Text Embeddings

Matryoshka Representation Learning (MRL) is a widely adopted approach for training text encoders so they provide useful text representations at various sizes, available by simply truncating the resulting vectors at sizes pre-determined at training time. Recent works have shown that randomly truncating text embeddings has minimal impact in downstream performance unless vectors are reduced in size by at least 70%, suggesting that embeddings are already robust to truncation without the use of MRL. However, no prior work has compared random truncation to MRL, so it is unclear how the two methods compare as effective embedding reduction methods. In this paper, we study this by applying the same truncation used by MRL to models trained with and without MRL. Our results across several models and downstream tasks show that, unless heavily truncating embeddings (i.e. reducing their size by at least 80%), truncated embeddings of non-MRL models are competitive with, and often outperform models trained with MRL. This suggests that truncation robustness may not necessarily come from MRL, and that the choice of spending the additional training cost of MRL depends on whether heavy truncation is desired. We make our code available for reproduction.

The development of high-quality text embeddings is increasingly drifting toward an exclusionary future, defined by three critical barriers: prohibitive computational costs, a narrow linguistic focus that neglects most of the world's languages, and a lack of transparency from closed-source or open-weight models that stifles research. To dismantle these barriers, we introduce ML-Embed, a suite of inclusive and efficient models built upon a new framework: 3-Dimensional Matryoshka Learning (3D-ML). Our framework addresses the computational challenge with comprehensive efficiency across the entire model lifecycle. Beyond the storage benefits of Matryoshka Representation Learning (MRL) and flexible inference-time depth provided by Matryoshka Layer Learning (MLL), we introduce Matryoshka Embedding Learning (MEL) for enhanced parameter efficiency. To address the linguistic challenge, we curate a massively multilingual dataset and train a suite of models ranging from 140M to 8B parameters. In a direct commitment to transparency, we release all models, data, and code. Extensive evaluation on 430 tasks demonstrates that our models set new records on 9 of 17 evaluated MTEB benchmarks, with particularly strong results in low-resource languages, providing a reproducible blueprint for building globally equitable and computationally efficient AI systems.

Hidden states change substantially across the layers of modern language models, but most layer-wise analyses focus on one aspect of that change. We propose Layer-wise Representation Dynamics (LRD), a framework with three layer-wise measurement families: Frenet (Grassmann speed and curvature) for global subspace motion, Neighborhood Retention Score (NRS) for local nearest-neighbor retention, and Graph Filtration Mutual Information (GFMI) for alignment with the final layer. Applying LRD to 31 models (encoder-based and decoder-based embedders, plus base LLMs) on 30 MTEB tasks reveals architectural and task-level differences that are not apparent from final-layer representations alone. We then use LRD for two applications: label-free model selection and inference-time layer pruning. For selection, all three model-level scores correlate positively with downstream MTEB performance, with end-to-end subspace displacement (d_{0,L}) the strongest, and the same direction holds on a smaller base-LLM MMLU panel. For pruning, GFMI is the only measurement-guided rule that beats Random at the 15% and 20% budgets and has the best median change at every budget. Frenet is effective only at the lightest budget, while NRS does not transfer from model selection to pruning. These results show that layer-wise structure provides signal for both interpretation and deployment decisions.

Large language models (LLMs) can convincingly imitate human writing styles, yet it remains unclear how much stylistic information is encoded in embeddings from any language model and retained after LLM rewriting. We investigate these questions in French, using a controlled literary dataset to quantify the effect of stylistic variation via changes in embedding dispersion. We observe that embeddings reliably capture authorial stylistic features and that these signals persist after rewriting, while also exhibiting LLM-specific patterns. These analytical results offer promising directions for authorship imitation detection in the era of language models.

Modern AI is opening the door to collective decision-making in which participants express their views as free-form text rather than voting on a fixed set of candidates. A natural idea is to embed these opinions in a vector space so that the substantial literature on facility location problems and fair clustering can be brought to bear. But standard text embeddings measure semantic similarity, whereas distances in facility location problems and fair clustering require what we call \textit{preferential similarity}: a participant's agreement with a piece of text should be inversely related to their distance from it. Off-the-shelf embeddings inherit a coarse preference signal through a correlation between semantic and preferential similarity, but fail to capture preferences when the correlation breaks. We formalize this as an invariance problem: text embedding models encode both a preference-relevant signal (stance and values) and semantic nuisance (style and wording), and the two are observationally correlated, so a geometry that relies on nuisance can appear preference-correct even when it is not. We show that synthetic training data designed to break this correlation provably shifts the optimal scorer away from nuisance-dominated cosine and significantly improves preference prediction across 11 online deliberation datasets.

Natural Language Processing is rapidly evolving into a primary instrument for Computational Social Science, with researchers increasingly using embeddings to measure latent constructs such as novelty, creativity, and bias. However, this transition faces a fundamental validity challenge: the ''Proxy Presumption,'' or the reliance on geometric properties (e.g., cosine distance) as direct measures of social concepts. We argue that without explicit validation, unsupervised representations remain entangled mixtures of the target construct ($C$) and confounding attributes ($Z$) like topic, style, and authorship. To bridge the gap between semantic embeddings and valid social measures, we introduce the Construct Validity Protocol (CVP). Drawing on causal representation learning and psychometrics, the CVP offers a rigorous pipeline from conceptualization to quantitative verification. We further propose Counterfactual Neutralization, a novel method using LLMs to reduce confounding in embedding space. By providing a standardized Validity Suite -- including tests for discriminant, incremental, and predictive validity -- this work offers the community a toolkit to transform heuristic proxies into robust, scientifically defensible instruments.

Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode semantic intent indirectly through geometric constraints or model updates, limiting interpretability and flexibility. We introduce LLM-augmented semantic steering, which enables analysts to express semantic intent by grouping a small set of example documents within the projection. A large language model externalizes this intent as natural-language representations and selectively extends it to related documents; the resulting semantic information is then incorporated into document representations via text augmentation or embedding-level blending, without retraining the underlying models. A case study illustrates how the same corpus can be reorganized from different semantic perspectives, while simulation-based evaluation shows that semantic steering improves global and local alignment with target semantic structures using only minimal interaction. Embedding-level blending further enables continuous and controllable steering of projection layouts. These results position projection spaces as intent-dependent semantic workspaces that can be reshaped through explicit, interpretable, language-mediated interaction.

Large language models (LLMs) have been widely explored for embedding generation. While recent studies show that in-context learning (ICL) effectively enhances the representational capability of LLMs by prepending a few task-related demonstrations, it causes substantial token overhead due to the increased sequence length. In this work, we propose EPIC, a novel embedding-based in-context prompt training strategy that leverages ICL to generate high-quality embeddings while reducing computational burden during both training and inference. This approach replaces discrete text demonstrations with their corresponding continuous embeddings, which not only encourages the LLM to align semantically-related text pairs during contrastive learning, but also requires the model to interpret demonstration embeddings as part of the in-context prompt. Consequently, EPIC-trained models achieve excellent embedding performance both with or without in-context prompts at inference time. Comprehensive experiments demonstrate that our method establishes new state-of-the-art results on the MTEB benchmark, surpassing frontier models trained solely on publicly available retrieval data. Extensive ablation studies further validate the effectiveness and necessity of our mechanism.

For constructing text embeddings, mean pooling, which averages token embeddings, is the standard approach. This paper examines whether mean pooling actually works well in real models. First, we note that mean pooling can collapse information beyond the first-order statistics of the token embeddings, such as second-order statistics that capture their spatial structure, potentially mapping distinct token embedding distributions to similar text embeddings. Motivated by this concern, we propose a simple metric to quantify such a collapse induced by mean pooling. Then, using this metric, we empirically measure how often this collapse occurs in actual models and texts, and find that modern text encoders are robust to this collapse. In particular, contrastive fine-tuned text encoders tend to be less prone to the collapse than their pretrained backbone models. We also find that the robustness of these text encoders lies in the concentration of token embeddings within each text. In addition, we find that robustness to the collapse, as quantified by our proposed metric, correlates with downstream task performance. Overall, our findings offer a new perspective on why modern text encoders remain effective despite relying on seemingly coarse mean pooling.

Word embeddings are fundamental to natural language processing, yet traditional approaches represent each word with a single vector, creating representational bottlenecks for polysemous words and limiting semantic expressiveness. While multi-anchor representations have shown promise by representing words as combinations of multiple vectors, they have been limited to small-scale models due to computational inefficiency and lack of integration with modern transformer architectures. We introduce Adaptive Dictionary Embeddings (ADE), a framework that successfully scales multi-anchor word representations to large language models. ADE makes three key contributions: (1) Vocabulary Projection (VP), which transforms the costly two-stage anchor lookup into a single efficient matrix operation; (2) Grouped Positional Encoding (GPE), a novel positional encoding scheme where anchors of the same word share positional information, preserving semantic coherence while enabling anchor-level variation; and (3) context-aware anchor reweighting, which leverages self-attention to dynamically compose anchor contributions based on sequence context. We integrate these components into the Segment-Aware Transformer (SAT), which provides context-aware reweighting of anchor contributions at inference time. We evaluate ADE on AG News and DBpedia-14 text classification benchmarks. With 98.7% fewer trainable parameters than DeBERTa-v3-base, ADE surpasses DeBERTa on DBpedia-14 (98.06% vs. 97.80%) and approaches it on AG News (90.64% vs. 94.50%), while compressing the embedding layer over 40x -- demonstrating that multi-anchor representations are a practical and parameter-efficient alternative to single-vector embeddings in modern transformer architectures.

Retrieval-Augmented Generation (RAG) systems depend on the geometric properties of vector representations to retrieve contextually appropriate evidence. When source documents interleave multiple topics within contiguous text, standard vectorization produces embedding spaces in which semantically distinct content occupies overlapping neighborhoods. We term this condition semantic entanglement. We formalize entanglement as a model-relative measure of cross-topic overlap in embedding space and define an Entanglement Index (EI) as a quantitative proxy. We argue that higher EI constrains attainable Top-K retrieval precision under cosine similarity retrieval. To address this, we introduce the Semantic Disentanglement Pipeline (SDP), a four-stage preprocessing framework that restructures documents prior to embedding. We further propose context-conditioned preprocessing, in which document structure is shaped by patterns of operational use, and a continuous feedback mechanism that adapts document structure based on agent performance. We evaluate SDP on a real-world enterprise healthcare knowledge base comprising over 2,000 documents across approximately 25 sub-domains. Top-K retrieval precision improves from approximately 32% under fixed-token chunking to approximately 82% under SDP, while mean EI decreases from 0.71 to 0.14. We do not claim that entanglement fully explains RAG failure, but that it captures a distinct preprocessing failure mode that downstream optimization cannot reliably correct once encoded into the vector space.

Recent text embedding models are often adapted to specialized domains via contrastive pre-finetuning (PFT) on a naive collection of scattered, heterogeneous tasks. However, this approach often introduces task-induced bias alongside domain knowledge, leading to uncontrolled representation shifts that distort the pretrained embedding geometry and cause substantial performance degradation. To address this issue, we propose REZE, a representation regularization framework that explicitly controls representation shift during embedding pre-finetuning. REZE operates on the relations of anchor-positive pairs and decomposes them in an eigenspace. It then measures task-wise dispersion along each eigencomponent to identify task-variant directions and applies adaptive soft-shrinkage to suppress task-induced noise while preserving task-invariant semantic structure, without inference-time overhead. Experiments across multiple embedding backbones and specialized benchmarks show that REZE outperforms standard pre-finetuning and isotropy-oriented post-hoc regularization in most settings, remaining stable where existing PFT variants collapse. Embedding space analyses further confirm that REZE induces controlled shifts aligned with the original embedding manifold, underscoring representation shift control as a key principle for robust embedding pre-finetuning under heterogeneous supervision.

While dense biomedical embeddings achieve strong performance, their opaque dimensions limit transparency in biomedical NLP. Recent question-based interpretable embeddings represent text through binary answers to natural-language questions, but existing approaches rely primarily on corpus-driven signals, often capturing topical or stylistic differences rather than fine-grained biomedical distinctions. We propose QIME, an ontology-grounded framework for interpretable biomedical text embeddings in which each dimension corresponds to an explicit biomedical-domain yes/no question. QIME leverages a biomedical ontology to guide contrastive question generation from semantic clusters, producing atomic, domain-grounded questions. It constructs embeddings via similarity-based semantic activation with MMR-based diversity-aware dimension selection, yielding sparse representations efficiently. Experiments on biomedical clustering, STS and retrieval benchmarks show that QIME consistently outperforms prior interpretable embedding methods and substantially narrows the gap to strong black-box biomedical encoders. It also imposes substantially lower cognitive burden than existing methods, providing concise and domain-specific interpretations. The code is available at https://github.com/L1nzh/QIME.

Financial text embeddings must distinguish changes in event status, perspective, and obligations even when passages share similar wording. NMIXX adapts existing encoders through 18.8k source-linked triplets: paraphrases and Korean-English translations preserve meaning, while targeted financial rewrites introduce semantic contrasts. We examine this recipe across seven backbones on English and Korean financial and general-domain semantic textual similarity (STS), and analyze the composition and passage lengths of KorFinSTS. BGE-M3 attains the highest adapted financial correlations in this comparison, improving from 0.1969 to 0.2967 on FinSTS and from 0.0512 to 0.2732 on KorFinSTS. Its general English and Korean correlations decrease by 0.0391 and 0.0463. Across the seven models, five improve their mean financial correlation, but all reduce their mean general-domain correlation. Per-language comparisons and benchmark-weight sensitivity analysis reveal differences obscured by a single aggregate score. The study contributes a finance-specific supervision design and evidence for evaluating adaptation jointly with retained general semantic capability; direct cross-language retrieval remains outside its evaluation scope.

FastText remains a practical choice for industrial word representation because it can synthesize vectors for out-of-vocabulary words from character n-grams. Its original hash-bucket implementation, however, couples two engineering compromises that become painful at large scale: unrelated n-grams collide into the same row, while increasing the bucket count quickly turns the input matrix into the dominant memory cost. This paper presents a memory-efficient FastText variant based on an exact-then-compress principle: first give every observed word and n-gram an explicit identity, then compress only those rows whose learned vectors and lexical structure justify sharing. Concretely, we replace hash buckets with collision-free double-array trie indexes and compress the resulting n-gram matrix through structurally constrained prefix and suffix merging followed by mark-compact row reorganization. Unlike arbitrary hashing, the proposed method shares rows only after a high cosine-similarity test, preserving interpretable n-gram identities while reducing the number of live rows. We describe the full training and serving pipeline, including UTF-8 aware n-gram enumeration, double-array trie lookup, memory-mapped model loading, and vector reconstruction for words and sentences. On a large Chinese vocabulary benchmark with 30.1M words and 287.4M extracted n-grams, the compressed model reduces memory from 145.2GB to 28.9GB, improves load time from 12.3 minutes to 3.2 minutes, and preserves downstream quality within 0.3 points of a hash-free model. We position the result as a compact lexical memory layer for LLM-era retrieval systems and release the implementation as an extended FastText prototype.