Computer Science ›› 2026, Vol. 53 ›› Issue (4): 337-346.doi: 10.11896/jsjkx.251000136

• Artificial Intelligence • Previous Articles     Next Articles

Category-Theoretic Semantic Representation: Systematic Review and Compositional Mechanism Analysis

LI Yidan1, CUI Jianying1, XIONG Minghui2   

  1. 1 Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China
    2 Digital Rule of Law Laboratory, Zhejiang University, Hangzhou 310008, China
  • Received:2025-10-28 Revised:2026-01-26 Online:2026-04-15 Published:2026-04-08
  • About author:LI Yidan,born in 1994,Ph.Dcandidate.Her main research interests include formal semantics,category theory,artificial intelligence logic and natural language processing.
    CUI Jianying,born in 1975,Ph.D,associate professor,Ph.D supervisor.Her main research interests include formal argumentation theory,artificial intelligence logic and natural language processing.
  • Supported by:
    Major Program of National Social Science Foundation of China(19ZDA042).

Abstract: Semantic representation is a central challenge in natural language processing (NLP).Existing approaches can be broa-dly categorized into two paradigms:symbolic and connectionist methods.Although the latter have achieved remarkable practical success,they suffer from theoretical limitations-commonly referred to as the “compositionality crisis” in compositional modeling and semantic interpretability.In existing methods,categorical compositional distributional semantics provides a principled mathematical framework for unifying symbolic syntactic structure with distributed semantics via type-driven composition.From a categorical perspective,this paper surveys category-theoretic approaches to semantic representation along the conceptual line of “category theory-composition-quantum computation”.Unlike surveys organized by models or tasks,it focuses on semantic composition mechanisms,comparing sentence-level models from a compositional viewpoint,analyzing the limitations of distributed approaches,and outlining the theoretical shift toward compositional distributional semantics.Building on this,string diagram-based frameworks such as DisCoCat and DisCoCirc are presented,clarifying their formal properties and quantum extensions,offering a unified view of symbolic,connectionist,and quantum semantics.

Key words: Category theory, String diagrams, Compositional semantics, Quantum computing, Interpretability

CLC Number: 

  • B819
[1]MIKOLOV T,CHEN K,CORRADO G,et al.Efficient estimation of word representations in vector space[C]//Proceedings of the 1st International Conference on Learning Representations.2013.
[2]PENNINGTON J,SOCHER R,MANNING C D.GloVe:Global vectors for word representation[C]//Proceedings of the Conference on Empirical Methods in Natural Language Processing.2014:1532-1543.
[3]PETERS M E,NEUMANN M,IYYER M,et al.Deep contextualized word representations[C]//Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics:Human Language Technologies.2018:2227-2237.
[4]DEVLIN J,CHANG M W,LEE K,et al.BERT:Pre-training of deep bidirectional transformers for language understanding[C]//Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics:Human Language Technologies,2019:4171-4186.
[5]MITCHELL J,LAPATA M.Vector-based models of semantic composition[C]//Proceedings of ACL-08:Human Language Technologies.2008:236-244.
[6]BLACOE W,LAPATA M.A comparison of vector-based representations for semantic composition[C]//Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Lear-ning.2012:546-556.
[7]DE FELICE G.Categorical tools for natural language processing[J].arXiv:2212.06636,2022.
[8]TULL S,LORENZ R,CLARK S,et al.Towards compositional interpretability for XAI[J].arXiv:2406.17583,2024.
[9]LI R,ZHAO X,MO M F.A brief overview of universal sentence representation methods:A linguistic view[J].ACM Computing Surveys,2022,55(3):1-42.
[10]ARORA S,LIANG Y,MA T.A simple but tough-to-beat baseline for sentence embeddings[C]//Proceedings of the 5th International Conference on Learning Representations.2017.
[11]RÜCKLÉ A,EGER S,PEYRARD M,et al.Concatenated p-mean word embeddings as universal cross-lingual sentence representations[C]//Proceedings of the 2018 Conference.2018.
[12]LE Q V,MIKOLOV T.Distributed representations of sentences and documents[C]//Proceedings of the 31st International Conference on Machine Learning.2014:1188-1196.
[13]HILL F,CHO K,KORHONEN A.Learning distributed repre-sentations of sentences from unlabelled data[C]//Proceedings of the Conference of the North American Chapter of the Asso-ciation for Computational Linguistics:Human Language Techno-logies.2016:1367-1377.
[14]ZHANG M,WU Y,LI W K,et al.Learning universal sentence representations with mean-max attention autoencoder[C]//Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing.2018.
[15]CHEN Q,WANG W,ZHANG Q L,et al.Ditto:A simple and efficient approach to improve sentence embeddings[C]//Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing.2023.
[16]KIROS R,ZHU Y,SALAKHUTDINOV R,et al.Skip-thought vectors[C]//Proceedings of the Advances in Neural Information Processing Systems.2015.
[17]LOGESWARAN L,LEE H.An efficient framework for learning sentence representations[C]//Proceedings of the 6th International Conference on Learning Representations.2018.
[18]NIE A,BENNETT E D,GOODMAN N D.DisSent:Sentence representation learning from explicit discourse relations[C]//Proceedings of the 2017 Conference.2017.
[19]SILEO D,VAN DE CRUYS T,PRADEL C,et al.Mining discourse markers for unsupervised sentence representation lear-ning[C]//Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics:Human Language Technologies.2019:3477-3486.
[20]KIROS J,CHAN W.InferLite:Simple universal sentence representations from natural language inference data[C]//Procee-dings of the Conference on Empirical Methods in Natural Language Processing.2018.
[21]REIMERS N,GUREVYCH I.Sentence-BERT:Sentence em-beddings using siamese BERT-networks[C]//Proceedings of the Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing(EMNLP-IJCNLP).2019.
[22]JERNITE Y,BOWMAN S R,SONTAG D.Discourse-based objectives for fast unsupervised sentence representation learning[J].arXiv:1705.00557,2017.
[23]SUBRAMANIAN S,TRISCHLER A,BENGIO Y,et al.Lear-ning general purpose distributed sentence representations via large scale multi-task learning[C]//Proceedings of the 6th International Conference on Learning Representations.2018.
[24]CER D,YANG Y,KONG S Y,et al.Universal sentence encoder for English[C]//Proceedings of the Conference on Empirical Methods in Natural Language Processing.2018:169-174.
[25]SCHOPF T,SCHNEIDER D,MATTHES F.Efficient domainadaptation of sentence embeddings using adapters[J].arXiv:2307.03104,2023.
[26]SOCHER R,PERELYGIN A,WU J,et al.Recursive deep mo-dels for semantic compositionality over a sentiment treebank[C]//Proceedings of the Conference on Empirical Methods in Natural Language Processing.2013:1631-1642.
[27]TAI K S,SOCHER R,MANNING C D.Improved semantic representations from tree-structured long short-term memory networks[C]//Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7thInternatio-nal Joint Conference on Natural Language Processing.2015:1556-1566.
[28]GEHRING J,AULI M,GRANGIER D,et al.Convolutional sequence to sequence learning[C]//Proceedings of the 34th International Conference on Machine Learning.2017:1243-1252.
[29]COECKE B,SADRZADEH M,CLARK S.Mathematical foundations for a compositional distributional model of meaning[J].arXiv:1003.4394,2010.
[30]LAN Z,CHEN M,GOODMAN S,et al.ALBERT:A lite BERT for self-supervised learning of language representations[J].arXiv:1909.11942,2019.
[31]OPENAI.GPT-5 system card[EB/OL].https://openai.com/-index/gpt-5-system-card/.
[32]RUSSELL B.The principles of mathematics[M].London:Routledge,1903.
[33]AJDUKIEWICZ K.Die syntaktische Konnexität[J].StudiaPhilosophica,1935,1:1-27.
[34]BAR-HILLEL Y.Logical syntax and semantics[J].Language,1954,30(2):230.
[35]EILENBERG S,MAC LANE S.General theory of naturalequivalences[J].Transactions of the American Mathematical Society,1945,58:231-294.
[36]LAWVERE F W.Functorial semantics of algebraic theories[J].Proceedings of the National Academy of Sciences of the United States of America,1963,50(5):869-872.
[37]LAMBEK J.On the calculus of syntactic types[C]//Structure of Language and Its Mathematical Aspects.Providence:American Mathematical Society,1961:166-178.
[38]COECKE B,GREFENSTETTE E,SADRZADEH M.Lambekvs.Lambek:Functorial vector space semantics and string diagrams for Lambek calculus[J].Annals of Pure and Applied Logic,2013,164(11):1079-1100.
[39]JOYAL A,STREET R.The geometry of tensor calculus II[R].Unpublished manuscript,1995.
[40]KARTSAKLIS D,FAN I,YEUNG R,et al.Lambeq:An efficient high-level Python library for quantum NLP[J].arXiv:2110.04236,2021.
[41]DE FELICE G,DI LAVORE E,ROMÁN M,et al.Functorial language games for question answering[C]//Proceedings of the 3rd Annual International Applied Category Theory Conference(ACT 2020).2020:311-321.
[42]TOUMI A,DE FELICE G.Higher-order DisCoCat(Peirce-Lambek-Montague semantics)[J].arXiv:2311.17813,2023.
[43]ZENG W,COECKE B.Quantum algorithms for compositional natural language processing[J].Electronic Proceedings in Theo-retical Computer Science,2016,221:67-75.
[44]YEUNG R,KARTSAKLIS D.A CCG-based version of the DisCoCat framework[J].arXiv:2105.07720,2021.
[45]COECKE B.The mathematics of text structure[C]//The Interplay of Mathematics,Logic,and Linguistics.2021:181-217.
[46]WANG-MASCIANICA V,LIU J,COECKE B.Distilling textinto circuits[J].arXiv:2301.10595,2023.
[47]LAAKKONEN T,MEICHANETZIDIS K,COECKE B.Quantum algorithms for compositional text processing[J].Electronic Proceedings in Theoretical Computer Science,2024,406:162-196.
[48]LE DU S,HERNÁNDEZ SANTANA S,SCARPA G.A gentle introduction to quantum natural language processing[J].arXiv:2202.11766,2022.
[49]SORDONI A,NIE J Y,BENGIO Y.Modeling term dependen-cies with quantum language models for IR[C]//Proceedings of the 36th International ACM SIGIR Conference on Research and Development in Information Retrieval.2013:653-662.
[50]XIE M,HOU Y,ZHANG P,et al.Modeling quantum entanglements in quantum language models[C]//Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence.2015.
[51]LI Q,MELUCCI M,TIWARI P.Quantum language model-based query expansion[C]//Proceedings of the 2018 ACM SIGIR International Conference on Theory of Information Retrieval.2018:183-186.
[52]JIANG Y,ZHANG P,GAO H,et al.A quantum interference inspired neural matching model for ad-hoc retrieval[C]//Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval.2020:19-28.
[53]PASIN A,CUNHA W,GONÇALVES M A,et al.A quantum annealing instance selection approach for efficient and effective transformer fine-tuning[C]//Proceedings of the 2024 ACM SIGIR International Conference on Theory of Information Retrieval.2024:205-214.
[54]LI Q,WANG B,MELUCCI M.CNM:An interpretable com-plex-valued network for matching[C]//Proceedings of the Conference of the North American Chapter of the Association for Computational Linguistics:Human Language Technologies.2019:4139-4148.
[55]MANSKY B,WÖRLE F,STEIN J K,et al.Adapting the DisCoCat-model for question answering in the Chinese language[C]//Proceedings of the IEEE International Conference on Quantum Computing and Engineering.2023:591-600.
[56]DUNEAU T,BRUHN S,MATOS G,et al.Scalable and interpretable quantum natural language processing:An implementation on trapped ions[J].arXiv:2409.08777,2024.
[57]ZHANG P,ZHANG J,MA X,et al.TextTN:Probabilistic encoding of language on tensor network[C]//Proceedings of the International Conference on Learning Representations.2021.
[58]RUSKANDA F Z,ABIWARDANI M R,AL BARI M A,et al.Quantum representation for sentiment classification[C]//Proceedings of the IEEE International Conference on Quantum Computing and Engineering.2022:67-78.
[59]QU Z,MENG Y,MUHAMMAD G,et al.QMFND:A quantum multimodal fusion-based fake news detection model for social media[J].Information Fusion,2024,104:102172.
[60]MEICHANETZIDIS K,TOUMI A,DE FELICE G,et al.Grammar-aware question-answering on quantum computers[J].ar-Xiv:2012.03756,2020.
[61]MEICHANETZIDIS K,TOUMI A,DE FELICE G,et al.Grammar-aware sentence classification on quantum computers[J].Quantum Machine Intelligence,2023,5(1):10.
[62]NIETO V.Towards machine translation with quantum computers[D].Stockholm:University of Stockholm,2021.
[63]BRADLEY T,TERILLA J,VLASSOPOULOS Y.An enriched category theory of language:from syntax to semantics[J].La Matematica,2022,1(2):551-580.
[64]LIU J,SHAIKH R A,RODATZ B,et al.A pipeline for discourse circuits from CCG[J].arXiv:2311.17892,2023.
[65]LIU T,WEI Y,WANG J.Research on distributional compositional categorical model in both classical and quantum natural language processing[C]//Proceedings of the SNPD 2024.2024:1-6.
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