Pith. sign in

REVIEW 3 major objections 4 minor 21 references

Capturing Symmetry and Antisymmetry in Language Models through Symmetry-Aware Training Objectives

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Retrained encoders learn swap-relation entailment that LLMs miss

desk verdict The template-bound benchmark makes the paper's central claims unsubstantiated, but the RotatE-inspired metric is a germ of a good idea. read the letter →

arxiv 2504.16312 v1 pith:MGHPS45B submitted 2025-04-22 cs.CL

Zhangdie Yuan , Andreas Vlachos This is my paper · ORCID
classification cs.CL
keywords symmetricrelationsantisymmetricnaturallanguageinferencecontrastivelearningk-nearestneighborsencoderretrainingWikidataRotatE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether language models understand that some relations remain true when their arguments are swapped (symmetric relations) while others become false (antisymmetric relations). It constructs a natural-language-inference benchmark from Wikidata triples in which each premise asserts a relation and each hypothesis swaps the two entities. On that benchmark, pretrained encoders such as RoBERTa hover at the 50 percent random baseline, even after MNLI fine-tuning. The authors then retrain the encoder alone with a contrastive objective built on a symmetry-aware distance metric borrowed from the RotatE knowledge-graph embedding method, reaching 100 percent accuracy on both lexicalized and delexicalized versions with only dozens of training examples. They conclude that retraining the encoder, instead of a classification head, teaches swapped-entity entailment while forgetting less of the model's prior knowledge than standard fine-tuning.

What carries the argument

The load-bearing object is a symmetry-aware distance metric between a premise embedding $p$ and a hypothesis embedding $h$, $d_\ell(p,h)=1-\operatorname{sim}(h,\,p\circ \ell)$, where $\circ$ is the element-wise (Hadamard) product with a label embedding $\ell$. This metric is asymmetric in its arguments: $d_\ell(p,h)\neq d_\ell(h,p)$ in general, which makes 'p entails h' and 'h entails p' distinguishable. In the k-NN variant, each sample's label embedding is recovered as the element-wise ratio $h\oslash p$ of the hypothesis and premise embeddings, and training pulls same-label ratios together while pushing different-label ratios apart; at inference, test labels come from a majority vote over the $k$ nearest training label embeddings. The fixed version of this metric is what lets the encoder learn the semantic distinction with only 48-64 training examples, because the rotational asymmetry is supplied by the metric rather than learned from data.

What would settle it

Take the same 14 relations and build a test set from naturally occurring, paraphrased sentences with swapped arguments; if the retrained encoder, frozen and probed by k-NN, drops from 100 percent toward chance on that set, the claimed mastery of symmetric and antisymmetric semantics is an artifact of the template format.

Watch

Extended reading notes

Core claim

The central discovery is that the missing relational competence is not in the classification head but in the encoder's geometry: pretrained sentence encoders place a sentence and its swapped-argument counterpart at symmetric distances, so entailment and contradiction cannot be told apart. The paper's fix is a distance metric defined on sentence embeddings, $d_\ell(p,h)=1-\operatorname{sim}(h,\,p\circ \ell)$, that treats swapping the premise and hypothesis as a rotation in embedding space, exactly as RotatE rotates one entity into another in knowledge-graph embeddings. Training the encoder with this metric, using random label embeddings or a k-NN voting scheme that infers label embeddings as element-wise ratios $h\oslash p$, brings accuracy to 100 percent on the new benchmark, matches the accuracy of a fine-tuned classification head, and does so with far fewer samples (48-64 vs. 336) while producing a smaller drop on MNLI after training (as low as -5.8 percent, versus -11.2 percent for fine-tuning). The authors' conclusion is that retraining the encoder through symmetry-aware objectives captures symmetric and antisymmetric relations that pretrained models miss, with better few-shot efficiency and knowledge retention than head fine-tuning.

Load-bearing premise

The benchmark labels are assigned from Wikidata's declared relation property and the sentences are produced by fixed templates, so if template-based pairs do not reflect genuine relational understanding then both the chance-level pretrained scores and the perfect retrained scores are test artifacts.

Editorial extensions

If this is right

  • Retraining the encoder alone, without any classification head or adapter, is enough to reach 100 percent accuracy on both lexicalized and delexicalized versions of the new symmetry benchmark.
  • The fixed RotatE-derived distance metric reduces the data needed to roughly an eighth of what fine-tuning requires (48-64 samples vs. 336), an efficiency gain the paper attributes to the metric already encoding the directionality of relations.
  • The retrained encoder forgets less prior knowledge: the measured drop on MNLI is up to 5.4 percentage points smaller than with fine-tuning in the reported settings.
  • The approach transfers across encoder sizes and pretraining pipelines (RoBERTa-Large, MiniLM 6/12 layers, all-MiniLM 6/12 layers), which the paper reads as evidence the method is general rather than model-specific.

Reading between the lines

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

  • Because the benchmark labels come mechanically from Wikidata's property declarations and the sentences from fixed templates (the paper's own stated limitation), the 100 percent scores should be read as a proof that the encoder can learn the declared relational axioms, not yet as evidence it would do so on the open-ended linguistic variety of natural text.
  • One untested corollary of the rotation-based distance is that the same objective could inject other knowledge-graph axiomatics—transitivity, irreflexivity, or hierarchy—into sentence encoders with similarly few examples; the paper only exercises symmetry and antisymmetry.
  • A natural stress test would apply the method to context-dependent relations such as 'x helps y' or 'x likes y', where symmetry is not a fixed property of the relation; success would require the metric to use the actual entity meanings rather than the relation label alone.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces a Wikidata-derived NLI dataset for evaluating symmetric and antisymmetric relations, reports that pretrained LLMs perform near chance on it, and proposes retraining the encoder with a contrastive objective and an asymmetric, RotatE-inspired distance metric, optionally combined with k-NN. The authors report 100% accuracy on both lexicalized and delexicalized versions with tens of training examples, claim parity with fine-tuned classification heads, and report improved retention on MNLI. The central claim is that retraining encoders with symmetry-aware objectives yields a reusable encoder that understands relational symmetry and antisymmetry better than standard fine-tuning.

Significance. If the empirical results were valid, the paper would offer a practical, few-shot method for injecting relational symmetry and antisymmetry into sentence encoders, with a released dataset as a useful resource. The directional distance metric derived from RotatE is an interesting idea, and the paper is clearly written. However, the evaluation is undermined by a template shortcut: because every relation is rendered by exactly one template and labels are assigned mechanically from the Wikidata property type, the benchmark can be solved by recognizing the relation phrase alone. The near-chance pretrained results and the 100% retrained results therefore do not establish an understanding of symmetry and antisymmetry in any general sense, and the paper's own Limitations section partially concedes this. The current significance is accordingly low.

major comments (3)
  1. [Appendix A.2, Table 3, Limitations] The dataset construction makes the NLI label a deterministic function of the relation phrase. For each of the 14 properties, exactly one natural-language template is used (Table 3), and Appendix A.2 assigns 'Entailment' to every symmetric property and 'Contradiction' to every antisymmetric property, regardless of the entities. A model that maps the template phrase (e.g., 'is a child of' vs. 'is a sibling of') to a label reaches 100% without comparing premise and hypothesis direction or inspecting the entity swap; the delexicalized version still contains the template word. The paper's own Limitations paragraph concedes that the dataset 'lack[s] syntactic diversity' and that the challenge is 'far from resolved,' yet the abstract and conclusion assert enhanced 'understanding of symmetric and antisymmetric relations.' This template shortcut is load-bearing because the near-chance pretrained results, the few-shot 100% accuracies, and the forgetting comparisons are all computed on this same benchmark.
  2. [Table 2, Section 3.2] The catastrophic-forgetting comparison is confounded by unequal training budgets. Random Label Embeddings uses 48 training samples, k-NN uses 64, k-NN with Learnt Distance Metric uses 400, and Fine-Tuning uses 336; the reported MNLI drops (5.8%, 7.7%, 21.5%, 11.2%) are therefore not comparable as measures of the training objective. Matching the number of training samples or training steps, or reporting forgetting as a function of update count, is needed before claiming improved knowledge retention.
  3. [Section 3.1, Table 2] The few-shot efficiency claim is not substantiated. The paper reports the number of training samples at which 100% accuracy is reached, but it does not describe how these counts were selected, whether they are minimal, or the variance across random seeds; no significance tests or error bars are given. Given the template shortcut, reaching 100% with 48 examples is consistent with memorizing the 14 relation templates rather than learning a reusable relational bias.
minor comments (4)
  1. [Section 1] There is a typo in the introduction: 'antisyemmetric' should be 'antisymmetric'.
  2. [References] The two references to Lin and Ng (2022a) and (2022b) appear to be the same paper with the same title and venue; they should be merged or clearly distinguished.
  3. [Appendix C] The appendix says hyperparameters are detailed below, but the k-NN with Learnt Distance Metric setting is missing its hyperparameters (learning rate, batch size, margin, k).
  4. [Tables 2 and 4] All accuracies are point estimates with no confidence intervals or significance tests; given the repeated 100% values, the tables should report run-level variability or at least multiple seeds.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the template-only benchmark is a validity limitation that the paper acknowledges, not a circular reduction.

full rationale

The paper's pipeline is a standard supervised benchmark study: Wikidata properties define the labels, the generated NLI pairs instantiate those definitions, a subset is used to retrain an encoder (Eqs. 3-6), and held-out accuracy is measured. No equation rewrites a predicted quantity back into the training labels by construction: Eq. 4 is a distance function, Eq. 5 is a contrastive loss, and Eq. 6 computes label embeddings from input pairs, none of which assumes the test label. The near-chance pretrained results are external probes, and the catastrophic-forgetting comparison is measured on MNLI, an independent dataset. The legitimate weakness is the benchmark's template determinism (Appendix A.2-A.3, Table 3): because each relation has one manually written template and the label is read off the Wikidata property, a model can achieve high accuracy by template recognition. The paper itself flags this in the Limitations section, stating that the datasets 'lack syntactic diversity' and that 'the challenge of capturing symmetry and antisymmetry with LLMs is far from resolved.' That is a validity or external-generalization shortcoming, not a circularity in the derivation. No load-bearing self-citation or uniqueness theorem is invoked. Therefore no circular step is established.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical or theoretical entities are introduced. The central claim relies on the Wikidata-derived dataset and on assumptions about how template-based sentences and element-wise embedding operations preserve relational semantics.

free parameters (4)
  • margin = 0.5
    Margin in the contrastive losses of Equations 3 and 5; chosen by hand and used for all retraining methods. Results may depend on it.
  • k = 3
    Number of neighbors used in k-NN inference for both k-NN variants; chosen by hand.
  • learning_rate = 2e-05
    Learning rate for retraining runs; reported in Appendix C. Standard but unvaried.
  • batch_size = 16
    Batch size for retraining; reported in Appendix C.
assumptions (5)
  • domain assumption Wikidata's symmetric and antisymmetric property declarations are correct and map directly to natural-language entailment and contradiction.
    Dataset labeling in Appendix A.2 assigns 'Entailment' for symmetric and 'Contradiction' for antisymmetric relations solely from the Wikidata property.
  • domain assumption Template-based conversion of triples into sentences preserves the logical relation semantics.
    Appendix A.3 and B use fixed templates; the paper's limitations note the resulting lack of syntactic diversity.
  • domain assumption The swapped-subject/object NLI formulation is a valid probe of relational symmetry understanding.
    Task definition in Section 2.1; if the formulation introduces artifacts such as unnatural sentence pairs, the near-chance results may not reflect general model competence.
  • domain assumption Element-wise product and division of real-valued sentence embeddings are meaningful compositional operators for encoding relations.
    Equations 4 and 6 borrow RotatE's complex-space operation and apply it to dense sentence embeddings without justification; this is central to the distance metric.
  • domain assumption MNLI performance drop is a valid measure of catastrophic forgetting in this comparison.
    Section 3.1 uses MNLI accuracy drop (Delta) as the forgetting metric; different training setups (encoder-only vs. head) may interact with the metric.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Capturing Symmetry and Antisymmetry in Language Models through Symmetry-Aware Training Objectives." pith.science (2026). https://pith.science/paper/MGHPS45B

@misc{pith2026250416312,
  author       = {Pith},
  title        = {Pith review of: Capturing Symmetry and Antisymmetry in Language Models through Symmetry-Aware Training Objectives},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MGHPS45B}},
  note         = {Machine review of arXiv:2504.16312}
}
read the original abstract

Capturing symmetric (e.g., country borders another country) and antisymmetric (e.g., parent_of) relations is crucial for a variety of applications. This paper tackles this challenge by introducing a novel Wikidata-derived natural language inference dataset designed to evaluate large language models (LLMs). Our findings reveal that LLMs perform comparably to random chance on this benchmark, highlighting a gap in relational understanding. To address this, we explore encoder retraining via contrastive learning with k-nearest neighbors. The retrained encoder matches the performance of fine-tuned classification heads while offering additional benefits, including greater efficiency in few-shot learning and improved mitigation of catastrophic forgetting.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

21 extracted references · 6 canonical work pages

  1. [1]

    Moustafa Alzantot, Yash Sharma, Ahmed Elgohary, Bo-Jhang Ho, Mani Srivastava, and Kai-Wei Chang. 2018. Generating natural language adversarial examples. arXiv preprint arXiv:1804.07998

    arXiv 2018

  2. [2]

    a is b" fail to learn

    Lukas Berglund, Meg Tong, Max Kaufmann, Mikita Balesni, Asa Cooper Stickland, Tomasz Korbak, and Owain Evans. 2023. The reversal curse: Llms trained on" a is b" fail to learn" b is a". arXiv preprint arXiv:2309.12288

    arXiv 2023

  3. [3]

    Nicola De Cao, Wilker Aziz, and Ivan Titov. 2021. Editing factual knowledge in language models. arXiv preprint arXiv:2104.08164

    arXiv 2021

  4. [4]

    Robert M French. 1999. Catastrophic forgetting in connectionist networks. Trends in cognitive sciences, 3(4):128--135

    1999

  5. [5]

    Yaroslav Fyodorov, Yoad Winter, and Nissim Francez. 2000. A natural logic inference system

    work page 2000

  6. [6]

    Max Glockner, Ieva Stali \=u nait \.e , James Thorne, Gisela Vallejo, Andreas Vlachos, and Iryna Gurevych. 2023. Ambifc: Fact-checking ambiguous claims with evidence. Transactions of the Association for Computational Linguistics

    work page 2023

  7. [7]

    Zhijiang Guo, Michael Schlichtkrull, and Andreas Vlachos. 2022. https://doi.org/10.1162/tacl_a_00454 A survey on automated fact-checking . Transactions of the Association for Computational Linguistics, 10:178--206

    doi:10.1162/tacl_a_00454 2022

  8. [8]

    Sudipta Kar, Giuseppe Castellucci, Simone Filice, Shervin Malmasi, and Oleg Rokhlenko. 2022. Preventing catastrophic forgetting in continual learning of new natural language tasks. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3137--3145

    work page 2022

Show all 21 references
  1. [9]

    Ruixi Lin and Hwee Tou Ng. 2022 a . Does bert know that the is-a relation is transitive? In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 94--99

    2022

  2. [10]

    Ruixi Lin and Hwee Tou Ng. 2022 b . https://doi.org/10.18653/v1/2022.acl-short.11 Does BERT know that the IS -a relation is transitive? In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 94--99, Dublin, Ir...

    2022 doi

  3. [11]

    Thomas McCoy, Paul Smolensky, Tal Linzen, Jianfeng Gao, and Asli Celikyilmaz

    R. Thomas McCoy, Paul Smolensky, Tal Linzen, Jianfeng Gao, and Asli Celikyilmaz. 2023. https://doi.org/10.1162/tacl_a_00567 How much do language models copy from their training data? evaluating linguistic novelty in text generation using RAVEN . Transactions of the Association...

    2023 doi

  4. [12]

    Nils Reimers and Iryna Gurevych. 2019. Sentence-bert: Sentence embeddings using siamese bert-networks. arXiv preprint arXiv:1908.10084

    2019 arXiv

  5. [13]

    Sebastian Riedel, Limin Yao, Andrew McCallum, and Benjamin M Marlin. 2013. Relation extraction with matrix factorization and universal schemas. In Proceedings of the 2013 conference of the North American chapter of the association for computational linguistics: human language ...

    2013

  6. [14]

    Maarten Sap, Vered Shwartz, Antoine Bosselut, Yejin Choi, and Dan Roth. 2020. Commonsense reasoning for natural language processing. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics: Tutorial Abstracts, pages 27--33

    2020

  7. [15]

    Shane Storks, Qiaozi Gao, and Joyce Y Chai. 2019. Recent advances in natural language inference: A survey of benchmarks, resources, and approaches. arXiv preprint arXiv:1904.01172

    2019 arXiv

  8. [16]

    Zhiqing Sun, Zhi-Hong Deng, Jian-Yun Nie, and Jian Tang. 2019. Rotate: Knowledge graph embedding by relational rotation in complex space. arXiv preprint arXiv:1902.10197

    2019 arXiv

  9. [17]

    Denny Vrande c i \'c and Markus Kr \"o tzsch. 2014. Wikidata: a free collaborative knowledgebase. Communications of the ACM, 57(10):78--85

    2014

  10. [18]

    Wenhui Wang, Furu Wei, Li Dong, Hangbo Bao, Nan Yang, and Ming Zhou. 2020. Minilm: Deep self-attention distillation for task-agnostic compression of pre-trained transformers. Advances in Neural Information Processing Systems, 33:5776--5788

    2020

  11. [19]

    Xiaozhi Wang, Tianyu Gao, Zhaocheng Zhu, Zhengyan Zhang, Zhiyuan Liu, Juanzi Li, and Jian Tang. 2021. Kepler: A unified model for knowledge embedding and pre-trained language representation. Transactions of the Association for Computational Linguistics, 9:176--194

    2021

  12. [20]

    URL: " 'urlintro :=

    ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year eprint doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before...

  13. [21]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.