Daily Papers

3D shape completion methods typically assume scans are pre-aligned to a canonical frame. This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17% and Chamfer distance ell1 on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion. Project page: https://sime-completion.github.io.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP. When the similarity is measured by dot-product between dual-encoder vectors or ell_2-distance, there already exist many scalable and efficient search methods. But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor. The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF. However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model. In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder. Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix. Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation. Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

We propose MESA and DMESA as novel feature matching methods, which utilize Segment Anything Model (SAM) to effectively mitigate matching redundancy. The key insight of our methods is to establish implicit-semantic area matching prior to point matching, based on advanced image understanding of SAM. Then, informative area matches with consistent internal semantic are able to undergo dense feature comparison, facilitating precise inside-area point matching. Specifically, MESA adopts a sparse matching framework and first obtains candidate areas from SAM results through a novel Area Graph (AG). Then, area matching among the candidates is formulated as graph energy minimization and solved by graphical models derived from AG. To address the efficiency issue of MESA, we further propose DMESA as its dense counterpart, applying a dense matching framework. After candidate areas are identified by AG, DMESA establishes area matches through generating dense matching distributions. The distributions are produced from off-the-shelf patch matching utilizing the Gaussian Mixture Model and refined via the Expectation Maximization. With less repetitive computation, DMESA showcases a speed improvement of nearly five times compared to MESA, while maintaining competitive accuracy. Our methods are extensively evaluated on five datasets encompassing indoor and outdoor scenes. The results illustrate consistent performance improvements from our methods for five distinct point matching baselines across all datasets. Furthermore, our methods exhibit promise generalization and improved robustness against image resolution variations. The code is publicly available at https://github.com/Easonyesheng/A2PM-MESA.

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n points in a metric space (P,d) where each point belongs to one of the ell different demographics (i.e., P = P_1 uplus P_2 uplus cdots uplus P_ell) and a set of ell intervals [alpha_1, beta_1], cdots, [alpha_ell, beta_ell] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ell_p-clustering cost (i.e., (sum_{vin P} d(v,C)^p)^{1/p}) such that for each group iin ell, |Ccap P_i| in [alpha_i, beta_i]. In particular, the fair range ell_p-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range ell_p-clustering for all values of pin [1,infty).

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Detection Transformers (DETR) have recently set new benchmarks in object detection. However, their performance in detecting rotated objects lags behind established oriented object detectors. Our analysis identifies a key observation: the boundary discontinuity and square-like problem in bipartite matching poses an issue with assigning appropriate ground truths to predictions, leading to duplicate low-confidence predictions. To address this, we introduce a Hausdorff distance-based cost for bipartite matching, which more accurately quantifies the discrepancy between predictions and ground truths. Additionally, we find that a static denoising approach impedes the training of rotated DETR, especially as the quality of the detector's predictions begins to exceed that of the noised ground truths. To overcome this, we propose an adaptive query denoising method that employs bipartite matching to selectively eliminate noised queries that detract from model improvement. When compared to models adopting a ResNet-50 backbone, our proposed model yields remarkable improvements, achieving +4.18 AP_{50}, +4.59 AP_{50}, and +4.99 AP_{50} on DOTA-v2.0, DOTA-v1.5, and DIOR-R, respectively.

We propose AffineGlue, a method for joint two-view feature matching and robust estimation that reduces the combinatorial complexity of the problem by employing single-point minimal solvers. AffineGlue selects potential matches from one-to-many correspondences to estimate minimal models. Guided matching is then used to find matches consistent with the model, suffering less from the ambiguities of one-to-one matches. Moreover, we derive a new minimal solver for homography estimation, requiring only a single affine correspondence (AC) and a gravity prior. Furthermore, we train a neural network to reject ACs that are unlikely to lead to a good model. AffineGlue is superior to the SOTA on real-world datasets, even when assuming that the gravity direction points downwards. On PhotoTourism, the AUC@10{\deg} score is improved by 6.6 points compared to the SOTA. On ScanNet, AffineGlue makes SuperPoint and SuperGlue achieve similar accuracy as the detector-free LoFTR.

In this work, we show that it is possible to extract significant amounts of alignment training data from a post-trained model -- useful to steer the model to improve certain capabilities such as long-context reasoning, safety, instruction following, and maths. While the majority of related work on memorisation has focused on measuring success of training data extraction through string matching, we argue that embedding models are better suited for our specific goals. Distances measured through a high quality embedding model can identify semantic similarities between strings that a different metric such as edit distance will struggle to capture. In fact, in our investigation, approximate string matching would have severely undercounted (by a conservative estimate of 10times) the amount of data that can be extracted due to trivial artifacts that deflate the metric. Interestingly, we find that models readily regurgitate training data that was used in post-training phases such as SFT or RL. We show that this data can be then used to train a base model, recovering a meaningful amount of the original performance. We believe our work exposes a possibly overlooked risk towards extracting alignment data. Finally, our work opens up an interesting discussion on the downstream effects of distillation practices: since models seem to be regurgitating aspects of their training set, distillation can therefore be thought of as indirectly training on the model's original dataset.

Unsupervised hashing methods typically aim to preserve the similarity between data points in a feature space by mapping them to binary hash codes. However, these methods often overlook the fact that the similarity between data points in the continuous feature space may not be preserved in the discrete hash code space, due to the limited similarity range of hash codes. The similarity range is bounded by the code length and can lead to a problem known as similarity collapse. That is, the positive and negative pairs of data points become less distinguishable from each other in the hash space. To alleviate this problem, in this paper a novel Similarity Distribution Calibration (SDC) method is introduced. SDC aligns the hash code similarity distribution towards a calibration distribution (e.g., beta distribution) with sufficient spread across the entire similarity range, thus alleviating the similarity collapse problem. Extensive experiments show that our SDC outperforms significantly the state-of-the-art alternatives on coarse category-level and instance-level image retrieval. Code is available at https://github.com/kamwoh/sdc.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

Given a database of bit strings A_1,ldots,A_min {0,1}^n, a fundamental data structure task is to estimate the distances between a given query Bin {0,1}^n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is epsilon-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, - For Hamming distance, our data structure answers any query in widetilde O(mk+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/log k}); - For edit distance, our data structure answers any query in widetilde O(mk^2+n) time and each estimate deviates from the true distance by at most widetilde O(k/e^{epsilon/(log k log n)}). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Vector Similarity Search (VSS) in high-dimensional spaces is rapidly emerging as core functionality in next-generation database systems for numerous data-intensive services -- from embedding lookups in large language models (LLMs), to semantic information retrieval and recommendation engines. Current benchmarks, however, evaluate VSS primarily on the recall-latency trade-off against a ground truth defined solely by distance metrics, neglecting how retrieval quality ultimately impacts downstream tasks. This disconnect can mislead both academic research and industrial practice. We present Iceberg, a holistic benchmark suite for end-to-end evaluation of VSS methods in realistic application contexts. From a task-centric view, Iceberg uncovers the Information Loss Funnel, which identifies three principal sources of end-to-end performance degradation: (1) Embedding Loss during feature extraction; (2) Metric Misuse, where distances poorly reflect task relevance; (3) Data Distribution Sensitivity, highlighting index robustness across skews and modalities. For a more comprehensive assessment, Iceberg spans eight diverse datasets across key domains such as image classification, face recognition, text retrieval, and recommendation systems. Each dataset, ranging from 1M to 100M vectors, includes rich, task-specific labels and evaluation metrics, enabling assessment of retrieval algorithms within the full application pipeline rather than in isolation. Iceberg benchmarks 13 state-of-the-art VSS methods and re-ranks them based on application-level metrics, revealing substantial deviations from traditional rankings derived purely from recall-latency evaluations. Building on these insights, we define a set of task-centric meta-features and derive an interpretable decision tree to guide practitioners in selecting and tuning VSS methods for their specific workloads.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

Recent efforts in fine-tuning language models often rely on automatic data selection, commonly using Nearest Neighbors retrieval from large datasets. However, we theoretically show that this approach tends to select redundant data, limiting its effectiveness or even hurting performance. To address this, we introduce SIFT, a data selection algorithm designed to reduce uncertainty about the model's response given a prompt, which unifies ideas from retrieval and active learning. Whereas Nearest Neighbor retrieval typically fails in the presence of information duplication, SIFT accounts for information duplication and optimizes the overall information gain of the selected examples. We focus our evaluations on fine-tuning at test-time for prompt-specific language modeling on the Pile dataset, and show that SIFT consistently outperforms Nearest Neighbor retrieval, with minimal computational overhead. Moreover, we show that our uncertainty estimates can predict the performance gain of test-time fine-tuning, and use this to develop an adaptive algorithm that invests test-time compute proportional to realized performance gains. We provide the activeft (Active Fine-Tuning) library which can be used as a drop-in replacement for Nearest Neighbor retrieval.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

In embedding-based retrieval, Approximate Nearest Neighbor (ANN) search enables efficient retrieval of similar items from large-scale datasets. While maximizing recall of relevant items is usually the goal of retrieval systems, a low precision may lead to a poor search experience. Unlike lexical retrieval, which inherently limits the size of the retrieved set through keyword matching, dense retrieval via ANN search has no natural cutoff. Moreover, the cosine similarity scores of embedding vectors are often optimized via contrastive or ranking losses, which make them difficult to interpret. Consequently, relying on top-K or cosine-similarity cutoff is often insufficient to filter out irrelevant results effectively. This issue is prominent in product search, where the number of relevant products is often small. This paper introduces a novel relevance filtering component (called "Cosine Adapter") for embedding-based retrieval to address this challenge. Our approach maps raw cosine similarity scores to interpretable scores using a query-dependent mapping function. We then apply a global threshold on the mapped scores to filter out irrelevant results. We are able to significantly increase the precision of the retrieved set, at the expense of a small loss of recall. The effectiveness of our approach is demonstrated through experiments on both public MS MARCO dataset and internal Walmart product search data. Furthermore, online A/B testing on the Walmart site validates the practical value of our approach in real-world e-commerce settings.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Worldwide image geolocalization-the task of predicting GPS coordinates from images taken anywhere on Earth-poses a fundamental challenge due to the vast diversity in visual content across regions. While recent approaches adopt a two-stage pipeline of retrieving candidates and selecting the best match, they typically rely on simplistic similarity heuristics and point-wise supervision, failing to model spatial relationships among candidates. In this paper, we propose GeoRanker, a distance-aware ranking framework that leverages large vision-language models to jointly encode query-candidate interactions and predict geographic proximity. In addition, we introduce a multi-order distance loss that ranks both absolute and relative distances, enabling the model to reason over structured spatial relationships. To support this, we curate GeoRanking, the first dataset explicitly designed for geographic ranking tasks with multimodal candidate information. GeoRanker achieves state-of-the-art results on two well-established benchmarks (IM2GPS3K and YFCC4K), significantly outperforming current best methods.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention mechanisms to simulate soft alignment, with no training signals to explicitly encourage alignment. The learned attention matrices are also dense and lacks interpretability. We propose Graph Optimal Transport (GOT), a principled framework that germinates from recent advances in Optimal Transport (OT). In GOT, cross-domain alignment is formulated as a graph matching problem, by representing entities into a dynamically-constructed graph. Two types of OT distances are considered: (i) Wasserstein distance (WD) for node (entity) matching; and (ii) Gromov-Wasserstein distance (GWD) for edge (structure) matching. Both WD and GWD can be incorporated into existing neural network models, effectively acting as a drop-in regularizer. The inferred transport plan also yields sparse and self-normalized alignment, enhancing the interpretability of the learned model. Experiments show consistent outperformance of GOT over baselines across a wide range of tasks, including image-text retrieval, visual question answering, image captioning, machine translation, and text summarization.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

Existing perceptual similarity metrics assume an image and its reference are well aligned. As a result, these metrics are often sensitive to a small alignment error that is imperceptible to the human eyes. This paper studies the effect of small misalignment, specifically a small shift between the input and reference image, on existing metrics, and accordingly develops a shift-tolerant similarity metric. This paper builds upon LPIPS, a widely used learned perceptual similarity metric, and explores architectural design considerations to make it robust against imperceptible misalignment. Specifically, we study a wide spectrum of neural network elements, such as anti-aliasing filtering, pooling, striding, padding, and skip connection, and discuss their roles in making a robust metric. Based on our studies, we develop a new deep neural network-based perceptual similarity metric. Our experiments show that our metric is tolerant to imperceptible shifts while being consistent with the human similarity judgment.

Mehta and Panigrahi (2012) proposed Online Matching with Stochastic Rewards, which generalizes the Online Bipartite Matching problem of Karp, Vazirani, and Vazirani (1990) by associating the edges with success probabilities. This new feature captures the pay-per-click model in online advertising. Recently, Huang and Zhang (2020) studied this problem under the online primal dual framework using the Configuration Linear Program (LP), and got the best known competitive ratios of the Stochastic Balance algorithm. Their work suggests that the more expressive Configuration LP is more suitable for this problem than the Matching LP. This paper advances the theory of Configuration LP in two directions. Our technical contribution includes a characterization of the joint matching outcome of an offline vertex and all its neighbors. This characterization may be of independent interest, and is aligned with the spirit of Configuration LP. By contrast, previous analyses of Ranking generally focus on only one neighbor. Second, we designed a Stochastic Configuration LP that captures a stochastic benchmark proposed by Goyal and Udwani (2020), who used a Path-based LP. The Stochastic Configuration LP is smaller and simpler than the Path-based LP. Moreover, using the new LP we improved the competitive ratio of Stochastic Balance from 0.596 to 0.611 when the success probabilities are infinitesimal, and to 0.613 when the success probabilities are further equal.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Vector search systems, pivotal in AI applications, often rely on the Hierarchical Navigable Small Worlds (HNSW) algorithm. However, the behaviour of HNSW under real-world scenarios using vectors generated with deep learning models remains under-explored. Existing Approximate Nearest Neighbours (ANN) benchmarks and research typically has an over-reliance on simplistic datasets like MNIST or SIFT1M and fail to reflect the complexity of current use-cases. Our investigation focuses on HNSW's efficacy across a spectrum of datasets, including synthetic vectors tailored to mimic specific intrinsic dimensionalities, widely-used retrieval benchmarks with popular embedding models, and proprietary e-commerce image data with CLIP models. We survey the most popular HNSW vector databases and collate their default parameters to provide a realistic fixed parameterisation for the duration of the paper. We discover that the recall of approximate HNSW search, in comparison to exact K Nearest Neighbours (KNN) search, is linked to the vector space's intrinsic dimensionality and significantly influenced by the data insertion sequence. Our methodology highlights how insertion order, informed by measurable properties such as the pointwise Local Intrinsic Dimensionality (LID) or known categories, can shift recall by up to 12 percentage points. We also observe that running popular benchmark datasets with HNSW instead of KNN can shift rankings by up to three positions for some models. This work underscores the need for more nuanced benchmarks and design considerations in developing robust vector search systems using approximate vector search algorithms. This study presents a number of scenarios with varying real world applicability which aim to better increase understanding and future development of ANN algorithms and embedding

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 the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

We investigate composed image retrieval with text feedback. Users gradually look for the target of interest by moving from coarse to fine-grained feedback. However, existing methods merely focus on the latter, i.e., fine-grained search, by harnessing positive and negative pairs during training. This pair-based paradigm only considers the one-to-one distance between a pair of specific points, which is not aligned with the one-to-many coarse-grained retrieval process and compromises the recall rate. In an attempt to fill this gap, we introduce a unified learning approach to simultaneously modeling the coarse- and fine-grained retrieval by considering the multi-grained uncertainty. The key idea underpinning the proposed method is to integrate fine- and coarse-grained retrieval as matching data points with small and large fluctuations, respectively. Specifically, our method contains two modules: uncertainty modeling and uncertainty regularization. (1) The uncertainty modeling simulates the multi-grained queries by introducing identically distributed fluctuations in the feature space. (2) Based on the uncertainty modeling, we further introduce uncertainty regularization to adapt the matching objective according to the fluctuation range. Compared with existing methods, the proposed strategy explicitly prevents the model from pushing away potential candidates in the early stage, and thus improves the recall rate. On the three public datasets, i.e., FashionIQ, Fashion200k, and Shoes, the proposed method has achieved +4.03%, +3.38%, and +2.40% Recall@50 accuracy over a strong baseline, respectively.

Enterprises often own large collections of structured data in the form of large databases or an enterprise data lake. Such data collections come with limited metadata and strict access policies that could limit access to the data contents and, therefore, limit the application of classic retrieval and analysis solutions. As a result, there is a need for solutions that can effectively utilize the available metadata. In this paper, we study the problem of matching table metadata to a business glossary containing data labels and descriptions. The resulting matching enables the use of an available or curated business glossary for retrieval and analysis without or before requesting access to the data contents. One solution to this problem is to use manually-defined rules or similarity measures on column names and glossary descriptions (or their vector embeddings) to find the closest match. However, such approaches need to be tuned through manual labeling and cannot handle many business glossaries that contain a combination of simple as well as complex and long descriptions. In this work, we leverage the power of large language models (LLMs) to design generic matching methods that do not require manual tuning and can identify complex relations between column names and glossaries. We propose methods that utilize LLMs in two ways: a) by generating additional context for column names that can aid with matching b) by using LLMs to directly infer if there is a relation between column names and glossary descriptions. Our preliminary experimental results show the effectiveness of our proposed methods.

Visual Place Recognition (VPR) is a critical task in computer vision, traditionally enhanced by re-ranking retrieval results with image matching. However, recent advancements in VPR methods have significantly improved performance, challenging the necessity of re-ranking. In this work, we show that modern retrieval systems often reach a point where re-ranking can degrade results, as current VPR datasets are largely saturated. We propose using image matching as a verification step to assess retrieval confidence, demonstrating that inlier counts can reliably predict when re-ranking is beneficial. Our findings shift the paradigm of retrieval pipelines, offering insights for more robust and adaptive VPR systems. The code is available at https://github.com/FarInHeight/To-Match-or-Not-to-Match.

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.

Transformers struggle with length generalisation, displaying poor performance even on basic tasks. We test whether these limitations can be explained through two key failures of the self-attention mechanism. The first is the inability to fully remove irrelevant information. The second is tied to position, even if the dot product between a key and query is highly negative (i.e. an irrelevant key) learned positional biases may unintentionally up-weight such information - dangerous when distances become out of distribution. Put together, these two failure cases lead to compounding generalisation difficulties. We test whether they can be mitigated through the combination of a) selective sparsity - completely removing irrelevant keys from the attention softmax and b) contextualised relative distance - distance is only considered as between the query and the keys that matter. We show how refactoring the attention mechanism with these two mitigations in place can substantially improve generalisation capabilities of decoder only transformers.

Dense feature matching is an important computer vision task that involves estimating all correspondences between two images of a 3D scene. In this paper, we revisit robust losses for matching from a Markov chain perspective, yielding theoretical insights and large gains in performance. We begin by constructing a unifying formulation of matching as a Markov chain, based on which we identify two key stages which we argue should be decoupled for matching. The first is the coarse stage, where the estimated result needs to be globally consistent. The second is the refinement stage, where the model needs precise localization capabilities. Inspired by the insight that these stages concern distinct issues, we propose a coarse matcher following the regression-by-classification paradigm that provides excellent globally consistent, albeit not exactly localized, matches. This is followed by a local feature refinement stage using well-motivated robust regression losses, yielding extremely precise matches. Our proposed approach, which we call RoMa, achieves significant improvements compared to the state-of-the-art. Code is available at https://github.com/Parskatt/RoMa

We address the problem of detecting and mapping all books in a collection of images to entries in a given book catalogue. Instead of performing independent retrieval for each book detected, we treat the image-text mapping problem as a many-to-many matching process, looking for the best overall match between the two sets. We combine a state-of-the-art segmentation method (SAM) to detect book spines and extract book information using a commercial OCR. We then propose a two-stage approach for text-image matching, where CLIP embeddings are used first for fast matching, followed by a second slower stage to refine the matching, employing either the Hungarian Algorithm or a BERT-based model trained to cope with noisy OCR input and partial text matches. To evaluate our approach, we publish a new dataset of annotated bookshelf images that covers the whole book collection of a public library in Spain. In addition, we provide two target lists of book metadata, a closed-set of 15k book titles that corresponds to the known library inventory, and an open-set of 2.3M book titles to simulate an open-world scenario. We report results on two settings, on one hand on a matching-only task, where the book segments and OCR is given and the objective is to perform many-to-many matching against the target lists, and a combined detection and matching task, where books must be first detected and recognised before they are matched to the target list entries. We show that both the Hungarian Matching and the proposed BERT-based model outperform a fuzzy string matching baseline, and we highlight inherent limitations of the matching algorithms as the target increases in size, and when either of the two sets (detected books or target book list) is incomplete. The dataset and code are available at https://github.com/llabres/library-dataset

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

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.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

Dataset distillation has emerged as a powerful approach for reducing data requirements in deep learning. Among various methods, distribution matching-based approaches stand out for their balance of computational efficiency and strong performance. However, existing distance metrics used in distribution matching often fail to accurately capture distributional differences, leading to unreliable measures of discrepancy. In this paper, we reformulate dataset distillation as a minmax optimization problem and introduce Neural Characteristic Function Discrepancy (NCFD), a comprehensive and theoretically grounded metric for measuring distributional differences. NCFD leverages the Characteristic Function (CF) to encapsulate full distributional information, employing a neural network to optimize the sampling strategy for the CF's frequency arguments, thereby maximizing the discrepancy to enhance distance estimation. Simultaneously, we minimize the difference between real and synthetic data under this optimized NCFD measure. Our approach, termed Neural Characteristic Function Matching (), inherently aligns the phase and amplitude of neural features in the complex plane for both real and synthetic data, achieving a balance between realism and diversity in synthetic samples. Experiments demonstrate that our method achieves significant performance gains over state-of-the-art methods on both low- and high-resolution datasets. Notably, we achieve a 20.5\% accuracy boost on ImageSquawk. Our method also reduces GPU memory usage by over 300times and achieves 20times faster processing speeds compared to state-of-the-art methods. To the best of our knowledge, this is the first work to achieve lossless compression of CIFAR-100 on a single NVIDIA 2080 Ti GPU using only 2.3 GB of memory.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate query features and performs a one-time optimization over a small set of initial queries to learn a routing strategy that guides future routing. We provide theoretical guarantees demonstrating that our algorithm achieves a competitive ratio of 1 - o(1) under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55times in overall performance, 1.85times in cost efficiency, and nearly 4.25times in throughput. Our code is available at https://github.com/fzwark/PORT.

One-to-one set matching is a key design for DETR to establish its end-to-end capability, so that object detection does not require a hand-crafted NMS (non-maximum suppression) to remove duplicate detections. This end-to-end signature is important for the versatility of DETR, and it has been generalized to broader vision tasks. However, we note that there are few queries assigned as positive samples and the one-to-one set matching significantly reduces the training efficacy of positive samples. We propose a simple yet effective method based on a hybrid matching scheme that combines the original one-to-one matching branch with an auxiliary one-to-many matching branch during training. Our hybrid strategy has been shown to significantly improve accuracy. In inference, only the original one-to-one match branch is used, thus maintaining the end-to-end merit and the same inference efficiency of DETR. The method is named H-DETR, and it shows that a wide range of representative DETR methods can be consistently improved across a wide range of visual tasks, including DeformableDETR, PETRv2, PETR, and TransTrack, among others. The code is available at: https://github.com/HDETR

This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without re-encoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validated that every memory node now has a chance to contribute, and experimentally showed that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at 20+ FPS for multiple objects without bells and whistles.

In this work, by re-examining the "matching" nature of Anomaly Detection (AD), we propose a new AD framework that simultaneously enjoys new records of AD accuracy and dramatically high running speed. In this framework, the anomaly detection problem is solved via a cascade patch retrieval procedure that retrieves the nearest neighbors for each test image patch in a coarse-to-fine fashion. Given a test sample, the top-K most similar training images are first selected based on a robust histogram matching process. Secondly, the nearest neighbor of each test patch is retrieved over the similar geometrical locations on those "global nearest neighbors", by using a carefully trained local metric. Finally, the anomaly score of each test image patch is calculated based on the distance to its "local nearest neighbor" and the "non-background" probability. The proposed method is termed "Cascade Patch Retrieval" (CPR) in this work. Different from the conventional patch-matching-based AD algorithms, CPR selects proper "targets" (reference images and locations) before "shooting" (patch-matching). On the well-acknowledged MVTec AD, BTAD and MVTec-3D AD datasets, the proposed algorithm consistently outperforms all the comparing SOTA methods by remarkable margins, measured by various AD metrics. Furthermore, CPR is extremely efficient. It runs at the speed of 113 FPS with the standard setting while its simplified version only requires less than 1 ms to process an image at the cost of a trivial accuracy drop. The code of CPR is available at https://github.com/flyinghu123/CPR.

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

Intersection over Union (IoU) is the most popular evaluation metric used in the object detection benchmarks. However, there is a gap between optimizing the commonly used distance losses for regressing the parameters of a bounding box and maximizing this metric value. The optimal objective for a metric is the metric itself. In the case of axis-aligned 2D bounding boxes, it can be shown that IoU can be directly used as a regression loss. However, IoU has a plateau making it infeasible to optimize in the case of non-overlapping bounding boxes. In this paper, we address the weaknesses of IoU by introducing a generalized version as both a new loss and a new metric. By incorporating this generalized IoU (GIoU) as a loss into the state-of-the art object detection frameworks, we show a consistent improvement on their performance using both the standard, IoU based, and new, GIoU based, performance measures on popular object detection benchmarks such as PASCAL VOC and MS COCO.

Objective assessment of source-separation systems still mismatches subjective human perception, especially when leakage and self-distortion interact. We introduce the Perceptual Separation (PS) and Perceptual Match (PM), the first pair of measures that functionally isolate these two factors. Our intrusive method begins with generating a bank of fundamental distortions for each reference waveform signal in the mixture. Distortions, references, and their respective system outputs from all sources are then independently encoded by a pre-trained self-supervised learning model. These representations are aggregated and projected onto a manifold via diffusion maps, which aligns Euclidean distances on the manifold with dissimilarities of the encoded waveforms. On this manifold, the PM measures the Mahalanobis distance from each output to its attributed cluster that consists of its reference and distortions embeddings, capturing self-distortion. The PS accounts for the Mahalanobis distance of the output to the attributed and to the closest non-attributed clusters, quantifying leakage. Both measures are differentiable and granular, operating at a resolution as low as 50 frames per second. We further derive, for both measures, deterministic error radius and non-asymptotic, high-probability confidence intervals (CIs). Experiments on English, Spanish, and music mixtures show that the PS and PM nearly always achieve the highest linear correlation coefficients with human mean-opinion scores than 14 competitors, reaching as high as 86.36% for speech and 87.21% for music. We observe, at worst, an error radius of 1.39% and a probabilistic 95% CI of 12.21% for these coefficients, which improves reliable and informed evaluation. Using mutual information, the measures complement each other most as their values decrease, suggesting they are jointly more informative as system performance degrades.

The lightweight "local-match-global" matching introduced by SRe2L successfully creates a distilled dataset with comprehensive information on the full 224x224 ImageNet-1k. However, this one-sided approach is limited to a particular backbone, layer, and statistics, which limits the improvement of the generalization of a distilled dataset. We suggest that sufficient and various "local-match-global" matching are more precise and effective than a single one and has the ability to create a distilled dataset with richer information and better generalization. We call this perspective "generalized matching" and propose Generalized Various Backbone and Statistical Matching (G-VBSM) in this work, which aims to create a synthetic dataset with densities, ensuring consistency with the complete dataset across various backbones, layers, and statistics. As experimentally demonstrated, G-VBSM is the first algorithm to obtain strong performance across both small-scale and large-scale datasets. Specifically, G-VBSM achieves a performance of 38.7% on CIFAR-100 with 128-width ConvNet, 47.6% on Tiny-ImageNet with ResNet18, and 31.4% on the full 224x224 ImageNet-1k with ResNet18, under images per class (IPC) 10, 50, and 10, respectively. These results surpass all SOTA methods by margins of 3.9%, 6.5%, and 10.1%, respectively.

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.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Fairness and relevance are two important aspects of recommender systems (RSs). Typically, they are evaluated either (i) separately by individual measures of fairness and relevance, or (ii) jointly using a single measure that accounts for fairness with respect to relevance. However, approach (i) often does not provide a reliable joint estimate of the goodness of the models, as it has two different best models: one for fairness and another for relevance. Approach (ii) is also problematic because these measures tend to be ad-hoc and do not relate well to traditional relevance measures, like NDCG. Motivated by this, we present a new approach for jointly evaluating fairness and relevance in RSs: Distance to Pareto Frontier (DPFR). Given some user-item interaction data, we compute their Pareto frontier for a pair of existing relevance and fairness measures, and then use the distance from the frontier as a measure of the jointly achievable fairness and relevance. Our approach is modular and intuitive as it can be computed with existing measures. Experiments with 4 RS models, 3 re-ranking strategies, and 6 datasets show that existing metrics have inconsistent associations with our Pareto-optimal solution, making DPFR a more robust and theoretically well-founded joint measure for assessing fairness and relevance. Our code: https://github.com/theresiavr/DPFR-recsys-evaluation

In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without reordering elements over time, it is possible to construct a hash table that achieves far better expected search complexities (both amortized and worst-case) than were previously thought possible. Along the way, we disprove the central conjecture left by Yao in his seminal paper ``Uniform Hashing is Optimal''. All of our results come with matching lower bounds.

Semantic correspondence methods have advanced to obtaining high-quality correspondences employing complicated networks, aiming to maximize the model capacity. However, despite the performance improvements, they may remain constrained by the scarcity of training keypoint pairs, a consequence of the limited training images and the sparsity of keypoints. This paper builds on the hypothesis that there is an inherent data-hungry matter in learning semantic correspondences and uncovers the models can be more trained by employing densified training pairs. We demonstrate a simple machine annotator reliably enriches paired key points via machine supervision, requiring neither extra labeled key points nor trainable modules from unlabeled images. Consequently, our models surpass current state-of-the-art models on semantic correspondence learning benchmarks like SPair-71k, PF-PASCAL, and PF-WILLOW and enjoy further robustness on corruption benchmarks. Our code is available at https://github.com/naver-ai/matchme.

Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55% of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

Most text-based information retrieval (IR) systems index objects by words or phrases. These discrete systems have been augmented by models that use embeddings to measure similarity in continuous space. But continuous-space models are typically used just to re-rank the top candidates. We consider the problem of end-to-end continuous retrieval, where standard approximate nearest neighbor (ANN) search replaces the usual discrete inverted index, and rely entirely on distances between learned embeddings. By training simple models specifically for retrieval, with an appropriate model architecture, we improve on a discrete baseline by 8% and 26% (MAP) on two similar-question retrieval tasks. We also discuss the problem of evaluation for retrieval systems, and show how to modify existing pairwise similarity datasets for this purpose.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

The goal of product mapping is to decide, whether two listings from two different e-shops describe the same products. Existing datasets of matching and non-matching pairs of products, however, often suffer from incomplete product information or contain only very distant non-matching products. Therefore, while predictive models trained on these datasets achieve good results on them, in practice, they are unusable as they cannot distinguish very similar but non-matching pairs of products. This paper introduces two new datasets for product mapping: ProMapCz consisting of 1,495 Czech product pairs and ProMapEn consisting of 1,555 English product pairs of matching and non-matching products manually scraped from two pairs of e-shops. The datasets contain both images and textual descriptions of the products, including their specifications, making them one of the most complete datasets for product mapping. Additionally, the non-matching products were selected in two phases, creating two types of non-matches -- close non-matches and medium non-matches. Even the medium non-matches are pairs of products that are much more similar than non-matches in other datasets -- for example, they still need to have the same brand and similar name and price. After simple data preprocessing, several machine learning algorithms were trained on these and two the other datasets to demonstrate the complexity and completeness of ProMap datasets. ProMap datasets are presented as a golden standard for further research of product mapping filling the gaps in existing ones.

Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which limits the suitability of the algorithm for larger values of k depending on the size of the collection. Optimizations targeted at the Euclidean k-Means algorithm largely do not apply because the cosine distance is not a metric. We therefore propose an efficient indexing structure to improve the scalability of Spherical k-Means with respect to k. Our approach exploits the sparsity of the input vectors and the convergence behavior of k-Means to reduce the number of comparisons on each iteration significantly.

Per-object distance estimation is critical in surveillance and autonomous driving, where safety is crucial. While existing methods rely on geometric or deep supervised features, only a few attempts have been made to leverage self-supervised learning. In this respect, our paper draws inspiration from Masked Image Modeling (MiM) and extends it to multi-object tasks. While MiM focuses on extracting global image-level representations, it struggles with individual objects within the image. This is detrimental for distance estimation, as objects far away correspond to negligible portions of the image. Conversely, our strategy, termed Masked Object Modeling (MoM), enables a novel application of masking techniques. In a few words, we devise an auxiliary objective that reconstructs the portions of the image pertaining to the objects detected in the scene. The training phase is performed in a single unified stage, simultaneously optimizing the masking objective and the downstream loss (i.e., distance estimation). We evaluate the effectiveness of MoM on a novel reference architecture (DistFormer) on the standard KITTI, NuScenes, and MOTSynth datasets. Our evaluation reveals that our framework surpasses the SoTA and highlights its robust regularization properties. The MoM strategy enhances both zero-shot and few-shot capabilities, from synthetic to real domain. Finally, it furthers the robustness of the model in the presence of occluded or poorly detected objects. Code is available at https://github.com/apanariello4/DistFormer

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Image-Text Matching (ITM) task, a fundamental vision-language (VL) task, suffers from the inherent ambiguity arising from multiplicity and imperfect annotations. Deterministic functions are not sufficiently powerful to capture ambiguity, prompting the exploration of probabilistic embeddings to tackle the challenge. However, the existing probabilistic ITM approach encounters two key shortcomings; the burden of heavy computations due to the Monte Carlo approximation, and the loss saturation issue in the face of abundant false negatives. To overcome the issues, this paper presents an improved Probabilistic Cross-Modal Embeddings (named PCME++) by introducing a new probabilistic distance with a closed-form solution. In addition, two optimization techniques are proposed to enhance PCME++ further: first, the incorporation of pseudo-positives to prevent the loss saturation problem under massive false negatives; second, mixed sample data augmentation for probabilistic matching. Experimental results on MS-COCO Caption and two extended benchmarks, CxC and ECCV Caption, demonstrate the effectiveness of PCME++ compared to state-of-the-art ITM methods. The robustness of PCME++ is also evaluated under noisy image-text correspondences. In addition, the potential applicability of PCME++ in automatic prompt tuning for zero-shot classification is shown. The code is available at https://github.com/naver-ai/pcmepp.

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity of the induced distribution of the (normalized) features on the hypersphere. We prove that, asymptotically, the contrastive loss optimizes these properties, and analyze their positive effects on downstream tasks. Empirically, we introduce an optimizable metric to quantify each property. Extensive experiments on standard vision and language datasets confirm the strong agreement between both metrics and downstream task performance. Remarkably, directly optimizing for these two metrics leads to representations with comparable or better performance at downstream tasks than contrastive learning. Project Page: https://tongzhouwang.info/hypersphere Code: https://github.com/SsnL/align_uniform , https://github.com/SsnL/moco_align_uniform

Many learning algorithms such as kernel machines, nearest neighbors, clustering, or anomaly detection, are based on the concept of 'distance' or 'similarity'. Before similarities are used for training an actual machine learning model, we would like to verify that they are bound to meaningful patterns in the data. In this paper, we propose to make similarities interpretable by augmenting them with an explanation in terms of input features. We develop BiLRP, a scalable and theoretically founded method to systematically decompose similarity scores on pairs of input features. Our method can be expressed as a composition of LRP explanations, which were shown in previous works to scale to highly nonlinear functions. Through an extensive set of experiments, we demonstrate that BiLRP robustly explains complex similarity models, e.g. built on VGG-16 deep neural network features. Additionally, we apply our method to an open problem in digital humanities: detailed assessment of similarity between historical documents such as astronomical tables. Here again, BiLRP provides insight and brings verifiability into a highly engineered and problem-specific similarity model.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional filters. The proposed algorithm combines dense embeddings with discrete filtering attributes, enabling fast retrieval in high-dimensional spaces. Designed specifically for CPU-based systems, our disk-based approach offers a cost-effective solution for large-scale similarity search. We demonstrate the effectiveness of our method through a case study, showcasing its potential for various practical uses.

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score. Because it does not differentiate the fidelity and diversity aspects of the generated images, recent papers have introduced variants of precision and recall metrics to diagnose those properties separately. In this paper, we show that even the latest version of the precision and recall metrics are not reliable yet. For example, they fail to detect the match between two identical distributions, they are not robust against outliers, and the evaluation hyperparameters are selected arbitrarily. We propose density and coverage metrics that solve the above issues. We analytically and experimentally show that density and coverage provide more interpretable and reliable signals for practitioners than the existing metrics. Code: https://github.com/clovaai/generative-evaluation-prdc.

Entity resolution is a widely studied problem with several proposals to match records across relations. Matching textual content is a widespread task in many applications, such as question answering and search. While recent methods achieve promising results for these two tasks, there is no clear solution for the more general problem of matching textual content and structured data. We introduce a framework that supports this new task in an unsupervised setting for any pair of corpora, being relational tables or text documents. Our method builds a fine-grained graph over the content of the corpora and derives word embeddings to represent the objects to match in a low dimensional space. The learned representation enables effective and efficient matching at different granularity, from relational tuples to text sentences and paragraphs. Our flexible framework can exploit pre-trained resources, but it does not depends on their existence and achieves better quality performance in matching content when the vocabulary is domain specific. We also introduce optimizations in the graph creation process with an "expand and compress" approach that first identifies new valid relationships across elements, to improve matching, and then prunes nodes and edges, to reduce the graph size. Experiments on real use cases and public datasets show that our framework produces embeddings that outperform word embeddings and fine-tuned language models both in results' quality and in execution times.

Large-scale visual localization systems continue to rely on 3D point clouds built from image collections using structure-from-motion. While the 3D points in these models are represented using local image features, directly matching a query image's local features against the point cloud is challenging due to the scale of the nearest-neighbor search problem. Many recent approaches to visual localization have thus proposed a hybrid method, where first a global (per image) embedding is used to retrieve a small subset of database images, and local features of the query are matched only against those. It seems to have become common belief that global embeddings are critical for said image-retrieval in visual localization, despite the significant downside of having to compute two feature types for each query image. In this paper, we take a step back from this assumption and propose Constrained Approximate Nearest Neighbors (CANN), a joint solution of k-nearest-neighbors across both the geometry and appearance space using only local features. We first derive the theoretical foundation for k-nearest-neighbor retrieval across multiple metrics and then showcase how CANN improves visual localization. Our experiments on public localization benchmarks demonstrate that our method significantly outperforms both state-of-the-art global feature-based retrieval and approaches using local feature aggregation schemes. Moreover, it is an order of magnitude faster in both index and query time than feature aggregation schemes for these datasets. Code will be released.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

In this paper, we address the challenge of matching semantically similar keypoints across image pairs. Existing research indicates that the intermediate output of the UNet within the Stable Diffusion (SD) can serve as robust image feature maps for such a matching task. We demonstrate that by employing a basic prompt tuning technique, the inherent potential of Stable Diffusion can be harnessed, resulting in a significant enhancement in accuracy over previous approaches. We further introduce a novel conditional prompting module that conditions the prompt on the local details of the input image pairs, leading to a further improvement in performance. We designate our approach as SD4Match, short for Stable Diffusion for Semantic Matching. Comprehensive evaluations of SD4Match on the PF-Pascal, PF-Willow, and SPair-71k datasets show that it sets new benchmarks in accuracy across all these datasets. Particularly, SD4Match outperforms the previous state-of-the-art by a margin of 12 percentage points on the challenging SPair-71k dataset.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

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.

Establishing semantic correspondences between images is a fundamental yet challenging task in computer vision. Traditional feature-metric methods enhance visual features but may miss complex inter-correlation relationships, while recent correlation-metric approaches are hindered by high computational costs due to processing 4D correlation maps. We introduce MambaMatcher, a novel method that overcomes these limitations by efficiently modeling high-dimensional correlations using selective state-space models (SSMs). By implementing a similarity-aware selective scan mechanism adapted from Mamba's linear-complexity algorithm, MambaMatcher refines the 4D correlation map effectively without compromising feature map resolution or receptive field. Experiments on standard semantic correspondence benchmarks demonstrate that MambaMatcher achieves state-of-the-art performance.

Advances in embedding models for text, image, audio, and video drive progress across multiple domains, including retrieval-augmented generation, recommendation systems, vehicle/person reidentification, and face recognition. Many applications in these domains require an efficient method to retrieve items that are close to a given query in the embedding space while satisfying a filter condition based on the item's attributes, a problem known as Filtered Approximate Nearest Neighbor Search (FANNS). In this work, we present a comprehensive survey and taxonomy of FANNS methods and analyze how they are benchmarked in the literature. By doing so, we identify a key challenge in the current FANNS landscape: the lack of diverse and realistic datasets, particularly ones derived from the latest transformer-based text embedding models. To address this, we introduce a novel dataset consisting of embedding vectors for the abstracts of over 2.7 million research articles from the arXiv repository, accompanied by 11 real-world attributes such as authors and categories. We benchmark a wide range of FANNS methods on our novel dataset and find that each method has distinct strengths and limitations; no single approach performs best across all scenarios. ACORN, for example, supports various filter types and performs reliably across dataset scales but is often outperformed by more specialized methods. SeRF shows excellent performance for range filtering on ordered attributes but cannot handle categorical attributes. Filtered-DiskANN and UNG excel on the medium-scale dataset but fail on the large-scale dataset, highlighting the challenge posed by transformer-based embeddings, which are often more than an order of magnitude larger than earlier embeddings. We conclude that no universally best method exists.

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.

Scholars studying organizations often work with multiple datasets lacking shared unique identifiers or covariates. In such situations, researchers may turn to approximate string matching methods to combine datasets. String matching, although useful, faces fundamental challenges. Even when two strings appear similar to humans, fuzzy matching often does not work because it fails to adapt to the informativeness of the character combinations presented. Worse, many entities have multiple names that are dissimilar (e.g., "Fannie Mae" and "Federal National Mortgage Association"), a case where string matching has little hope of succeeding. This paper introduces data from a prominent employment-related networking site (LinkedIn) as a tool to address these problems. We propose interconnected approaches to leveraging the massive amount of information from LinkedIn regarding organizational name-to-name links. The first approach builds a machine learning model for predicting matches from character strings, treating the trillions of user-contributed organizational name pairs as a training corpus: this approach constructs a string matching metric that explicitly maximizes match probabilities. A second approach identifies relationships between organization names using network representations of the LinkedIn data. A third approach combines the first and second. We document substantial improvements over fuzzy matching in applications, making all methods accessible in open-source software ("LinkOrgs").

This paper presents a new approach to image similarity search in the context of fashion, a domain with inherent ambiguity due to the multiple ways in which images can be considered similar. We introduce the concept of Referred Visual Search (RVS), where users provide additional information to define the desired similarity. We present a new dataset, LAION-RVS-Fashion, consisting of 272K fashion products with 842K images extracted from LAION, designed explicitly for this task. We then propose an innovative method for learning conditional embeddings using weakly-supervised training, achieving a 6% increase in Recall at one (R@1) against a gallery with 2M distractors, compared to classical approaches based on explicit attention and filtering. The proposed method demonstrates robustness, maintaining similar R@1 when dealing with 2.5 times as many distractors as the baseline methods. We believe this is a step forward in the emerging field of Referred Visual Search both in terms of accessible data and approach. Code, data and models are available at https://www.github.com/Simon-Lepage/CondViT-LRVSF .

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

Aligned text-image encoders such as CLIP have become the de facto model for vision-language tasks. Furthermore, modality-specific encoders achieve impressive performances in their respective domains. This raises a central question: does an alignment exist between uni-modal vision and language encoders since they fundamentally represent the same physical world? Analyzing the latent spaces structure of vision and language models on image-caption benchmarks using the Centered Kernel Alignment (CKA), we find that the representation spaces of unaligned and aligned encoders are semantically similar. In the absence of statistical similarity in aligned encoders like CLIP, we show that a possible matching of unaligned encoders exists without any training. We frame this as a seeded graph-matching problem exploiting the semantic similarity between graphs and propose two methods - a Fast Quadratic Assignment Problem optimization, and a novel localized CKA metric-based matching/retrieval. We demonstrate the effectiveness of this on several downstream tasks including cross-lingual, cross-domain caption matching and image classification. Code available at github.com/mayug/0-shot-llm-vision.

Data selection is crucial for optimizing language model (LM) performance on specific tasks, yet most existing methods fail to effectively consider the target task distribution. Current approaches either ignore task-specific requirements entirely or rely on approximations that fail to capture the nuanced patterns needed for tasks like Autoformalization or code generation. Methods that do consider the target distribution often rely on simplistic, sometimes noisy, representations, like hashed n-gram features, which can lead to collisions and introduce noise. We introduce ZIP-FIT, a data selection framework that uses gzip compression to directly measure alignment between potential training data and the target task distribution. In extensive evaluations on Autoformalization and Python code generation, ZIP-FIT significantly outperforms leading baselines like DSIR and D4. Models trained on ZIP-FIT-selected data achieve their lowest cross-entropy loss up to 85.1\% faster than baselines, demonstrating that better task alignment leads to more efficient learning. In addition, ZIP-FIT performs selection up to 65.8\% faster than DSIR and two orders of magnitude faster than D4. Notably, ZIP-FIT shows that smaller, well-aligned datasets often outperform larger but less targeted ones, demonstrating that a small amount of higher quality data is superior to a large amount of lower quality data. Our results imply that task-aware data selection is crucial for efficient domain adaptation, and that compression offers a principled way to measure task alignment. By showing that targeted data selection can dramatically improve task-specific performance, our work provides new insights into the relationship between data quality, task alignment, and model learning efficiency.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency, the basic structure of these models is Bi-encoder in most cases. However, this simple structure may cause serious information loss during the encoding of documents since the queries are agnostic. To address this problem, we design a method to mimic the queries on each of the documents by an iterative clustering process and represent the documents by multiple pseudo queries (i.e., the cluster centroids). To boost the retrieval process using approximate nearest neighbor search library, we also optimize the matching function with a two-step score calculation procedure. Experimental results on several popular ranking and QA datasets show that our model can achieve state-of-the-art results.

This study explores the concept of equivariance in vision-language foundation models (VLMs), focusing specifically on the multimodal similarity function that is not only the major training objective but also the core delivery to support downstream tasks. Unlike the existing image-text similarity objective which only categorizes matched pairs as similar and unmatched pairs as dissimilar, equivariance also requires similarity to vary faithfully according to the semantic changes. This allows VLMs to generalize better to nuanced and unseen multimodal compositions. However, modeling equivariance is challenging as the ground truth of semantic change is difficult to collect. For example, given an image-text pair about a dog, it is unclear to what extent the similarity changes when the pixel is changed from dog to cat? To this end, we propose EqSim, a regularization loss that can be efficiently calculated from any two matched training pairs and easily pluggable into existing image-text retrieval fine-tuning. Meanwhile, to further diagnose the equivariance of VLMs, we present a new challenging benchmark EqBen. Compared to the existing evaluation sets, EqBen is the first to focus on "visual-minimal change". Extensive experiments show the lack of equivariance in current VLMs and validate the effectiveness of EqSim. Code is available at https://github.com/Wangt-CN/EqBen.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients whilst a central entity/server orchestrates the computations (again, without having access to the samples). To achieve this feat, we take advantage of the geometric properties of the Wasserstein distance -- in particular, the triangle inequality -- and that of the associated {\em geodesics}: our algorithm, FedWad (for Federated Wasserstein Distance), iteratively approximates the Wasserstein distance by manipulating and exchanging distributions from the space of geodesics in lieu of the input samples. In addition to establishing the convergence properties of FedWad, we provide empirical results on federated coresets and federate optimal transport dataset distance, that we respectively exploit for building a novel federated model and for boosting performance of popular federated learning algorithms.

Multimodal retrieval is becoming a crucial component of modern AI applications, yet its evaluation lags behind the demands of more realistic and challenging scenarios. Existing benchmarks primarily probe surface-level semantic correspondence (e.g., object-text matching) while failing to assess the deeper reasoning required to capture complex relationships between visual and textual information. To address this gap, we introduce MR^2-Bench, a reasoning-intensive benchmark for multimodal retrieval. MR^2-Bench presents the following critical values: 1) all tasks are reasoning-driven, going beyond shallow matching to effectively assess models' capacity for logical, spatial, and causal inference; 2) it features diverse multimodal data, such as natural images, diagrams, and visual puzzles, enabling comprehensive evaluation across content types; 3) it supports complex queries and documents containing multiple images and covers diverse retrieval scenarios, more accurately reflecting real-world applications. Our benchmark contains 1,309 curated queries, derived either from manual collection and annotation or from selective consolidation of public datasets. Despite achieving strong results on existing benchmarks, current state-of-the-art models still struggle on MR^2-Bench: for example, the leading Seed1.6-Embedding model attains a Recall@1 of 77.78 on MMEB, but only 9.91 on MR^2-Bench. This substantial performance gap highlights both the increased challenge posed by our benchmark and the pressing need for further advances in reasoning-intensive multimodal retrieval. The dataset and evaluation code will be made publicly available at https://github.com/VectorSpaceLab/MR2-Bench.

English. This document aims to study the best algorithms to verify the belonging of a specific document to a related domain by comparing different methods for calculating the distance between two vectors. This study has been made possible with the help of the structures made available by the Apache Spark framework. Starting from the study illustrated in the publication "New frontier of textual classification: Big data and distributed calculus" by Massimiliano Morrelli et al., We wanted to carry out a study on the possible implementation of a solution capable of calculating the Similarity of a sentence using the distributed environment. Italiano. Il presente documento persegue l'obiettivo di studiare gli algoritmi migliori per verificare l'appartenenza di un determinato documento a un relativo dominio tramite un confronto di diversi metodi per il calcolo della distanza fra due vettori. Tale studio \`e stato condotto con l'ausilio delle strutture messe a disposizione dal framework Apache Spark. Partendo dallo studio illustrato nella pubblicazione "Nuova frontiera della classificazione testuale: Big data e calcolo distribuito" di Massimiliano Morrelli et al., si \`e voluto realizzare uno studio sulla possibile implementazione di una soluzione in grado di calcolare la Similarit\`a di una frase sfruttando l'ambiente distribuito.

We introduce a lightweight and accurate architecture for resource-efficient visual correspondence. Our method, dubbed XFeat (Accelerated Features), revisits fundamental design choices in convolutional neural networks for detecting, extracting, and matching local features. Our new model satisfies a critical need for fast and robust algorithms suitable to resource-limited devices. In particular, accurate image matching requires sufficiently large image resolutions - for this reason, we keep the resolution as large as possible while limiting the number of channels in the network. Besides, our model is designed to offer the choice of matching at the sparse or semi-dense levels, each of which may be more suitable for different downstream applications, such as visual navigation and augmented reality. Our model is the first to offer semi-dense matching efficiently, leveraging a novel match refinement module that relies on coarse local descriptors. XFeat is versatile and hardware-independent, surpassing current deep learning-based local features in speed (up to 5x faster) with comparable or better accuracy, proven in pose estimation and visual localization. We showcase it running in real-time on an inexpensive laptop CPU without specialized hardware optimizations. Code and weights are available at www.verlab.dcc.ufmg.br/descriptors/xfeat_cvpr24.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

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.

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

Retrieval-augmented Generation (RAG) has primarily been studied in limited settings, such as factoid question answering; more challenging, reasoning-intensive benchmarks have seen limited success from minimal RAG. In this work, we challenge this prevailing view on established, reasoning-intensive benchmarks: MMLU, MMLU Pro, AGI Eval, GPQA, and MATH. We identify a key missing component in prior work: a usable, web-scale datastore aligned with the breadth of pretraining data. To this end, we introduce CompactDS: a diverse, high-quality, web-scale datastore that achieves high retrieval accuracy and subsecond latency on a single-node. The key insights are (1) most web content can be filtered out without sacrificing coverage, and a compact, high-quality subset is sufficient; and (2) combining in-memory approximate nearest neighbor (ANN) retrieval and on-disk exact search balances speed and recall. Using CompactDS, we show that a minimal RAG pipeline achieves consistent accuracy improvements across all benchmarks and model sizes (8B--70B), with relative gains of 10% on MMLU, 33% on MMLU Pro, 14% on GPQA, and 19% on MATH. No single data source suffices alone, highlighting the importance of diversity of sources (web crawls, curated math, academic papers, textbooks). Finally, we show that our carefully designed in-house datastore matches or outperforms web search engines such as Google Search, as well as recently proposed, complex agent-based RAG systems--all while maintaining simplicity, reproducibility, and self-containment. We release CompactDS and our retrieval pipeline, supporting future research exploring retrieval-based AI systems.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Selecting a suitable training dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this data selection problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution, given some unlabeled target samples. Due to the large scale and dimensionality of the raw text data, existing methods use simple heuristics to select data that are similar to a high-quality reference corpus (e.g., Wikipedia), or leverage experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. Crucially, we work in a reduced feature space to make importance weight estimation tractable over the space of text. To determine an appropriate feature space, we first show that KL reduction, a data metric that measures the proximity between selected data and the target in a feature space, has high correlation with average accuracy on 8 downstream tasks (r=0.89) when computed with simple n-gram features. From this observation, we present Data Selection with Importance Resampling (DSIR), an efficient and scalable algorithm that estimates importance weights in a reduced feature space (e.g., n-gram features in our instantiation) and selects data with importance resampling according to these weights. When training general-domain models (target is Wikipedia + books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark. When performing continued pretraining towards a specific domain, DSIR performs comparably to expert curated data across 8 target distributions.

Few-shot fine-grained classification and person search appear as distinct tasks and literature has treated them separately. But a closer look unveils important similarities: both tasks target categories that can only be discriminated by specific object details; and the relevant models should generalize to new categories, not seen during training. We propose a novel unified Query-Guided Network (QGN) applicable to both tasks. QGN consists of a Query-guided Siamese-Squeeze-and-Excitation subnetwork which re-weights both the query and gallery features across all network layers, a Query-guided Region Proposal subnetwork for query-specific localisation, and a Query-guided Similarity subnetwork for metric learning. QGN improves on a few recent few-shot fine-grained datasets, outperforming other techniques on CUB by a large margin. QGN also performs competitively on the person search CUHK-SYSU and PRW datasets, where we perform in-depth analysis.

Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely used Ford-Fulkerson algorithm for computing maximum flows by seeding Ford-Fulkerson with predicted flows. Our proposed method offers strong theoretical performance in terms of the quality of the prediction. We then consider image segmentation, a common use-case of flows in computer vision, and complement our theoretical analysis with strong empirical results.

Product quantization (PQ) is a widely used technique for ad-hoc retrieval. Recent studies propose supervised PQ, where the embedding and quantization models can be jointly trained with supervised learning. However, there is a lack of appropriate formulation of the joint training objective; thus, the improvements over previous non-supervised baselines are limited in reality. In this work, we propose the Matching-oriented Product Quantization (MoPQ), where a novel objective Multinoulli Contrastive Loss (MCL) is formulated. With the minimization of MCL, we are able to maximize the matching probability of query and ground-truth key, which contributes to the optimal retrieval accuracy. Given that the exact computation of MCL is intractable due to the demand of vast contrastive samples, we further propose the Differentiable Cross-device Sampling (DCS), which significantly augments the contrastive samples for precise approximation of MCL. We conduct extensive experimental studies on four real-world datasets, whose results verify the effectiveness of MoPQ. The code is available at https://github.com/microsoft/MoPQ.

Fuzzy similarity join is an important database operator widely used in practice. So far the research community has focused exclusively on optimizing fuzzy join scalability. However, practitioners today also struggle to optimize fuzzy-join quality, because they face a daunting space of parameters (e.g., distance-functions, distance-thresholds, tokenization-options, etc.), and often have to resort to a manual trial-and-error approach to program these parameters in order to optimize fuzzy-join quality. This key challenge of automatically generating high-quality fuzzy-join programs has received surprisingly little attention thus far. In this work, we study the problem of "auto-program" fuzzy-joins. Leveraging a geometric interpretation of distance-functions, we develop an unsupervised Auto-FuzzyJoin framework that can infer suitable fuzzy-join programs on given input tables, without requiring explicit human input such as labeled training data. Using Auto-FuzzyJoin, users only need to provide two input tables L and R, and a desired precision target tau (say 0.9). Auto-FuzzyJoin leverages the fact that one of the input is a reference table to automatically program fuzzy-joins that meet the precision target tau in expectation, while maximizing fuzzy-join recall (defined as the number of correctly joined records). Experiments on both existing benchmarks and a new benchmark with 50 fuzzy-join tasks created from Wikipedia data suggest that the proposed Auto-FuzzyJoin significantly outperforms existing unsupervised approaches, and is surprisingly competitive even against supervised approaches (e.g., Magellan and DeepMatcher) when 50\% of ground-truth labels are used as training data.

Recently, Qiao, Duan, and Cheng~(2019) proposed a distributed nearest-neighbor classification method, in which a massive dataset is split into smaller groups, each processed with a k-nearest-neighbor classifier, and the final class label is predicted by a majority vote among these groupwise class labels. This paper shows that the distributed algorithm with k=1 over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions, for both regression and classification problems. Roughly speaking, distributed 1-nearest-neighbor rules with M groups has a performance comparable to standard Theta(M)-nearest-neighbor rules. In the analysis, alternative rules with a refined aggregation method are proposed and shown to attain exact minimax optimal rates.

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.

The k-Nearest Neighbor (kNN) classification approach is conceptually simple - yet widely applied since it often performs well in practical applications. However, using a global constant k does not always provide an optimal solution, e.g., for datasets with an irregular density distribution of data points. This paper proposes an adaptive kNN classifier where k is chosen dynamically for each instance (point) to be classified, such that the expected accuracy of classification is maximized. We define the expected accuracy as the accuracy of a set of structurally similar observations. An arbitrary similarity function can be used to find these observations. We introduce and evaluate different similarity functions. For the evaluation, we use five different classification tasks based on geo-spatial data. Each classification task consists of (tens of) thousands of items. We demonstrate, that the presented expected accuracy measures can be a good estimator for kNN performance, and the proposed adaptive kNN classifier outperforms common kNN and previously introduced adaptive kNN algorithms. Also, we show that the range of considered k can be significantly reduced to speed up the algorithm without negative influence on classification accuracy.