Semantic Geometry of Sentence Embeddings (2025)

Abstract: Sentence embeddings are central to modern natural language processing, powering tasks such as clustering, semantic search, and retrieval-augmented generation. Yet, they remain largely opaque: their internal features are not directly interpretable, and users lack fine-grained control for downstream tasks. To address this issue, we introduce a formal framework to characterize the organization of features in sentence embeddings through information-theoretic means. Building on this foundation, we develop a method to identify interpretable feature directions and show how they can be composed to capture richer semantic structures. Experiments on both synthetic and real-world datasets confirm the presence of this semantic geometry and highlight the utility of our approach for enhancing interpretability and fine-grained control in sentence embeddings.

## introduction sentence embeddings have become a cornerstone of modern ai applications and form the foundation for tasks involving sentence similarity and retrieval @xcite . they are essential to semantic search engines, power retrieval-augmented generation, and are core to a wide range of traditional natural language processing tasks, ranging from clustering to paraphrasing @xcite . yet, despite their ability to capture rich semantic relationships, tasks on sentence embeddings are typically reduced to a single scalar similarity score @xcite . this practice obscures the internal structure of embeddings: the features and components that drive similarity remain hidden. this limits both performance and interpretability. users lack fine-grained control over operations and cannot interpret why two sentences are considered similar or dissimilar. understanding this internal structure is not only key to improve performance on downstream tasks, but also to enhance transparency, safety, and alignment with human values @xcite . the internal structure of sentences has long been a central topic in semantics, with a focus on how meaning arises from constituent parts. at the core of this tradition is the principle of compositionality, which holds that the meaning of a sentence is a function of the meanings of its components and their syntactic combination @xcite . early approaches to sentence representations reflected this idea through additive or compositional models of features @xcite . more recently, distributional semantics has shifted this inquiry into vector spaces, where sentence embedding models capture emergent semantic structures consistent with hypotheses such as distributional inclusion @xcite . modern sentence embedding models have been based on transformer models, whose strength been the learning of intermediate representations, which encode deeper features @xcite . the complexity of these spaces however, as led to difficulties in identifying these features at scale @xcite . it is also not sure if these features are interpretable or map to compositional units which emerge as by-products of training. although a semantic geometry and organization of features has been clearly identified with word vectors, such as not yet been the case for sentences @xcite @xcite . in this paper, we propose a framework to characterize the semantic organisation of sentence representations and its interpretability. on this basis, we make the following contributions: ## background in this section, we provide background on modern sentence embedding models, their training and interpretability. ## the structure of sentence embeddings in the previous section, we saw how sentence representation models aimed at capturing semantic similarities. in the following section, we will study the emergent spaces that emerge from this objective. ## identifying features the previous section established that the pmi kernel induces a structured decomposition of sentence embeddings into latent features. we now turn to the problem of identifying these features in a tractable and interpretable way. ## experiments we now present experiments to empirically test the properties introduced above. our full code can be found on github, and the dataset can be accessed on hugging face. additional implementation details are provided in appendix b and further results in appendix c . ## discussion and conclusion a central insight of this work is that even simple operations, i.e. identifying a prototype of a feautre f , can reveal meaningful structure in sentence embeddings. our results suggest that sentence embeddings are not uniformly dispersed but rather organize into latent semantic regions, with meaningful ordering and overlap. if such structure can be identified reliably, it opens the door to scalable, per-model interpretability: semantic clusters could be extracted automatically, visualized on the hypersphere, and used to explain similarity, entailment, or category membership in embedding-based systems. understanding the internal geometry of sentence embeddings is critical for modern information retrieval and nlp pipelines, particularly as ai-augmented applications, such as semantic search, retrieval-augmented generation, and recommendation, where safety and ethical applications. are paramount. the uncovered representational geometry could also be relevant across other disciplines. it notably bears a striking resemblance to cognitive theories of similarity, reflecting tversky's work on feature-based similarity @xcite or conceptual spaces @xcite @xcite .