Embedding models, which transform inputs into dense vector representations, are pivotal for capturing semantic information across various domains and modalities. Text embedding models represent words and sentences as vectors, strategically positioning semantically similar texts in close proximity within the embedding space (Gao et al., 2021; Le and Mikolov, 2014; Reimers and Gurevych, 2019). Recent research has focused on developing general-purpose embedding models capable of excelling in diverse downstream tasks, including information retrieval, clustering, and classification (Cer et al., 2018; Muennighoff et al., 2023). Leveraging their vast pre-training knowledge, large language models (LLMs) have emerged as a promising avenue for constructing such general-purpose embedding models, with the potential to significantly enhance performance across a broad spectrum of applications (Anil et al., 2023a,b; Brown et al., 2020). The integration of LLMs has revolutionized the development of high-quality embedding models through two primary approaches. Firstly, LLMs have been employed to refine training datasets by generating higher quality examples. Techniques such as hard negative mining (Lee et al., 2024) and synthetic data generation (Dai et al., 2022; Wang et al., 2023) enable the distillation of LLM knowledge into smaller, more efficient embedding models, leading to substantial performance gains. Secondly, recognizing that the embedding model parameters are frequently initialized from language models (Devlin et al., 2019; Karpukhin et al., 2020), researchers have explored leveraging LLM parameters directly for initialization (Ni et al., 2021).

Personalized item recommendation typically suffers from data sparsity, which is most often addressed by learning vector representations of users and items via low-rank matrix factorization. While this effectively densifies the matrix by assuming users and movies can be represented by linearly dependent latent features, it does not capture more complicated interactions. For example, vector representations struggle with set-theoretic relationships, such as negation and intersection, e.g. recommending a movie that is "comedy and action, but not romance". In this work, we formulate the problem of personalized item recommendation as matrix completion where rows are set-theoretically dependent. To capture this set-theoretic dependence we represent each user and attribute by a hyper-rectangle or box (i.e. a Cartesian product of intervals). Box embeddings can intuitively be understood as trainable Venn diagrams, and thus not only inherently represent similarity (via the Jaccard index), but also naturally and faithfully support arbitrary set-theoretic relationships. Queries involving set-theoretic constraints can be efficiently computed directly on the embedding space by performing geometric operations on the representations. We empirically demonstrate the superiority of box embeddings over vector-based neural methods on both simple and complex item recommendation queries by up to 30 \% overall.

Long-context language models (LCLMs) have the potential to revolutionize our approach to tasks traditionally reliant on external tools like retrieval systems or databases. Leveraging LCLMs' ability to natively ingest and process entire corpora of information offers numerous advantages. It enhances user-friendliness by eliminating the need for specialized knowledge of tools, provides robust end-to-end modeling that minimizes cascading errors in complex pipelines, and allows for the application of sophisticated prompting techniques across the entire system. To assess this paradigm shift, we introduce LOFT, a benchmark of real-world tasks requiring context up to millions of tokens designed to evaluate LCLMs' performance on in-context retrieval and reasoning. Our findings reveal LCLMs' surprising ability to rival state-of-the-art retrieval and RAG systems, despite never having been explicitly trained for these tasks. However, LCLMs still face challenges in areas like compositional reasoning that are required in SQL-like tasks. Notably, prompting strategies significantly influence performance, emphasizing the need for continued research as context lengths grow. Overall, LOFT provides a rigorous testing ground for LCLMs, showcasing their potential to supplant existing paradigms and tackle novel tasks as model capabilities scale.

Text embedding models represent natural language as dense vectors, positioning semantically similar text near each other within the embedding space (Gao et al., 2021; Le and Mikolov, 2014; Reimers and Gurevych, 2019). These embeddings are commonly used for a wide range of downstream tasks including document retrieval, sentence similarity, classification, and clustering (Muennighoff et al., 2023). Instead of building separate embedding models for each downstream task, recent efforts seek to create a single embedding model supporting many tasks. The recent development of general-purpose text embedding models presents a challenge: these models require large amounts of training data to comprehensively cover desired domains and skills. Recent embedding efforts have focused on using extensive collections of training examples (Li et al., 2023; Wang et al., 2022).

Learning vector representations for words is one of the most fundamental topics in NLP, capable of capturing syntactic and semantic relationships useful in a variety of downstream NLP tasks. Vector representations can be limiting, however, in that typical scoring such as dot product similarity intertwines position and magnitude of the vector in space. Exciting innovations in the space of representation learning have proposed alternative fundamental representations, such as distributions, hyperbolic vectors, or regions. Our model, Word2Box, takes a region-based approach to the problem of word representation, representing words as $n$-dimensional rectangles. These representations encode position and breadth independently and provide additional geometric operations such as intersection and containment which allow them to model co-occurrence patterns vectors struggle with. We demonstrate improved performance on various word similarity tasks, particularly on less common words, and perform a qualitative analysis exploring the additional unique expressivity provided by Word2Box.

Knowledge bases often consist of facts which are harvested from a variety of sources, many of which are noisy and some of which conflict, resulting in a level of uncertainty for each triple. Knowledge bases are also often incomplete, prompting the use of embedding methods to generalize from known facts, however, existing embedding methods only model triple-level uncertainty, and reasoning results lack global consistency. To address these shortcomings, we propose BEUrRE, a novel uncertain knowledge graph embedding method with calibrated probabilistic semantics. BEUrRE models each entity as a box (i.e. axis-aligned hyperrectangle) and relations between two entities as affine transforms on the head and tail entity boxes. The geometry of the boxes allows for efficient calculation of intersections and volumes, endowing the model with calibrated probabilistic semantics and facilitating the incorporation of relational constraints. Extensive experiments on two benchmark datasets show that BEUrRE consistently outperforms baselines on confidence prediction and fact ranking due to its probabilistic calibration and ability to capture high-order dependencies among facts.

Neural entity typing models typically represent entity types as vectors in a high-dimensional space, but such spaces are not well-suited to modeling these types' complex interdependencies. We study the ability of box embeddings, which represent entity types as d-dimensional hyperrectangles, to represent hierarchies of fine-grained entity type labels even when these relationships are not defined explicitly in the ontology. Our model represents both types and entity mentions as boxes. Each mention and its context are fed into a BERT-based model to embed that mention in our box space; essentially, this model leverages typological clues present in the surface text to hypothesize a type representation for the mention. Soft box containment can then be used to derive probabilities, both the posterior probability of a mention exhibiting a given type and the conditional probability relations between types themselves. We compare our approach with a strong vector-based typing model, and observe state-of-the-art performance on several entity typing benchmarks. In addition to competitive typing performance, our box-based model shows better performance in prediction consistency (predicting a supertype and a subtype together) and confidence (i.e., calibration), implying that the box-based model captures the latent type hierarchies better than the vector-based model does.

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly promising example of such an embedding as they are closed under intersection and their volume can be calculated easily, allowing them to naturally represent calibrated probability distributions. The benefits of geometric embeddings also introduce a problem of local identifiability, however, where whole neighborhoods of parameters result in equivalent loss which impedes learning. Prior work addressed some of these issues by using an approximation to Gaussian convolution over the box parameters, however, this intersection operation also increases the sparsity of the gradient. In this work, we model the box parameters with min and max Gumbel distributions, which were chosen such that space is still closed under the operation of the intersection. The calculation of the expected intersection volume involves all parameters, and we demonstrate experimentally that this drastically improves the ability of such models to learn.

The recent work of Clark et al. introduces the AI2 Reasoning Challenge (ARC) and the associated ARC dataset that partitions open domain, complex science questions into an Easy Set and a Challenge Set. That paper includes an analysis of 100 questions with respect to the types of knowledge and reasoning required to answer them; however, it does not include clear definitions of these types, nor does it offer information about the quality of the labels. We propose a comprehensive set of definitions of knowledge and reasoning types necessary for answering the questions in the ARC dataset. Using ten annotators and a sophisticated annotation interface, we analyze the distribution of labels across the Challenge Set and statistics related to them. Additionally, we demonstrate that although naive information retrieval methods return sentences that are irrelevant to answering the query, sufficient supporting text is often present in the (ARC) corpus. Evaluating with human-selected relevant sentences improves the performance of a neural machine comprehension model by 42 points.