Daily Papers

Alchemical relative binding free energy (RBFE) calculations are limited by the fixed-charge approximation of classical force fields. Hybrid machine learning interatomic potential/molecular mechanics (MLIP/MM) schemes correct ligand strain, but under mechanical embedding still describe ligand--environment electrostatics with static point charges. Electrostatic embedding schemes coupling machine-learned charges to the MM environment have been proposed and validated against QM/MM for simple systems, but not tested in a production alchemical workflow. We take the electrostatic embedding scheme of Semelak et al.\ and evaluate it on protein--ligand RBFE. We trained a TensorNet2 model, AceFF-2-RESP-1, on 10^{6} conformations from the AceFF dataset, jointly predicting energies, forces and Restrained Electrostatic Potential (RESP) charges. We chose RESP over MBIS for commensurability with the AMBER-family force field it couples to. The predicted charges enter the short-range direct-space part of the particle mesh Ewald sum, with Thole damping to prevent polarization catastrophes during alchemical transformations. We tested the scheme across five targets from the Wang et al.\ benchmark set, fixed in advance by a prior study, with three replicates per edge and matched protocols. Electrostatic embedding improved every accuracy and correlation metric for TYK2 (ΔΔG RMSE 0.86 rightarrow 0.45~kcal/mol against GAFF2), but performed comparably to the classical and mechanical-embedding baselines for CDK2, thrombin, p38 and JNK1. Standard single-molecule energy and charge benchmarks were not good predictors of this target-dependent outcome. TYK2 combined good ΔΔG accuracy with the lowest force error on the Schrödinger benchmark, but this pattern did not hold for the other targets.

Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range electrostatic effects. We present a new electrostatic foundation model for molecular chemistry that extends the MACE architecture with explicit treatment of long-range interactions and electrostatic induction. Our approach combines local many-body geometric features with a non-self-consistent field formalism that updates learnable charge and spin densities through polarisable iterations to model induction, followed by global charge equilibration via learnable Fukui functions to control total charge and total spin. This design enables an accurate and physical description of systems with varying charge and spin states while maintaining computational efficiency. Trained on the OMol25 dataset of 100 million hybrid DFT calculations, our models achieve chemical accuracy across diverse benchmarks, with accuracy competitive with hybrid DFT on thermochemistry, reaction barriers, conformational energies, and transition metal complexes. Notably, we demonstrate that the inclusion of long-range electrostatics leads to a large improvement in the description of non-covalent interactions and supramolecular complexes over non-electrostatic models, including sub-kcal/mol prediction of molecular crystal formation energy in the X23-DMC dataset and a fourfold improvement over short-ranged models on protein-ligand interactions. The model's ability to handle variable charge and spin states, respond to external fields, provide interpretable spin-resolved charge densities, and maintain accuracy from small molecules to protein-ligand complexes positions it as a versatile tool for computational molecular chemistry and drug discovery.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

Text embeddings are useful features in many applications such as semantic search and computing text similarity. Previous work typically trains models customized for different use cases, varying in dataset choice, training objective and model architecture. In this work, we show that contrastive pre-training on unsupervised data at scale leads to high quality vector representations of text and code. The same unsupervised text embeddings that achieve new state-of-the-art results in linear-probe classification also display impressive semantic search capabilities and sometimes even perform competitively with fine-tuned models. On linear-probe classification accuracy averaging over 7 tasks, our best unsupervised model achieves a relative improvement of 4% and 1.8% over previous best unsupervised and supervised text embedding models respectively. The same text embeddings when evaluated on large-scale semantic search attains a relative improvement of 23.4%, 14.7%, and 10.6% over previous best unsupervised methods on MSMARCO, Natural Questions and TriviaQA benchmarks, respectively. Similarly to text embeddings, we train code embedding models on (text, code) pairs, obtaining a 20.8% relative improvement over prior best work on code search.

We introduce the first method for translating text embeddings from one vector space to another without any paired data, encoders, or predefined sets of matches. Our unsupervised approach translates any embedding to and from a universal latent representation (i.e., a universal semantic structure conjectured by the Platonic Representation Hypothesis). Our translations achieve high cosine similarity across model pairs with different architectures, parameter counts, and training datasets. The ability to translate unknown embeddings into a different space while preserving their geometry has serious implications for the security of vector databases. An adversary with access only to embedding vectors can extract sensitive information about the underlying documents, sufficient for classification and attribute inference.

Recently, Transformer-like deep architectures have shown strong performance on tabular data problems. Unlike traditional models, e.g., MLP, these architectures map scalar values of numerical features to high-dimensional embeddings before mixing them in the main backbone. In this work, we argue that embeddings for numerical features are an underexplored degree of freedom in tabular DL, which allows constructing more powerful DL models and competing with GBDT on some traditionally GBDT-friendly benchmarks. We start by describing two conceptually different approaches to building embedding modules: the first one is based on a piecewise linear encoding of scalar values, and the second one utilizes periodic activations. Then, we empirically demonstrate that these two approaches can lead to significant performance boosts compared to the embeddings based on conventional blocks such as linear layers and ReLU activations. Importantly, we also show that embedding numerical features is beneficial for many backbones, not only for Transformers. Specifically, after proper embeddings, simple MLP-like models can perform on par with the attention-based architectures. Overall, we highlight embeddings for numerical features as an important design aspect with good potential for further improvements in tabular DL.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

We introduce EmbeddingGemma, a new lightweight, open text embedding model based on the Gemma 3 language model family. Our innovative training recipe strategically captures knowledge from larger models via encoder-decoder initialization and geometric embedding distillation. We improve model robustness and expressiveness with a spread-out regularizer, and ensure generalizability by merging checkpoints from varied, optimized mixtures. Evaluated on the Massive Text Embedding Benchmark (MTEB) across multilingual, English, and code domains, EmbeddingGemma (300M) achieves state-of-the-art results. Notably, it outperforms prior top models, both proprietary and open, with fewer than 500M parameters, and provides performance comparable to models double its size, offering an exceptional performance-to-cost ratio. Remarkably, this lead persists when quantizing model weights or truncating embedding outputs. This makes EmbeddingGemma particularly well-suited for low-latency and high-throughput use cases such as on-device applications. We provide ablation studies exploring our key design choices. We release EmbeddingGemma to the community to promote further research.

A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons for their benefits, especially when used in combination. Here we treat the embeddings of images as point particles and consider model optimization as a dynamic process on this system of particles. Our dynamic model combines an attractive force for similar images, a locally dispersive force to avoid local collapse, and a global dispersive force to achieve a globally-homogeneous distribution of particles. The dynamic perspective highlights the advantage of using a delayed-parameter image embedding (a la BYOL) together with multiple views of the same image. It also uses a purely-dynamic local dispersive force (Brownian motion) that shows improved performance over other methods and does not require knowledge of other particle coordinates. The method is called MSBReg which stands for (i) a Multiview centroid loss, which applies an attractive force to pull different image view embeddings toward their centroid, (ii) a Singular value loss, which pushes the particle system toward spatially homogeneous density, (iii) a Brownian diffusive loss. We evaluate downstream classification performance of MSBReg on ImageNet as well as transfer learning tasks including fine-grained classification, multi-class object classification, object detection, and instance segmentation. In addition, we also show that applying our regularization term to other methods further improves their performance and stabilize the training by preventing a mode collapse.

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs.

Text autoencoders are often used for unsupervised conditional text generation by applying mappings in the latent space to change attributes to the desired values. Recently, Mai et al. (2020) proposed Emb2Emb, a method to learn these mappings in the embedding space of an autoencoder. However, their method is restricted to autoencoders with a single-vector embedding, which limits how much information can be retained. We address this issue by extending their method to Bag-of-Vectors Autoencoders (BoV-AEs), which encode the text into a variable-size bag of vectors that grows with the size of the text, as in attention-based models. This allows to encode and reconstruct much longer texts than standard autoencoders. Analogous to conventional autoencoders, we propose regularization techniques that facilitate learning meaningful operations in the latent space. Finally, we adapt Emb2Emb for a training scheme that learns to map an input bag to an output bag, including a novel loss function and neural architecture. Our empirical evaluations on unsupervised sentiment transfer show that our method performs substantially better than a standard autoencoder.

Large, carefully partitioned datasets are essential to train neural networks and standardize performance benchmarks. As a result, we have set up new repositories to make our electron microscopy datasets available to the wider community. There are three main datasets containing 19769 scanning transmission electron micrographs, 17266 transmission electron micrographs, and 98340 simulated exit wavefunctions, and multiple variants of each dataset for different applications. To visualize image datasets, we trained variational autoencoders to encode data as 64-dimensional multivariate normal distributions, which we cluster in two dimensions by t-distributed stochastic neighbor embedding. In addition, we have improved dataset visualization with variational autoencoders by introducing encoding normalization and regularization, adding an image gradient loss, and extending t-distributed stochastic neighbor embedding to account for encoded standard deviations. Our datasets, source code, pretrained models, and interactive visualizations are openly available at https://github.com/Jeffrey-Ede/datasets.

With hundreds of thousands of language models available on Huggingface today, efficiently evaluating and utilizing these models across various downstream, tasks has become increasingly critical. Many existing methods repeatedly learn task-specific representations of Large Language Models (LLMs), which leads to inefficiencies in both time and computational resources. To address this, we propose EmbedLLM, a framework designed to learn compact vector representations, of LLMs that facilitate downstream applications involving many models, such as model routing. We introduce an encoder-decoder approach for learning such embeddings, along with a systematic framework to evaluate their effectiveness. Empirical results show that EmbedLLM outperforms prior methods in model routing both in accuracy and latency. Additionally, we demonstrate that our method can forecast a model's performance on multiple benchmarks, without incurring additional inference cost. Extensive probing experiments validate that the learned embeddings capture key model characteristics, e.g. whether the model is specialized for coding tasks, even without being explicitly trained on them. We open source our dataset, code and embedder to facilitate further research and application.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

The specialized language and complex concepts in physics pose significant challenges for information extraction through Natural Language Processing (NLP). Central to effective NLP applications is the text embedding model, which converts text into dense vector representations for efficient information retrieval and semantic analysis. In this work, we introduce PhysBERT, the first physics-specific text embedding model. Pre-trained on a curated corpus of 1.2 million arXiv physics papers and fine-tuned with supervised data, PhysBERT outperforms leading general-purpose models on physics-specific tasks including the effectiveness in fine-tuning for specific physics subdomains.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Vector embeddings derived from large language models (LLMs) show promise in capturing latent information from the literature. Interestingly, these can be integrated into material embeddings, potentially useful for data-driven predictions of materials properties. We investigate the extent to which LLM-derived vectors capture the desired information and their potential to provide insights into material properties without additional training. Our findings indicate that, although LLMs can be used to generate representations reflecting certain property information, extracting the embeddings requires identifying the optimal contextual clues and appropriate comparators. Despite this restriction, it appears that LLMs still have the potential to be useful in generating meaningful materials-science representations.

Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries. Building on these developments, we introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations with non-parameterized geometric variability, based on recently proposed Equivariant Neural Field architectures. In enf2enf, input geometries are encoded into latent point cloud embeddings that inherently preserve geometric grounding and capture local phenomena. The resulting representations are then combined with global parameters and directly decoded into continuous output fields, thus efficiently modeling the coupling between geometry and physics. By leveraging the inductive biases of locality and translation invariance, our approach is able to capture fine-scale physical features as well as complex shape variations, thereby enhancing generalization and physical compliance. Extensive experiments on a high-fidelity aerodynamic dataset, a hyper-elastic material benchmark, and multi-element airfoil geometries, demonstrate that the proposed model achieves superior or competitive performance compared to state-of-the-art graph based, operator learning, and neural field methods. Notably, our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes while maintaining high accuracy on full-scale discretizations.

Transformer architectures rely on explicit position encodings in order to preserve a notion of word order. In this paper, we argue that existing work does not fully utilize position information. For example, the initial proposal of a sinusoid embedding is fixed and not learnable. In this paper, we first review absolute position embeddings and existing methods for relative position embeddings. We then propose new techniques that encourage increased interaction between query, key and relative position embeddings in the self-attention mechanism. Our most promising approach is a generalization of the absolute position embedding, improving results on SQuAD1.1 compared to previous position embeddings approaches. In addition, we address the inductive property of whether a position embedding can be robust enough to handle long sequences. We demonstrate empirically that our relative position embedding method is reasonably generalized and robust from the inductive perspective. Finally, we show that our proposed method can be adopted as a near drop-in replacement for improving the accuracy of large models with a small computational budget.

Semantic segmentation is a computer vision task that associates a label with each pixel in an image. Modern approaches tend to introduce class embeddings into semantic segmentation for deeply utilizing category semantics, and regard supervised class masks as final predictions. In this paper, we explore the mechanism of class embeddings and have an insight that more explicit and meaningful class embeddings can be generated based on class masks purposely. Following this observation, we propose ECENet, a new segmentation paradigm, in which class embeddings are obtained and enhanced explicitly during interacting with multi-stage image features. Based on this, we revisit the traditional decoding process and explore inverted information flow between segmentation masks and class embeddings. Furthermore, to ensure the discriminability and informativity of features from backbone, we propose a Feature Reconstruction module, which combines intrinsic and diverse branches together to ensure the concurrence of diversity and redundancy in features. Experiments show that our ECENet outperforms its counterparts on the ADE20K dataset with much less computational cost and achieves new state-of-the-art results on PASCAL-Context dataset. The code will be released at https://gitee.com/mindspore/models and https://github.com/Carol-lyh/ECENet.

We introduce llama-embed-nemotron-8b, an open-weights text embedding model that achieves state-of-the-art performance on the Multilingual Massive Text Embedding Benchmark (MMTEB) leaderboard as of October 21, 2025. While recent models show strong performance, their training data or methodologies are often not fully disclosed. We aim to address this by developing a fully open-source model, publicly releasing its weights and detailed ablation studies, and planning to share the curated training datasets. Our model demonstrates superior performance across all major embedding tasks -- including retrieval, classification and semantic textual similarity (STS) -- and excels in challenging multilingual scenarios, such as low-resource languages and cross-lingual setups. This state-of-the-art performance is driven by a novel data mix of 16.1 million query-document pairs, split between 7.7 million samples from public datasets and 8.4 million synthetically generated examples from various open-weight LLMs. One of our key contributions is a detailed ablation study analyzing core design choices, including a comparison of contrastive loss implementations, an evaluation of synthetic data generation (SDG) strategies, and the impact of model merging. The llama-embed-nemotron-8b is an instruction-aware model, supporting user-defined instructions to enhance performance for specific use-cases. This combination of top-tier performance, broad applicability, and user-driven flexibility enables it to serve as a universal text embedding solution.

The paper presents an O(N log N)-implementation of t-SNE -- an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots and that normally runs in O(N^2). The new implementation uses vantage-point trees to compute sparse pairwise similarities between the input data objects, and it uses a variant of the Barnes-Hut algorithm - an algorithm used by astronomers to perform N-body simulations - to approximate the forces between the corresponding points in the embedding. Our experiments show that the new algorithm, called Barnes-Hut-SNE, leads to substantial computational advantages over standard t-SNE, and that it makes it possible to learn embeddings of data sets with millions of objects.

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and, in addition to encoding surprisingly good syntactic and semantic information, have been proven useful as extra features in many downstream NLP tasks.

Embedding models have been crucial in enabling various downstream tasks such as semantic similarity, information retrieval, and clustering. Recently, there has been a surge of interest in developing universal text embedding models that can generalize across tasks (e.g., MTEB). However, progress in learning universal multimodal embedding models has been relatively slow despite their importance. In this work, we aim to explore the potential for building universal embeddings capable of handling a wide range of downstream tasks. Our contributions are twofold: (1) MMEB (Massive Multimodal Embedding Benchmark), which covers 4 meta-tasks (i.e. classification, visual question answering, multimodal retrieval, and visual grounding) and 36 datasets, including 20 training and 16 evaluation datasets, and (2) VLM2Vec (Vision-Language Model -> Vector), a contrastive training framework that converts any state-of-the-art vision-language model into an embedding model via training on MMEB. Unlike previous models such as CLIP and BLIP, VLM2Vec can process any combination of images and text to generate a fixed-dimensional vector based on task instructions. We build a series of VLM2Vec models on Phi-3.5-V and evaluate them on MMEB's evaluation split. Our results show that \model achieves an absolute average improvement of 10% to 20% over existing multimodal embedding models on both in-distribution and out-of-distribution datasets in MMEB.

Building predictive models for companies often relies on inference using historical data of companies in the same industry sector. However, companies are similar across a variety of dimensions that should be leveraged in relevant prediction problems. This is particularly true for large, complex organizations which may not be well defined by a single industry and have no clear peers. To enable prediction using company information across a variety of dimensions, we create an embedding of company stocks, Stock2Vec, which can be easily added to any prediction model that applies to companies with associated stock prices. We describe the process of creating this rich vector representation from stock price fluctuations, and characterize what the dimensions represent. We then conduct comprehensive experiments to evaluate this embedding in applied machine learning problems in various business contexts. Our experiment results demonstrate that the four features in the Stock2Vec embedding can readily augment existing cross-company models and enhance cross-company predictions.

In the process of numerically modeling natural languages, developing language embeddings is a vital step. However, it is challenging to develop functional embeddings for resource-poor languages such as Sinhala, for which sufficiently large corpora, effective language parsers, and any other required resources are difficult to find. In such conditions, the exploitation of existing models to come up with an efficacious embedding methodology to numerically represent text could be quite fruitful. This paper explores the effectivity of several one-tiered and two-tiered embedding architectures in representing Sinhala text in the sentiment analysis domain. With our findings, the two-tiered embedding architecture where the lower-tier consists of a word embedding and the upper-tier consists of a sentence embedding has been proven to perform better than one-tier word embeddings, by achieving a maximum F1 score of 88.04% in contrast to the 83.76% achieved by word embedding models. Furthermore, embeddings in the hyperbolic space are also developed and compared with Euclidean embeddings in terms of performance. A sentiment data set consisting of Facebook posts and associated reactions have been used for this research. To effectively compare the performance of different embedding systems, the same deep neural network structure has been trained on sentiment data with each of the embedding systems used to encode the text associated.

Ad-hoc search calls for the selection of appropriate answers from a massive-scale corpus. Nowadays, the embedding-based retrieval (EBR) becomes a promising solution, where deep learning based document representation and ANN search techniques are allied to handle this task. However, a major challenge is that the ANN index can be too large to fit into memory, given the considerable size of answer corpus. In this work, we tackle this problem with Bi-Granular Document Representation, where the lightweight sparse embeddings are indexed and standby in memory for coarse-grained candidate search, and the heavyweight dense embeddings are hosted in disk for fine-grained post verification. For the best of retrieval accuracy, a Progressive Optimization framework is designed. The sparse embeddings are learned ahead for high-quality search of candidates. Conditioned on the candidate distribution induced by the sparse embeddings, the dense embeddings are continuously learned to optimize the discrimination of ground-truth from the shortlisted candidates. Besides, two techniques: the contrastive quantization and the locality-centric sampling are introduced for the learning of sparse and dense embeddings, which substantially contribute to their performances. Thanks to the above features, our method effectively handles massive-scale EBR with strong advantages in accuracy: with up to +4.3% recall gain on million-scale corpus, and up to +17.5% recall gain on billion-scale corpus. Besides, Our method is applied to a major sponsored search platform with substantial gains on revenue (+1.95%), Recall (+1.01%) and CTR (+0.49%). Our code is available at https://github.com/microsoft/BiDR.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is represented by an irregular point cloud rather than a simple vector, making it difficult to directly quantify and compare biological differences between individuals. Nonlinear methods such as kernels and neural networks achieve predictive accuracy but act as black boxes, offering little biological interpretability. To address these limitations, we adapt the Linear Optimal Transport (LOT) framework to this setting, embedding irregular point clouds into a fixed-dimensional Euclidean space while preserving distributional structure. This embedding provides a principled linear representation that preserves optimal transport geometry while enabling downstream analysis. It also forms a registration between any two patients, enabling direct comparison of their cellular distributions. Within this space, LOT enables: (i) accurate and interpretable classification of COVID-19 patient states, where classifier weights map back to specific markers and spatial regions driving predictions; and (ii) synthetic data generation for patient-derived organoids, exploiting the linearity of the LOT embedding. LOT barycenters yield averaged cellular profiles representing combined conditions or samples, supporting drug interaction testing. Together, these results establish LOT as a unified framework that bridges predictive performance, interpretability, and generative modeling. By transforming heterogeneous point clouds into structured embeddings directly traceable to the original data, LOT opens new opportunities for understanding immune variation and treatment effects in high-dimensional biological systems.

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical methods have been applied successfully in the past, the primary challenge in solving these equations arises from the frequency of electromagnetic fields, which depends on the shape and size of the objects to be resolved. Since the domain of influence for these equations is compactly supported, even a small perturbation in frequency necessitates a new discretization of Maxwell's equations, resulting in substantial computational costs. In this work, we investigate the potential of neural operators, particularly the Deep Operator Network (DeepONet) and its variants, as a surrogate model for Maxwell's equations. Existing DeepONet implementations are restricted to real-valued data in R^n, but since the time-harmonic Maxwell's equations yield solutions in the complex domain C^n, a specialized architecture is required to handle complex algebra. We propose a formulation of DeepONet for complex data, define the forward pass in the complex domain, and adopt a reparametrized version of DeepONet for more efficient training. We also propose a unified framework to combine a plurality of DeepONets, trained for multiple electromagnetic field components, to incorporate the boundary condition. We conduct computational experiments on a 3D metallic sphere without singularities and on a metallic almond-shaped target to demonstrate the effectiveness of the proposed method for problems involving singularity-prone solutions. As shown by computational experiments, our method significantly enhances the efficiency of predicting scattered fields from a spherical object at arbitrary high frequencies.

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as features, especially for neural-network-based models. Directly feeding raw Gaussian parameters into learning frameworks fails to address the non-unique and heterogeneous nature of the Gaussian parameterization, yielding highly data-dependent models. This challenge motivates us to explore a more principled approach to represent 3D Gaussian Splatting in neural networks that preserves the underlying color and geometric structure while enforcing unique mapping and channel homogeneity. In this paper, we propose an embedding representation of 3DGS based on continuous submanifold fields that encapsulate the intrinsic information of Gaussian primitives, thereby benefiting the learning of 3DGS.

Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational costs. To better understand LLM scaling, we study representational differences between LLMs and their smaller counterparts, with the goal of replicating the representational qualities of larger models in the smaller models. We observe a geometric phenomenon which we term embedding condensation, where token embeddings collapse into a narrow cone-like subspace in some language models. Through systematic analyses across multiple Transformer families, we show that small models such as GPT2 and Qwen3-0.6B exhibit severe condensation, whereas the larger models such as GPT2-xl and Qwen3-32B are more resistant to this phenomenon. Additional observations show that embedding condensation is not reliably mitigated by knowledge distillation from larger models. To fight against it, we formulate a dispersion loss that explicitly encourages embedding dispersion during training. Experiments demonstrate that it mitigates condensation, recovers dispersion patterns seen in larger models, and yields performance gains across 10 benchmarks. We believe this work offers a principled path toward improving smaller Transformers without additional parameters.

Embedding projections are popular for visualizing large datasets and models. However, people often encounter "friction" when using embedding visualization tools: (1) barriers to adoption, e.g., tedious data wrangling and loading, scalability limits, no integration of results into existing workflows, and (2) limitations in possible analyses, without integration with external tools to additionally show coordinated views of metadata. In this paper, we present Embedding Atlas, a scalable, interactive visualization tool designed to make interacting with large embeddings as easy as possible. Embedding Atlas uses modern web technologies and advanced algorithms -- including density-based clustering, and automated labeling -- to provide a fast and rich data analysis experience at scale. We evaluate Embedding Atlas with a competitive analysis against other popular embedding tools, showing that Embedding Atlas's feature set specifically helps reduce friction, and report a benchmark on its real-time rendering performance with millions of points. Embedding Atlas is available as open source to support future work in embedding-based analysis.

While paragraph embedding models are remarkably effective for downstream classification tasks, what they learn and encode into a single vector remains opaque. In this paper, we investigate a state-of-the-art paragraph embedding method proposed by Zhang et al. (2017) and discover that it cannot reliably tell whether a given sentence occurs in the input paragraph or not. We formulate a sentence content task to probe for this basic linguistic property and find that even a much simpler bag-of-words method has no trouble solving it. This result motivates us to replace the reconstruction-based objective of Zhang et al. (2017) with our sentence content probe objective in a semi-supervised setting. Despite its simplicity, our objective improves over paragraph reconstruction in terms of (1) downstream classification accuracies on benchmark datasets, (2) faster training, and (3) better generalization ability.

Equivariant Transformers such as Equiformer have demonstrated the efficacy of applying Transformers to the domain of 3D atomistic systems. However, they are still limited to small degrees of equivariant representations due to their computational complexity. In this paper, we investigate whether these architectures can scale well to higher degrees. Starting from Equiformer, we first replace SO(3) convolutions with eSCN convolutions to efficiently incorporate higher-degree tensors. Then, to better leverage the power of higher degrees, we propose three architectural improvements -- attention re-normalization, separable S^2 activation and separable layer normalization. Putting this all together, we propose EquiformerV2, which outperforms previous state-of-the-art methods on the large-scale OC20 dataset by up to 12% on forces, 4% on energies, offers better speed-accuracy trade-offs, and 2times reduction in DFT calculations needed for computing adsorption energies.

Word embeddings and language models have transformed natural language processing (NLP) by facilitating the representation of linguistic elements in continuous vector spaces. This review visits foundational concepts such as the distributional hypothesis and contextual similarity, tracing the evolution from sparse representations like one-hot encoding to dense embeddings including Word2Vec, GloVe, and fastText. We examine both static and contextualized embeddings, underscoring advancements in models such as ELMo, BERT, and GPT and their adaptations for cross-lingual and personalized applications. The discussion extends to sentence and document embeddings, covering aggregation methods and generative topic models, along with the application of embeddings in multimodal domains, including vision, robotics, and cognitive science. Advanced topics such as model compression, interpretability, numerical encoding, and bias mitigation are analyzed, addressing both technical challenges and ethical implications. Additionally, we identify future research directions, emphasizing the need for scalable training techniques, enhanced interpretability, and robust grounding in non-textual modalities. By synthesizing current methodologies and emerging trends, this survey offers researchers and practitioners an in-depth resource to push the boundaries of embedding-based language models.

Embeddings have emerged as a standard representational interface linking foundation models with downstream systems. Most embedding benchmarks assess representations through discriminative tasks or geometric criteria centered on separability in embedding space. However, strong performance on such evaluations does not establish whether content compressed into an embedding remains accessible to a downstream generator. To address this gap, we introduce the Generative Embedding Benchmark (GEB), in which a decoder answers questions using only a frozen embedding and question text, without access to the original image or intermediate visual features. Answer quality under this readout measures generative information: the answer-relevant content recoverable from an embedding. GEB includes a curated visual-question-answering dataset with a 1,800-item development split and a held-out 900-item test split covering natural images, scene text, and visual documents. Using a common decoder and training recipe, we evaluate seven public embedding models in visual-only and vision-language joint modes. On the test set, visual-only scores range from 28.25 to 33.21; with image-question joint encoding, all five VLM-based embedding models score higher, and the best reaches 65.56. Matched embeddings also outperform text-only inputs, zero embeddings, and shuffled embeddings. Natural-image information is much easier to recover than scene text or visual-document information, while a Qwen3-VL-2B reference with access to the original image reaches 84.30. Together, these results show that generative readout exposes information bottlenecks that separability-based evaluation does not capture.

This paper presents a comprehensive analysis of various static word embeddings for Hungarian, including traditional models such as Word2Vec, FastText, as well as static embeddings derived from BERT-based models using different extraction methods. We evaluate these embeddings on both intrinsic and extrinsic tasks to provide a holistic view of their performance. For intrinsic evaluation, we employ a word analogy task, which assesses the embeddings ability to capture semantic and syntactic relationships. Our results indicate that traditional static embeddings, particularly FastText, excel in this task, achieving high accuracy and mean reciprocal rank (MRR) scores. Among the BERT-based models, the X2Static method for extracting static embeddings demonstrates superior performance compared to decontextualized and aggregate methods, approaching the effectiveness of traditional static embeddings. For extrinsic evaluation, we utilize a bidirectional LSTM model to perform Named Entity Recognition (NER) and Part-of-Speech (POS) tagging tasks. The results reveal that embeddings derived from dynamic models, especially those extracted using the X2Static method, outperform purely static embeddings. Notably, ELMo embeddings achieve the highest accuracy in both NER and POS tagging tasks, underscoring the benefits of contextualized representations even when used in a static form. Our findings highlight the continued relevance of static word embeddings in NLP applications and the potential of advanced extraction methods to enhance the utility of BERT-based models. This piece of research contributes to the understanding of embedding performance in the Hungarian language and provides valuable insights for future developments in the field. The training scripts, evaluation codes, restricted vocabulary, and extracted embeddings will be made publicly available to support further research and reproducibility.

In the large language model (LLM) revolution, embedding is a key component of various systems. For example, it is used to retrieve knowledge or memories for LLMs, to build content moderation filters, etc. As such cases span from English to other natural or programming languages, from retrieval to classification and beyond, it is desirable to build a unified embedding model rather than dedicated ones for each scenario. In this work, we make an initial step towards this goal, demonstrating that multiple languages (both natural and programming) pre-trained transformer decoders can embed universally when finetuned on limited English data. We provide a comprehensive practice with thorough evaluations. On English MTEB, our models achieve competitive performance on different embedding tasks by minimal training data. On other benchmarks, such as multilingual classification and code search, our models (without any supervision) perform comparably to, or even surpass heavily supervised baselines and/or APIs. These results provide evidence of a promising path towards building powerful unified embedders that can be applied across tasks and languages.

Compact models often lose the structure of their embedding space. The issue shows up when the capacity is tight or the data spans several languages. Such collapse makes it difficult for downstream tasks to build on the resulting representation. Existing compression methods focus on aligning model outputs at a superficial level but fail to preserve the underlying manifold structure. This mismatch often leads to semantic drift in the compact model, causing both task behavior and linguistic properties to deviate from the reference model. To address those issues, we provide a new framework called Embedding Consistency Regulation (ECR). This framework first derives a set of semantic anchors from teacher embeddings (computed once offline). Then, the compact model learns to maintain consistent geometry around these anchors, without relying on matching logits or internal features. ECR adds only a small projection step at inference, without altering the decoding architecture or its runtime behavior. In experiments on a 100K multilingual corpus, ECR consistently stabilizes training and preserves semantic structure across tasks and languages. It also produces a more compact and task-aligned representation space, enabling low-capacity models to learn cleaner manifolds than conventional baselines. ECR works without teacher outputs and is compatible with, but independent of, distillation. Taken together, our results show that ECR helps compact models better follow task requirements and makes them easier to deploy under strict efficiency or privacy limits.

We introduce EELBERT, an approach for compression of transformer-based models (e.g., BERT), with minimal impact on the accuracy of downstream tasks. This is achieved by replacing the input embedding layer of the model with dynamic, i.e. on-the-fly, embedding computations. Since the input embedding layer accounts for a significant fraction of the model size, especially for the smaller BERT variants, replacing this layer with an embedding computation function helps us reduce the model size significantly. Empirical evaluation on the GLUE benchmark shows that our BERT variants (EELBERT) suffer minimal regression compared to the traditional BERT models. Through this approach, we are able to develop our smallest model UNO-EELBERT, which achieves a GLUE score within 4% of fully trained BERT-tiny, while being 15x smaller (1.2 MB) in size.

Text embeddings are essential components in modern NLP pipelines. While numerous embedding models have been proposed, their performance varies across domains. This variability motivates the use of ensemble techniques to combine complementary strengths. However, most existing ensemble methods operate on deterministic embeddings and fail to account for model-specific uncertainty, limiting their robustness and reliability in downstream applications. To address these limitations, we propose Uncertainty-driven Embedding Convolution (UEC). UEC first transforms deterministic embeddings into probabilistic ones in a post-hoc manner. It then computes adaptive ensemble weights based on embedding uncertainty, grounded in a Bayes-optimal solution under a surrogate loss. Additionally, UEC employs an uncertainty-aware similarity function that directly incorporates uncertainty into the similarity scoring, providing a theoretically grounded and efficient surrogate to distributional distances. Extensive experiments on diverse benchmarks demonstrate that UEC consistently improves both performance and robustness by leveraging principled uncertainty modeling.

Scalable Vector Graphics (SVGs) function both as visual images and as structured code that encode rich geometric and layout information, yet most methods rasterize them and discard this symbolic organization. At the same time, recent sentence embedding methods produce strong text representations but do not naturally extend to visual or structured modalities. We propose a training-free, instruction-guided multimodal embedding framework that uses a Multimodal Large Language Model (MLLM) to map text, raster images, and SVG code into an aligned embedding space. We control the direction of embeddings through modality-specific instructions and structural SVG cues, eliminating the need for learned projection heads or contrastive training. Our method has two key components: (1) Multimodal Explicit One-word Limitation (mEOL), which instructs the MLLM to summarize any multimodal input into a single token whose hidden state serves as a compact semantic embedding. (2) A semantic SVG rewriting module that assigns meaningful identifiers and simplifies nested SVG elements through visual reasoning over the rendered image, exposing geometric and relational cues hidden in raw code. Using a repurposed VGBench, we build the first text-to-SVG retrieval benchmark and show that our training-free embeddings outperform encoder-based and training-based multimodal baselines. These results highlight prompt-level control as an effective alternative to parameter-level training for structure-aware multimodal retrieval. Project page: https://scene-the-ella.github.io/meol/

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.

Foundation models have established unified representations for natural language processing, yet this paradigm remains largely unexplored for tabular data. Existing methods face fundamental limitations: LLM-based approaches lack retrieval-compatible vector outputs, whereas text embedding models often fail to capture tabular structure and numerical semantics. To bridge this gap, we first introduce the Tabular Embedding Benchmark (TabBench), a comprehensive suite designed to evaluate the tabular understanding capability of embedding models. We then propose TabEmbed, the first generalist embedding model that unifies tabular classification and retrieval within a shared embedding space. By reformulating diverse tabular tasks as semantic matching problems, TabEmbed leverages large-scale contrastive learning with positive-aware hard negative mining to discern fine-grained structural and numerical nuances. Experimental results on TabBench demonstrate that TabEmbed significantly outperforms state-of-the-art text embedding models, establishing a new baseline for universal tabular representation learning. Code and datasets are publicly available at https://github.com/qiangminjie27/TabEmbed and https://huggingface.co/datasets/qiangminjie27/TabBench.

Video Joint Embedding Predictive Architectures (V-JEPA) learn generalizable off-the-shelf video representation by predicting masked regions in latent space with an exponential moving average (EMA)-updated teacher. While EMA prevents representation collapse, it complicates scalable model selection and couples teacher and student architectures. We revisit masked-latent prediction and show that a frozen teacher suffices. Concretely, we (i) train a target encoder with a simple pixel-reconstruction objective under V-JEPA masking, then (ii) freeze it and train a student to predict the teacher's latents on masked regions. This leads to a two-stage, unregularized scheme that we refer to as SALT (Static-teacher Asymmetric Latent Training). SALT decouples optimization into pixel reconstruction (teacher) and masked latent prediction (student), increasing transparency, efficiency, and scalability while preserving the ability of representation to generalize under frozen evaluation. Empirically, our student models outperform recently proposed V-JEPA 2 encoders under frozen backbone evaluation across diverse benchmarks. They are also more compute-optimal: at matched pretraining FLOPs, our method achieves higher probing accuracy, and its scaling curves dominate V-JEPA's accuracy-FLOPs Pareto frontier. Finally, we find that student quality is remarkably robust to teacher quality: high-performing students emerge even with small, sub-optimal teachers. This points to a compute budget allocation that should overwhelmingly favor the student. These results position SALT as a simple, scalable, and compute-efficient alternative to EMA-based self-distillation for video representation learning.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

A new trend uses LLMs as dense text encoders via contrastive learning. However, since LLM embeddings predict the probability distribution of the next token, they are inherently generative and distributive, conflicting with contrastive learning, which requires embeddings to capture full-text semantics and align via cosine similarity. This discrepancy hinders the full utilization of LLMs' pre-training capabilities, resulting in inefficient learning. In response to this issue, we propose AutoRegEmbed, a new contrastive learning method built on embedding conditional probability distributions, which integrates two core tasks: information compression and conditional distribution alignment. The information compression task encodes text into the embedding space, ensuring that the embedding vectors capture global semantics. The conditional distribution alignment task focuses on aligning text embeddings with positive samples embeddings by leveraging the conditional distribution of embeddings while simultaneously reducing the likelihood of generating negative samples from text embeddings, thereby achieving embedding alignment and uniformity. Experimental results demonstrate that our method significantly outperforms traditional contrastive learning approaches and achieves performance comparable to state-of-the-art models when using the same amount of data.

In this paper, we introduce a mesh-free two-level hybrid Tucker tensor format for approximation of multivariate functions, which combines the product Chebyshev interpolation with the ALS-based Tucker decomposition of the tensor of Chebyshev coefficients. It allows to avoid the expenses of the rank-structured approximation of function-related tensors defined on large spacial grids, while benefiting from the Tucker decomposition of the rather small core tensor of Chebyshev coefficients. This leads to nearly optimal Tucker rank parameters which are close to the results for well established Tucker-ALS algorithm applied to the large grid-based tensors. These rank parameters inherited from the Tucker-ALS decomposition of the coefficient tensor can be much less than the polynomial degrees of the initial Chebyshev interpolant via function independent basis set. Furthermore, the tensor product Chebyshev polynomials discretized on a tensor grid leads to a low-rank two-level orthogonal algebraic Tucker tensor that approximates the initial function with controllable accuracy. It is shown that our techniques could be gainfully applied to the long-range part of the electrostatic potential of multi-particle systems approximated in the range-separated tensor format. Error and complexity estimates of the proposed methods are presented. We demonstrate the efficiency of the suggested method numerically on examples of the long-range components of multi-particle interaction potentials generated by 3D Newton kernel for large bio-molecule systems and lattice-type compounds.

Embedding models are a cornerstone of modern AI. Driven by Multimodal Large Language Models (MLLMs), they have made great progress in architecture and data curation, while the holistic paradigm is still limited to SSC, i.e., single input, singular embedding, contrastive supervision, which collapses rich, multifaceted inputs into monolithic embeddings and fails to fully exploit MLLM capabilities. In this paper, we tailor one Parallel Decoupling Framework (PDF) for multimodal embedding learning, by utilizing the proprietary steerability of MLLMs, i.e., their ability to flexibly generate quite differentiated response under explicit instructions. Concretely, PDF conditions a shared MLLM backbone on distinct, learnable prefixes to roll out multiple parallel paths for one input, then relies on these paths to obtain parallel embeddings. To promote full parallel diversity, we employ Mutual Information Minimization (MIM) as an explicit constraint, coupled with per-path contrastive supervision to maintain semantic alignment. Such dual-objectives force PDF to yield robust semantic coverage and a generalizable embedding space. Ultimately, the remarkable embedding space are accessible at inference via one single forward pass, incurring negligible computational overhead. We instantiate PDF on multiple MLLM backbones and prove its effectiveness on MMEB benchmark. Significant gains are consistently achieved across various resolutions and model sizes, e.g., boosting the VLM2Vec-LLaVA-1.6-LR model by a remarkable +8.9% (7B), while the VLM2Vec-Qwen2VL models by +4.2% (2B) and +3.1% (7B). In terms of efficiency, our 2B model surpasses its baseline by +2.6% using only half the computational budget.

In this paper, we propose KaLM-Embedding-V2, a versatile and compact embedding model, which achieves impressive performance in general-purpose text embedding tasks by leveraging superior training techniques and data. Our key innovations include: (1) To better align the architecture with representation learning, we remove the causal attention mask and adopt a fully bidirectional transformer with simple yet effective mean-pooling to produce fixed-length embeddings; (2) We employ a multi-stage training pipeline: (i) pre-training on large-scale weakly supervised open-source corpora; (ii) fine-tuning on high-quality retrieval and non-retrieval datasets; and (iii) model-soup parameter averaging for robust generalization. Besides, we introduce a focal-style reweighting mechanism that concentrates learning on difficult samples and an online hard-negative mixing strategy to continuously enrich hard negatives without expensive offline mining; (3) We collect over 20 categories of data for pre-training and 100 categories of data for fine-tuning, to boost both the performance and generalization of the embedding model. Extensive evaluations on the Massive Text Embedding Benchmark (MTEB) Chinese and English show that our model significantly outperforms others of comparable size, and competes with 3x, 14x, 18x, and 26x larger embedding models, setting a new standard for a versatile and compact embedding model with less than 1B parameters.

Positional embeddings (PE) play a crucial role in Vision Transformers (ViTs) by providing spatial information otherwise lost due to the permutation invariant nature of self attention. While absolute positional embeddings (APE) have shown theoretical advantages over relative positional embeddings (RPE), particularly due to the ability of sinusoidal functions to preserve spatial inductive biases like monotonicity and shift invariance, a fundamental challenge arises when mapping a 2D grid to a 1D sequence. Existing methods have mostly overlooked or never explored the impact of patch ordering in positional embeddings. To address this, we propose LOOPE, a learnable patch-ordering method that optimizes spatial representation for a given set of frequencies, providing a principled approach to patch order optimization. Empirical results show that our PE significantly improves classification accuracy across various ViT architectures. To rigorously evaluate the effectiveness of positional embeddings, we introduce the "Three Cell Experiment", a novel benchmarking framework that assesses the ability of PEs to retain relative and absolute positional information across different ViT architectures. Unlike standard evaluations, which typically report a performance gap of 4 to 6% between models with and without PE, our method reveals a striking 30 to 35% difference, offering a more sensitive diagnostic tool to measure the efficacy of PEs. Our experimental analysis confirms that the proposed LOOPE demonstrates enhanced effectiveness in retaining both relative and absolute positional information.

Contextualized embeddings based on large language models (LLMs) are available for various languages, but their coverage is often limited for lower resourced languages. Training LLMs for such languages is often difficult due to insufficient data and high computational cost. Especially for very low resource languages, static word embeddings thus still offer a viable alternative. There is, however, a notable lack of comprehensive repositories with such embeddings for diverse languages. To address this, we present LowREm, a centralized repository of static embeddings for 87 low-resource languages. We also propose a novel method to enhance GloVe-based embeddings by integrating multilingual graph knowledge, utilizing another source of knowledge. We demonstrate the superior performance of our enhanced embeddings as compared to contextualized embeddings extracted from XLM-R on sentiment analysis. Our code and data are publicly available under https://huggingface.co/DFKI.

Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned embeddings controls predictive performance for a fixed trained model. We show that population risk can be bounded by two factors: (i) the intrinsic dimension of the embedding distribution, which determines the convergence rate of empirical embedding distribution to the population distribution in Wasserstein distance, and (ii) the sensitivity of the downstream mapping from embeddings to predictions, characterized by Lipschitz constants. Together, these yield an embedding-dependent error bound that does not rely on parameter counts or hypothesis class complexity. At the final embedding layer, architectural sensitivity vanishes and the bound is dominated by embedding dimension, explaining its strong empirical correlation with generalization performance. Experiments across architectures and datasets validate the theory and demonstrate the utility of embedding-based diagnostics.

With the growing popularity of RAG, the capabilities of embedding models are gaining increasing attention. Embedding models are primarily trained through contrastive loss learning, with negative examples being a key component. Previous work has proposed various hard negative mining strategies, but these strategies are typically employed as preprocessing steps. In this paper, we propose the conan-embedding model, which maximizes the utilization of more and higher-quality negative examples. Specifically, since the model's ability to handle preprocessed negative examples evolves during training, we propose dynamic hard negative mining method to expose the model to more challenging negative examples throughout the training process. Secondly, contrastive learning requires as many negative examples as possible but is limited by GPU memory constraints. Therefore, we use a Cross-GPU balancing Loss to provide more negative examples for embedding training and balance the batch size across multiple tasks. Moreover, we also discovered that the prompt-response pairs from LLMs can be used for embedding training. Our approach effectively enhances the capabilities of embedding models, currently ranking first on the Chinese leaderboard of Massive text embedding benchmark

This paper presents E5, a family of state-of-the-art text embeddings that transfer well to a wide range of tasks. The model is trained in a contrastive manner with weak supervision signals from our curated large-scale text pair dataset (called CCPairs). E5 can be readily used as a general-purpose embedding model for any tasks requiring a single-vector representation of texts such as retrieval, clustering, and classification, achieving strong performance in both zero-shot and fine-tuned settings. We conduct extensive evaluations on 56 datasets from the BEIR and MTEB benchmarks. For zero-shot settings, E5 is the first model that outperforms the strong BM25 baseline on the BEIR retrieval benchmark without using any labeled data. When fine-tuned, E5 obtains the best results on the MTEB benchmark, beating existing embedding models with 40x more parameters.

Vietnam ranks among the top countries in terms of both internet traffic and online toxicity. As a result, implementing embedding models for recommendation and content control duties in applications is crucial. However, a lack of large-scale test datasets, both in volume and task diversity, makes it tricky for scientists to effectively evaluate AI models before deploying them in real-world, large-scale projects. To solve this important problem, we introduce a Vietnamese benchmark, VN-MTEB for embedding models, which we created by translating a large number of English samples from the Massive Text Embedding Benchmark using our new automated framework. We leverage the strengths of large language models (LLMs) and cutting-edge embedding models to conduct translation and filtering processes to retain high-quality samples, guaranteeing a natural flow of language and semantic fidelity while preserving named entity recognition (NER) and code snippets. Our comprehensive benchmark consists of 41 datasets from six tasks specifically designed for Vietnamese text embeddings. In our analysis, we find that bigger and more complex models using Rotary Positional Embedding outperform those using Absolute Positional Embedding in embedding tasks. Datasets are available at HuggingFace: https://huggingface.co/collections/GreenNode/vn-mteb-68871433f0f7573b8e1a6686

Decoder-only large language model (LLM)-based embedding models are beginning to outperform BERT or T5-based embedding models in general-purpose text embedding tasks, including dense vector-based retrieval. In this work, we introduce the NV-Embed model with a variety of architectural designs and training procedures to significantly enhance the performance of LLM as a versatile embedding model, while maintaining its simplicity and reproducibility. For model architecture, we propose a latent attention layer to obtain pooled embeddings, which consistently improves retrieval and downstream task accuracy compared to mean pooling or using the last <EOS> token embedding from LLMs. To enhance representation learning, we remove the causal attention mask of LLMs during contrastive training. For model training, we introduce a two-stage contrastive instruction-tuning method. It first applies contrastive training with instructions on retrieval datasets, utilizing in-batch negatives and curated hard negative examples. At stage-2, it blends various non-retrieval datasets into instruction tuning, which not only enhances non-retrieval task accuracy but also improves retrieval performance. Combining these techniques, our NV-Embed model, using only publicly available data, has achieved a record-high score of 69.32, ranking No. 1 on the Massive Text Embedding Benchmark (MTEB) (as of May 24, 2024), with 56 tasks, encompassing retrieval, reranking, classification, clustering, and semantic textual similarity tasks. Notably, our model also attains the highest score of 59.36 on 15 retrieval tasks in the MTEB benchmark (also known as BEIR). We will open-source the model at: https://huggingface.co/nvidia/NV-Embed-v1.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer architecture in which a particular embedding vector's dimension scales with its query frequency. Through theoretical analysis and systematic experiments, we demonstrate that using mixed dimensions can drastically reduce the memory usage, while maintaining and even improving the ML performance. Empirically, we show that the proposed mixed dimension layers improve accuracy by 0.1% using half as many parameters or maintain it using 16X fewer parameters for click-through rate prediction task on the Criteo Kaggle dataset.

One persistent obstacle in industrial quality inspection is the detection of anomalies. In real-world use cases, two problems must be addressed: anomalous data is sparse and the same types of anomalies need to be detected on previously unseen objects. Current anomaly detection approaches can be trained with sparse nominal data, whereas domain generalization approaches enable detecting objects in previously unseen domains. Utilizing those two observations, we introduce the hybrid task of domain generalization on sparse classes. To introduce an accompanying dataset for this task, we present a modification of the well-established MVTec AD dataset by generating three new datasets. In addition to applying existing methods for benchmark, we design two embedding-based approaches, Spatial Embedding MLP (SEMLP) and Labeled PatchCore. Overall, SEMLP achieves the best performance with an average image-level AUROC of 87.2 % vs. 80.4 % by MIRO. The new and openly available datasets allow for further research to improve industrial anomaly detection.

Code embeddings capture the semantic representations of code and are crucial for various code-related large language model (LLM) applications, such as code search. Previous training primarily relies on optimizing the InfoNCE loss by comparing positive natural language (NL)-code pairs with in-batch negatives. However, due to the sparse nature of code contexts, training solely by comparing the major differences between positive and negative pairs may fail to capture deeper semantic nuances. To address this issue, we propose a novel order-augmented strategy for improved code search (OASIS). It leverages order-based similarity labels to train models to capture subtle differences in similarity among negative pairs. Extensive benchmark evaluations demonstrate that our OASIS model significantly outperforms previous state-of-the-art models focusing solely on major positive-negative differences. It underscores the value of exploiting subtle differences among negative pairs with order labels for effective code embedding training.

The tradeoff between precision and performance in molecular simulations can nowadays be addressed by machine-learned force fields (MLFF), which combine ab initio accuracy with force field numerical efficiency. Different from conventional force fields however, incorporating relevant electronic degrees of freedom into MLFFs becomes important. Here, we implement an equivariant transformer that embeds molecular net charge and spin state without additional neural network parameters. The model trained on a singlet/triplet non-correlated CH2 dataset can identify different spin states and shows state-of-the-art extrapolation capability. Therein, self-attention sensibly captures non-local effects, which, as we show, can be finely tuned over the network hyper-parameters. We indeed found that Softmax activation functions utilised in the self-attention mechanism of graph networks outperformed ReLU-like functions in prediction accuracy. Increasing the attention temperature from τ= d to 2d further improved the extrapolation capability, indicating a weighty role of nonlocality. Additionally, a weight initialisation method was purposed that sensibly accelerated the training process.

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems constrain to smaller ensembles and lower-capacity networks, significantly deteriorating their performance and properties. We introduce Packed-Ensembles (PE), a strategy to design and train lightweight structured ensembles by carefully modulating the dimension of their encoding space. We leverage grouped convolutions to parallelize the ensemble into a single shared backbone and forward pass to improve training and inference speeds. PE is designed to operate within the memory limits of a standard neural network. Our extensive research indicates that PE accurately preserves the properties of DE, such as diversity, and performs equally well in terms of accuracy, calibration, out-of-distribution detection, and robustness to distribution shift. We make our code available at https://github.com/ENSTA-U2IS/torch-uncertainty.

A creative idea is often born from transforming, combining, and modifying ideas from existing visual examples capturing various concepts. However, one cannot simply copy the concept as a whole, and inspiration is achieved by examining certain aspects of the concept. Hence, it is often necessary to separate a concept into different aspects to provide new perspectives. In this paper, we propose a method to decompose a visual concept, represented as a set of images, into different visual aspects encoded in a hierarchical tree structure. We utilize large vision-language models and their rich latent space for concept decomposition and generation. Each node in the tree represents a sub-concept using a learned vector embedding injected into the latent space of a pretrained text-to-image model. We use a set of regularizations to guide the optimization of the embedding vectors encoded in the nodes to follow the hierarchical structure of the tree. Our method allows to explore and discover new concepts derived from the original one. The tree provides the possibility of endless visual sampling at each node, allowing the user to explore the hidden sub-concepts of the object of interest. The learned aspects in each node can be combined within and across trees to create new visual ideas, and can be used in natural language sentences to apply such aspects to new designs.

A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector representations. While the robustness with respect to changes of continuous inputs is well-understood, the situation is less clear when considering discrete changes, for instance replacing a word by another in an input sentence. Our work formally proves that popular embedding schemes, such as concatenation, TF-IDF, and Paragraph Vector (a.k.a. doc2vec), exhibit robustness in the H\"older or Lipschitz sense with respect to the Hamming distance. We provide quantitative bounds for these schemes and demonstrate how the constants involved are affected by the length of the document. These findings are exemplified through a series of numerical examples.

Static and contextual multilingual embeddings have complementary strengths. Static embeddings, while less expressive than contextual language models, can be more straightforwardly aligned across multiple languages. We combine the strengths of static and contextual models to improve multilingual representations. We extract static embeddings for 40 languages from XLM-R, validate those embeddings with cross-lingual word retrieval, and then align them using VecMap. This results in high-quality, highly multilingual static embeddings. Then we apply a novel continued pre-training approach to XLM-R, leveraging the high quality alignment of our static embeddings to better align the representation space of XLM-R. We show positive results for multiple complex semantic tasks. We release the static embeddings and the continued pre-training code. Unlike most previous work, our continued pre-training approach does not require parallel text.

One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product of training large language models (LLMs). One major drawback of this type of representation is their incomprehensibility to humans. Understanding the embedding space is crucial for several important needs, including the need to debug the embedding method and compare it to alternatives, and the need to detect biases hidden in the model. In this paper, we present a novel method of understanding embeddings by transforming a latent embedding space into a comprehensible conceptual space. We present an algorithm for deriving a conceptual space with dynamic on-demand granularity. We devise a new evaluation method, using either human rater or LLM-based raters, to show that the conceptualized vectors indeed represent the semantics of the original latent ones. We show the use of our method for various tasks, including comparing the semantics of alternative models and tracing the layers of the LLM. The code is available online https://github.com/adiSimhi/Interpreting-Embedding-Spaces-by-Conceptualization.

Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In addition, it needs to construct the similarity graph for samples, which suffers from the curse of dimensionality when the data are high-dimensional. To address these two challenges, we introduce Deep Spectral Clustering (DSC), which consists of two main modules: the spectral embedding module and the greedy Kmeans module. The former module learns to efficiently embed raw samples into the spectral embedding space using deep neural networks and power iteration. The latter module improves the cluster structures of Kmeans on the learned spectral embeddings by a greedy optimization strategy, which iteratively reveals the direction of the worst cluster structures and optimizes embeddings in this direction. To jointly optimize spectral embeddings and clustering, we seamlessly integrate the two modules and optimize them in an end-to-end manner. Experimental results on seven real-world datasets demonstrate that DSC achieves state-of-the-art clustering performance.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

For convolutional neural network models that optimize an image embedding, we propose a method to highlight the regions of images that contribute most to pairwise similarity. This work is a corollary to the visualization tools developed for classification networks, but applicable to the problem domains better suited to similarity learning. The visualization shows how similarity networks that are fine-tuned learn to focus on different features. We also generalize our approach to embedding networks that use different pooling strategies and provide a simple mechanism to support image similarity searches on objects or sub-regions in the query image.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite of pre-trained decoder-only language models. Our innovation is an algorithm that produces optimal configurations of model sizes, data quantities, and fine-tuning methods for text-embedding models at different computational budget levels. The resulting recipe, which we obtain through extensive experiments, can be used by practitioners to make informed design choices for their embedding models. Specifically, our findings suggest that full fine-tuning and low-rank adaptation fine-tuning produce optimal models at lower and higher computational budgets respectively.

A crucial component of many deep learning applications (such as FAQ and RAG) is dense retrieval, in which embedding models are used to convert raw text to numerical vectors and then get the most similar text by MIPS (Maximum Inner Product Search). Some text embedding benchmarks (e.g. MTEB, BEIR, and AIR-Bench) have been established to evaluate embedding models accurately. Thanks to these benchmarks, we can use SOTA models; however, the deployment and application of these models in industry were hampered by their large vector dimensions and numerous parameters. To alleviate this problem, 1) we present a distillation technique that can enable a smaller student model to achieve good performance. 2) Inspired by MRL we present a training approach of reducing the vector dimensions based on its own vectors or its teacher vectors. 3) We do simple yet effective alignment training between images and text to make our model a multimodal encoder. We trained Stella and Jasper models using the technologies above and achieved high scores on the MTEB leaderboard. We release the model and data at Hugging Face Hub (https://huggingface.co/infgrad/jasper_en_vision_language_v1) and the training logs are at https://api.wandb.ai/links/dunnzhang0/z8jqoqpb.

Word embeddings are an essential component in a wide range of natural language processing applications. However, distributional semantic models are known to struggle when only a small number of context sentences are available. Several methods have been proposed to obtain higher-quality vectors for these words, leveraging both this context information and sometimes the word forms themselves through a hybrid approach. We show that the current tasks do not suffice to evaluate models that use word-form information, as such models can easily leverage word forms in the training data that are related to word forms in the test data. We introduce 3 new tasks, allowing for a more balanced comparison between models. Furthermore, we show that hyperparameters that have largely been ignored in previous work can consistently improve the performance of both baseline and advanced models, achieving a new state of the art on 4 out of 6 tasks.

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

LLM-based text embedders have substantially improved retrieval and semantic representation quality, but their deployment remains costly: large backbone models slow down embedding inference, while high-dimensional full-precision embeddings impose substantial storage and bandwidth overhead on large-scale indexes. In this paper, we present BITEMBED, an extreme low-bit framework for LLM-based text embedding that jointly targets encoding efficiency and vector storage. BITEMBED converts pretrained LLM backbones into BitNet-style embedding encoders with ternary weights, quantized activations, and lightweight normalization refinement. The converted model is adapted to representation learning through continual contrastive pre-training, followed by supervised contrastive fine-tuning with both similarity-distribution distillation and attention-relation distillation from a full-precision teacher. Beyond quantizing the backbone, BITEMBED further trains output embeddings to support multiple storage precisions meeting different storage needs in various scenarios. Experiments on MMTEB (eng, v2) with Qwen3-0.6B and Gemma3-270M show that BITEMBED is largely comparable to full precision teacher embedders. Moreover, BITEMBED flexibly obtains text embeddings of various precisions, achieving a trade-off between performance and storage cost.

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

Recent advancements in Large Language Models (LLMs) have drawn increasing attention since the learned embeddings pretrained on large-scale datasets have shown powerful ability in various downstream applications. However, whether the learned knowledge by LLMs can be transferred to clinical cardiology remains unknown. In this work, we aim to bridge this gap by transferring the knowledge of LLMs to clinical Electrocardiography (ECG). We propose an approach for cardiovascular disease diagnosis and automatic ECG diagnosis report generation. We also introduce an additional loss function by Optimal Transport (OT) to align the distribution between ECG and language embedding. The learned embeddings are evaluated on two downstream tasks: (1) automatic ECG diagnosis report generation, and (2) zero-shot cardiovascular disease detection. Our approach is able to generate high-quality cardiac diagnosis reports and also achieves competitive zero-shot classification performance even compared with supervised baselines, which proves the feasibility of transferring knowledge from LLMs to the cardiac domain.

Accurate and scalable machine-learned inter-atomic potentials (MLIPs) are essential for molecular simulations ranging from drug discovery to new material design. Current state-of-the-art models enforce roto-translational symmetries through equivariant neural network architectures, a hard-wired inductive bias that can often lead to reduced flexibility, computational efficiency, and scalability. In this work, we introduce TransIP: Transformer-based Inter-Atomic Potentials, a novel training paradigm for interatomic potentials achieving symmetry compliance without explicit architectural constraints. Our approach guides a generic non-equivariant Transformer-based model to learn SO(3)-equivariance by optimizing its representations in the embedding space. Trained on the recent Open Molecules (OMol25) collection, a large and diverse molecular dataset built specifically for MLIPs and covering different types of molecules (including small organics, biomolecular fragments, and electrolyte-like species), TransIP attains comparable performance in machine-learning force fields versus state-of-the-art equivariant baselines. Further, compared to a data augmentation baseline, TransIP achieves 40% to 60% improvement in performance across varying OMol25 dataset sizes. More broadly, our work shows that learned equivariance can be a powerful and efficient alternative to equivariant or augmentation-based MLIP models.

We introduce SemCSE, an unsupervised method for learning semantic embeddings of scientific texts. Building on recent advances in contrastive learning for text embeddings, our approach leverages LLM-generated summaries of scientific abstracts to train a model that positions semantically related summaries closer together in the embedding space. This resulting objective ensures that the model captures the true semantic content of a text, in contrast to traditional citation-based approaches that do not necessarily reflect semantic similarity. To validate this, we propose a novel benchmark designed to assess a model's ability to understand and encode the semantic content of scientific texts, demonstrating that our method enforces a stronger semantic separation within the embedding space. Additionally, we evaluate SemCSE on the comprehensive SciRepEval benchmark for scientific text embeddings, where it achieves state-of-the-art performance among models of its size, thus highlighting the benefits of a semantically focused training approach.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often found, largely by focusing on extremal filter responses. In this paper, we show that this approach can favor easy-to-interpret cases that are not necessarily representative of the average behavior of a representation. A more realistic but harder-to-study hypothesis is that semantic representations are distributed, and thus filters must be studied in conjunction. In order to investigate this idea while enabling systematic visualization and quantification of multiple filter responses, we introduce the Net2Vec framework, in which semantic concepts are mapped to vectorial embeddings based on corresponding filter responses. By studying such embeddings, we are able to show that 1., in most cases, multiple filters are required to code for a concept, that 2., often filters are not concept specific and help encode multiple concepts, and that 3., compared to single filter activations, filter embeddings are able to better characterize the meaning of a representation and its relationship to other concepts.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings. Our code is available at https://github.com/aktsonthalia/rankable-vision-embeddings.

We present QZhou-Embedding, a general-purpose contextual text embedding model with exceptional text representation capabilities. Built upon the Qwen2.5-7B-Instruct foundation model, we designed a unified multi-task framework comprising specialized data transformation and training strategies. The data transformation scheme enables the incorporation of more diverse textual training datasets, while the task-specific training strategies enhance model learning efficiency. We developed a data synthesis pipeline leveraging LLM API, incorporating techniques such as paraphrasing, augmentation, and hard negative example generation to improve the semantic richness and sample difficulty of the training set. Additionally, we employ a two-stage training strategy, comprising initial retrieval-focused pretraining followed by full-task fine-tuning, enabling the embedding model to extend its capabilities based on robust retrieval performance. Our model achieves state-of-the-art results on the MTEB and CMTEB benchmarks, ranking first on both leaderboards (August 27 2025), and simultaneously achieves state-of-the-art performance on tasks including reranking, clustering, etc. Our findings demonstrate that higher-quality, more diverse data is crucial for advancing retrieval model performance, and that leveraging LLMs generative capabilities can further optimize data quality for embedding model breakthroughs. Our model weights are released on HuggingFace under Apache 2.0 license. For reproducibility, we provide evaluation code and instructions on GitHub.

Automated and semi-automated techniques in biomedical electron microscopy (EM) enable the acquisition of large datasets at a high rate. Segmentation methods are therefore essential to analyze and interpret these large volumes of data, which can no longer completely be labeled manually. In recent years, deep learning algorithms achieved impressive results in both pixel-level labeling (semantic segmentation) and the labeling of separate instances of the same class (instance segmentation). In this review, we examine how these algorithms were adapted to the task of segmenting cellular and sub-cellular structures in EM images. The special challenges posed by such images and the network architectures that overcame some of them are described. Moreover, a thorough overview is also provided on the notable datasets that contributed to the proliferation of deep learning in EM. Finally, an outlook of current trends and future prospects of EM segmentation is given, especially in the area of label-free learning.

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Recent multimodal embedding approaches leveraging multimodal large language models (MLLMs) fine-tuned with contrastive learning (CL) have shown promising results, yet the underlying reasons behind their superiority remain underexplored. This work argues that a crucial advantage of MLLM-based approaches stems from implicit cross-modal alignment achieved during generative pretraining, where the language decoder learns to exploit multimodal signals within a shared representation space for generating unimodal outputs. Through analysis of anisotropy and kernel similarity structure, we empirically confirm that latent alignment emerges within MLLM representations, allowing CL to serve as a lightweight refinement stage. Leveraging this insight, we propose a Language-Centric Omnimodal Embedding framework, termed LCO-Emb. Extensive experiments across diverse backbones and benchmarks demonstrate its effectiveness, achieving state-of-the-art performance across modalities. Furthermore, we identify a Generation-Representation Scaling Law (GRSL), showing that the representational capabilities gained through contrastive refinement scales positively with the MLLM's generative capabilities. This suggests that improving generative abilities evolves as an effective paradigm for enhancing representation quality. We provide a theoretical explanation of GRSL, which formally links the MLLM's generative quality to the upper bound on its representation performance, and validate it on a challenging, low-resource visual-document retrieval task, showing that continual generative pretraining before CL can further enhance the potential of a model's embedding capabilities. Codes, models, and resources are available at https://github.com/LCO-Embedding/LCO-Embedding.

The blind application of machine learning runs the risk of amplifying biases present in data. Such a danger is facing us with word embedding, a popular framework to represent text data as vectors which has been used in many machine learning and natural language processing tasks. We show that even word embeddings trained on Google News articles exhibit female/male gender stereotypes to a disturbing extent. This raises concerns because their widespread use, as we describe, often tends to amplify these biases. Geometrically, gender bias is first shown to be captured by a direction in the word embedding. Second, gender neutral words are shown to be linearly separable from gender definition words in the word embedding. Using these properties, we provide a methodology for modifying an embedding to remove gender stereotypes, such as the association between between the words receptionist and female, while maintaining desired associations such as between the words queen and female. We define metrics to quantify both direct and indirect gender biases in embeddings, and develop algorithms to "debias" the embedding. Using crowd-worker evaluation as well as standard benchmarks, we empirically demonstrate that our algorithms significantly reduce gender bias in embeddings while preserving the its useful properties such as the ability to cluster related concepts and to solve analogy tasks. The resulting embeddings can be used in applications without amplifying gender bias.

Masked visual modeling has attracted much attention due to its promising potential in learning generalizable representations. Typical approaches urge models to predict specific contents of masked tokens, which can be intuitively considered as teaching a student (the model) to solve given problems (predicting masked contents). Under such settings, the performance is highly correlated with mask strategies (the difficulty of provided problems). We argue that it is equally important for the model to stand in the shoes of a teacher to produce challenging problems by itself. Intuitively, patches with high values of reconstruction loss can be regarded as hard samples, and masking those hard patches naturally becomes a demanding reconstruction task. To empower the model as a teacher, we propose Hard Patches Mining (HPM), predicting patch-wise losses and subsequently determining where to mask. Technically, we introduce an auxiliary loss predictor, which is trained with a relative objective to prevent overfitting to exact loss values. Also, to gradually guide the training procedure, we propose an easy-to-hard mask strategy. Empirically, HPM brings significant improvements under both image and video benchmarks. Interestingly, solely incorporating the extra loss prediction objective leads to better representations, verifying the efficacy of determining where is hard to reconstruct. The code is available at https://github.com/Haochen-Wang409/HPM.

Text embedding models have been popular for information retrieval applications such as semantic search and Question-Answering systems based on Retrieval-Augmented Generation (RAG). Those models are typically Transformer models that are fine-tuned with contrastive learning objectives. Many papers introduced new embedding model architectures and training approaches, however, one of the key ingredients, the process of mining negative passages, remains poorly explored or described. One of the challenging aspects of fine-tuning embedding models is the selection of high quality hard-negative passages for contrastive learning. In this paper we propose a family of positive-aware mining methods that leverage the positive relevance score for more effective false negatives removal. We also provide a comprehensive ablation study on hard-negative mining methods over their configurations, exploring different teacher and base models. We demonstrate the efficacy of our proposed methods by introducing the NV-Retriever-v1 model, which scores 60.9 on MTEB Retrieval (BEIR) benchmark and 0.65 points higher than previous methods. The model placed 1st when it was published to MTEB Retrieval on July 07, 2024.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

OWL (Web Ontology Language) ontologies which are able to formally represent complex knowledge and support semantic reasoning have been widely adopted across various domains such as healthcare and bioinformatics. Recently, ontology embeddings have gained wide attention due to its potential to infer plausible new knowledge and approximate complex reasoning. However, existing methods face notable limitations: geometric model-based embeddings typically overlook valuable textual information, resulting in suboptimal performance, while the approaches that incorporate text, which are often based on language models, fail to preserve the logical structure. In this work, we propose a new ontology embedding method OnT, which tunes a Pretrained Language Model (PLM) via geometric modeling in a hyperbolic space for effectively incorporating textual labels and simultaneously preserving class hierarchies and other logical relationships of Description Logic EL. Extensive experiments on four real-world ontologies show that OnT consistently outperforms the baselines including the state-of-the-art across both tasks of prediction and inference of axioms. OnT also demonstrates strong potential in real-world applications, indicated by its robust transfer learning abilities and effectiveness in real cases of constructing a new ontology from SNOMED CT. Data and code are available at https://github.com/HuiYang1997/OnT.

Large language models exhibit impressive zero-shot capabilities across a wide range of downstream tasks. However, they struggle to function as off-the-shelf embedding models, leading to suboptimal performance on massive text embedding benchmarks. In this paper, we identify a potential cause underlying this deficiency. Our motivation stems from an unexpected observation: text embeddings tend to align with frequent but uninformative tokens when projected onto the vocabulary space. We argue that this excessive expression of high-frequency tokens suppresses the model's ability to capture nuanced semantics. To address this, we introduce EmbedFilter, a simple linear transformation designed to refine text embeddings derived from LLMs directly. Specifically, we uncover that the unembedding matrix within LLMs encodes a latent space that is actively writing these frequent tokens into embedding space. By filtering out this subspace, EmbedFilter suppress the influence of high-frequency tokens, thereby enhancing semantic representations. As a compelling byproduct, this enables an inherent dimensionality reduction, lowering index storage and speedup retrieval while fully preserving the refined embedding quality. Our experiments across multiple LLM backbones demonstrate that LLMs equipped with EmbedFilter achieve superior zero-shot downstream performance even with significantly reduced embedding dimensions. We hope our findings provide deeper insights into the mechanisms of LLM-based representations and inspire more principled designs to improve text embeddings training. Our code is available at https://github.com/CentreChen/EmbFilter.

Topic models have been prevalent for decades with various applications. However, existing topic models commonly suffer from the notorious topic collapsing: discovered topics semantically collapse towards each other, leading to highly repetitive topics, insufficient topic discovery, and damaged model interpretability. In this paper, we propose a new neural topic model, Embedding Clustering Regularization Topic Model (ECRTM). Besides the existing reconstruction error, we propose a novel Embedding Clustering Regularization (ECR), which forces each topic embedding to be the center of a separately aggregated word embedding cluster in the semantic space. This enables each produced topic to contain distinct word semantics, which alleviates topic collapsing. Regularized by ECR, our ECRTM generates diverse and coherent topics together with high-quality topic distributions of documents. Extensive experiments on benchmark datasets demonstrate that ECRTM effectively addresses the topic collapsing issue and consistently surpasses state-of-the-art baselines in terms of topic quality, topic distributions of documents, and downstream classification tasks.

Quantitative microstructural characterization is fundamental to materials science, where electron micrograph (EM) provides indispensable high-resolution insights. However, progress in deep learning-based EM characterization has been hampered by the scarcity of large-scale, diverse, and expert-annotated datasets, due to acquisition costs, privacy concerns, and annotation complexity. To address this issue, we introduce UniEM-3M, the first large-scale and multimodal EM dataset for instance-level understanding. It comprises 5,091 high-resolution EMs, about 3 million instance segmentation labels, and image-level attribute-disentangled textual descriptions, a subset of which will be made publicly available. Furthermore, we are also releasing a text-to-image diffusion model trained on the entire collection to serve as both a powerful data augmentation tool and a proxy for the complete data distribution. To establish a rigorous benchmark, we evaluate various representative instance segmentation methods on the complete UniEM-3M and present UniEM-Net as a strong baseline model. Quantitative experiments demonstrate that this flow-based model outperforms other advanced methods on this challenging benchmark. Our multifaceted release of a partial dataset, a generative model, and a comprehensive benchmark -- available at huggingface -- will significantly accelerate progress in automated materials analysis.

LLM-based text embedders typically encode the semantic content of their input. However, embedding tasks require mapping diverse inputs to similar outputs. Typically, this input-output is addressed by training embedding models with paired data using contrastive learning. In this work, we propose a novel self-supervised approach, LLM2Vec-Gen, which adopts a different paradigm: rather than encoding the input, we learn to represent the model's potential response. Specifically, we add trainable special tokens to the LLM's vocabulary, append them to input, and optimize them to represent the LLM's response in a fixed-length sequence. Training is guided by the LLM's own completion for the query, along with an unsupervised embedding teacher that provides distillation targets. This formulation helps to bridge the input-output gap and transfers LLM capabilities such as safety alignment and reasoning to embedding tasks. Crucially, the LLM backbone remains frozen and training requires only unlabeled queries. LLM2Vec-Gen achieves state-of-the-art self-supervised performance on the Massive Text Embedding Benchmark (MTEB), improving by 9.3% over the best unsupervised embedding teacher. We also observe up to 43.2% reduction in harmful content retrieval and 29.3% improvement in reasoning capabilities for embedding tasks. Finally, the learned embeddings are interpretable and can be decoded into text to reveal their semantic content.

Fine-grained and instance-level recognition methods are commonly trained and evaluated on specific domains, in a model per domain scenario. Such an approach, however, is impractical in real large-scale applications. In this work, we address the problem of universal image embedding, where a single universal model is trained and used in multiple domains. First, we leverage existing domain-specific datasets to carefully construct a new large-scale public benchmark for the evaluation of universal image embeddings, with 241k query images, 1.4M index images and 2.8M training images across 8 different domains and 349k classes. We define suitable metrics, training and evaluation protocols to foster future research in this area. Second, we provide a comprehensive experimental evaluation on the new dataset, demonstrating that existing approaches and simplistic extensions lead to worse performance than an assembly of models trained for each domain separately. Finally, we conducted a public research competition on this topic, leveraging industrial datasets, which attracted the participation of more than 1k teams worldwide. This exercise generated many interesting research ideas and findings which we present in detail. Project webpage: https://cmp.felk.cvut.cz/univ_emb/

Text embeddings have attracted growing interest due to their effectiveness across a wide range of natural language processing (NLP) tasks, such as retrieval, classification, clustering, bitext mining, and summarization. With the emergence of pretrained language models (PLMs), general-purpose text embeddings (GPTE) have gained significant traction for their ability to produce rich, transferable representations. The general architecture of GPTE typically leverages PLMs to derive dense text representations, which are then optimized through contrastive learning on large-scale pairwise datasets. In this survey, we provide a comprehensive overview of GPTE in the era of PLMs, focusing on the roles PLMs play in driving its development. We first examine the fundamental architecture and describe the basic roles of PLMs in GPTE, i.e., embedding extraction, expressivity enhancement, training strategies, learning objectives, and data construction. Then, we describe advanced roles enabled by PLMs, such as multilingual support, multimodal integration, code understanding, and scenario-specific adaptation. Finally, we highlight potential future research directions that move beyond traditional improvement goals, including ranking integration, safety considerations, bias mitigation, structural information incorporation, and the cognitive extension of embeddings. This survey aims to serve as a valuable reference for both newcomers and established researchers seeking to understand the current state and future potential of GPTE.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Learning embedding table plays a fundamental role in Click-through rate(CTR) prediction from the view of the model performance and memory usage. The embedding table is a two-dimensional tensor, with its axes indicating the number of feature values and the embedding dimension, respectively. To learn an efficient and effective embedding table, recent works either assign various embedding dimensions for feature fields and reduce the number of embeddings respectively or mask the embedding table parameters. However, all these existing works cannot get an optimal embedding table. On the one hand, various embedding dimensions still require a large amount of memory due to the vast number of features in the dataset. On the other hand, decreasing the number of embeddings usually suffers from performance degradation, which is intolerable in CTR prediction. Finally, pruning embedding parameters will lead to a sparse embedding table, which is hard to be deployed. To this end, we propose an optimal embedding table learning framework OptEmbed, which provides a practical and general method to find an optimal embedding table for various base CTR models. Specifically, we propose pruning the redundant embeddings regarding corresponding features' importance by learnable pruning thresholds. Furthermore, we consider assigning various embedding dimensions as one single candidate architecture. To efficiently search the optimal embedding dimensions, we design a uniform embedding dimension sampling scheme to equally train all candidate architectures, meaning architecture-related parameters and learnable thresholds are trained simultaneously in one supernet. We then propose an evolution search method based on the supernet to find the optimal embedding dimensions for each field. Experiments on public datasets show that OptEmbed can learn a compact embedding table which can further improve the model performance.

Multimodal representation learning models have demonstrated successful operation across complex tasks, and the integration of vision-language models (VLMs) has further enabled embedding models with instruction-following capabilities. However, existing embedding models lack visual-interactive capabilities to specify regions of interest from users (e.g., point, bounding box, mask), which have been explored in generative models to broaden their human-interactive applicability. Equipping embedding models with visual interactions not only would unlock new applications with localized grounding of user intent, which remains unexplored, but also enable the models to learn entity-level information within images to complement their global representations for conventional embedding tasks. In this paper, we propose a novel Visual-InteRactive Text-Image Universal Embedder (VIRTUE) that extends the capabilities of the segmentation model and the vision-language model to the realm of representation learning. In VIRTUE, the segmentation model can process visual prompts that pinpoint specific regions within an image, thereby enabling the embedder to handle complex and ambiguous scenarios more precisely. To evaluate the visual-interaction ability of VIRTUE, we introduce a large-scale Segmentation-and-Scene Caption Retrieval (SCaR) benchmark comprising 1M samples that aims to retrieve the text caption by jointly considering the entity with a specific object and image scene. VIRTUE consistently achieves a state-of-the-art performance with significant improvements across 36 universal MMEB (3.1%-8.5%) and five visual-interactive SCaR (15.2%-20.3%) tasks.

In this report, we introduce Eddy-VL 1.9B, a compressed multimodal embedding model built on Qwen3-VL-Embedding-2B for offline, edge-deployable vision-language retrieval. Eddy-VL targets air-gapped forensic and investigative settings where cloud APIs are unavailable and low latency is essential. Compression combines (i) probe-driven structural pruning that removes four redundant text-decoder layers (28 to 24) ranked by adjacent-layer linear CKA, and (ii) layered knowledge distillation with hole-covering teacher-student mappings, mid-layer attention-map 1-CKA, and final-layer MSE and cosine losses with Matryoshka dimensions {128, 256, 512, 1024, 2048}. The released model contains 1,926,188,032 parameters (3.85 GB bf16), representing approximately 9.5% fewer parameters than the 2.13B teacher model. Empirical evaluations on MMEB-V2 (78 tasks, VLM2Vec protocol) show that Eddy-VL achieves an overall score of 63.2 compared with 68.9 for the teacher, retaining 91.7% of the teacher's performance while recovering 6.4 of the 12.1 points lost through pruning alone (56.8). Compositional reasoning performance remains close to the teacher on SugarCrepe (86.1 vs. 86.4), MR2-Bench (24.5 vs. 24.7), and ARO (59.5 vs. 60.4), while Winoground group performance (6.8 vs. 8.5) remains the primary limitation. Depth pruning also reduces forward latency by approximately 10% (150.0 to 136.4 ms per image on NVIDIA DGX Spark using FlashAttention-2). We present the architecture, compression methodology, training procedures, and evaluation results, demonstrating the effectiveness of Eddy-VL for multimodal retrieval under constrained edge deployment. Model weights and inference code are publicly available on Hugging Face.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.

Document embeddings and similarity measures underpin content-based recommender systems, whereby a document is commonly represented as a single generic embedding. However, similarity computed on single vector representations provides only one perspective on document similarity that ignores which aspects make two documents alike. To address this limitation, aspect-based similarity measures have been developed using document segmentation or pairwise multi-class document classification. While segmentation harms the document coherence, the pairwise classification approach scales poorly to large scale corpora. In this paper, we treat aspect-based similarity as a classical vector similarity problem in aspect-specific embedding spaces. We represent a document not as a single generic embedding but as multiple specialized embeddings. Our approach avoids document segmentation and scales linearly w.r.t.the corpus size. In an empirical study, we use the Papers with Code corpus containing 157,606 research papers and consider the task, method, and dataset of the respective research papers as their aspects. We compare and analyze three generic document embeddings, six specialized document embeddings and a pairwise classification baseline in the context of research paper recommendations. As generic document embeddings, we consider FastText, SciBERT, and SPECTER. To compute the specialized document embeddings, we compare three alternative methods inspired by retrofitting, fine-tuning, and Siamese networks. In our experiments, Siamese SciBERT achieved the highest scores. Additional analyses indicate an implicit bias of the generic document embeddings towards the dataset aspect and against the method aspect of each research paper. Our approach of aspect-based document embeddings mitigates potential risks arising from implicit biases by making them explicit.

We present a novel dual-head deep learning architecture for protein-protein interaction modeling that enables simultaneous prediction of binding affinity (ΔG) and mutation-induced affinity changes (ΔΔG) using only protein sequence information. Our approach offers a significant advancement over existing methods by employing specialized prediction heads that operate on a shared representation network, allowing direct and optimized prediction of both values. To ensure robust generalization, we integrated complementary datasets from SKEMPI v2 and PDBbind with a rigorous protein domain-based splitting strategy that prevents information leakage between training and validation sets. Our architecture combines transformer-based encoders with a novel cross-attention mechanism that processes paired protein sequences directly, without requiring any structural information. The network embeds input sequences using ESM3 representations, then employs a learnable sliced window embedding layer to manage variable-length sequences efficiently. A multi-layer transformer encoder with bidirectional self-attention captures intra-protein patterns, while cross-attention layers enable explicit modeling of interactions between protein pairs. This shared representation network feeds into separate ΔG and ΔΔG prediction heads, allowing task-specific optimization while leveraging common features. The model achieves ΔΔG validation of Pearson correlation at 0.485, while maintaining strong ΔG predictions (Pearson: 0.638). While existing approaches require protein structure data and binding interface information, our model eliminates these constraints. This provides a critical advantage for the numerous proteins with unknown structures or those challenging to crystallize, such as viral and intrinsically disordered proteins.

Text embedding models have emerged as powerful tools for transforming sentences into fixed-sized feature vectors that encapsulate semantic information. While these models are essential for tasks like information retrieval, semantic clustering, and text re-ranking, most existing open-source models, especially those built on architectures like BERT, struggle to represent lengthy documents and often resort to truncation. One common approach to mitigate this challenge involves splitting documents into smaller paragraphs for embedding. However, this strategy results in a much larger set of vectors, consequently leading to increased memory consumption and computationally intensive vector searches with elevated latency. To address these challenges, we introduce Jina Embeddings 2, an open-source text embedding model capable of accommodating up to 8192 tokens. This model is designed to transcend the conventional 512-token limit and adeptly process long documents. Jina Embeddings 2 not only achieves state-of-the-art performance on a range of embedding-related tasks in the MTEB benchmark but also matches the performance of OpenAI's proprietary ada-002 model. Additionally, our experiments indicate that an extended context can enhance performance in tasks such as NarrativeQA.

Language grounding to vision is an active field of research aiming to enrich text-based representations of word meanings by leveraging perceptual knowledge from vision. Despite many attempts at language grounding, it is still unclear how to effectively inject visual knowledge into the word embeddings of a language in such a way that a proper balance of textual and visual knowledge is maintained. Some common concerns are the following. Is visual grounding beneficial for abstract words or is its contribution only limited to concrete words? What is the optimal way of bridging the gap between text and vision? How much do we gain by visually grounding textual embeddings? The present study addresses these questions by proposing a simple yet very effective grounding approach for pre-trained word embeddings. Our model aligns textual embeddings with vision while largely preserving the distributional statistics that characterize word use in text corpora. By applying a learned alignment, we are able to generate visually grounded embeddings for unseen words, including abstract words. A series of evaluations on word similarity benchmarks shows that visual grounding is beneficial not only for concrete words, but also for abstract words. We also show that our method for visual grounding offers advantages for contextualized embeddings, but only when these are trained on corpora of relatively modest size. Code and grounded embeddings for English are available at https://github.com/Hazel1994/Visually_Grounded_Word_Embeddings_2.

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.