Category-Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics

Edward Grefenstette

Home/Archive/arXiv

arXiv · 1311.1539

Category-Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics

Edward Grefenstette

View original source ↗Read source document ↗Export metadata ↓

Abstract

This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over these contexts and represents them as vectors in high dimensional spaces. The problem of compositionality for such models concerns itself with how to produce representations for larger units of text by composing the representations of smaller units of text. This thesis focuses on a particular approach to this compositionality problem, namely using the categorical framework developed by Coecke, Sadrzadeh, and Clark, which combines syntactic analysis formalisms with distributional semantic representations of meaning to produce syntactically motivated composition operations. This thesis shows how this approach can be theoretically extended and practically implemented to produce concrete compositional distributional models of natural language semantics. It furthermore demonstrates that such models can perform on par with, or better than, other competing approaches in the field of natural language processing. There are three principal contributions to computational linguistics in this thesis. The first is to extend the DisCoCat framework on the syntactic front and semantic front, incorporating a number of syntactic analysis formalisms and providing learning procedures allowing for the generation of concrete compositional distributional models. The second contribution is to evaluate the models developed from the procedures presented here, showing that they outperform other compositional distributional models present in the literature. The third contribution is to show how using category theory to solve linguistic problems forms a sound basis for research, illustrated by examples of work on this topic, that also suggest directions for future research.

Explore related subjects

cs.CL cs.LG math.CT math.LO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Edward Grefenstette. 2013-11-06. Category-Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics. https://arxiv.org/abs/1311.1539

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

SafetyFlow: An Agent-Flow System for Automated LLM Safety Benchmarking

The rapid proliferation of large language models (LLMs) has intensified the requirement for reliable safety evaluation to uncover model vulnerabilities. To this end, numerous LLM safety evaluation benchmarks are proposed. However, existing benchmarks generally rely on labor-intensive manual curation, which causes excessive time and resource consumption. They also exhibit significant redundancy and limited difficulty. To alleviate these problems, we introduce SafetyFlow, the first agent-flow system designed to automate the construction of LLM safety benchmarks. SafetyFlow can automatically build a comprehensive safety benchmark in only four days without any human intervention by orchestrating seven specialized agents, significantly reducing time and resource cost. Equipped with versatile tools, the agents of SafetyFlow ensure process and cost controllability while integrating human expertise into the automatic pipeline. The final constructed dataset, SafetyFlowBench, contains 23,446 queries with low redundancy and strong discriminative power. Our contribution includes the first fully automated benchmarking pipeline and a comprehensive safety benchmark. We evaluate the safety of 49 advanced LLMs on our dataset and conduct extensive experiments to validate our efficacy and efficiency.

cs.CL↗

arXiv2026

Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs

Large language models are known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy to detect such behaviour, but existing methods lack a unified framework to assess reliability at both the prompt and answer level. We introduce a geometric framework which quantifies language model uncertainty at both levels by explicitly modelling a prompt-conditioned semantic distribution in answer embedding space. Our approach is black-box and sampling-based; we generate multiple answers per prompt, and use archetypal analysis to estimate a geometric support for the answer distribution. At the prompt level, we approximate the distribution entropy to quantify uncertainty; for each individual answer, we then use notions of atypicality to assess its reliability relative to the batch. We employ our framework to not only detect hallucinations but correct them, by selecting the batch example deemed most reliable. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. Beyond pure performance, we suggest the theoretical grounding of our work provides support for semantic distributions as useful objects of study for language model uncertainty.

cs.CL↗

arXiv2026

Calibrated Confidence Expression for Radiology Report Generation

Safe deployment of Large Vision-Language Models (LVLMs) in radiology report generation requires not only accurate predictions but also clinically interpretable indicators of when outputs should be thoroughly reviewed, enabling selective radiologist verification and reducing the risk of hallucinated findings influencing clinical decisions. One intuitive approach to this is verbalized confidence, where the model explicitly states its certainty. However, current state-of-the-art language models are often overconfident, and research on calibration in multimodal settings such as radiology report generation is limited. To address this gap, we introduce ConRad (Confidence Calibration for Radiology Reports), a reinforcement learning framework for fine-tuning medical LVLMs to produce calibrated verbalized confidence estimates alongside radiology reports. We study two settings: a single report-level confidence score and a sentence-level variant assigning a confidence to each claim. Both are trained using the GRPO algorithm with reward functions based on the logarithmic scoring rule, which incentivizes truthful self-assessment by penalizing miscalibration and guarantees optimal calibration under reward maximization. Experimentally, ConRad substantially improves calibration and outperforms competing methods. In a clinical evaluation we show that ConRad's report level scores are well aligned with clinicians' judgment. By highlighting full reports or low-confidence statements for targeted review, ConRad can support safer clinical integration of AI-assistance for report generation.

cs.CL↗