Daily Papers

Monocular-to-stereo conversion synthesizes stereoscopic content from 2D videos for immersive 3D experiences. In modern Depth-Image-Based Rendering (DIBR) approaches, stereo inpainting of disocclusions is the critical bottleneck. Training-based methods achieve superior quality but rely on scarce stereo pairs or synthetic data with domain gaps. We address this through the first self-supervised framework learning from monocular videos via cycle consistency. Our key contribution is the Geometric Reciprocity Theorem (GRT): under the nearest-neighbor DIBR formulation, the disocclusion mask when synthesizing a target view equals the mask of pixels lost when warping back from target to source, enabling analytical computation of test-time disocclusion masks directly from monocular images. This yields train-test consistency for the stated warping formulation, supporting self-supervised learning from unlimited monocular videos and substantial improvements over training-free and supervised state-of-the-art methods. Project page: https://visual-ai.github.io/grt/

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k=1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p_i is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P_{1:i-1} = {p_1, \dots, p_{i-1}} or within p_i's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1\times--10\times speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries -- enabling k-NN searches within any subset P_{1:m} (m \leq n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

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 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.

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

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.

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 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.

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes D-dimensional vectors into D-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size (k). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the long-standing inference bottleneck of kNN, establishing a new structural paradigm for graph-based nonparametric learning.

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory consumption. Recently, a method called RaBitQ achieves the state-of-the-art performance among these methods. It produces better empirical performance in both accuracy and efficiency when using the same compression rate and provides rigorous theoretical guarantees. However, the method is only designed for compressing vectors at high compression rates (32x) and lacks support for achieving higher accuracy by using more space. In this paper, we introduce a new quantization method to address this limitation by extending RaBitQ. The new method inherits the theoretical guarantees of RaBitQ and achieves the asymptotic optimality in terms of the trade-off between space and error bounds as to be proven in this study. Additionally, we present efficient implementations of the method, enabling its application to ANN queries to reduce both space and time consumption. Extensive experiments on real-world datasets confirm that our method consistently outperforms the state-of-the-art baselines in both accuracy and efficiency when using the same amount of memory.

Approximate Nearest Neighbor Search (ANNS), as the core of vector databases (VectorDBs), has become widely used in modern AI and ML systems, powering applications from information retrieval to bio-informatics. While graph-based ANNS methods achieve high query efficiency, their scalability is constrained by the available host memory. Recent disk-based ANNS approaches mitigate memory usage by offloading data to Solid-State Drives (SSDs). However, they still suffer from issues such as long I/O traversal path, misalignment with storage I/O granularity, and high in-memory indexing overhead, leading to significant I/O latency and ultimately limiting scalability for large-scale vector search. In this paper, we propose PageANN, a disk-based approximate nearest neighbor search (ANNS) framework designed for high performance and scalability. PageANN introduces a page-node graph structure that aligns logical graph nodes with physical SSD pages, thereby shortening I/O traversal paths and reducing I/O operations. Specifically, similar vectors are clustered into page nodes, and a co-designed disk data layout leverages this structure with a merging technique to store only representative vectors and topology information, avoiding unnecessary reads. To further improve efficiency, we design a memory management strategy that combines lightweight indexing with coordinated memory-disk data allocation, maximizing host memory utilization while minimizing query latency and storage overhead. Experimental results show that PageANN significantly outperforms state-of-the-art (SOTA) disk-based ANNS methods, achieving 1.85x-10.83x higher throughput and 51.7%-91.9% lower latency across different datasets and memory budgets, while maintaining comparable high recall accuracy.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

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.

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 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.

Approximate Nearest Neighbors (ANN) search is a crucial task in several applications like recommender systems and information retrieval. Current state-of-the-art ANN libraries, although being performance-oriented, often lack modularity and ease of use. This translates into them not being fully suitable for easy prototyping and testing of research ideas, an important feature to enable. We address these limitations by introducing kANNolo, a novel research-oriented ANN library written in Rust and explicitly designed to combine usability with performance effectively. kANNolo is the first ANN library that supports dense and sparse vector representations made available on top of different similarity measures, e.g., euclidean distance and inner product. Moreover, it also supports vector quantization techniques, e.g., Product Quantization, on top of the indexing strategies implemented. These functionalities are managed through Rust traits, allowing shared behaviors to be handled abstractly. This abstraction ensures flexibility and facilitates an easy integration of new components. In this work, we detail the architecture of kANNolo and demonstrate that its flexibility does not compromise performance. The experimental analysis shows that kANNolo achieves state-of-the-art performance in terms of speed-accuracy trade-off while allowing fast and easy prototyping, thus making kANNolo a valuable tool for advancing ANN research. Source code available on GitHub: https://github.com/TusKANNy/kannolo.

Consider a random uniform sample of n points in a compact region A of Euclidean d-space, d geq 2, with a smooth or (when d=2) polygonal boundary. Fix k bf N. Let T_{n,k} be the threshold r at which the geometric graph on these n vertices with distance parameter r becomes k-connected. We show that if d=2 then n (pi/|A|) T_{n,1}^2 - log n is asymptotically standard Gumbel. For (d,k) neq (2,1), it is n (theta_d/|A|) T_{n,k}^d - (2-2/d) log n - (4-2k-2/d) log log n that converges in distribution to a nondegenerate limit, where theta_d is the volume of the unit ball. The limit is Gumbel with scale parameter 2 except when (d,k)=(2,2) where the limit is two component extreme value distributed. The different cases reflect the fact that boundary effects are more more important in some cases than others. We also give similar results for the largest k-nearest neighbour link U_{n,k} in the sample, and show T_{n,k}=U_{n,k} with high probability. We provide estimates on rates of convergence and give similar results for Poisson samples in A. Finally, we give similar results even for non-uniform samples, with a less explicit sequence of centring constants.

Nearest neighbour based methods have proved to be one of the most successful self-supervised learning (SSL) approaches due to their high generalization capabilities. However, their computational efficiency decreases when more than one neighbour is used. In this paper, we propose a novel contrastive SSL approach, which we call All4One, that reduces the distance between neighbour representations using ''centroids'' created through a self-attention mechanism. We use a Centroid Contrasting objective along with single Neighbour Contrasting and Feature Contrasting objectives. Centroids help in learning contextual information from multiple neighbours whereas the neighbour contrast enables learning representations directly from the neighbours and the feature contrast allows learning representations unique to the features. This combination enables All4One to outperform popular instance discrimination approaches by more than 1% on linear classification evaluation for popular benchmark datasets and obtains state-of-the-art (SoTA) results. Finally, we show that All4One is robust towards embedding dimensionalities and augmentations, surpassing NNCLR and Barlow Twins by more than 5% on low dimensionality and weak augmentation settings. The source code would be made available soon.

Approximate nearest neighbor (ANN) graph indices such as HNSW and Vamana construct their edge topology in full-precision or high-fidelity quantized metric spaces, relegating binary quantization (BQ) to a post-hoc distance estimator during search. This paper asks a different question: Can binary quantization define the graph topology itself -- and if so, under what conditions? We study this question through QuIVer (Quantized Index for Vector Retrieval), a training-free ANN graph index that performs Vamana edge selection, diversity pruning, and beam-search navigation entirely within a 2-bit Sign-Magnitude BQ metric space, accessing float32 vectors only for final reranking. Systematic evaluation on twelve million-scale datasets reveals a sharp applicability boundary: BQ-native topology is highly effective on cosine-native contrastive-learning embeddings (>=88% Recall@10 at ef=64 across five datasets, 384--3072 dimensions), moderately effective on multimodal CLIP data (71--78%), and empirically unsuitable for Euclidean-native or structureless distributions (<15%). Our results suggest an empirical "impossible triangle" between aggressive compression, high throughput, and universal data compatibility. The central contribution is not merely the system, but the boundary it reveals: falsifiable criteria for when industrial vector search systems can safely trade metric fidelity for compact BQ-native navigation. On compatible workloads, the system benefits are substantial: QuIVer's BQ-native hot path (<1.3 GB for 1M vectors) yields 2.5--5.5x higher multi-threaded throughput than DiskANN Rust and HNSW variants at matched recall, with 4.7x less hot memory and no codebook or rotation training (unlike PQ/OPQ/RaBitQ).

Approximate nearest neighbor search (ANNS) is a fundamental building block in information retrieval with graph-based indices being the current state-of-the-art and widely used in the industry. Recent advances in graph-based indices have made it possible to index and search billion-point datasets with high recall and millisecond-level latency on a single commodity machine with an SSD. However, existing graph algorithms for ANNS support only static indices that cannot reflect real-time changes to the corpus required by many key real-world scenarios (e.g. index of sentences in documents, email, or a news index). To overcome this drawback, the current industry practice for manifesting updates into such indices is to periodically re-build these indices, which can be prohibitively expensive. In this paper, we present the first graph-based ANNS index that reflects corpus updates into the index in real-time without compromising on search performance. Using update rules for this index, we design FreshDiskANN, a system that can index over a billion points on a workstation with an SSD and limited memory, and support thousands of concurrent real-time inserts, deletes and searches per second each, while retaining >95% 5-recall@5. This represents a 5-10x reduction in the cost of maintaining freshness in indices when compared to existing methods.

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.

K-Nearest Neighbors (KNN) is one of the most used ML classifiers. However, if we observe closely, standard distance-weighted KNN and relative variants assume all 'k' neighbors are equally reliable. In heterogeneous feature space, this becomes a limitation that hinders reliability in predicting true levels of the observation. We propose DW-KNN (Double Weighted KNN), a transparent and robust variant that integrates exponential distance with neighbor validity. This enables instance-level interpretability, suppresses noisy or mislabeled samples, and reduces hyperparameter sensitivity. Comprehensive evaluation on 9 data-sets helps to demonstrate that DW-KNN achieves 0.8988 accuracy on average. It ranks 2nd among six methods and within 0.2% of the best-performing Ensemble KNN. It also exhibits the lowest cross-validation variance (0.0156), indicating reliable prediction stability. Statistical significance test confirmed (p < 0.001) improvement over compactness weighted KNN (+4.09\%) and Kernel weighted KNN (+1.13\%). The method provides a simple yet effective alternative to complex adaptive schemes, particularly valuable for high-stakes applications requiring explainable predictions.

Grid-based approaches to approximate nearest neighbor (ANN) search have been absent from modern scaling analyses. We present a systematic characterization of a multiprobe grid algorithm with respect to dataset size N and dimensionality d. Our experiments reveal a previously unreported d-scaling crossover on the GloVe embedding family, in which multiprobe grid search maintains an approximately constant dimensional scaling exponent while other graph-, tree-, and partitioning-based methods exhibit degrading throughput. The advantage comes with near-linear query scaling in N, but also with lower indexing cost than competing ANN methods. Our results suggest that grid-based methods such as multiprobe grid may be competitive in rebuild-heavy or high-dimensional settings where indexing cost and dimensional robustness dictate performance. More broadly, recent work has formalized self-attention as an ANN operation. Thus, the N- and d-scaling properties of ANN algorithms may guide cost analysis of efficient transformer architectures. Code is available at: https://github.com/weiz345/MultiProbeANN.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Approximate nearest-neighbor search (ANNS) algorithms have become increasingly critical for recent AI applications, particularly in retrieval-augmented generation (RAG) and agent-based LLM applications. In this paper, we present CRINN, a new paradigm for ANNS algorithms. CRINN treats ANNS optimization as a reinforcement learning problem where execution speed serves as the reward signal. This approach enables the automatic generation of progressively faster ANNS implementations while maintaining accuracy constraints. Our experimental evaluation demonstrates CRINN's effectiveness across six widely-used NNS benchmark datasets. When compared against state-of-the-art open-source ANNS algorithms, CRINN achieves best performance on three of them (GIST-960-Euclidean, MNIST-784-Euclidean, and GloVe-25-angular), and tied for first place on two of them (SIFT-128-Euclidean and GloVe-25-angular). The implications of CRINN's success reach well beyond ANNS optimization: It validates that LLMs augmented with reinforcement learning can function as an effective tool for automating sophisticated algorithmic optimizations that demand specialized knowledge and labor-intensive manual refinement.Code can be found at https://github.com/deepreinforce-ai/CRINN

A vector database is used to store high-dimensional data that cannot be characterized by traditional DBMS. Although there are not many articles describing existing or introducing new vector database architectures, the approximate nearest neighbor search problem behind vector databases has been studied for a long time, and considerable related algorithmic articles can be found in the literature. This article attempts to comprehensively review relevant algorithms to provide a general understanding of this booming research area. The basis of our framework categorises these studies by the approach of solving ANNS problem, respectively hash-based, tree-based, graph-based and quantization-based approaches. Then we present an overview of existing challenges for vector databases. Lastly, we sketch how vector databases can be combined with large language models and provide new possibilities.

We present a geometric framework for filtered approximate nearest neighbor (ANN) search. Filtering a proximity graph by a metadata predicate produces a subgraph, a fiber, whose connectivity and geometry can differ sharply from the full graph. Using local signals, we propose a two-phase search algorithm that combines full-graph exploration with filtered-neighbor descent when the local geometry is favorable. These signals also classify search failures into three regimes: topological cuts, geometric folds, and genuine basins. A key observation is that all three share a common resolution: restarting the search in a fiber-present cluster near the query. To support this, we introduce a lightweight anchor structure that identifies such regions and restarts the search accordingly. We show empirically that the method outperforms FAISS HNSW on filtered search and the three failure regimes separate cleanly and shift predictably with filter selectivity.

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

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.

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.

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.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning method from the pre-deep learning era, as an augmentation to modern neural network based approaches. As a lazy learning method, k-NN simply aggregates the distance between the test image and top-k neighbors in a training set. We adopt k-NN with pre-trained visual representations produced by either supervised or self-supervised methods in two steps: (1) Leverage k-NN predicted probabilities as indications for easy vs. hard examples during training. (2) Linearly interpolate the k-NN predicted distribution with that of the augmented classifier. Via extensive experiments on a wide range of classification tasks, our study reveals the generality and flexibility of k-NN integration with additional insights: (1) k-NN achieves competitive results, sometimes even outperforming a standard linear classifier. (2) Incorporating k-NN is especially beneficial for tasks where parametric classifiers perform poorly and / or in low-data regimes. We hope these discoveries will encourage people to rethink the role of pre-deep learning, classical methods in computer vision. Our code is available at: https://github.com/KMnP/nn-revisit.

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.

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.

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.

Leveraging nearest neighbor retrieval for self-supervised representation learning has proven beneficial with object-centric images. However, this approach faces limitations when applied to scene-centric datasets, where multiple objects within an image are only implicitly captured in the global representation. Such global bootstrapping can lead to undesirable entanglement of object representations. Furthermore, even object-centric datasets stand to benefit from a finer-grained bootstrapping approach. In response to these challenges, we introduce a novel Cross-Image Object-Level Bootstrapping method tailored to enhance dense visual representation learning. By employing object-level nearest neighbor bootstrapping throughout the training, CrIBo emerges as a notably strong and adequate candidate for in-context learning, leveraging nearest neighbor retrieval at test time. CrIBo shows state-of-the-art performance on the latter task while being highly competitive in more standard downstream segmentation tasks. Our code and pretrained models are publicly available at https://github.com/tileb1/CrIBo.

Self-supervised learning algorithms based on instance discrimination train encoders to be invariant to pre-defined transformations of the same instance. While most methods treat different views of the same image as positives for a contrastive loss, we are interested in using positives from other instances in the dataset. Our method, Nearest-Neighbor Contrastive Learning of visual Representations (NNCLR), samples the nearest neighbors from the dataset in the latent space, and treats them as positives. This provides more semantic variations than pre-defined transformations. We find that using the nearest-neighbor as positive in contrastive losses improves performance significantly on ImageNet classification, from 71.7% to 75.6%, outperforming previous state-of-the-art methods. On semi-supervised learning benchmarks we improve performance significantly when only 1% ImageNet labels are available, from 53.8% to 56.5%. On transfer learning benchmarks our method outperforms state-of-the-art methods (including supervised learning with ImageNet) on 8 out of 12 downstream datasets. Furthermore, we demonstrate empirically that our method is less reliant on complex data augmentations. We see a relative reduction of only 2.1% ImageNet Top-1 accuracy when we train using only random crops.

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.

Learning scientific document representations can be substantially improved through contrastive learning objectives, where the challenge lies in creating positive and negative training samples that encode the desired similarity semantics. Prior work relies on discrete citation relations to generate contrast samples. However, discrete citations enforce a hard cut-off to similarity. This is counter-intuitive to similarity-based learning, and ignores that scientific papers can be very similar despite lacking a direct citation - a core problem of finding related research. Instead, we use controlled nearest neighbor sampling over citation graph embeddings for contrastive learning. This control allows us to learn continuous similarity, to sample hard-to-learn negatives and positives, and also to avoid collisions between negative and positive samples by controlling the sampling margin between them. The resulting method SciNCL outperforms the state-of-the-art on the SciDocs benchmark. Furthermore, we demonstrate that it can train (or tune) models sample-efficiently, and that it can be combined with recent training-efficient methods. Perhaps surprisingly, even training a general-domain language model this way outperforms baselines pretrained in-domain.

Despite significant advances, the performance of state-of-the-art continual learning approaches hinges on the unrealistic scenario of fully labeled data. In this paper, we tackle this challenge and propose an approach for continual semi-supervised learning--a setting where not all the data samples are labeled. A primary issue in this scenario is the model forgetting representations of unlabeled data and overfitting the labeled samples. We leverage the power of nearest-neighbor classifiers to nonlinearly partition the feature space and flexibly model the underlying data distribution thanks to its non-parametric nature. This enables the model to learn a strong representation for the current task, and distill relevant information from previous tasks. We perform a thorough experimental evaluation and show that our method outperforms all the existing approaches by large margins, setting a solid state of the art on the continual semi-supervised learning paradigm. For example, on CIFAR-100 we surpass several others even when using at least 30 times less supervision (0.8% vs. 25% of annotations). Finally, our method works well on both low and high resolution images and scales seamlessly to more complex datasets such as ImageNet-100. The code is publicly available on https://github.com/kangzhiq/NNCSL

In neural Information Retrieval (IR), ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than 9\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Convolutional neural networks (CNNs) have been widely used in efficient image super-resolution. However, for CNN-based methods, performance gains often require deeper networks and larger feature maps, which increase complexity and inference costs. Inspired by LoRA's success in fine-tuning large language models, we explore its application to lightweight models and propose Distillation-Supervised Convolutional Low-Rank Adaptation (DSCLoRA), which improves model performance without increasing architectural complexity or inference costs. Specifically, we integrate ConvLoRA into the efficient SR network SPAN by replacing the SPAB module with the proposed SConvLB module and incorporating ConvLoRA layers into both the pixel shuffle block and its preceding convolutional layer. DSCLoRA leverages low-rank decomposition for parameter updates and employs a spatial feature affinity-based knowledge distillation strategy to transfer second-order statistical information from teacher models (pre-trained SPAN) to student models (ours). This method preserves the core knowledge of lightweight models and facilitates optimal solution discovery under certain conditions. Experiments on benchmark datasets show that DSCLoRA improves PSNR and SSIM over SPAN while maintaining its efficiency and competitive image quality. Notably, DSCLoRA ranked first in the Overall Performance Track of the NTIRE 2025 Efficient Super-Resolution Challenge. Our code and models are made publicly available at https://github.com/Yaozzz666/DSCF-SR.

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne

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.

Molecular relational learning, whose goal is to learn the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. Recently, graph neural networks have recently shown great success in molecular relational learning by modeling a molecule as a graph structure, and considering atom-level interactions between two molecules. Despite their success, existing molecular relational learning methods tend to overlook the nature of chemistry, i.e., a chemical compound is composed of multiple substructures such as functional groups that cause distinctive chemical reactions. In this work, we propose a novel relational learning framework, called CGIB, that predicts the interaction behavior between a pair of graphs by detecting core subgraphs therein. The main idea is, given a pair of graphs, to find a subgraph from a graph that contains the minimal sufficient information regarding the task at hand conditioned on the paired graph based on the principle of conditional graph information bottleneck. We argue that our proposed method mimics the nature of chemical reactions, i.e., the core substructure of a molecule varies depending on which other molecule it interacts with. Extensive experiments on various tasks with real-world datasets demonstrate the superiority of CGIB over state-of-the-art baselines. Our code is available at https://github.com/Namkyeong/CGIB.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

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.

Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while still relying on the same backbone architecture. In the meantime, sparse representation learning fueled by traditional inverted indexing techniques has seen a growing interest, inheriting from desirable IR priors such as explicit lexical matching. While some architectural variants have been proposed, a lesser effort has been put in the training of such models. In this work, we build on SPLADE -- a sparse expansion-based retriever -- and show to which extent it is able to benefit from the same training improvements as dense models, by studying the effect of distillation, hard-negative mining as well as the Pre-trained Language Model initialization. We furthermore study the link between effectiveness and efficiency, on in-domain and zero-shot settings, leading to state-of-the-art results in both scenarios for sufficiently expressive models.

Boundary point detection aims to outline the external contour structure of clusters and enhance the inter-cluster discrimination, thus bolstering the performance of the downstream classification and clustering tasks. However, existing boundary point detectors are sensitive to density heterogeneity or cannot identify boundary points in concave structures and high-dimensional manifolds. In this work, we propose a robust and efficient boundary point detection method based on Local Direction Dispersion (LoDD). The core of boundary point detection lies in measuring the difference between boundary points and internal points. It is a common observation that an internal point is surrounded by its neighbors in all directions, while the neighbors of a boundary point tend to be distributed only in a certain directional range. By considering this observation, we adopt density-independent K-Nearest Neighbors (KNN) method to determine neighboring points and design a centrality metric LoDD using the eigenvalues of the covariance matrix to depict the distribution uniformity of KNN. We also develop a grid-structure assumption of data distribution to determine the parameters adaptively. The effectiveness of LoDD is demonstrated on synthetic datasets, real-world benchmarks, and application of training set split for deep learning model and hole detection on point cloud data. The datasets and toolkit are available at: https://github.com/ZPGuiGroupWhu/lodd.

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

Multi-document summarization (MDS) is a difficult task in Natural Language Processing, aiming to summarize information from several documents. However, the source documents are often insufficient to obtain a qualitative summary. We propose a retriever-guided model combined with non-parametric memory for summary generation. This model retrieves relevant candidates from a database and then generates the summary considering the candidates with a copy mechanism and the source documents. The retriever is implemented with Approximate Nearest Neighbor Search (ANN) to search large databases. Our method is evaluated on the MultiXScience dataset which includes scientific articles. Finally, we discuss our results and possible directions for future work.

Link prediction, a fundamental task on graphs, has proven indispensable in various applications, e.g., friend recommendation, protein analysis, and drug interaction prediction. However, since datasets span a multitude of domains, they could have distinct underlying mechanisms of link formation. Evidence in existing literature underscores the absence of a universally best algorithm suitable for all datasets. In this paper, we endeavor to explore principles of link prediction across diverse datasets from a data-centric perspective. We recognize three fundamental factors critical to link prediction: local structural proximity, global structural proximity, and feature proximity. We then unearth relationships among those factors where (i) global structural proximity only shows effectiveness when local structural proximity is deficient. (ii) The incompatibility can be found between feature and structural proximity. Such incompatibility leads to GNNs for Link Prediction (GNN4LP) consistently underperforming on edges where the feature proximity factor dominates. Inspired by these new insights from a data perspective, we offer practical instruction for GNN4LP model design and guidelines for selecting appropriate benchmark datasets for more comprehensive evaluations.

k-nearest-neighbor machine translation has demonstrated remarkable improvements in machine translation quality by creating a datastore of cached examples. However, these improvements have been limited to high-resource language pairs, with large datastores, and remain a challenge for low-resource languages. In this paper, we address this issue by combining representations from multiple languages into a single datastore. Our results consistently demonstrate substantial improvements not only in low-resource translation quality (up to +3.6 BLEU), but also for high-resource translation quality (up to +0.5 BLEU). Our experiments show that it is possible to create multilingual datastores that are a quarter of the size, achieving a 5.3x speed improvement, by using linguistic similarities for datastore creation.

Modern semantic search and retrieval-augmented generation (RAG) systems rely predominantly on in-memory approximate nearest neighbor (ANN) indexes over high-precision floating-point vectors, resulting in escalating operational cost and inherent trade-offs between latency, throughput, and retrieval accuracy. This paper analyzes the architectural limitations of the dominant "HNSW + float32 + cosine similarity" stack and evaluates existing cost-reduction strategies, including storage disaggregation and lossy vector quantization, which inevitably sacrifice either performance or accuracy. We introduce and empirically evaluate an alternative information-theoretic architecture based on maximally informative binarization (MIB), efficient bitwise distance metrics, and an information-theoretic scoring (ITS) mechanism. Unlike conventional ANN systems, this approach enables exhaustive search over compact binary representations, allowing deterministic retrieval and eliminating accuracy degradation under high query concurrency. Using the MAIR benchmark across 14 datasets and 10,038 queries, we compare this architecture against Elasticsearch, Pinecone, PGVector, and Qdrant. Results demonstrate retrieval quality comparable to full-precision systems, while achieving substantially lower latency and maintaining constant throughput at high request rates. We show that this architectural shift enables a truly serverless, cost-per-query deployment model, challenging the necessity of large in-memory ANN indexes for high-quality semantic search.

The widespread enthusiasm for deep learning has recently expanded into the domain of tabular data. Recognizing that the advancement in deep tabular methods is often inspired by classical methods, e.g., integration of nearest neighbors into neural networks, we investigate whether these classical methods can be revitalized with modern techniques. We revisit a differentiable version of K-nearest neighbors (KNN) -- Neighbourhood Components Analysis (NCA) -- originally designed to learn a linear projection to capture semantic similarities between instances, and seek to gradually add modern deep learning techniques on top. Surprisingly, our implementation of NCA using SGD and without dimensionality reduction already achieves decent performance on tabular data, in contrast to the results of using existing toolboxes like scikit-learn. Further equipping NCA with deep representations and additional training stochasticity significantly enhances its capability, being on par with the leading tree-based method CatBoost and outperforming existing deep tabular models in both classification and regression tasks on 300 datasets. We conclude our paper by analyzing the factors behind these improvements, including loss functions, prediction strategies, and deep architectures. The code is available at https://github.com/qile2000/LAMDA-TALENT.

Substantial efforts have been devoted more recently to presenting various methods for object detection in optical remote sensing images. However, the current survey of datasets and deep learning based methods for object detection in optical remote sensing images is not adequate. Moreover, most of the existing datasets have some shortcomings, for example, the numbers of images and object categories are small scale, and the image diversity and variations are insufficient. These limitations greatly affect the development of deep learning based object detection methods. In the paper, we provide a comprehensive review of the recent deep learning based object detection progress in both the computer vision and earth observation communities. Then, we propose a large-scale, publicly available benchmark for object DetectIon in Optical Remote sensing images, which we name as DIOR. The dataset contains 23463 images and 192472 instances, covering 20 object classes. The proposed DIOR dataset 1) is large-scale on the object categories, on the object instance number, and on the total image number; 2) has a large range of object size variations, not only in terms of spatial resolutions, but also in the aspect of inter- and intra-class size variability across objects; 3) holds big variations as the images are obtained with different imaging conditions, weathers, seasons, and image quality; and 4) has high inter-class similarity and intra-class diversity. The proposed benchmark can help the researchers to develop and validate their data-driven methods. Finally, we evaluate several state-of-the-art approaches on our DIOR dataset to establish a baseline for future research.

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.

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.

Embedding-based search is widely used in applications such as recommendation and retrieval-augmented generation (RAG). Recently, there is a growing demand to support these capabilities over personal data stored locally on devices. However, maintaining the necessary data structure associated with the embedding-based search is often infeasible due to its high storage overhead. For example, indexing 100 GB of raw data requires 150 to 700 GB of storage, making local deployment impractical. Reducing this overhead while maintaining search quality and latency becomes a critical challenge. In this paper, we present LEANN, a storage-efficient approximate nearest neighbor (ANN) search index optimized for resource-constrained personal devices. LEANN combines a compact graph-based structure with an efficient on-the-fly recomputation strategy to enable fast and accurate retrieval with minimal storage overhead. Our evaluation shows that LEANN reduces index size to under 5% of the original raw data, achieving up to 50 times smaller storage than standard indexes, while maintaining 90% top-3 recall in under 2 seconds on real-world question answering benchmarks.

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.

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.

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.

The advent of deep perceptual networks brought about a paradigm shift in machine vision and image perception. Image apprehension lately carried out by hand-crafted features in the latent space have been replaced by deep features acquired from supervised networks for improved understanding. However, such deep networks require strict supervision with a substantial amount of the labeled data for authentic training process. These methods perform poorly in domains lacking labeled data especially in case of remote sensing image retrieval. Resolving this, we propose an unsupervised encoder-decoder feature for remote sensing image matching (RSIM). Moreover, we replace the conventional distance metrics with a deep discriminator network to identify the similarity of the image pairs. To the best of our knowledge, discriminator network has never been used before for solving RSIM problem. Results have been validated with two publicly available benchmark remote sensing image datasets. The technique has also been investigated for content-based remote sensing image retrieval (CBRSIR); one of the widely used applications of RSIM. Results demonstrate that our technique supersedes the state-of-the-art methods used for unsupervised image matching with mean average precision (mAP) of 81%, and image retrieval with an overall improvement in mAP score of about 12%.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

Building effective dense retrieval systems remains difficult when relevance supervision is not available. Recent work has looked to overcome this challenge by using a Large Language Model (LLM) to generate hypothetical documents that can be used to find the closest real document. However, this approach relies solely on the LLM to have domain-specific knowledge relevant to the query, which may not be practical. Furthermore, generating hypothetical documents can be inefficient as it requires the LLM to generate a large number of tokens for each query. To address these challenges, we introduce Real Document Embeddings from Relevance Feedback (ReDE-RF). Inspired by relevance feedback, ReDE-RF proposes to re-frame hypothetical document generation as a relevance estimation task, using an LLM to select which documents should be used for nearest neighbor search. Through this re-framing, the LLM no longer needs domain-specific knowledge but only needs to judge what is relevant. Additionally, relevance estimation only requires the LLM to output a single token, thereby improving search latency. Our experiments show that ReDE-RF consistently surpasses state-of-the-art zero-shot dense retrieval methods across a wide range of low-resource retrieval datasets while also making significant improvements in latency per-query.

Conducting text retrieval in a dense learned representation space has many intriguing advantages over sparse retrieval. Yet the effectiveness of dense retrieval (DR) often requires combination with sparse retrieval. In this paper, we identify that the main bottleneck is in the training mechanisms, where the negative instances used in training are not representative of the irrelevant documents in testing. This paper presents Approximate nearest neighbor Negative Contrastive Estimation (ANCE), a training mechanism that constructs negatives from an Approximate Nearest Neighbor (ANN) index of the corpus, which is parallelly updated with the learning process to select more realistic negative training instances. This fundamentally resolves the discrepancy between the data distribution used in the training and testing of DR. In our experiments, ANCE boosts the BERT-Siamese DR model to outperform all competitive dense and sparse retrieval baselines. It nearly matches the accuracy of sparse-retrieval-and-BERT-reranking using dot-product in the ANCE-learned representation space and provides almost 100x speed-up.

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

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.

Recent text-to-image models have achieved impressive results. However, since they require large-scale datasets of text-image pairs, it is impractical to train them on new domains where data is scarce or not labeled. In this work, we propose using large-scale retrieval methods, in particular, efficient k-Nearest-Neighbors (kNN), which offers novel capabilities: (1) training a substantially small and efficient text-to-image diffusion model without any text, (2) generating out-of-distribution images by simply swapping the retrieval database at inference time, and (3) performing text-driven local semantic manipulations while preserving object identity. To demonstrate the robustness of our method, we apply our kNN approach on two state-of-the-art diffusion backbones, and show results on several different datasets. As evaluated by human studies and automatic metrics, our method achieves state-of-the-art results compared to existing approaches that train text-to-image generation models using images only (without paired text data)

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

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

Linear probes are widely used in interpretability research and often compared by cosine similarity. The Mahalanobis cosine similarity (MCS) between two directions, which reweights the inner product by test data covariance, is a natural task-aware refinement. Ying et al. (2026) report that a probe's MCS to a reference probe trained on the out-of-distribution (OOD) data near-perfectly linearly predicts the probe's OOD AUROC (R^2 = 0.98). Here, we extend this empirical finding across models, layers, and concept domains, and prove this general phenomenon in closed form: For balanced classes whose projections are Gaussian, OOD AUROC and MCS to the reference probe are linear because both are sigmoid-shaped functions of the probe's signal-to-noise ratio (SNR) on the test data. The theory also predicts when this linearity fails, which we verify empirically. MCS offers a theoretically grounded and empirically effective alternative to Euclidean cosine similarity for comparing linear probes.

We introduce a highly performant 3D object detector for point clouds using the DETR framework. The prior attempts all end up with suboptimal results because they fail to learn accurate inductive biases from the limited scale of training data. In particular, the queries often attend to points that are far away from the target objects, violating the locality principle in object detection. To address the limitation, we introduce a novel 3D Vertex Relative Position Encoding (3DV-RPE) method which computes position encoding for each point based on its relative position to the 3D boxes predicted by the queries in each decoder layer, thus providing clear information to guide the model to focus on points near the objects, in accordance with the principle of locality. In addition, we systematically improve the pipeline from various aspects such as data normalization based on our understanding of the task. We show exceptional results on the challenging ScanNetV2 benchmark, achieving significant improvements over the previous 3DETR in AP_{25}/AP_{50} from 65.0\%/47.0\% to 77.8\%/66.0\%, respectively. In addition, our method sets a new record on ScanNetV2 and SUN RGB-D datasets.Code will be released at http://github.com/yichaoshen-MS/V-DETR.

We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines p-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a p-adic distance on k-mer prefixes, which captures hierarchical positional structure, and a compositional L_1 distance on k-mer frequencies, which captures local sequence content. The two distances jointly parameterise a bi-filtered Vietoris--Rips complex, and per-sequence topological summaries from this bi-filtration serve as features for standard machine learning classifiers. We establish theoretical guarantees for the construction: stability under metric perturbations and invariance to the choice of prime, alongside a result that explains why a single p-adic axis is topologically uninformative and why the bi-filtration recovers nontrivial homology. On twelve genomic benchmarks (28 to 500 sequences, 3 to 7 classes), pVR outperforms four established alignment-free baselines on three of six low-sample datasets, with gains of up to 21 percentage points; it underperforms only on a SARS-CoV-2 variant benchmark whose point-mutation divergence violates the hierarchical assumption, and all methods saturate in the large-sample regime. pVR also outperforms zero-shot frozen embeddings from the 500M-parameter Nucleotide Transformer v2 by 6.7 to 11.4 percentage points on three low-sample benchmarks. The pVR codebase is publicly available at https://github.com/MAHI-Group/pVR.