Daily Papers

Despite the central role of attention heads in Transformers, we lack tools to understand why a model attends to a particular token. To address this, we study the query-key (QK) space -- the bilinear joint embedding space between queries and keys. We present a contrastive covariance method to decompose the QK space into low-rank, human-interpretable components. It is when features in keys and queries align in these low-rank subspaces that high attention scores are produced. We first study our method both analytically and empirically in a simplified setting. We then apply our method to large language models to identify human-interpretable QK subspaces for categorical semantic features and binding features. Finally, we demonstrate how attention scores can be attributed to our identified features.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains.

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.

Reconstruction and joint embedding have emerged as two leading paradigms in Self Supervised Learning (SSL). Reconstruction methods focus on recovering the original sample from a different view in input space. On the other hand, joint embedding methods align the representations of different views in latent space. Both approaches offer compelling advantages, yet practitioners lack clear guidelines for choosing between them. In this work, we unveil the core mechanisms that distinguish each paradigm. By leveraging closed form solutions for both approaches, we precisely characterize how the view generation process, e.g. data augmentation, impacts the learned representations. We then demonstrate that, unlike supervised learning, both SSL paradigms require a minimal alignment between augmentations and irrelevant features to achieve asymptotic optimality with increasing sample size. Our findings indicate that in scenarios where these irrelevant features have a large magnitude, joint embedding methods are preferable because they impose a strictly weaker alignment condition compared to reconstruction based methods. These results not only clarify the trade offs between the two paradigms but also substantiate the empirical success of joint embedding approaches on real world challenging datasets.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes. However, we believe that the potential offered by this paradigm is not yet fully exploited. In this work, we propose to utilize the structure of the space spanned by the attributes using a set of relations. We devise objective functions to preserve these relations in the embedding space, thereby inducing semanticity to the embedding space. Through extensive experimental evaluation on five benchmark datasets, we demonstrate that inducing semanticity to the embedding space is beneficial for zero-shot learning. The proposed approach outperforms the state-of-the-art on the standard zero-shot setting as well as the more realistic generalized zero-shot setting. We also demonstrate how the proposed approach can be useful for making approximate semantic inferences about an image belonging to a category for which attribute information is not available.

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing image classifier and a semantic word embedding model, which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.

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.

Zero-shot learning (ZSL) models rely on learning a joint embedding space where both textual/semantic description of object classes and visual representation of object images can be projected to for nearest neighbour search. Despite the success of deep neural networks that learn an end-to-end model between text and images in other vision problems such as image captioning, very few deep ZSL model exists and they show little advantage over ZSL models that utilise deep feature representations but do not learn an end-to-end embedding. In this paper we argue that the key to make deep ZSL models succeed is to choose the right embedding space. Instead of embedding into a semantic space or an intermediate space, we propose to use the visual space as the embedding space. This is because that in this space, the subsequent nearest neighbour search would suffer much less from the hubness problem and thus become more effective. This model design also provides a natural mechanism for multiple semantic modalities (e.g., attributes and sentence descriptions) to be fused and optimised jointly in an end-to-end manner. Extensive experiments on four benchmarks show that our model significantly outperforms the existing models. Code is available at https://github.com/lzrobots/DeepEmbeddingModel_ZSL

Bilinear pooling (BLP) refers to a family of operations recently developed for fusing features from different modalities predominantly developed for VQA models. A bilinear (outer-product) expansion is thought to encourage models to learn interactions between two feature spaces and has experimentally outperformed `simpler' vector operations (concatenation and element-wise-addition/multiplication) on VQA benchmarks. Successive BLP techniques have yielded higher performance with lower computational expense and are often implemented alongside attention mechanisms. However, despite significant progress in VQA, BLP methods have not been widely applied to more recently explored video question answering (video-QA) tasks. In this paper, we begin to bridge this research gap by applying BLP techniques to various video-QA benchmarks, namely: TVQA, TGIF-QA, Ego-VQA and MSVD-QA. We share our results on the TVQA baseline model, and the recently proposed heterogeneous-memory-enchanced multimodal attention (HME) model. Our experiments include both simply replacing feature concatenation in the existing models with BLP, and a modified version of the TVQA baseline to accommodate BLP we name the `dual-stream' model. We find that our relatively simple integration of BLP does not increase, and mostly harms, performance on these video-QA benchmarks. Using recently proposed theoretical multimodal fusion taxonomies, we offer insight into why BLP-driven performance gain for video-QA benchmarks may be more difficult to achieve than in earlier VQA models. We suggest a few additional `best-practices' to consider when applying BLP to video-QA. We stress that video-QA models should carefully consider where the complex representational potential from BLP is actually needed to avoid computational expense on `redundant' fusion.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Reconstructing interacting hands from a single RGB image is a very challenging task. On the one hand, severe mutual occlusion and similar local appearance between two hands confuse the extraction of visual features, resulting in the misalignment of estimated hand meshes and the image. On the other hand, there are complex spatial relationship between interacting hands, which significantly increases the solution space of hand poses and increases the difficulty of network learning. In this paper, we propose a decoupled iterative refinement framework to achieve pixel-alignment hand reconstruction while efficiently modeling the spatial relationship between hands. Specifically, we define two feature spaces with different characteristics, namely 2D visual feature space and 3D joint feature space. First, we obtain joint-wise features from the visual feature map and utilize a graph convolution network and a transformer to perform intra- and inter-hand information interaction in the 3D joint feature space, respectively. Then, we project the joint features with global information back into the 2D visual feature space in an obfuscation-free manner and utilize the 2D convolution for pixel-wise enhancement. By performing multiple alternate enhancements in the two feature spaces, our method can achieve an accurate and robust reconstruction of interacting hands. Our method outperforms all existing two-hand reconstruction methods by a large margin on the InterHand2.6M dataset.

Joint Embedding Predictive Architectures (JEPA) have emerged as a powerful framework for learning general-purpose representations. However, these models often lack interpretability and suffer from inefficiencies due to dense embedding representations. We propose SparseJEPA, an extension that integrates sparse representation learning into the JEPA framework to enhance the quality of learned representations. SparseJEPA employs a penalty method that encourages latent space variables to be shared among data features with strong semantic relationships, while maintaining predictive performance. We demonstrate the effectiveness of SparseJEPA by training on the CIFAR-100 dataset and pre-training a lightweight Vision Transformer. The improved embeddings are utilized in linear-probe transfer learning for both image classification and low-level tasks, showcasing the architecture's versatility across different transfer tasks. Furthermore, we provide a theoretical proof that demonstrates that the grouping mechanism enhances representation quality. This was done by displaying that grouping reduces Multiinformation among latent-variables, including proofing the Data Processing Inequality for Multiinformation. Our results indicate that incorporating sparsity not only refines the latent space but also facilitates the learning of more meaningful and interpretable representations. In further work, hope to further extend this method by finding new ways to leverage the grouping mechanism through object-centric representation learning.

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.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y, g cdot y), where g is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G:= (R_m times Z_n times Z_n), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

Profiting from large-scale training datasets, advances in neural architecture design and efficient inference, joint embeddings have become the dominant approach for tackling cross-modal retrieval. In this work we first show that, despite their effectiveness, state-of-the-art joint embeddings suffer significantly from the longstanding "hubness problem" in which a small number of gallery embeddings form the nearest neighbours of many queries. Drawing inspiration from the NLP literature, we formulate a simple but effective framework called Querybank Normalisation (QB-Norm) that re-normalises query similarities to account for hubs in the embedding space. QB-Norm improves retrieval performance without requiring retraining. Differently from prior work, we show that QB-Norm works effectively without concurrent access to any test set queries. Within the QB-Norm framework, we also propose a novel similarity normalisation method, the Dynamic Inverted Softmax, that is significantly more robust than existing approaches. We showcase QB-Norm across a range of cross modal retrieval models and benchmarks where it consistently enhances strong baselines beyond the state of the art. Code is available at https://vladbogo.github.io/QB-Norm/.

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x in R^d per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality epsilon-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5times fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

We consider the problem of predicting how the likelihood of an outcome of interest for a patient changes over time as we observe more of the patient data. To solve this problem, we propose a supervised contrastive learning framework that learns an embedding representation for each time step of a patient time series. Our framework learns the embedding space to have the following properties: (1) nearby points in the embedding space have similar predicted class probabilities, (2) adjacent time steps of the same time series map to nearby points in the embedding space, and (3) time steps with very different raw feature vectors map to far apart regions of the embedding space. To achieve property (3), we employ a nearest neighbor pairing mechanism in the raw feature space. This mechanism also serves as an alternative to data augmentation, a key ingredient of contrastive learning, which lacks a standard procedure that is adequately realistic for clinical tabular data, to our knowledge. We demonstrate that our approach outperforms state-of-the-art baselines in predicting mortality of septic patients (MIMIC-III dataset) and tracking progression of cognitive impairment (ADNI dataset). Our method also consistently recovers the correct synthetic dataset embedding structure across experiments, a feat not achieved by baselines. Our ablation experiments show the pivotal role of our nearest neighbor pairing.

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.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Joint embedding spaces have significantly advanced music understanding and generation by linking text and audio through multimodal contrastive learning. However, these approaches face large memory requirement limitations due to relying on large batch sizes to effectively utilize negative samples. Further, multimodal joint embedding spaces suffer from a modality gap wherein embeddings from different modalities lie in different manifolds of the embedding space. To address these challenges, we propose Siamese Language-Audio Pretraining (SLAP), a novel multimodal pretraining framework that allows learning powerful representations without negative samples. SLAP adapts the Bootstrap Your Own Latent (BYOL) paradigm for multimodal audio-text training, promoting scalability in training multimodal embedding spaces. We illustrate the ability of our model to learn meaningful relationships between music and text -- specifically, we show that SLAP outperforms CLAP on tasks such as text-music retrieval and zero-shot classification. We also observe competitive downstream performance on several MIR tasks, including with larger or supervised models (genre and instrument classification, auto-tagging). Additionally, our approach has attractive properties, such as a quantifiably reduced modality gap and improved robustness to batch size variations on retrieval performance. Finally, its novel formulation unlocks large-scale training on a single GPU through gradient accumulation.

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural network layers. This makes it hard to use hyperbolic embeddings in downstream tasks. Here, we bridge this gap in a principled manner by combining the formalism of Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks such as gated recurrent units. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

In this paper, we show that a binary latent space can be explored for compact yet expressive image representations. We model the bi-directional mappings between an image and the corresponding latent binary representation by training an auto-encoder with a Bernoulli encoding distribution. On the one hand, the binary latent space provides a compact discrete image representation of which the distribution can be modeled more efficiently than pixels or continuous latent representations. On the other hand, we now represent each image patch as a binary vector instead of an index of a learned cookbook as in discrete image representations with vector quantization. In this way, we obtain binary latent representations that allow for better image quality and high-resolution image representations without any multi-stage hierarchy in the latent space. In this binary latent space, images can now be generated effectively using a binary latent diffusion model tailored specifically for modeling the prior over the binary image representations. We present both conditional and unconditional image generation experiments with multiple datasets, and show that the proposed method performs comparably to state-of-the-art methods while dramatically improving the sampling efficiency to as few as 16 steps without using any test-time acceleration. The proposed framework can also be seamlessly scaled to 1024 times 1024 high-resolution image generation without resorting to latent hierarchy or multi-stage refinements.

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.

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.

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.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

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.

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.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

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.

Learning manipulable representations of the world and its dynamics is central to AI. Joint-Embedding Predictive Architectures (JEPAs) offer a promising blueprint, but lack of practical guidance and theory has led to ad-hoc R&D. We present a comprehensive theory of JEPAs and instantiate it in {\bf LeJEPA}, a lean, scalable, and theoretically grounded training objective. First, we identify the isotropic Gaussian as the optimal distribution that JEPAs' embeddings should follow to minimize downstream prediction risk. Second, we introduce a novel objective--{\bf Sketched Isotropic Gaussian Regularization} (SIGReg)--to constrain embeddings to reach that ideal distribution. Combining the JEPA predictive loss with SIGReg yields LeJEPA with numerous theoretical and practical benefits: (i) single trade-off hyperparameter, (ii) linear time and memory complexity, (iii) stability across hyper-parameters, architectures (ResNets, ViTs, ConvNets) and domains, (iv) heuristics-free, e.g., no stop-gradient, no teacher-student, no hyper-parameter schedulers, and (v) distributed training-friendly implementation requiring only approx50 lines of code. Our empirical validation covers 10+ datasets, 60+ architectures, all with varying scales and domains. As an example, using imagenet-1k for pretraining and linear evaluation with frozen backbone, LeJEPA reaches 79\% with a ViT-H/14. We hope that the simplicity and theory-friendly ecosystem offered by LeJEPA will reestablish self-supervised pre-training as a core pillar of AI research (https://github.com/rbalestr-lab/lejepa{GitHub repo}).

Joint Embedding Predictive Architectures (JEPAs) learn representations able to solve numerous downstream tasks out-of-the-box. JEPAs combine two objectives: (i) a latent-space prediction term, i.e., the representation of a slightly perturbed sample must be predictable from the original sample's representation, and (ii) an anti-collapse term, i.e., not all samples should have the same representation. While (ii) is often considered as an obvious remedy to representation collapse, we uncover that JEPAs' anti-collapse term does much more--it provably estimates the data density. In short, any successfully trained JEPA can be used to get sample probabilities, e.g., for data curation, outlier detection, or simply for density estimation. Our theoretical finding is agnostic of the dataset and architecture used--in any case one can compute the learned probabilities of sample x efficiently and in closed-form using the model's Jacobian matrix at x. Our findings are empirically validated across datasets (synthetic, controlled, and Imagenet) and across different Self Supervised Learning methods falling under the JEPA family (I-JEPA and DINOv2) and on multimodal models, such as MetaCLIP. We denote the method extracting the JEPA learned density as {\bf JEPA-SCORE}.

Joint-Embedding Self Supervised Learning (JE-SSL) has seen a rapid development, with the emergence of many method variations but only few principled guidelines that would help practitioners to successfully deploy them. The main reason for that pitfall comes from JE-SSL's core principle of not employing any input reconstruction therefore lacking visual cues of unsuccessful training. Adding non informative loss values to that, it becomes difficult to deploy SSL on a new dataset for which no labels can help to judge the quality of the learned representation. In this study, we develop a simple unsupervised criterion that is indicative of the quality of the learned JE-SSL representations: their effective rank. Albeit simple and computationally friendly, this method -- coined RankMe -- allows one to assess the performance of JE-SSL representations, even on different downstream datasets, without requiring any labels. A further benefit of RankMe is that it does not have any training or hyper-parameters to tune. Through thorough empirical experiments involving hundreds of training episodes, we demonstrate how RankMe can be used for hyperparameter selection with nearly no reduction in final performance compared to the current selection method that involve a dataset's labels. We hope that RankMe will facilitate the deployment of JE-SSL towards domains that do not have the opportunity to rely on labels for representations' quality assessment.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Shape-Text matching is an important task of high-level shape understanding. Current methods mainly represent a 3D shape as multiple 2D rendered views, which obviously can not be understood well due to the structural ambiguity caused by self-occlusion in the limited number of views. To resolve this issue, we directly represent 3D shapes as point clouds, and propose to learn joint embedding of point clouds and texts by bidirectional matching between parts from shapes and words from texts. Specifically, we first segment the point clouds into parts, and then leverage optimal transport method to match parts and words in an optimized feature space, where each part is represented by aggregating features of all points within it and each word is abstracted by its contextual information. We optimize the feature space in order to enlarge the similarities between the paired training samples, while simultaneously maximizing the margin between the unpaired ones. Experiments demonstrate that our method achieves a significant improvement in accuracy over the SOTAs on multi-modal retrieval tasks under the Text2Shape dataset. Codes are available at https://github.com/JLUtangchuan/Parts2Words.

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot product function. In this paper, we propose a new representation learning framework for dense retrieval. Instead of learning a vector for each query and document, our framework learns a multivariate distribution and uses negative multivariate KL divergence to compute the similarity between distributions. For simplicity and efficiency reasons, we assume that the distributions are multivariate normals and then train large language models to produce mean and variance vectors for these distributions. We provide a theoretical foundation for the proposed framework and show that it can be seamlessly integrated into the existing approximate nearest neighbor algorithms to perform retrieval efficiently. We conduct an extensive suite of experiments on a wide range of datasets, and demonstrate significant improvements compared to competitive dense retrieval models.

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

Recent advances in vision-language models (VLMs) have demonstrated remarkable zero-shot capabilities, yet adapting these models to specialized domains remains a significant challenge. Building on recent theoretical insights suggesting that independently trained VLMs are related by a canonical transformation, we extend this understanding to the concept of domains. We hypothesize that image features across disparate domains are related by a canonicalized geometric transformation that can be recovered using a small set of anchors. Few-shot classification provides a natural setting for this alignment, as the limited labeled samples serve as the anchors required to estimate this transformation. Motivated by this hypothesis, we introduce BiCLIP, a framework that applies a targeted transformation to multimodal features to enhance cross-modal alignment. Our approach is characterized by its extreme simplicity and low parameter footprint. Extensive evaluations across 11 standard benchmarks, including EuroSAT, DTD, and FGVCAircraft, demonstrate that BiCLIP consistently achieves state-of-the-art results. Furthermore, we provide empirical verification of existing geometric findings by analyzing the orthogonality and angular distribution of the learned transformations, confirming that structured alignment is the key to robust domain adaptation. Code is available at https://github.com/QuantitativeImagingLaboratory/BilinearCLIP

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.

Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, large-capacity models, and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-the-shelf image matcher, together with a rapid nonparametric clustering, to construct a graph representing intra- and inter-image keypoint relations. A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inverse-compositional loss, that eliminates the need for a regularization term over the predicted transformations (and thus also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/

Large Language Model (LLM) pretraining, finetuning, and evaluation rely on input-space reconstruction and generative capabilities. Yet, it has been observed in vision that embedding-space training objectives, e.g., with Joint Embedding Predictive Architectures (JEPAs), are far superior to their input-space counterpart. That mismatch in how training is achieved between language and vision opens up a natural question: {\em can language training methods learn a few tricks from the vision ones?} The lack of JEPA-style LLM is a testimony of the challenge in designing such objectives for language. In this work, we propose a first step in that direction where we develop LLM-JEPA, a JEPA based solution for LLMs applicable both to finetuning and pretraining. Thus far, LLM-JEPA is able to outperform the standard LLM training objectives by a significant margin across models, all while being robust to overfiting. Those findings are observed across numerous datasets (NL-RX, GSM8K, Spider, RottenTomatoes) and various models from the Llama3, OpenELM, Gemma2 and Olmo families. Code: https://github.com/rbalestr-lab/llm-jepa.

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.

Large-scale embedding-based retrieval (EBR) is the cornerstone of search-related industrial applications. Given a user query, the system of EBR aims to identify relevant information from a large corpus of documents that may be tens or hundreds of billions in size. The storage and computation turn out to be expensive and inefficient with massive documents and high concurrent queries, making it difficult to further scale up. To tackle the challenge, we propose a binary embedding-based retrieval (BEBR) engine equipped with a recurrent binarization algorithm that enables customized bits per dimension. Specifically, we compress the full-precision query and document embeddings, formulated as float vectors in general, into a composition of multiple binary vectors using a lightweight transformation model with residual multilayer perception (MLP) blocks. We can therefore tailor the number of bits for different applications to trade off accuracy loss and cost savings. Importantly, we enable task-agnostic efficient training of the binarization model using a new embedding-to-embedding strategy. We also exploit the compatible training of binary embeddings so that the BEBR engine can support indexing among multiple embedding versions within a unified system. To further realize efficient search, we propose Symmetric Distance Calculation (SDC) to achieve lower response time than Hamming codes. We successfully employed the introduced BEBR to Tencent products, including Sogou, Tencent Video, QQ World, etc. The binarization algorithm can be seamlessly generalized to various tasks with multiple modalities. Extensive experiments on offline benchmarks and online A/B tests demonstrate the efficiency and effectiveness of our method, significantly saving 30%~50% index costs with almost no loss of accuracy at the system level.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

In the context of few-shot classification, the goal is to train a classifier using a limited number of samples while maintaining satisfactory performance. However, traditional metric-based methods exhibit certain limitations in achieving this objective. These methods typically rely on a single distance value between the query feature and support feature, thereby overlooking the contribution of shallow features. To overcome this challenge, we propose a novel approach in this paper. Our approach involves utilizing a multi-output embedding network that maps samples into distinct feature spaces. The proposed method extracts feature vectors at different stages, enabling the model to capture both global and abstract features. By utilizing these diverse feature spaces, our model enhances its performance. Moreover, employing a self-attention mechanism improves the refinement of features at each stage, leading to even more robust representations and improved overall performance. Furthermore, assigning learnable weights to each stage significantly improved performance and results. We conducted comprehensive evaluations on the MiniImageNet and FC100 datasets, specifically in the 5-way 1-shot and 5-way 5-shot scenarios. Additionally, we performed cross-domain tasks across eight benchmark datasets, achieving high accuracy in the testing domains. These evaluations demonstrate the efficacy of our proposed method in comparison to state-of-the-art approaches. https://github.com/FatemehAskari/MSENet

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

The emergence of similar representations between independently trained neural models has sparked significant interest in the representation learning community, leading to the development of various methods to obtain communication between latent spaces. "Latent space communication" can be achieved in two ways: i) by independently mapping the original spaces to a shared or relative one; ii) by directly estimating a transformation from a source latent space to a target one. In this work, we combine the two into a novel method to obtain latent space translation through the relative space. By formalizing the invertibility of angle-preserving relative representations and assuming the scale invariance of decoder modules in neural models, we can effectively use the relative space as an intermediary, independently projecting onto and from other semantically similar spaces. Extensive experiments over various architectures and datasets validate our scale invariance assumption and demonstrate the high accuracy of our method in latent space translation. We also apply our method to zero-shot stitching between arbitrary pre-trained text and image encoders and their classifiers, even across modalities. Our method has significant potential for facilitating the reuse of models in a practical manner via compositionality.

Joint Embedding Predictive Architectures (JEPAs) offer a compelling framework for learning world models in compact latent spaces, yet existing methods remain fragile, relying on complex multi-term losses, exponential moving averages, pre-trained encoders, or auxiliary supervision to avoid representation collapse. In this work, we introduce LeWorldModel (LeWM), the first JEPA that trains stably end-to-end from raw pixels using only two loss terms: a next-embedding prediction loss and a regularizer enforcing Gaussian-distributed latent embeddings. This reduces tunable loss hyperparameters from six to one compared to the only existing end-to-end alternative. With ~15M parameters trainable on a single GPU in a few hours, LeWM plans up to 48x faster than foundation-model-based world models while remaining competitive across diverse 2D and 3D control tasks. Beyond control, we show that LeWM's latent space encodes meaningful physical structure through probing of physical quantities. Surprise evaluation confirms that the model reliably detects physically implausible events.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

Self-supervised learning on large-scale multi-modal datasets allows learning semantically meaningful embeddings in a joint multi-modal representation space without relying on human annotations. These joint embeddings enable zero-shot cross-modal tasks like retrieval and classification. However, these methods often struggle to generalize well on out-of-domain data as they ignore the semantic structure present in modality-specific embeddings. In this context, we propose a novel Semantic-Structure-Preserving Consistency approach to improve generalizability by preserving the modality-specific relationships in the joint embedding space. To capture modality-specific semantic relationships between samples, we propose to learn multiple anchors and represent the multifaceted relationship between samples with respect to their relationship with these anchors. To assign multiple anchors to each sample, we propose a novel Multi-Assignment Sinkhorn-Knopp algorithm. Our experimentation demonstrates that our proposed approach learns semantically meaningful anchors in a self-supervised manner. Furthermore, our evaluation on MSR-VTT and YouCook2 datasets demonstrates that our proposed multi-anchor assignment based solution achieves state-of-the-art performance and generalizes to both inand out-of-domain datasets. Code: https://github.com/Swetha5/Multi_Sinkhorn_Knopp

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Video-text retrieval is a class of cross-modal representation learning problems, where the goal is to select the video which corresponds to the text query between a given text query and a pool of candidate videos. The contrastive paradigm of vision-language pretraining has shown promising success with large-scale datasets and unified transformer architecture, and demonstrated the power of a joint latent space. Despite this, the intrinsic divergence between the visual domain and textual domain is still far from being eliminated, and projecting different modalities into a joint latent space might result in the distorting of the information inside the single modality. To overcome the above issue, we present a novel mechanism for learning the translation relationship from a source modality space S to a target modality space T without the need for a joint latent space, which bridges the gap between visual and textual domains. Furthermore, to keep cycle consistency between translations, we adopt a cycle loss involving both forward translations from S to the predicted target space T', and backward translations from T' back to S. Extensive experiments conducted on MSR-VTT, MSVD, and DiDeMo datasets demonstrate the superiority and effectiveness of our LaT approach compared with vanilla state-of-the-art methods.

The unsupervised task of Joint Alignment (JA) of images is beset by challenges such as high complexity, geometric distortions, and convergence to poor local or even global optima. Although Vision Transformers (ViT) have recently provided valuable features for JA, they fall short of fully addressing these issues. Consequently, researchers frequently depend on expensive models and numerous regularization terms, resulting in long training times and challenging hyperparameter tuning. We introduce the Spatial Joint Alignment Model (SpaceJAM), a novel approach that addresses the JA task with efficiency and simplicity. SpaceJAM leverages a compact architecture with only 16K trainable parameters and uniquely operates without the need for regularization or atlas maintenance. Evaluations on SPair-71K and CUB datasets demonstrate that SpaceJAM matches the alignment capabilities of existing methods while significantly reducing computational demands and achieving at least a 10x speedup. SpaceJAM sets a new standard for rapid and effective image alignment, making the process more accessible and efficient. Our code is available at: https://bgu-cs-vil.github.io/SpaceJAM/.

We present FIND, a generalized interface for aligning foundation models' embeddings. As shown in teaser figure, a lightweight transformer interface without tuning any foundation model weights is enough for a unified image (segmentation) and dataset-level (retrieval) understanding. The proposed interface has the following favorable attributes: (1) Generalizable. It applies to various tasks spanning retrieval, segmentation, etc., under the same architecture and weights. (2) Prototypable. Different tasks are able to be implemented through prototyping attention masks and embedding types. (3) Extendable. The proposed interface is adaptive to new tasks, and new models. (4) Interleavable. With the benefit of multi-task multi-modal training, the proposed interface creates an interleaved shared embedding space. In light of the interleaved embedding space, we introduce the FIND-Bench, which introduces new training and evaluation annotations to the COCO dataset for interleave segmentation and retrieval. Our approach achieves state-of-the-art performance on FIND-Bench and competitive performance on standard retrieval and segmentation settings. The training, evaluation, and demo code as well as the dataset have been released at https://github.com/UX-Decoder/FIND.

This paper demonstrates an approach for learning highly semantic image representations without relying on hand-crafted data-augmentations. We introduce the Image-based Joint-Embedding Predictive Architecture (I-JEPA), a non-generative approach for self-supervised learning from images. The idea behind I-JEPA is simple: from a single context block, predict the representations of various target blocks in the same image. A core design choice to guide I-JEPA towards producing semantic representations is the masking strategy; specifically, it is crucial to (a) sample target blocks with sufficiently large scale (semantic), and to (b) use a sufficiently informative (spatially distributed) context block. Empirically, when combined with Vision Transformers, we find I-JEPA to be highly scalable. For instance, we train a ViT-Huge/14 on ImageNet using 16 A100 GPUs in under 72 hours to achieve strong downstream performance across a wide range of tasks, from linear classification to object counting and depth prediction.

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.

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.

Generative models and vision encoders have largely advanced on separate tracks, optimized for different goals and grounded in different mathematical principles. Yet, they share a fundamental property: latent space Gaussianity. Generative models map Gaussian noise to images, while encoders map images to semantic embeddings whose coordinates empirically behave as Gaussian. We hypothesize that both are views of a shared latent source, the Universal Normal Embedding (UNE): an approximately Gaussian latent space from which encoder embeddings and DDIM-inverted noise arise as noisy linear projections. To test our hypothesis, we introduce NoiseZoo, a dataset of per-image latents comprising DDIM-inverted diffusion noise and matching encoder representations (CLIP, DINO). On CelebA, linear probes in both spaces yield strong, aligned attribute predictions, indicating that generative noise encodes meaningful semantics along linear directions. These directions further enable faithful, controllable edits (e.g., smile, gender, age) without architectural changes, where simple orthogonalization mitigates spurious entanglements. Taken together, our results provide empirical support for the UNE hypothesis and reveal a shared Gaussian-like latent geometry that concretely links encoding and generation. Code and data are available https://rbetser.github.io/UNE/

Many applications of cross-modal music retrieval are related to connecting sheet music images to audio recordings. A typical and recent approach to this is to learn, via deep neural networks, a joint embedding space that correlates short fixed-size snippets of audio and sheet music by means of an appropriate similarity structure. However, two challenges that arise out of this strategy are the requirement of strongly aligned data to train the networks, and the inherent discrepancies of musical content between audio and sheet music snippets caused by local and global tempo differences. In this paper, we address these two shortcomings by designing a cross-modal recurrent network that learns joint embeddings that can summarize longer passages of corresponding audio and sheet music. The benefits of our method are that it only requires weakly aligned audio-sheet music pairs, as well as that the recurrent network handles the non-linearities caused by tempo variations between audio and sheet music. We conduct a number of experiments on synthetic and real piano data and scores, showing that our proposed recurrent method leads to more accurate retrieval in all possible configurations.

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

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.

Despite significant recent advances in the field of face recognition, implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors. Our method uses a deep convolutional network trained to directly optimize the embedding itself, rather than an intermediate bottleneck layer as in previous deep learning approaches. To train, we use triplets of roughly aligned matching / non-matching face patches generated using a novel online triplet mining method. The benefit of our approach is much greater representational efficiency: we achieve state-of-the-art face recognition performance using only 128-bytes per face. On the widely used Labeled Faces in the Wild (LFW) dataset, our system achieves a new record accuracy of 99.63%. On YouTube Faces DB it achieves 95.12%. Our system cuts the error rate in comparison to the best published result by 30% on both datasets. We also introduce the concept of harmonic embeddings, and a harmonic triplet loss, which describe different versions of face embeddings (produced by different networks) that are compatible to each other and allow for direct comparison between each other.

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.

The development of data-dependent heuristics and representations for biological sequences that reflect their evolutionary distance is critical for large-scale biological research. However, popular machine learning approaches, based on continuous Euclidean spaces, have struggled with the discrete combinatorial formulation of the edit distance that models evolution and the hierarchical relationship that characterises real-world datasets. We present Neural Distance Embeddings (NeuroSEED), a general framework to embed sequences in geometric vector spaces, and illustrate the effectiveness of the hyperbolic space that captures the hierarchical structure and provides an average 22% reduction in embedding RMSE against the best competing geometry. The capacity of the framework and the significance of these improvements are then demonstrated devising supervised and unsupervised NeuroSEED approaches to multiple core tasks in bioinformatics. Benchmarked with common baselines, the proposed approaches display significant accuracy and/or runtime improvements on real-world datasets. As an example for hierarchical clustering, the proposed pretrained and from-scratch methods match the quality of competing baselines with 30x and 15x runtime reduction, respectively.

Multimodal self-supervised learning is getting more and more attention as it allows not only to train large networks without human supervision but also to search and retrieve data across various modalities. In this context, this paper proposes a self-supervised training framework that learns a common multimodal embedding space that, in addition to sharing representations across different modalities, enforces a grouping of semantically similar instances. To this end, we extend the concept of instance-level contrastive learning with a multimodal clustering step in the training pipeline to capture semantic similarities across modalities. The resulting embedding space enables retrieval of samples across all modalities, even from unseen datasets and different domains. To evaluate our approach, we train our model on the HowTo100M dataset and evaluate its zero-shot retrieval capabilities in two challenging domains, namely text-to-video retrieval, and temporal action localization, showing state-of-the-art results on four different datasets.

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via the 1-Wasserstein distance, using only paired data. This two-step approach minimizes an upper bound on the 1-Wasserstein distance between joint distributions, reducing reliance on scarce paired samples while enabling fast one-step generation. Theoretically, we establish non-asymptotic error bounds and demonstrate a key benefit of unpaired data: enhanced geometric fidelity in generated outputs. Furthermore, by extending the scope of its two core steps, LSDM provides a coherent statistical perspective that connects to a broad class of latent-space approaches. Notably, Latent Diffusion Models (LDMs) can be viewed as a variant of LSDM, in which joint distribution matching is achieved indirectly via score matching. Consequently, our results also provide theoretical insights into the consistency of LDMs. Empirical evaluations on real-world image tasks, including class-conditional generation and image super-resolution, demonstrate the effectiveness of LSDM in leveraging unpaired data to enhance generation quality.

Building cross-modal applications is challenging due to limited paired multi-modal data. Recent works have shown that leveraging a pre-trained multi-modal contrastive representation space enables cross-modal tasks to be learned from uni-modal data. This is based on the assumption that contrastive optimization makes embeddings from different modalities interchangeable. However, this assumption is under-explored due to the poorly understood geometry of the multi-modal contrastive space, where a modality gap exists. In our study, we provide a theoretical explanation of this space's geometry and introduce a three-step method, C^3 (Connect, Collapse, Corrupt), to bridge the modality gap, enhancing the interchangeability of embeddings. Our C^3 method significantly improves cross-modal learning from uni-modal data, achieving state-of-the-art results on zero-shot image / audio / video captioning and text-to-image generation.

The joint-embedding predictive architecture (JEPA) recently has shown impressive results in extracting visual representations from unlabeled imagery under a masking strategy. However, we reveal its disadvantages, notably its insufficient understanding of local semantics. This deficiency originates from masked modeling in the embedding space, resulting in a reduction of discriminative power and can even lead to the neglect of critical local semantics. To bridge this gap, we introduce DMT-JEPA, a novel masked modeling objective rooted in JEPA, specifically designed to generate discriminative latent targets from neighboring information. Our key idea is simple: we consider a set of semantically similar neighboring patches as a target of a masked patch. To be specific, the proposed DMT-JEPA (a) computes feature similarities between each masked patch and its corresponding neighboring patches to select patches having semantically meaningful relations, and (b) employs lightweight cross-attention heads to aggregate features of neighboring patches as the masked targets. Consequently, DMT-JEPA demonstrates strong discriminative power, offering benefits across a diverse spectrum of downstream tasks. Through extensive experiments, we demonstrate our effectiveness across various visual benchmarks, including ImageNet-1K image classification, ADE20K semantic segmentation, and COCO object detection tasks. Code is available at: https://github.com/DMTJEPA/DMTJEPA.

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

High-dimensional vector embeddings are widely used in retrieval systems, yet dimensionality reduction (DR) is seldom applied due to its tendency to distort nearest-neighbor (NN) structure critical for search. Existing DR techniques such as PCA and UMAP optimize global or manifold-preserving criteria, rather than retrieval-specific objectives. We present MPAD: Maximum Pairwise Absolute Difference, an unsupervised DR method that explicitly preserves approximate NN relations by maximizing the margin between k-NNs and non-k-NNs under a soft orthogonality constraint. This design enables MPAD to retain ANN-relevant geometry without supervision or changes to the original embedding model. Experiments across multiple domains show that MPAD consistently outperforms standard DR methods in preserving neighborhood structure, enabling more accurate search in reduced dimensions.

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

Universal multimodal embedding models play a critical role in tasks such as interleaved image-text retrieval, multimodal RAG, and multimodal clustering. However, our empirical results indicate that existing LMM-based embedding models trained with the standard InfoNCE loss exhibit a high degree of overlap in similarity distribution between positive and negative pairs, making it challenging to distinguish hard negative pairs effectively. To deal with this issue, we propose a simple yet effective framework that dynamically improves the embedding model's representation learning for negative pairs based on their discriminative difficulty. Within this framework, we train a series of models, named LLaVE, and evaluate them on the MMEB benchmark, which covers 4 meta-tasks and 36 datasets. Experimental results show that LLaVE establishes stronger baselines that achieve state-of-the-art (SOTA) performance while demonstrating strong scalability and efficiency. Specifically, LLaVE-2B surpasses the previous SOTA 7B models, while LLaVE-7B achieves a further performance improvement of 6.2 points. Although LLaVE is trained on image-text data, it can generalize to text-video retrieval tasks in a zero-shot manner and achieve strong performance, demonstrating its remarkable potential for transfer to other embedding tasks.

Learning vector representations (aka. embeddings) of users and items lies at the core of modern recommender systems. Ranging from early matrix factorization to recently emerged deep learning based methods, existing efforts typically obtain a user's (or an item's) embedding by mapping from pre-existing features that describe the user (or the item), such as ID and attributes. We argue that an inherent drawback of such methods is that, the collaborative signal, which is latent in user-item interactions, is not encoded in the embedding process. As such, the resultant embeddings may not be sufficient to capture the collaborative filtering effect. In this work, we propose to integrate the user-item interactions -- more specifically the bipartite graph structure -- into the embedding process. We develop a new recommendation framework Neural Graph Collaborative Filtering (NGCF), which exploits the user-item graph structure by propagating embeddings on it. This leads to the expressive modeling of high-order connectivity in user-item graph, effectively injecting the collaborative signal into the embedding process in an explicit manner. We conduct extensive experiments on three public benchmarks, demonstrating significant improvements over several state-of-the-art models like HOP-Rec and Collaborative Memory Network. Further analysis verifies the importance of embedding propagation for learning better user and item representations, justifying the rationality and effectiveness of NGCF. Codes are available at https://github.com/xiangwang1223/neural_graph_collaborative_filtering.

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.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

The performance of algorithms for neural architecture search strongly depends on the parametrization of the search space. We use contrastive learning to identify networks across different initializations based on their data Jacobians, and automatically produce the first architecture embeddings independent from the parametrization of the search space. Using our contrastive embeddings, we show that traditional black-box optimization algorithms, without modification, can reach state-of-the-art performance in Neural Architecture Search. As our method provides a unified embedding space, we perform for the first time transfer learning between search spaces. Finally, we show the evolution of embeddings during training, motivating future studies into using embeddings at different training stages to gain a deeper understanding of the networks in a search space.

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex hierarchical relationships in images with remarkably small dimensionality. To demonstrate hyperbolic embeddings' competence, we introduce a light-weight hyperbolic graph neural network for image segmentation, encompassing patch-level features in a very small embedding size. Our solution, Seg-HGNN, surpasses the current best unsupervised method by 2.5\%, 4\% on VOC-07, VOC-12 for localization, and by 0.8\%, 1.3\% on CUB-200, ECSSD for segmentation, respectively. With less than 7.5k trainable parameters, Seg-HGNN delivers effective and fast (approx 2 images/second) results on very standard GPUs like the GTX1650. This empirical evaluation presents compelling evidence of the efficacy and potential of hyperbolic representations for vision tasks.

The massive interest in deep neural networks (DNNs) for both computer vision and natural language processing has been sparked by the growth in computational power. However, this led to an increase in the memory footprint, to a point where it can be challenging to simply load a model on commodity devices such as mobile phones. To address this limitation, quantization is a favored solution as it maps high precision tensors to a low precision, memory efficient format. In terms of memory footprint reduction, its most effective variants are based on codebooks. These methods, however, suffer from two limitations. First, they either define a single codebook for each tensor, or use a memory-expensive mapping to multiple codebooks. Second, gradient descent optimization of the mapping favors jumps toward extreme values, hence not defining a proximal search. In this work, we propose to address these two limitations. First, we initially group similarly distributed neurons and leverage the re-ordered structure to either apply different scale factors to the different groups, or map weights that fall in these groups to several codebooks, without any mapping overhead. Second, stemming from this initialization, we propose a joint learning of the codebook and weight mappings that bears similarities with recent gradient-based post-training quantization techniques. Third, drawing estimation from straight-through estimation techniques, we introduce a novel gradient update definition to enable a proximal search of the codebooks and their mappings. The proposed jointly learnable codebooks and mappings (JLCM) method allows a very efficient approximation of any DNN: as such, a Llama 7B can be compressed down to 2Go and loaded on 5-year-old smartphones.

Traditional neural word embeddings are usually dependent on a richer diversity of vocabulary. However, the language models recline to cover major vocabularies via the word embedding parameters, in particular, for multilingual language models that generally cover a significant part of their overall learning parameters. In this work, we present a new compact embedding structure to reduce the memory footprint of the pre-trained language models with a sacrifice of up to 4% absolute accuracy. The embeddings vectors reconstruction follows a set of subspace embeddings and an assignment procedure via the contextual relationship among tokens from pre-trained language models. The subspace embedding structure calibrates to masked language models, to evaluate our compact embedding structure on similarity and textual entailment tasks, sentence and paraphrase tasks. Our experimental evaluation shows that the subspace embeddings achieve compression rates beyond 99.8% in comparison with the original embeddings for the language models on XNLI and GLUE benchmark suites.

Learning discriminative shape representations is a crucial issue for large-scale 3D shape retrieval. In this paper, we propose the Collaborative Inner Product Loss (CIP Loss) to obtain ideal shape embedding that discriminative among different categories and clustered within the same class. Utilizing simple inner product operation, CIP loss explicitly enforces the features of the same class to be clustered in a linear subspace, while inter-class subspaces are constrained to be at least orthogonal. Compared to previous metric loss functions, CIP loss could provide more clear geometric interpretation for the embedding than Euclidean margin, and is easy to implement without normalization operation referring to cosine margin. Moreover, our proposed loss term can combine with other commonly used loss functions and can be easily plugged into existing off-the-shelf architectures. Extensive experiments conducted on the two public 3D object retrieval datasets, ModelNet and ShapeNetCore 55, demonstrate the effectiveness of our proposal, and our method has achieved state-of-the-art results on both datasets.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

Image-based Joint-Embedding Predictive Architecture (I-JEPA) learns visual representations by predicting latent embeddings of masked regions from visible context. However, it treats all regions uniformly and independently, lacking an explicit notion of where or in what order predictions should be made. Inspired by human visual perception, which deploys attention selectively and sequentially from the most informative to secondary regions, we propose DSeq-JEPA, a Discriminative Sequential Joint-Embedding Predictive Architecture that bridges predictive and autoregressive self-supervised learning, integrating JEPA-style latent prediction with GPT-style sequential reasoning. Specifically, DSeq-JEPA (i) first identifies primary discriminative regions based on a transformer-derived saliency map, emphasizing the distribution of visual importance, and then (ii) predicts subsequent regions in this discriminative order, progressively forming a curriculum-like semantic progression from primary to secondary cues -- a form of GPT-style pre-training. Extensive experiments across diverse tasks, including image classification (ImageNet), fine-grained visual categorization (iNaturalist21, CUB-200-2011, Stanford-Cars), detection and segmentation (MS-COCO, ADE20K), and low-level reasoning tasks (Clevr/Count, Clevr/Dist), demonstrate that DSeq-JEPA consistently focuses on more discriminative and generalizable representations than I-JEPA variants. Project page: https://github.com/SkyShunsuke/DSeq-JEPA.

Given the success of Large Language Models (LLMs), there has been considerable interest in studying the properties of model activations. The literature overwhelmingly agrees that LLM representations are dominated by a few ``outlier dimensions'' with exceedingly high variance and magnitude. Several studies in Natural Language Processing (NLP) have sought to mitigate the impact of such outlier dimensions and force LLMs to be isotropic (i.e., have uniform variance across all dimensions in embedding space). Isotropy is thought to be a desirable property for LLMs that improves model performance and more closely aligns textual representations with human intuition. However, many of the claims regarding isotropy in NLP have been based on the average cosine similarity of embeddings, which has recently been shown to be a flawed measure of isotropy. In this paper, we propose I-STAR: IsoScore*-based STable Anisotropic Regularization, a novel regularization method that can be used to increase or decrease levels of isotropy in embedding space during training. I-STAR uses IsoScore*, the first accurate measure of isotropy that is both differentiable and stable on mini-batch computations. In contrast to several previous works, we find that decreasing isotropy in contextualized embeddings improves performance on the majority of tasks and models considered in this paper.

In this paper, we present a new embedding model, called M3-Embedding, which is distinguished for its versatility in Multi-Linguality, Multi-Functionality, and Multi-Granularity. It can support more than 100 working languages, leading to new state-of-the-art performances on multi-lingual and cross-lingual retrieval tasks. It can simultaneously perform the three common retrieval functionalities of embedding model: dense retrieval, multi-vector retrieval, and sparse retrieval, which provides a unified model foundation for real-world IR applications. It is able to process inputs of different granularities, spanning from short sentences to long documents of up to 8192 tokens. The effective training of M3-Embedding involves the following technical contributions. We propose a novel self-knowledge distillation approach, where the relevance scores from different retrieval functionalities can be integrated as the teacher signal to enhance the training quality. We also optimize the batching strategy, enabling a large batch size and high training throughput to ensure the discriminativeness of embeddings. To the best of our knowledge, M3-Embedding is the first embedding model which realizes such a strong versatility. The model and code will be publicly available at https://github.com/FlagOpen/FlagEmbedding.

Two competing paradigms exist for self-supervised learning of data representations. Joint Embedding Predictive Architecture (JEPA) is a class of architectures in which semantically similar inputs are encoded into representations that are predictive of each other. A recent successful approach that falls under the JEPA framework is self-distillation, where an online encoder is trained to predict the output of the target encoder, sometimes using a lightweight predictor network. This is contrasted with the Masked AutoEncoder (MAE) paradigm, where an encoder and decoder are trained to reconstruct missing parts of the input in the data space rather, than its latent representation. A common motivation for using the JEPA approach over MAE is that the JEPA objective prioritizes abstract features over fine-grained pixel information (which can be unpredictable and uninformative). In this work, we seek to understand the mechanism behind this empirical observation by analyzing the training dynamics of deep linear models. We uncover a surprising mechanism: in a simplified linear setting where both approaches learn similar representations, JEPAs are biased to learn high-influence features, i.e., features characterized by having high regression coefficients. Our results point to a distinct implicit bias of predicting in latent space that may shed light on its success in practice.

This work presents a novel framework for training Arabic nested embedding models through Matryoshka Embedding Learning, leveraging multilingual, Arabic-specific, and English-based models, to highlight the power of nested embeddings models in various Arabic NLP downstream tasks. Our innovative contribution includes the translation of various sentence similarity datasets into Arabic, enabling a comprehensive evaluation framework to compare these models across different dimensions. We trained several nested embedding models on the Arabic Natural Language Inference triplet dataset and assessed their performance using multiple evaluation metrics, including Pearson and Spearman correlations for cosine similarity, Manhattan distance, Euclidean distance, and dot product similarity. The results demonstrate the superior performance of the Matryoshka embedding models, particularly in capturing semantic nuances unique to the Arabic language. Results demonstrated that Arabic Matryoshka embedding models have superior performance in capturing semantic nuances unique to the Arabic language, significantly outperforming traditional models by up to 20-25\% across various similarity metrics. These results underscore the effectiveness of language-specific training and highlight the potential of Matryoshka models in enhancing semantic textual similarity tasks for Arabic NLP.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they serve as algebraic primitives that can be analysed without reference to input and can describe structures ranging from linear concepts to complicated manifolds. This work uses bilinear autoencoders to efficiently decompose representations into quadratic polynomials. We discuss improvements that induce importance ordering, clustering, and activation sparsity. This is an initial step toward nonlinear yet analysable latents through their algebraic properties.

Although Multimodal Large Language Models (MLLMs) have shown remarkable potential in Visual Document Retrieval (VDR) through generating high-quality multi-vector embeddings, the substantial storage overhead caused by representing a page with thousands of visual tokens limits their practicality in real-world applications. To address this challenge, we propose an auto-regressive generation approach, CausalEmbed, for constructing multi-vector embeddings. By incorporating iterative margin loss during contrastive training, CausalEmbed encourages the embedding models to learn compact and well-structured representations. Our method enables efficient VDR tasks using only dozens of visual tokens, achieving a 30-155x reduction in token count while maintaining highly competitive performance across various backbones and benchmarks. Theoretical analysis and empirical results demonstrate the unique advantages of auto-regressive embedding generation in terms of training efficiency and scalability at test time. As a result, CausalEmbed introduces a flexible test-time scaling strategy for multi-vector VDR representations and sheds light on the generative paradigm within multimodal document retrieval.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Self-Supervised learning (SSL) with Joint-Embedding Architectures (JEA) has led to outstanding performances. All instantiations of this paradigm were trained using strong and well-established hand-crafted data augmentations, leading to the general belief that they are required for the proper training and performance of such models. On the other hand, generative reconstruction-based models such as BEIT and MAE or Joint-Embedding Predictive Architectures such as I-JEPA have shown strong performance without using data augmentations except masking. In this work, we challenge the importance of invariance and data-augmentation in JEAs at scale. By running a case-study on a recent SSL foundation model - DINOv2 - we show that strong image representations can be obtained with JEAs and only cropping without resizing provided the training data is large enough, reaching state-of-the-art results and using the least amount of augmentation in the literature. Through this study, we also discuss the impact of compute constraints on the outcomes of experimental deep learning research, showing that they can lead to very different conclusions.

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this task; however, these methods often struggle with scalability and can be time-consuming when applied to large-scale dynamic graphs. Moreover, they tend to lack robustness and are vulnerable to real-world noisy data. To address these issues, we make three key contributions. First, to improve scalability, we propose temporal separated matrix factorization, where a single matrix is divided into multiple smaller matrices for independent factorization, resulting in faster computation. Second, to improve robustness, we introduce bi-clustering regularization, which jointly optimizes graph embedding and clustering, thereby filtering out noisy features from the graph embeddings. Third, to further enhance effectiveness and efficiency, we propose selective embedding updating, where we update only the embeddings of dynamic nodes while the embeddings of static nodes are fixed among different timestamps. Experimental results on six synthetic and five real-world benchmarks demonstrate the scalability, robustness and effectiveness of our proposed method. Source code is available at https://github.com/Clearloveyuan/DyG-MF.

Continuous Bag of Words (CBOW) is a powerful text embedding method. Due to its strong capabilities to encode word content, CBOW embeddings perform well on a wide range of downstream tasks while being efficient to compute. However, CBOW is not capable of capturing the word order. The reason is that the computation of CBOW's word embeddings is commutative, i.e., embeddings of XYZ and ZYX are the same. In order to address this shortcoming, we propose a learning algorithm for the Continuous Matrix Space Model, which we call Continual Multiplication of Words (CMOW). Our algorithm is an adaptation of word2vec, so that it can be trained on large quantities of unlabeled text. We empirically show that CMOW better captures linguistic properties, but it is inferior to CBOW in memorizing word content. Motivated by these findings, we propose a hybrid model that combines the strengths of CBOW and CMOW. Our results show that the hybrid CBOW-CMOW-model retains CBOW's strong ability to memorize word content while at the same time substantially improving its ability to encode other linguistic information by 8%. As a result, the hybrid also performs better on 8 out of 11 supervised downstream tasks with an average improvement of 1.2%.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. However, existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. In particular, we demonstrate that some random walk statistics can be informative features to characterize node identities and positions while supporting the inductive embedding inference. Experiments validate the superior performance of IRWE beyond various baselines for the transductive and inductive inference of identity and position embeddings.

GAN inversion and editing via StyleGAN maps an input image into the embedding spaces (W, W^+, and F) to simultaneously maintain image fidelity and meaningful manipulation. From latent space W to extended latent space W^+ to feature space F in StyleGAN, the editability of GAN inversion decreases while its reconstruction quality increases. Recent GAN inversion methods typically explore W^+ and F rather than W to improve reconstruction fidelity while maintaining editability. As W^+ and F are derived from W that is essentially the foundation latent space of StyleGAN, these GAN inversion methods focusing on W^+ and F spaces could be improved by stepping back to W. In this work, we propose to first obtain the precise latent code in foundation latent space W. We introduce contrastive learning to align W and the image space for precise latent code discovery. %The obtaining process is by using contrastive learning to align W and the image space. Then, we leverage a cross-attention encoder to transform the obtained latent code in W into W^+ and F, accordingly. Our experiments show that our exploration of the foundation latent space W improves the representation ability of latent codes in W^+ and features in F, which yields state-of-the-art reconstruction fidelity and editability results on the standard benchmarks. Project page: https://kumapowerliu.github.io/CLCAE.

In recent years supervised representation learning has provided state of the art or close to the state of the art results in semantic analysis tasks including ranking and information retrieval. The core idea is to learn how to embed items into a latent space such that they optimize a supervised objective in that latent space. The dimensions of the latent space have no clear semantics, and this reduces the interpretability of the system. For example, in personalization models, it is hard to explain why a particular item is ranked high for a given user profile. We propose a novel model of representation learning called Supervised Explicit Semantic Analysis (SESA) that is trained in a supervised fashion to embed items to a set of dimensions with explicit semantics. The model learns to compare two objects by representing them in this explicit space, where each dimension corresponds to a concept from a knowledge base. This work extends Explicit Semantic Analysis (ESA) with a supervised model for ranking problems. We apply this model to the task of Job-Profile relevance in LinkedIn in which a set of skills defines our explicit dimensions of the space. Every profile and job are encoded to this set of skills their similarity is calculated in this space. We use RNNs to embed text input into this space. In addition to interpretability, our model makes use of the web-scale collaborative skills data that is provided by users for each LinkedIn profile. Our model provides state of the art result while it remains interpretable.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

Universal multimodal embedding models have achieved great success in capturing semantic relevance between queries and candidates. However, current methods either condense queries and candidates into a single vector, potentially limiting the expressiveness for fine-grained information, or produce too many vectors that are prohibitively expensive for multi-vector retrieval. In this work, we introduce MetaEmbed, a new framework for multimodal retrieval that rethinks how multimodal embeddings are constructed and interacted with at scale. During training, a fixed number of learnable Meta Tokens are appended to the input sequence. At test-time, their last-layer contextualized representations serve as compact yet expressive multi-vector embeddings. Through the proposed Matryoshka Multi-Vector Retrieval training, MetaEmbed learns to organize information by granularity across multiple vectors. As a result, we enable test-time scaling in multimodal retrieval, where users can balance retrieval quality against efficiency demands by selecting the number of tokens used for indexing and retrieval interactions. Extensive evaluations on the Massive Multimodal Embedding Benchmark (MMEB) and the Visual Document Retrieval Benchmark (ViDoRe) confirm that MetaEmbed achieves state-of-the-art retrieval performance while scaling robustly to models with 32B parameters.

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.

Multimodal models have demonstrated powerful capabilities in complex tasks requiring multimodal alignment including zero-shot classification and cross-modal retrieval. However, existing models typically rely on millions of paired multimodal samples, which are prohibitively expensive or infeasible to obtain in many domains. In this work, we explore the feasibility of building multimodal models with limited amount of paired data by aligning pretrained unimodal foundation models. We show that high-quality alignment is possible with as few as tens of thousands of paired samplesx2013less than 1% of the data typically used in the field. To achieve this, we introduce STRUCTURE, an effective regularization technique that preserves the neighborhood geometry of the latent space of unimodal encoders. Additionally, we show that aligning last layers is often suboptimal and demonstrate the benefits of aligning the layers with the highest representational similarity across modalities. These two components can be readily incorporated into existing alignment methods, yielding substantial gains across 24 zero-shot image classification and retrieval benchmarks, with average relative improvement of 51.6% in classification and 91.8% in retrieval tasks. Our results highlight the effectiveness and broad applicability of our framework for limited-sample multimodal learning and offer a promising path forward for resource-constrained domains.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.