following the
format-correct reranking only, the enbancement is shown in Table 3 which suggests LLMs have the potential but are not ready to be directly deployed for the solution.
4.4 EMPIRICAL ANALYSIS OF GEOMETRIC CONDITIONS
Here, we mainly present two experimental analysis geometric conditions, i.e., (1) the weight of Estructure in the dominnteedominated encoder for cone, expressed in 3 preserve the monotonicity in the hyperbolic space, and (2) the relationship between structure loss and context loss in Liotat expressed in Eq Extensive experiments are placed in the appendix:
The analysis for investigating the role of sequential self-attention mechanism with graph neural
networks cesssae--psssingg mechanism in the commext-dominated encoder in Appendix [.2
The analysis of varying the number of sampled hops be found in Appendix [33
The analysis of the difference between Euclidean and Hyperbolic manners for the structure- dominated encoder in Appendix [.4
The analysis of the relationship between the hard negative sampling and random sampling is in Appendix L.5
First, we conduct the ablation study of the hyperbolic embedding to show its indispensability. In Table we can see that totally removing the strueture-dominated encoder (i.e., weight 0) usually induces the worst performance.
Second, conduct another ablation study for the ancestor, descendant, and sibling encoding and investigated their relationships. According to Eq. 10 we have / for all sampled neighbors in general, μ for sampled descendants only, for sampled ancestors only, and & for sampled siblings only. Taking the SemEval-Food dataset as an example, in Table we can observe that with all sampled nodes considered together, i.e, weight = 1111, the optimal results are obtained, compared with any ablation.

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Published as a conference paper at ICLR 2026
Table 4: Role of aatruttree in Performance of SS-MONO (w/o AD) on SemEval-Food dataset.
Total
Leaf
Non-leaf
Weight of Catructure
MR
MRR
R 10 [
MR L
MRR f
R 10 [
MR 4
MRR
R@ 10
350.737
0.399
0.259
190.833
0.551
0.426
1219.779
0.074
0.024
0.1
349.031
0.399
0.315
230.161
0.670
0.607
933.872
0.190
0.091
0.3
304.774
0.428
0.322
222.891
0.698
0.657
727.834
0.215
0.057
0.5
315.792
0.430
0.338
228.177
0.690
0.642
768.466
0.225
0.098
0.7
389.381
0.358
0.270
279.644
0.626
0.533
956.356
0.146
0.063
335.416
0.391
0.305
211.944
0.679
0.600
943.098
0.171
0.080
Table 5: Ablation study of weight combinations (B, μu, E) for objective function in Estructure
Weight..,....
Leaf
Non-teaf
MR 1
MRR
K011 1
R055
R:0100
1
Pi05 7
Pd
MR.
MRR 1
R3010
MR
MRR 1
R0
1111
315.79
0.430
0,161
0.283
0.338
0.338
0.119
0.071
228.18
0.690
0.642
768.47
0,235
0.098
1110
323.55
0.217
0.039
0.093
0.129
0.081
0.039
0.027
132.21
0.445
0.289
1254.94
0.041
0.005
100]
430,85
0.379
0.148
0.356
0.309
0.311
0.107
0.065
264.74
0.665
0.621
1289.10
0,145
0.053
1680
345.07
0.372
0.68
0.069
205.83
0.449
0.343
1236.25
0.008
0111
1500.86 85
11050
0.066
0.019
0.029
0.014
01008
0.006
1375.50
0.078
0.059
2180.90
0.038
0.086
1963.16
0.065
0.000
309.49
0.134
0.044
3757.18
RELATED WORK
Understanding complex graph structures with deep learning models has covered many tasks (e.g.. node classification (Fu et al. 2024), link prediction Tieu et al. 2023), graph classification (Fu al. 2022), graph generation (He et 2025), graph regression (Wang et al. 2025)) and multiple applications (e.g., fake news detection (Fu & He 2021), time-series attack (Lin et al. 2024), claim verification (Fang et al. 2025), multi-modal summarization (Ning al., 2025), ads recommen- dation (Zhang et al.) (025). data cleaning (Li et al. (025a)). As special (hierarchical, directed, and rext-attributed) graph structure, taxonomy paves the way for information retrieval. knowledge organization and question answering (Shen & Han, (022). Based on non-generative models, classic taxonomy expansion/completion methods like (Zhang et al.] [02TT] Wang et al.) 2022] Xue al., 2024) focus identifying the most suitable parent position and then adding the new item as the corresponding child node. Recently, the surge of large language models has inspired the exploration of graph structures, due to its broad world knowledge and reasoning ability (Wei et al. 2026 Li
let al. 2025b Fu et al.] 2025 Xu et al.) 2024). To start, Xu et al. (202)) proposed prompt tuning
BERT for finding the hypernym of incoming query and converting the hypernym prediction generation task. Later, Zeng et al. (2024a) introduced Chain-of-Larn Layer to iteratively prompt LLMs for inducing taxonomy structure from small of entities. Mishra et al. (2024) fine-tuned Low Rank Adapter with Proximal Policy Optimization (PPO) for generating the hypernym of a query. To explore the node contextual features along the taxonomy's 's structural semantics, we propose SS-MONO to integrate the structural semantics and with concept textual semantics with the affordable LLM usage.
6 CONCLUSION
In this paper, we explored the intersection of hyperbolic structures in LLM embeddings and the scientific taxonomy expansion problem. Our study revealed that while LLMs possess strong repre- sentational capacity, they fail to reliably support domain-specific taxonomy expansion. To bridge this gap, we proposed SS-MONO, self-supervise framework that borrows knowledge from LLMss but distills it into SLMs through structure- and semantics-aware training. Empirical results confirm that SS-MONO delivers substantial gains over both frozen LLMs and specialized deep learning models, establishing SLMs as practical and scalable alternative for taxonomy expansion.
ACKNOWLEDGMENT
This work is supported by National Science Foundation under Award No. 11--2117902. The views and conclusions are those the authors and should not be interpreted as representing the official policies of the funding agencies the government.
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Published as a conference paper at ICLR 2026
ETHICS STATEMENT
This work adheres to the ICLR Code of Ethics. Our study relies exclusively on publicly available datasets and does not involve human subjects, personally identifiable information, sensitive data. The findings are intended for scientific purposes only and do not pose foreseeable risks of harmful application or misuse. No conflicts of interest external sponsorships have influenced this work.
REPRODUCIBILITY STATEMENT
We have made significant efforts to ensure the reproducibility of our results. Detailed descriptions of the model architecture and training procedure are provided in Sections [ and 4.11 Additional hyperparameters, detailed introduction of baseline models, implementation details, and evaluation and G To further support reproducibility, we
metrics steps are documented in Appendices E F
provide code, configuration files, and data processing scripts in the anonymous GitHub repository https: / / com/ Lirr rirri ang/ MoMMono reproduce our experiments and validate our findings.
Together, these resources enable others to
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A
APPENDIX CONTENTS
Appendix
Limitation
Appendix
Hyperbolic Transformation Operations
Appendix
Brief Introduction of Cone and Aperture
Appendix Detailed Introduction of Non-LLM Baselines
Appendix
Implementation of LLM Baselines like DeepSeck-R1-8B, Llama-3.1-8B,
Gemma-2-4 9B, and GPT-4o mini for Taxonomy Expansion Task
Appendix
Evaluation Metrics
Appendix Comprchensive Case Study
Appendix More Analysis Geometric Conditions
Number of Candidate Edges for the Input of LLMs
Self-Attention and Graph Neural Network in
Encoder
Number of Hops
Euclidean Encoder and Hyperbolic Encoder
Hard Negative Sampling and Random Sampling
Appendix
Failed Example of L.LM Caribration
K.1
No Ranking Answer
K.2
Hallucinated Edges in the Existing Taxonomy
K.3
Shorten Ranking Answer
Appendix
Implementation Details of SS-MoNO
Taxonomy Expansion via Position Matching
Encode Contextualized Embeddings from Language Models
Neural Architecture and Hyperparameters
Reproducibility
Appendix
M
Generation and Verification of Edge Description
Appendix
Fine-Tuning LLM for Taxonomy Expansion Task
Appendix
LLM Augmented Descriptions with Non-Leaf Expansion
Appendix
The Use of LLMs
B
LIMITATION
While our method demonstrates strong performance and general applicability, several limitations should be acknowledged:
Fixed Sampling Depth. The strategy of uniformly sampling 3-hop neighbors may not adequately capture essential context in taxonomies requiring deeper hierarchical insights, nor avoid irrelevant noise in shallow hierarchies.
Dependence on LLMs. Our method explores the effectiveness of LLM augmentations, meaning inaccuracies or biases present in the LLMs can propagate into the taxonomy expansions.
LLM Model Size. Due to resource limitations, did not explore LLMs with more than 10B parameters. Investigating the ranking and retrieval capabilities of larger LLMs, both with and without fine-tuning, presents an interesting direction for future research.
C HYPERBOLIC TRANSFORMATION OPERATIONS
C.1 MOBIUS ADDITION ON POINCARÉ BALL
u 0. (1+ 2c(u, v) ( + - (1-clull3))
u DDd == [ < <1}. (14)
1 20(u, v) + |||2u| 2|
where and Tidl and
throughout.
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C.2 EXPONENTIAL MAP
Let D f E IR ||]]] < } be the d-dimensional Poincaré ball (curvature -1). Define the conformal factor A = --| The exponential map at æ E D' exp, T,D4 + D is
(xp +
tanh
+ O,
(15)
|
and ex) r. Here + denotes Möbius addition on the Poincaré ball (see Appendix C.I) and we identify T,I Fd
C.3 LOGARITHMIC MAP
The inverse operation (logarithmic map) log, DDd > TyD for E D is
log, (v)
arctanh @ vll) || A
(16)
x + yl
and (o) = O. Here, @ is the Mobius addition (details in Appendix hyperbolic tangent.
C.1
and arclanh is inverse
C.4 SPECIAL CASE AT THE ORIGIN.
Since A 1- and 0 D w. the exponential and logarithmic maps at the origin reduce
expo(v) = (| v
+ O,
expo (0) 0,
logo (y) = artanh(Iyy))
y # O,
logn(0) =
D CONE AND APERTURE
As stated in (Ganea al. 2018a), define cone width function Φ(-) that the resulting cones satisfies the transitivity of partial order in an embedding space, then, in our hyperbolic setting, we have
Vu, v D (0).v 6
()(r) c (d(w)
(17)
where @ (()) is the cone of point with the width function @(u). Morcover, the Poincaré entailment cone can be defined as
(
m E(u,v) ((u)}
(18)
where the half-aperture is p(u) = aresin k -1. ). || 2 E, and K is a hyperparameter. For any u. Da e)) E(u, u) is the angle between the half-lines we and Oū, defined by
E(u, v) = π LOwv.
(19)
This angle has the closed form
(u, v) (1+ [| ||u||2(1 (1+ 1| ||u||| ||u wll / ||u| 2|10) 2(, v)
B(u, v) = arccos
(20)
where O denotes the origin.
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E DETAILED INTRODUCTION OF NON-LLM BASELINES
Bilinear Model (Sutskever et al. 2009). A relational model infers whether particular unobserved relations are likely to be true.
Neural Tensor Network (Socher al. 2013). An expressive neural tensor network suitable for reasoning over relationships between two entities.
TaxoExpan (Shen et al. 2020). A taxonomy expansion model leverages graph neural networks for the egonet structure leamn node embeddings expand.
ARBORIST (Manzoor et al. 2020p. A taxonomy expansion model considers the heterogeneous relations encoded in the taxonomy context by integrating the embedding distance with geometric distance as the dynamic margin loss.
TMN Zhang et al. 2021). A ranking- ranking-based taxonomy completion model uses the triplet matching network and defines taxonomy completion as a parent-child edge ranking task.
QEN (Wang et 2022). A ranking-bass -based laxonomy completion model extends TMN by adding
siblings as additional signals.
TaxBox (Xue et al.
2024) A taxonomy expansion method that leverages box containment and
center closeness to design two specialized geometric scorers within the box embedding space.
F IMPLEMENTATION OF LLM BASELINES
Existing studies LLMs for knowledge graph completion primarily focus term prediction, where the model is given a sampled path from knowledge graph and tasked with predicting the next node (Sun al.) 2024 [Shwwag et al. 2024). However, the best of our knowledge, no prior work has explored the application of LLMs (not as a foundation model) to taxonomy expansion in the context of query-pos posttion ranking.
To address this gap, we investigate the performance of LLMs in retrieving and reranking the top k candidate positions, adapting the problem to a query positioon ranking setting. Evaluating an LLM's ability to retrieve and rerank an extensive list of candidate positions is nontrivial due to the task's inherent complexity.
Following the document retrieval setup in (Lee et al. 2024), we construct prompt that includes instructions, a list of taxonomy edges with corresponding indexes, and examples. However, incorpo- rating all candidate taxonomy edges in the prompt exceeds the context length of DeepSeck-R1-SP) Gemma-2-9B, and Llama-3-8B. even for the smallest dataset, SemEval- To address this limita- tion, we randomly sample 500 edges and instruct LLMs retrieve the top 10, returning each edge index and rank in defined format: < edge id > p:parent id-c:child < rank >> xx. For GPT-4o mini, conducted experiments multi-message input. For the other two datasets, which contain a substantially larger number of candidate edges, we randomly sampled 500 edges following the procedure described above to ensure the fcasibility and consistency of evaluation. For hyperparameter settings, we set the maximum number of generation tokens 1000 and the temperature 0.2. The detailed prompt template is shown in Block [
the SemEval-Food dataset using all 7,313 candidate edges as
Listing 1: Query-Positions Ranking Prompt Template for DeepSeek-R!
You will give the entire 1ist of edges in existing taxonomy. Ploase rorank the aiver candidate adges based the vinilarity neaning Lu quesy node, To speci
inaertion means parent Lean (i.w., the first term) of the edge is the hypernyn of the query tem, and the child tern (iee, the second tern) of the enge is the hypeaym of the query zern.
The volevent edees should zank nonnicg the query should be insorted between the nodes the most re revvent edges.
Each candidate edocs is
unique Lsentificr edge sedgez is the edge in the fornaz of sparent> +> schild>. If the child tarn is sapty, in means the pazeat tern the leaf node of the texonony.
format <odoc_idds sedeee where <odgo_id>
scre is the total 1ist of the existing edges in the zzmonony:
cedge_ (edge_id)
(chi nane sand send edge>
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Please securn top 10 candidate edgea based on the colevance the quary carn. rank candidate edges should be in the Formet of ledge_ldb dedge_. (or
query corn: andeninai
Daseripticn ot the query Abdoninal ecnsation disconfort, distress or agony in the abdoninal ragion.
provided candidate edges Sollowing fusnats "eedge_ibwegge.ce cankol, sedgg_idbedgee rancs2, ...).
Reranked Hist of candidate edges:
isedge_ baccge__idggeeinneee wwt.:eiggssnddeepp..o.
sedds__ddppppaing patpppppp---.aammm.... acuterrank>2,
cadge__.á>pppe wtt.ppperecculeppaiio...
<edge_idapt
cedge_idbprwigg btgbgppniigaanndggggggge. sysp diges:ive esvonit Inggniting
<edge sesppppann-sse ppannn-s-kaaok
<edge_id>p:en sego__dddp:signanaaae http::pcsgggnnaspptm...... vlgesttoeeeee::rrt--
<adoe__ babdonnn,,, acute-e:<ranko.,
cediee_ hallig___-ppppebliiiii teddine sesennk110]
Quary carn: (kvares q'quary_teem"] 1). Description quary torn: [kwarqu (Narrea"qquee sernggaa_eenddssereere dese_ddscrrpttonn Please zerank provided (Krargsl" "merggsinuuberr.o number_ot. stabber_tt_cendddee www.iiatteeaaeaococcooc sendldate edges tolloving cormati 1
cdae_idrodre__dee idernni_,, resae_serotac_ddrraa ...)" ".
3eranked 1ist candidate edges:
G EVALUATION METRICS
Following the same setting with (Zhang et al. 2021 Wang et al. 2022). we report the ranking- based evaluation metries to measure the performance of SS MONO with baseline models. We first sort all candidate positions based on the matching score F(H,, RIIM, R., Rs, R.) as Eq. Lq..aaan and then return the ranks of the ground-truth positions in the sorted candidate position list for each query node. The evaluation metrics include Mean Rank, Mean Reciprocal Rank, Recall@k k, and Precision @ k. In addition, we compare the metries by three categories, i.e., the leaf query nodes, the non-leaf query nodes, and the total query nodes (including both leaf and non-leaf query nodes).
Mean Rank (MR) measures the macro average ranking of ground-truth positions among all candidate positions. The lower Mean Rank is, the higher the ranking of the ground-truth position is among candidate positions.
Mean Reciprocal Rank (MRR) measures the macro average reciprocal rank of all ground-truth positions. Therefore, the higher the MRR is, the higher the ranking of the ground truth position is among all candidate positions.
@ecall@k k (R@ k) calculates the number of ground-truth positions in the top-k candidate positions, averaged by the total counts of ground-trute -ruth positions for all queries.
Precision @ (P@ k) calculates the number of ground-truth positions in the top-k candidate positions, averaged by the total number of queries times k.
H COMPREHENSIVE CASE STUDY
To further explain the performance, we generate the concrete prediction examples generated by SS-MoNG, SS-MONO(w/o AD), and QEN for the SemEval-Food dataset, shown in Table
For the leaf node insertion, SS-MONO correctly predicts the proper position at the top for query concepts "stinger" and "papaya juice". The actual position of query concept "mulmsey". i.e., "fortified wine pseudo leaf" is predicted at the second rank. SS-MONO correctly predicts the proper position at the top for query concepts "stinger". and "malmsey". However, the proper position is ranked third for "papaya juice". Therefore, we further investigate the description provided in the dataset for "malmsey" and "fortified wine". However, the raw input node description of "malmsey" does not imply or contain information related to alcohol by volume. With LLM -ugM-neteetedd candidate position description, SS-MONO captures information related to "malmsey" " with "fortified wine".
As for loafleaf insertion, compared with the baseline model QEN, SS-MONO achieves better rankings for query concepts containing multiple true insertion positions, e.g., "milk" " has 60 ground truth
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Table 6: Case Study: Top-10 Predicted Candidate Positions Generated by SS-MONO vs. SS-MONO
(w/o AD) vs. QEN. "p:" indicates the hypernym concept of the query concept, and "c:" indicates the hyponym concept of the query concept. The ground truth rank for non-leaf insertion is the mean rank.
bod
fee poin bod
oppoodi but
pakiis prodect guodds koe
sepeniii lod porkkkgyppesee
pilker quoede
prestisond poodds lodf
podeontt queads
pontas wdeehhoppenaii
prod praceppo leat
pomeeneecppato ind 2hoeraoecdo
and
prodt
produatle ind g for but
prestectinntT withi
proido leal
pranleppedd led
poaa poodo buff
sull wick cooras but
planaage cake placeaage colliorr peanesgecccteen gesorngeo 333333
las
ploceppnnd kod Fraed cppuradi laaf piealy
the ponds
plice spenail
gundd
ronpat
Groad Tachilakk
N5-Noso Caueey
pites copecad
poine cun--cppennt load
poleettedd coneegpoedd koaf
pret lnd
petiphhall preaii loal
podriking ang wa ventecppe pere les
pheggady oppcadi los
phomngr-cm creat
popore led
pompateppeatt loal
pondd las
pitua diabe poadd bauf
cadied aed basf
pcheorage caeed direned
powes d'acara pooddd
poodfe
pchnorape
viac lad
ado
plwch lnd
prockes
plrreegeoteee sells
pric la liggur
proflie lqurece pir i poopocpaskiial
pokk opoecopeakl
poiers prodacte yow
gropaic
1B1.01
QEN
Nor
Denk Uninyy
wrnge lua!
Pri pome
melrney porciabler lost
speiiing
poodl lauf
prodaricgeodd kud
sikee pesuls
poodunii pead loud
plach divetasaado haad
coann poiido and
porlical fi pra-cponniiat ind
pouse-pus als kuaf
poudchee poidk
pooma poido
diamaadd poido
gpoede
polettledd epond
spoeal buu
happddy gou
prine laa""
proeiiee ligen ponais lnd
prge to preeds lut
part cranvepeenbiii ind
ponced pooddo and
pharee besppe adi lad
prockcppouut leal
dark his mpenddppecden
arra mosoppaaae losl pupalo 1S1900
paleegunan
2110000
insertion positions and "frozen dessert" has 13 ground truth positions. However, SS-MON-- doesn't perform better than SS-MONO (w/o AD), but better than QEN.
I MORE ABLATION STUDY AND HYPERPARAMETER ANALYSIS
1.1 NUMBER OF CANDIDATE EDGES FOR THE INPUT OF DEEPSEEK-P R1-8B
The implementation (including prompt template and hyperparameter settings) is given in Appendix F In short, we prompt the LLM with a pool of randomly sampled candidate parent-chin child edges, then have it retrieve the top 10 and rank them in descending order. To assess how the quantity of candidate positions affects L.M ranking performance, we conduct an ablation study by varying the number of candidate edges per query concept, ranging from 100, 500, and 900.
Overall, the results in Table 7 show a clear non-monotonic trend. Increasing the pool size from 100 to 500 yields the strongest gains. R@1 I improves from 0.006 to 0.016 and P@) I from 0.014 to 0.033, indicating that many true parents of SemEval-Food concepts are recovered only when the LLM is allowed to propose moderately larger set of edges. However, further increasing to 900 candidates does not uniformly improve top-k accuracy: while 5/SR 10 and P@ 5/P@ 10 continue to rise slightly (0.023 and 0.009/0.005), R@1 1 and P@ 1 degrade compared the 500-candidate setting. This suggests that excessively large candidate sets dilute the signal with noisy or spurious edges, making it harder for the re-ranking module surface the correct parent in the very top positions. Interestingly, for non-leaf nodes, the 900-candidate setting shows a noticeable improvement in R@ 10 (0.023), implying that deeper or more structurally ambiguous nodes benefit from larger and more diverse candidate pool. These observations confirm that moderate candidate expansion provides the best balance between coverage and noise, whereas overly large L.MM-generale pools introduce diminishing or even negative returns in precision-oriented metrics.
1.2 SELF-ATTENTION IN CONTEXT-DOMINAN ENCODER
To demonstrate the effectiveness of the self-attention mechanism (SAM) employed in the Context- Dominated Encoder, we conducted comprehensive experiments evaluating three different aspects: (1) a baseline model without SAM (denoted by SS- SS-MoNo(w/o SAM)): (2) an ablation study replacing SAM with standard graph neural networks, specifically GAT and GCN; and (3) extended ablation
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Table Performance of DeepSeek-RI-s RI-BB with different numbers of candidate edges on SemEval- Food dataset.
Method
Total
Leaf
Non-leat
MR
MRR
RB5
R@10
P@11
PG5
P8101
MR.
MRR
R@:10
MR
MRR
R
DocpSoek-RR
0.006
0.001
DeepSeck-R1 81 500 DeepSoel-R1-a
0.016
0.01
11016
0,033
01007
0.005
0.025
0,005
0010
0.020
0.015
study integrating structure loss into GNNs, resulting in GAT+Cone and GCN+Cone variants. As presented in Table 8 the proposed SS-MoN consistently outperforms these ablation models across almost all evaluated metrics, with the exceptions being the Mean Rank (MR) for Total and Leaf nodes. It may suggest that the sequence- based self-attention mechanism is typically more effective than various subgraph-base based message passing mechanisms.
Table Ablation results comparing SS-Mono and its Graph Neural Network variants on taxonomy expansion.
Method
Total
Leaf
Non-leaf
MR
MRR
R:011
R05
RG
PG11
PIB5
PG110
MR.
MBR
RG
MR
MRR
R
0.119
0.998
SAM)
SS-Mono (GATT
57883
0.215
0.003
0.071
0.145
0.007
0.50
0.000
249.77
0.429
0.293
2278.94
0.039
0.003
MS-Mona (GAT Cones
615.33
0.167
0.016
0.029
0.074
0.014
0012
0.016
307.57
0.339
0.141
2133.04
0.02
0.03
SS-Mona
SS-Mono (GCN + Cone)
538.46
0.138
0.003
0.016
0.035
0.007
0.007
0.007
90.59
0.220
0.054
3469.03
0.0.0
0,012
1.3 NUMBER HOPS
In the experiment, show that the performance with sampling 3-hop neighbors for all datasets with a fair comparison, given the depth of (sub)trees not deep, c.g., ranging from to 8. Also, the fair depth to balance the useful information (near neighbors) and noise (far neighbors). To further justify the hyperparameter selection, we conducted experiments with 2-hop, 3-hop, and 4-hop sampling in Table 9 3-hop sampling shows the most compelling performance across most of the performance metrics.
Table 9: Performance comparison across different hop sizes for evidence expansion.
Method
Total
Leaf
Non-leaf
MR
MRR
RG
RG65
R@:00
P81
PG5
PG110
MR
MRR
RG:
MRR
RG:10
Zhop
321.49
0.383
0.145
0.238
0.289
0.304
0.100
0.061
255 335.07
0.637
0.567
682.51
0.172
0.059
3hop
228.18
4hop 305.02
0.406
0.141
0.244
0.293
0.297
0.103
0.061
217.74
0.617
0.546
779.33
0.232
0.082
1.4 EUCLIDEAN VS. HYPERBOLIC ENCODER IN STRUCTURE-DOMINATER ENCODER
To more thoroughly assess the contribution the hyperbolic encoder and nested entailment cone objective, we conduct ablation in which the structural encoder is replaced with purely Fu- clidean transformer architecture and the cone loss substituted with a Euclidean ordering-constrann objective:
1= max (0, d(g,p) d(p, c) m) + max (0. d(g, c) d(p.c) + m)}
where d(-) denotes the standard L2 distance. In this variant, we keep the same two-layer transformer encoder used SS-MONO but remove all hyperbolic components, including the Euclidean-to- hyperbolic projection and the nested entailment cone mechanism. The resulting representations fed directly into the Euclidean ordering loss, ensuring that the comparison isolates the geometric modeling choice rather than architectural differences.
Across all three datasets, as shown in Table I0 SS-MONO with the hyperbolic encoder consistently outperforms the Euclidean variant every metric in the Total, Leaf, and Non-leaf evaluations,
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underscoring the importance of hyperbolic representations and the cone-based objective for capturing hierarchical structure and achieving strong performance.
Table 10: Performance of SS-Mono with Hyperbolic and Euclidean Encoders on SemEval- Food, WordNet- Verb, and MeSH Datasets.
Leaf
Non-lcaf
MR.
MRR1
R
100
PATh
PolS:
PO-107
MR.
MRR1
R0
MR]
MRR1
101
SemmRaal-Foud
SS-Monn (Hyperbolic)
230.169
0,400
0,186
0.299
0.325
0.392
0,126
0.068
143,937
0.708
0.648
756.736
0.147
0.059
Mono (Luclidean)
654.712
0.175
0019
0.032
263.317
0.298
2560.572
0.800
WordNet-Verbb
SS-Mono (Hypcclalic)
1626.522
0.334
0,106
0.208
1.260
0.163
0.164
11,40
922.541
0.521
0.457
4651,311
0.122
0,835
McSH
SS Mono (Hypecholic)
456,20
0.427
0.074
0.197
0.288
0.173
0
1
390.717
0.570
0.476
540.551
0.334
0.166
SS-Mono (Fuclidean)
RV76
0.075
0,021
7038.220
0.099
13400.450
1.5 HARD NEGATIVE SAMPLING AND RANDOM SAMPLING
To evaluate whether our negative- sampling strategy introduces bias or overestimates robustness, we designed set of ablations that systematically vary the difficulty of negative examples. This analysis examines how different proportions of structurally local ("hard"" and globally sampled ("random") negatives affect model behavior.
We consider two types of negatives:
Hard negatives are constructed from the ego-network surrounding each candidate parent-child position. For given query node, we extract egonets around both the true parent- child edges and the alternative candidate positions, and collect all edges within these neighborhoods that are neither gold positions nor edges directly incident to the query. This produces pool of structurally plausible but incorrect placements that represent challenging local confounders.
Random negatives are sampled uniformly from the global candidate pool non-positive positions. These negatives represent structurally distant or unambiguous alternatives and provide broad coverage of the negative space.
We evaluate two sampling regimes that span a spectrum from structurally unbiased highly local. We form mixed batches in which proportion of negatives are hard negatives and the remainder are random negatives. We vary the hard-negative ratio across (0%, 10%, 30%, 50%, 70%, 90%) ). keeping all other hyperparameters and batch construction identical across settings. This setup directly tests whether increasing structural locality in the negative pool leads to artificially inflated performance.
The ablation results (in Table 11 demonstrate a non-monotonic relationship between the proportion of hard negatives and overall performance. On SemEval-Food for example, moderate ratios (10- 30%) provide consistent improvements, while higher ratios (250%) lead to performance degradation, particularly for non-leaf concepts. Importantly, the random-only configuration remains a strong and stable baseline, indicating that the model does not depend heavily structurally localized negatives to perform competitively.
Table 11: Effect of Hard Negative Sampling Ratio on SemEval-Food Dataset. Taking 0% ratio as the baseline, red means gain, blue means loss, and heat means degree.
Hadd Negative Samples
Non
MR.
MRR
R@91
RB51
R.110
PS11
P.8.T
P.:10
MR.
MRR 1
R4 10
MR. 1
MRR
R6:101
239.109
0.299
0.392
0.126
0.008
143.937
0.645
756.735
0.147
10%
233.354
0.391
0.199
0.322
0.334
0.419
0.135
0.070
108.495
0.749
0.696
$47.900
0.117
0.057
30%
268. 193
0.364
0.158
0.283
0.312
0331
0.119
0.066
107.20
0.717
0.644
1059.815
0.093
0.057
324.31
0.346
0.283
0.405
0.119
146.489
0.570
70%
359
0.330
0.141
0.251
0.289
097
105
0.051
114.738
0.583
0.166
1591.126
0,073
0.058
90%
0.277
0.167
161
0.070
0.045
151.653
0.423
2045.659
0.000
Two factors contribute the degradation observed high hard-negative ratios:
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Overemphasis highly ambiguous alternatives. When most negatives originate from local egonets, the loss becomes dominated by extremely subtle or nearly indistinguishable negative examples. This encourages the model to overfit to fine-gra ain-ngaieed structural patterns specific to the training taxonomy rather than learning generalizable cues.
Reduced coverage of the easy and medium negative space. Random negatives help establish a broad decision margin by teaching the model what clearly cannot be a parent/child. Excessive reliance on hard negatives reduces exposure to this broader negative space, leading to mistakes on simple or moderately difficult negatives during evaluation.
J TEMPLATE FOR LLM ACHIEVING CALIBRATION
In this section, the prompting template for reranking calibration by LLMs is provided Block] 2 We deploy L (Touvron et al. 2023) for the calibration.
Listing 2: LLM Calibration Prompt Template
Please rerank the given candi det edges where query tern
Inserted. The insersion in the tern ot the edge is the hypernyn of the query term, and the child teen is the hyponym ot the query tern. mezning the insertion neans the pazent term 1i.e., the first texa)) of the edge is the hyparzyn of the quezy bezn, and child
Floase verank given candidate edgts based the cimilarity
query nede. be speciric,
of edge the hyponyn of query Leen. tass with ten candidate edges as an example to varn you up- Atter the xam-up, I w.ll give you the arbitrary number queries and candidate adgas. Please make saze the number et your zeraaks consistent with number of the originel candidate eöges.
give you cenank
Bere 10 Candidate edges: cedge idpp:8d8-er111e cedgeoni mi milkkend-edgen <edge_ 1opp__iopp:80--11225 sedgsemiik +> scur milk <end-edge>
zeranking candidate
<edge 100p:10000-1661 <edge> poresoge gruel cead-edge>
Query asidophilus milx. Description ssed to treat gast enstiiin inal disorders. rerank provided rank>2, ...)",
quary asidophilus milk la formented by bacteria;
edges tolloxing "eedge idsedge <rank>), bddgeiidedge. idc
Beranked 1ist of candidate edges:
(ato__dddp:880::12332082 <edge_id>p:358. -:55pp888885553
Bere actual inguta:
mommbor_o__candddttt_.oomm Cancidate edgesiAn
(candidate_edgea)
Query (query_iecn).
Desoription of the query tern: (query tern descriptior)
Please serank provised cumber_ot_canee wtt.ooaaaddatteeeeeeeeeee candidate edges rollowing the rornat: "[Kosgo_id>>
edge_id <ranksi, [an___ddddaaddrraakeee ...)". Beranked 1ist candidate edges:
K FAILED EXAMPLE OF LLM CARIBRATION
K.1 No RANKING ANSWER
Two main cases are observed when no ranking answers are successfully parsed since LLMs refuse to generate edge indices provided in the input prompt. One case is LLM generating ideas or thoughts on how to solve the reranking task. The other case LLM generating python scripts trying to solve the reranking task. We will list one example output with long thoughts and Python scripts in Block 3 As a result, LLMs generation can hardly follow the format requirement in the Block 2
Listing 3: LLM Calibration Failed Case: No Ranking Answer, i.e., Generating Python Scripts
solve this problen, will conbination Leclin ligua to serank the given cand candidate idlate wdlgea based on their sinifarity to the quesy Lern X julpph""
lanquage preceasing (ILP) and nachine learoing
Becu'' approaclis
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#PPoproosssinge:
propzocesa the text daca by tokenizing words each edge converting
then Inwercaze.
e*Festure extractioness 1'11 extract testures tron each edge that are relevant to the query torn Vidulep"", includerNnlee Presence specific words like ("rourboa'", Mruugar"", Vminti', or \" crushed ica!* in the edge.Antts Antt Syntactic selatioaships betneen words, such as (fand)* or Movaet" Labeled
ceatures
Lzwin nachine learning relat relationshipe that are indicative of edges related to Viulep)", The nodel will be trained to predict the relevance each edge the given candi edges based their predicted rel relevance the query Vijulep'..
exModel Leaininges:
pattecna
quezy Lezn, And. seBerankinges: Once audel Leaaned, use it
implonentation Eython: "python
isgort
tron nits.tokenize ingort word word_tocen toceniiee
from sklearn, feature rant certiaatonnn lon, on.text text import "ridfVectoriver
tron sklearn.mode selection import train test split fron sclearn. Hnderrnndell import Legistideegreszior
skleasn.metrics
asouracy__cose
Pregrocess
det preprocees__ook textreeess__tttttieeee (text):
word_tokenizo (oox:.
'.Join(tokens"
Extrast
fron
def extract extiract_fetttres fest
teatures
it "bourban' in odgo or "xhiskey" in edge: Ceatures.append
Presence courbon/whiskey
K.2 HALLUCINATED EDGES IN THE EXISTING TAXONOMY
One example of hallucinated edges generated by LLMs is shown in Table 12 The LLM ReRanked List contains one hallucinated edge "p:620-c:375" by connecting two existing terms "p:620" from edge "p:620-c:" and "c:375" from edge "p: "p:1247=c:375".
Table 12: LLM Calibration Case: Hallucinated Edges. The hallucinated edge example is bolded.
Input List
p-247-e:
p:1284e::
p:540c
p:570-e:
3:35
pr020kr:
p3986-o:
1:337-c:
p:272e:
p:147-e::755
p:620ec:
p:510e::
p:570c
p:620-c:375
p:96-c
p:33.
p.222e:
p:127-c:
K.3
SHORTEN RANKING ANSWER
Some cases show that LLMs would shorten the reranked list by ranking several top edges and mentioning that all other edges are irrelevant. One example asking LLM to rerank 50 candidate positions is shown in Block
Listing 4: LLM Calibration Case: The Shorten Ranking Answer
To rerank the cendidate edgex for the query tern Veirrnnan toast t I will analyxe each edge and de calcllate simi larity score based on the description or the query cern, The sooced are subjective and may very depending individusl perepectives.
Scre'' analysie:
++gdgor:: 9:1364-c:966 sodge>toas: +> orange toss--onnd-sgee-laee Scores D (orançe toast is not related
cimnanon]
=xRdgess: p:1 364-n: cedgettoss: -> cend-edge Score: Ibasis bread, but flavor topping
menzloned)
.*Edgex+;
sedre>stuffing <ead-odgerlalte Score: Istufring rsiated toast
cinnamon!
.>Edgo*+: 9:1396-0: <odge>quist bread <ead-cdzerlalte Scorc: iquick
typo hreadd
Clavor topping sentioned)
...
26. >-SageAv: p:1096-cs142 <edgexquick bread muttinkend-edges (Socre:
21. .+Bdgo**: pi f12-c:1236 <eige>cracker +> seds crackerend-eege> (Secre: 5)
.+Bdger:: p:1096-c:737 kedgerquick bread jota
scores are: .Rddgexx p:412 6:971 eedgerrrackes > syster crackersend edges (Bocr::
top adeas
Addggass 2033 cedgeollriified butter -> kerd-edge> (Score: 5)
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=*dggun: 9:412-0:1236 sadgercracker -> cracker 18coze: 5)
These edges are the nost relevant to the topic of toast with cinnancn, as they involve types of breed or coppings that used in similar
ranking or importance of each edge in a real real-vorld scerario.
subject
systen may reflect relevance
L IMPLEMENTATION DETAILS OF SS-MONO
1.11 TAXONOMY EXPANSION VIA QUERY-POSITION MATCHING
Mochine Loominn
Query node (eg.. Geometric Deep Learning)
p [e.g. Machine Learning!
Marhiie Learning
Geametrix Dowp
Sibling node b node
Sibling
Learning
Child node
[c.g. Graph
Neural Networrk)
Groph Neural Network
Existing Teconomy
Query-Poshion Matching:
Expanded Taxonomy
Inserting q
position (p.c)
Figure Taxonomy Expansion Task via Query-Position Matching, If query g finds the best- matched position to insert, e.g., (p, c), then it will break the existing edge (p, c) and establish new edges (p, q) and (g, c).
Pseuce Node (empty, placeholseri
Which position matches best
Query g
Original Taxonomy
Original Taxonomy Pseudo Nodee
Secudo-Appencee Taxonomy
Finding the Best Position for Non-Leaf Insertion
Figure 4: Establishing Pseudo-Appended Taxonomy T from T for Unifying Non-Leaf Insertion and Leaf Insertion.
Given an existing taxonomy T = (V, E) and query node (i.c., a newly emerging concept that has not appeared in 7), the non-leaf taxonomy expansion task aims to expand the taxonomy to the new taxonomy Tg by inserting the query node appropriately. To be specific, the query node seeks match the best candidate position, i.e., an edge like (p. c) in T. and then adds new edges (p, g) and (g, c) by breaking the original edge (p, c). For illustration, non-leaf insertion example for expanding the existing taxonomy is illustrated in Figure
During the lon-leaf expansion task, to maintain the possibility of appending the query node as the leaf node, in (Zhang et al. (022), authors propose to append pseudo nodes to the existing taxonomy and make it pseulo-append taxonomy T. The pseudo nodes are empty placeholders with zero feature vectors. In this way, inserting leaf and non-leaf nodes into the existing taxonomy T can be unified by only inserting non-leaf nodes into the pseudo-append taxonomy T. The corresponding procedures are illustrated in Figure 4
L.2 ENCODE CONTEXTUALIZED EMBEDDINGS FROM LANGUAGE MODELS
We use DistiiBERT--aas-uunoen base-uncased (Sanh et al. 2019) as the backbone pre-trained language model (PLM) to encode the input concept description sentence. Here, we describe the steps to obtain the node feature embedding H R (V) ж from the input concept description sentence X. The first step feed the description sentence to the backbone PLM, PLM(X),, where Z R (V)())) Lxh and L is the maximum length of tokens in each description sentence. Then, an attention layer adapted pool the Z to node-level embedding H.
H softmax (ZW;) Tz
(21)
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where Ws Rmxh is the trainable parameter and m is the dimension size to which the L length tokens is compressed. H E [RIVU(o//xxxh, When m 1, we can get H E BR after squeezing.
L.3 NEURAL ARCHITECTURE AND HYPERPARAMETERS
The 2-layer transformer encoder is used for SAM with the number of attention heads 8. The hidden dimension of the SAM layer is 256. The dimension project from SS-MONO is trained by RiemannianAdam optimizer using cosine learning rate scheduler. The learning rate linearly warmed up from to 5 x 10-6 in the first 10% training steps. The margin y is set as 0.1. The initialization of curvature is set as and is set as a trainable parameter. The numbers of training epochs for SemEval-Food, WordNet-Verb. and MeSH are 50, 40, and 40.
L.4 REPRODUCIBILITY
The experiments are executed on a Tesla V100 (32GB) GPU machine. The implementation code can be found in https::/ggthub..... wtt.://thhh...o...aaaaaaaaaa Saanngg/S--MMMMM Mono
M EDGE DESCRIPTION GENERATION AND SANITY CHECKING
In this section, we demonstrate the procedure for generating edge descriptions and performing sanity check.
M.1 EDGE DESCRIPTION GENERATION
To provide relational context beyond standalone node definitions, we generate edge descriptions that aim to explicitly articulate the relationship between hypernym and its hyponym. These descriptions serve as lightweight relational signals that the structural encoder can consume. To reduce hallucinations,
tightly constrained prompt that requires all statements be grounded in the provided definitions and context. We deploy Gemma2:99 (Mesnard et al. 2024) for description generation. The prompt template can be found in Listing 5
Listing 5: Description Generation Prompt Template
parente :parent_nameil [parent_context.
Child corn: (shild_name)
dafinition: (chiia_daCination)
Snown children of [chils_nanc]: [chiis_ccntext]
Tasks Melte conciss renahionship explanet
describing
swlates Uhe pazent
Ground every statement
inventing unsupportes, racts. Mea:ion at least one concrete trast that ties tha child specifically the pazent cazegozy.
provides. derinitions/contee
Given the prompt, one of the generated edge descriptions in the food taxonomy is as follows. Parent (445): dairy product "dairy product milk and butter and cheese." Child (474): double creme - "double creme is cream with fat content of 48% or more." Generated description:
"Double creme is type of dairy product because it is made from cream, which falls under the broader category of dairy products defined by its inclusion in 'milk and butter and cheese." Specifically, double creme's high content (48% or more) distinguishes within the range of dairy products."
M.2 SANITY CHECKING OF GENERATED DESCRIPTIONS
We validate the quality and faithfulness generated edge descriptions using two-stage protocol: (i) leven-level lexical similarity and (ii) semantic evaluation via LLM-as-Judge.
The first one is for measuring from the token level for the capability of LLM to maintain old knowledge and bring knowledge, which efficient for scaled datasets.
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For the plausible cases according to the first manner, LLM-as-Judge is leveraged deeply analyze them by calling API.
Across both lexical and semantic evaluations, LLM LLM-generated edge descriptions are largely faithful, semantically aligned, and reliable as relational augmentation. Even among the tevest-ROUGE cases, only small minority exhibit semantic drift, validating L.LM-generated relationship descriptions practical and effective mechanism for transferring relational knowledge to smaller structural models. We extend as follows.
M.2.1 TOKEN-LEVEL LEXICAL SIMILARITY
We compute ROUGE-I, ROUGE-L, Novelty Ratio, and TF-IDF similarity between each edge description and the original term definitions. These metrics provide coarse measure of grounding new content introduced by the LLM.
ROUGE-1 and ROUGE-L: capturing unigram (ROUGH-1) and longest common (ROUGE-L)
subsequence overlap between the given terms' description and LLM generated edge description.
Novelty Ratio (i.e., 100% token overlap ratio): assessing how much content in the generated description is newly introduced versus grounded the original definition.
TF-IDF similarity: measuring global lexical similarity beyond direct token overlap.
Table 13 summarizes results across all three datasets. Novelty ratios typically exceed 50%, while ROUGE scores fall in the 20-40% range, suggesting that LLMs introduce meaningful relational content while remaining partially grounded.
Table 13: Lexical similarity evaluation of LLM-generated edge descriptions across three datasets.
SemEval-Food
WordNet-Verll
MeSH
Metric
Mcan
Std
Mcan
Std
Mcan
Std
ROUGE-1
0.3965
0.1091
0.3012
0.0814
0.4102
0.1008
ROUGE-L
0,2733
0.0865
0.2027
0,0624
0.2441
0,0662
Novelty Ratio
0.6129
0.1352
0.7169
0.1000
0,5286
0,1444
TF-IDF Similarity
0.6081
0.1412
0.5894
0.1703
0.6034
0.1305
M.2.2 LLM-AS-JUDGE SEMANTIC CONSISTENCY EVALUATION
Lexical metrics do not capture semantic correctness. To measure semantic alignment, we use GPT-4o as an LLM-as-Jun Judgeeee. To manage API cost, we evaluate only the 80 lowest-ROUGH edges per dataset since those are most likely to exhibit errors. Each edge receives three independent votes (Aligned / Partially Aligned Misaligned) using the prompt template in Listing
Listing 6: Description Sanity Check Prompt Template
Given the cenonipal kik style mode descrigt iors, decide whether the provided edge desoription is tactuslly correct, aligned with the parent/cnh /chi terms, and free oz hacincinated
You taxonony quality
Parent Torm: [pacont_tezm)
Parent Definitica: [paront_detiattion
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Published as a conference paper at ICLR 2026
ReCezencea to plactholder paoudo nodes (9.9.. "pseudo root" "psoudo leach) aze acceptable should nos be Flagged treated information solely For being placeholders lacking extrra detail.
Results are shown Table 14 Despite low lexical overlap, only a small fraction (510) of descriptions are misaligned, demonstrating that low-ROUGE generations can still be semantically correct.
Table 14: LLM-as-Judee semantic consistency evaluation on the 80 per dataset.
edge descriptions
Dataset
Aligned
Partial
Misaligned
Seooval-Food
47/80 (58.75%)
25/80 (31.25%)
8/80 (10.00%)
WordNet- Verb
36/80 (45.00%)
40/80 (50.00%)
4/80 ( (.000)
McSH
58/80 (72.50%)
19/80 (23.75%)
3/80 ( (3.55%
N FINE-TUNING LLM FOR TAXONOMY EXPANSION TASK
To test the adaptability of our pipeline off shelf language models, we adopt TinyLlama-La I- intermediate-stepy 1431 k-3T (Zhang et al., 2024) as representative lightweight LLM and attach LoRA adapter (Hu al. 2022) the last four transformer layers (for computational efficiency). Concretely, we fine-tune the attention and feed-forward projection modules (q_proj, k k_proj. v v_proj, o_proj, gate jate_projj_______ppppp up_proj, down_pro) while freezing the token embedding layer. The TinyLlama encoder is trained under the same learning objective as SS-Mono, using the loss in Eq. (14), ensuring a consistent optimization setup for comparison.
This experiment demonstrates that geometric encoder is compatible with pretrained LLM check- points: integrating an LLM encoder requires only minor architectural changes and remains computa- tionally lightweight. As shown in Table 15 the fine-tuned TinyLlama variant achieves comparable MR and MRR and notably improves leaf insertions, but it degrades performance on non-leaf nodes. These results suggest that our LLMM-SLM-disttilattonn design worse than (or even better than) LLM fine-tuning.
Table 15: Performance of SS-Mono with Fine-Tuned LinyLlama on SemEval-Food Dataset.
Meladd
Total
Leaf
Non-leaf
MR.
MRR
RG1 1f
R.511
R36
P6117
PG5
MR.
MER1
R40101
MR.
MRR1
R.0100
S5-Mano
239.169
143997
TlnyLluma tine caned)
253,9L1
0.373
0.122
0.241
0.309
0.277
0.101
0,065
73881
0.754
0.652
1139,808
0,080
0.045
O LLM AUGMENTED DESCRIPTIONS WITH NON-LEAF EXPANSION
We analyze why LLM- -uuum-eete Descriptions (AD) tend to improve leaf-node node insertion more consistently than non-leaf insertion, shown in Table Our observations indicate that this difference arises from how LLM-generated descriptions interact with the structural roles of different node types in taxonomy along three dimensions.
Leaf-node descriptions are structurally consistent and aligned with the insertion task. For leaf nodes, the -enerrreeteeed descriptions primarily emphasize the concept's global semantic identity, such as being terminal category or a fine- fine-grained subtype. Since leaf nodes do not have children, these descriptions remain concise, stable, and semantically homogeneous across examples. This consistency provides the scorer with clearer signals regarding the node's s appropriate position in the taxonomy.
Non-leaf descriptions exhibit higher diversity due to dual relational roles. Non-leaf nodes participate in both upward pparent-facing and downward Schild-facingg relationships. As a result, their descriptions must encode more heterogeneous and relationally complex information. Empirically,
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Published as a conference paper at ICLR 2026
LLMs produce wider range of phrasings for non-leaf nodes because the prompts must articulate how multiple concepts relate rather than describe an isolated entity. This broader linguistic variability increases variance in the augmented text representations.
Variability in AD interacts with fine-grained structural ranking and can dilute local signals. Intermediate insertion a fine-grained ranking problem in which the scorer must distinguish among many structurally similar alternatives. When ADs for non-leaf nodes exhibit high variance, the result- ing representations provide weaker less discriminative cues for resolving subtle local structural differences. In contrast, leaf-node insertion benefits from the more uniform and taxonomy-aligne descriptions.
To sum up, LLM Augmented Descriptions is, so far, a viable solution that provides additional knowledge for the existing taxonomy and can leveraged to improve the SLM's performance based on designed geometric deep learning constraints and self-supervised learning approach, as shown in the extensive experiments. Indeed, is not perfect and has the latent drawback discussed above, and more than willing to make it our future research direction. A few possible directions are listed below:
Incorporating external web knowledge for richer edge descriptions. Future extensions may integrate controlled web search so that the LLM can retrieve verifiable information about con- cept relationships. This has the potential to generate more accurate, edge-oriented descriptions, particularly for non-leaf nodes whose semantics depend on multiple relational contexts.
Leveraging local neighborhood structure during AD generation. Conditioning description generation on a node's s local subgraph- as siblings, parents, children, or subtree summaries- can better ground the textual output in the underlying taxonomy. Such structure-aware prompting may reduce semantic drift and lower variance in AD for non-leaf nodes.
Developing multi-step, grounded generation pipelines. A more robust AD pipeline can combine (i) local-structure grounding, (ii) retrieved external knowledge, and (iii) self-critique or refinement step. This multi-stage procedure aims to stabilize the textual signal, filter inconsistent relational statements, and produce richer, higher-fidelity descriptions that support fine-grained non-leaf' insertion.
P THE USE OF LLMS
As required by the ICLR 2026 Submission Policy, we made the following statement for the use of LLMs. We used large language models (LLMs) as controlled assistive tools for writing, specifically to check grammar and improve clarity. All outputs were reviewed and edited by the authors, who take full responsibility for the final content. Different LLMs were also included in experiments as part of evaluating their effectiveness for the taxonomy expansion task.
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Reviews:
[{"review_id": "2L0zitmfA7", "reviewer": "Reviewer_7uga", "summary": "This paper addresses the task of taxonomy expansion in scientific domains, specifically adding new concept nodes to an existing taxonomy (precisely in a directed acyclic hierarchy of concepts). The paper proposes a pipeline that borrows knowledge from an LLM and transfers it into SLM, which can then perform the taxonomy expansion efficiently. SS-MONO has three stages: (1) local taxonomy augmentation using an LLM - for each candidate insertion position in the taxonomy (parent node and a child node between which a new concept might be inserted) a pretained LLM is prompted to generate a textual explanation or description of local context (semantic features about the candidate position), (2) fine-tuning a SLM with geometric constraints to rank candidate insertion positions for a query concept (structure-dominated encoder that projects concept embeddings into hyperbolic space by nested entailment cones to keep hierarchical relationships, and a context-dominated encoder that embeds the textual descriptions) - here a key idea to enforce the monotonic ordering (child ≼ query ≼ parent in the embedding space) and (3) LLM-based calibrationof SLM score where to insert the new concept with use of second LLM call to re-rank the top-$k$ predicted positions. Experiments on three benchmarks demonstrate, in some cases, superiority and advantages of SS-MONO over other compared methods.", "questions": "- Can the authors provide more details or examples of the prompt and output used for the LLM when generating the candidate position descriptions? This is currently abstract in the paper. For instance, if the candidate position is between parent concept P and child concept C, do you prompt the LLM with something like “Explain the relationship between P and its subcategory C” or “Give a description of where C fits under P”? And does the LLM output a few sentences describing that taxonomic context? An example would help in understanding what knowledge the LLM is injecting. Additionally, did you observe any instances of the LLM outputting incorrect information about the taxonomy? If so, how did you mitigate that (e.g., do you simply trust whatever the LLM says, or do you have a way to sanity-check it)? Clarifying this will help assess the reliability of the augmentation. And could you please evaluate LLM with the same procedure (subtasks) as SLM (inference).\n- You introduce a complex hyperbolic constraint system for the structure-dominated encoder. Did you compare or ablate this against a simpler approach (for example, a Euclidean encoder or a transformer-based graph encoder without hyperbolic projection)? In Appendix I.1 you mention investigating the role of “geometric deep learning” – can you summarize those findings? It would be insightful to know how much the hyperbolic embedding improved things. Perhaps the model could also be trained in Euclidean space with a learned ordering constraint – would that fail or perform worse? \n- In cases where a concept has multiple true parent locations (non-leaf multi-attachments), how would you operationally use SS-MONO to attach it in all the correct places?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The paper presents a creative integration of ideas from different domains: it combines hyperbolic geometry (for representing hierarchical structure) with LLM-based semantic augmentation in a small-model pipeline. While hyperbolic embeddings have been used for hierarchical tasks before and others have leveraged language models for taxonomy expansion, this provides a limited but still novel work in how it brings these together. Especially the notion of “Structure-Semantic Monotonization” is a novel formulation to ensure monotonicity in latent space (with use of nested entailment cones to enforce transitivity). \n- The technical quality of the work appears high. The paper is thorough in justifying and evaluating the approach.\n- The training scheme is cleverly self-supervised, avoiding manual annotations (removal of nodes predict their insertion).", "weaknesses": "- Ironically, a method motivated by avoiding LLM usage still depends on LLMs at key points. The small model alone does a lot of the work, but the pipeline requires a capable LLM to provide the augmented descriptions and to perform final calibration. In the ablation without LLM augmentations (SS-MONO w/o AD), the small model’s performance, although competitive, is not clearly superior to the best prior methods. \n- The paper does not delve deeply into what the LLM-generated “textual explanations” look like or how consistent their quality is. This is a bit of a black box in the description. If the LLM outputs poor or hallucinated explanations for some candidate positions, does that ever confuse the SLM during training? One could imagine the LLM sometimes generating a misleading context (especially if the taxonomy contains very specialized terms that the LLM isn’t familiar with). The authors did not mention any filtering or human verification of the LLM outputs. It would strengthen the work to either demonstrate that these augmented descriptions are almost always accurate, or to describe measures to handle noise in those descriptions.\n- Due to my understanding, there is no comparison to one of the baseline scenarios when LLM are similarly asked in turns to perform similar steps lika SS-MONO (pair insertion evaluairion, re-ranking).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rUC8YW6Yg7", "reviewer": "Reviewer_orUz", "summary": "The paper introduces SS-MONO (Structure-Semantic Monotonization), a novel pipeline for efficient and accurate scientific taxonomy expansion. Recognizing the strong hyperbolicity in Large Language Model (LLM) embeddings, SS-MONO addresses the high computational cost and hallucination issues associated with directly using LLMs on domain-specific taxonomies. SS-MONO leverages LLM augmentation and distills this knowledge into Small Language Models (SLMs) through self-supervised fine-tuning enforced by geometric constraints. Key modules include a structure-dominated encoder using hyperbolic representation learning to preserve hierarchy (monotonicity) and a context-dominated encoder for contextual semantics. Experiments show that a fine-tuned SLM (e.g., DistilBERT-base-110M) consistently outperforms frozen LLMs and deep learning baselines on expansion tasks.", "questions": "1. Please update the bold format in all the experiment tables in the paper carefully. Currently many bolded numbers in the table are not exactly the one with the best value. This is very confusing and could lead to wrong conclusion.\n\n2. Please address the above two concerns I have.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Efficiency and Cost-Effectiveness\n\nSS-MONO implements an LLM-to-SLM distillation approach, fine-tuning a Small Language Model (SLM), such as DistilBERT-base-110M. This strategy provides a practical and economical alternative to the high computational costs and difficulties associated with directly using Large Language Models (LLMs) on domain-specific taxonomies.\n\n2. Structural Integrity and Superior Overall Performance\n\nThe pipeline utilizes hyperbolic representation learning in its structure-dominated encoder to enforce geometric constraints (monotonicity), which preserves the hierarchical order. This structural awareness allows the fine-tuned SLM to consistently outperform frozen LLMs and domain-specific deep learning baselines overall.\n\n3. Self-Supervised Training\n\nThe entire training process is self-supervised, guided by the existing taxonomy's topology. This design eliminates the need for expensive human labeling efforts for expansion tasks", "weaknesses": "1. Performance on Large-Scale Taxonomies\n\nThe methodology demonstrates significantly lower effectiveness on the large-scale WordNet-Verb dataset (13,936 nodes, depth 12) compared to smaller datasets. SS-MONO's overall average ranking on WordNet-Verb is 1626.52, which is not SOTA and substantially less favorable than its performance on SemEval-Food (239.17) and MeSH (436.82). Does this indicate that the proposed method could have issues in scalability and can be less effective on large-scale Taxonomies?\n\n2. Non-Leaf Volatility with LLM Augmentation Observed\n\nThe performance metrics show that including LLM Augmented Descriptions (AD) does not always enhance intermediate (non-leaf) expansion. For example, on WordNet-Verb, the Non-leaf R@10 metric decreases sharply from 0.099 (SS-MONO w/o AD) to 0.035 (full SS-MONO). Other datasets have the same observation. What could lead to the performance difference between leaf nodes and non-leaf nodes? Is it because non-leaf nodes have more complicated relationship and LLM can hardly have clear annotations?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "f9rUJVV242", "reviewer": "Reviewer_Ghyo", "summary": "The paper explores how SLMs can effectively perform scientific taxonomy expansion by leveraging geometric constraints and guidance from LLMs.  \nAuthors propose SS-MONO (Structure-Semantic Monotonization), which integrates three components: (1) local taxonomy augmentation by frozen LLMs, (2) self-supervised fine-tuning of an SLM (e.g., DistilBERT) with hyperbolic constraints to preserve hierarchical transitivity, and (3) LLM-based calibration.  \nExperiments on SemEval-Food, MeSH, and WordNet-Verb show that SS-MONO outperforms both traditional graph-based methods (e.g., TaxoExpan, TMN, QEN) and frozen LLMs like GPT-4o-mini, establishing SLMs as cost-efficient and competitive models for scientific taxonomy expansion.", "questions": "See weakness.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper presents a novel perspective that connects hyperbolic geometry in LLM embeddings with taxonomy reasoning.\n- The paper is well-motivated and technically detailed.\n- The self-supervised training approach removes the need for human annotation, and the idea of “borrowing knowledge” from LLMs while retaining the efficiency of SLMs is practically appealing.  \n- The empirical results are comprehensive and support the claim of the paper.", "weaknesses": "- The impact of geometric regularization compared to simpler fine-tuning is not explained in the main text. I think it’s worth discussing the main takeaway of the ablation studies in 4.2.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QYthe4ZZ8N", "reviewer": "Reviewer_APGH", "summary": "This paper introduces SS-Mono, a pipeline targeting efficient and accurate scientific taxonomy expansion by transferring hierarchical knowledge from Large Language Models to Small Language Models. SS-Mono integrates a local taxonomy augmentation phase using LLMs, a self-supervised geometric fine-tuning process with hyperbolic constraints, and LLM-based calibration for candidate ranking. The approach is evaluated on several taxonomy expansion benchmarks (SemEval-Food, WordNet-Verb, and MeSH), showing that a fine-tuned SLM outperforms both frozen LLMs and domain-specific baselines for both leaf and non-leaf node insertions.", "questions": "Q1: Have the authors conducted any systematic analysis of the types or frequency of semantic drift or spurious insertions caused by LLM-augmented edge descriptions? If not, can they provide statistics or example cases showing where LLM guidance introduces incorrect or misleading hierarchy insertions?\n\nQ2: Can the negative sampling strategy in self-supervised optimization be further detailed or ablated? Is there evidence that specific hard negative choices strongly affect generalization versus random negatives?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "S1: The structure of SS-Mono is modular and well-motivated: it combines structure-dominated (hyperbolic metric) and context-dominated (semantic, LLM-augmented) encoders. This dual design is well illustrated in Figure 1, which shows how LLMs are used to enrich edge semantics and how structural relations are composed.\n\nS2: Extensive experiments (see Tables 2 and 3) cover multiple datasets and include a wider range of both classical and recent baselines, including neural and LLM-based approaches. The results show consistent, substantial gains of SS-Mono, especially when augmented with LLM outputs, across MR, MRR, and Recall/Precision metrics.\n\nS3: Self-supervised training enables the model to leverage existing taxonomies without costly annotation. The mathematical formulations (see Equations 1-11 and Cone Loss in Section 3.2) are clear, concise, and consistent with state-of-the-art hyperbolic learning approaches.", "weaknesses": "W1: While the paper claims that \"LLMs have potential but are not ready to be directly deployed,\" the LLM calibration component appears to be more of an optional enhancement than a robust part of the pipeline. Figure 2 exposes high failure rates in LLM output for reranking (frequent hallucinated edges or incomplete lists), and Section 4.3 provides only a partial mitigation of this challenge. The improvements from LLM calibration, as shown in Table 3, are not always consistent or predictable.\n\nW2: The model relies on self-supervised negative sampling and LLM-augmented context for candidate positions. The precise method for sampling hard negatives is tailored closely to the taxonomy structure as described in Section 3.4, but it is unclear whether the negative sampling strategy introduces bias or overestimates the model’s robustness to challenging/far-out queries.\n\nW3: The pipeline discusses SLM fine-tuning with geometric constraints, but does not deeply analyze (or ablate) alternative LLM fine-tuning approaches (domain adaptation, prompt-tuning, etc.). This limits direct attribution of SLM’s advantages to the geometric approach, rather than simply to the smaller/faster architecture or training regime.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)