arXiv subjects

Haike Xu

Publications and source records attributed to Haike Xu.

14 recordsLinked to original sources

arXiv2026

Compact Geometric Representations of Hierarchies

Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space. Recent work of You et al. [NeurIPS '25] has extended this approach to hierarchical retrieval, where relevance is determined by the ancestor-descendant relationships in a Directed Acyclic Graph (DAG). While previous work has shown that valid embeddings exist when the number of descendants is small, these bounds degrade significantly for deep hierarchies, requiring dimensions as large as the total number of nodes. In this paper, we investigate compact reachability embeddings for more general graph classes and provide theoretical guarantees for representing hierarchies using embeddings whose dimension depends on structural graph parameters. We prove that for any directed tree, there exists a reachability embedding in constant dimension 3, independent of the tree's size or depth. We generalize this result to graphs characterized by treewidth $t$, constructing embeddings of dimension $O(t \log n)$, where $n$ is the number of nodes. Complementing these upper bounds, we provide matching or near-matching lower bounds, showing that dimension $\Omega(n)$ is necessary for general DAGs and $\Omega(t/\log(n/t))$ is required for graphs of treewidth $t$. We also obtain upper and lower bounds parameterized by the number of cross-edges in the DAG. We additionally show that our embeddings can be constructed on real world datasets, and that they give much smaller dimensions in high recall regimes compared to prior embeddings with theoretical guarantees.

stat.ML↗

arXiv2026

JAG: Joint Attribute Graphs for Filtered Nearest Neighbor Search

Despite filtered nearest neighbor search being a fundamental task in modern vector search systems, the performance of existing algorithms is highly sensitive to query selectivity and filter type. In particular, existing solutions excel either at specific filter categories (e.g., label equality) or within narrow selectivity bands (e.g., pre-filtering for low selectivity) and are therefore a poor fit for practical deployments that demand generalization to new filter types and unknown query selectivities. In this paper, we propose JAG (Joint Attribute Graphs), a graph-based algorithm designed to deliver robust performance across the entire selectivity spectrum and support diverse filter types. Our key innovation is the introduction of attribute and filter distances, which transform binary filter constraints into continuous navigational guidance. By constructing a proximity graph that jointly optimizes for both vector similarity and attribute proximity, JAG prevents navigational dead-ends and allows JAG to consistently outperform prior graph-based filtered nearest neighbor search methods. Our experimental results across five datasets and four filter types (Label, Range, Subset, Boolean) demonstrate that JAG significantly outperforms existing state-of-the-art baselines in both throughput and recall robustness.

cs.IR↗

arXiv2025

Even Faster Kernel Matrix Linear Algebra via Density Estimation

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the following up to $(1+\varepsilon)$ relative error: matrix-vector products, matrix-matrix products, the spectral norm, and sum of all entries. The runtimes of our algorithms depend on the dimension $d$, the number of points $n$, and the target error $\varepsilon$. Importantly, the dependence on $n$ in each case is far lower when accessing the kernel matrix through KDE queries as opposed to reading individual entries. Our improvements over existing best algorithms (particularly those of Backurs, Indyk, Musco, and Wagner '21) for these tasks reduce the polynomial dependence on $\varepsilon$, and additionally decreases the dependence on $n$ in the case of computing the sum of all entries of the kernel matrix. We complement our upper bounds with several lower bounds for related problems, which provide (conditional) quadratic time hardness results and additionally hint at the limits of KDE based approaches for the problems we study.

cs.DS↗

arXiv2025

Beyond Sequential Reranking: Reranker-Guided Search Improves Reasoning Intensive Retrieval

The widely used retrieve-and-rerank pipeline faces two critical limitations: they are constrained by the initial retrieval quality of the top-k documents, and the growing computational demands of LLM-based rerankers restrict the number of documents that can be effectively processed. We introduce Reranker-Guided-Search (RGS), a novel approach that bypasses these limitations by directly retrieving documents according to reranker preferences rather than following the traditional sequential reranking method. Our method uses a greedy search on proximity graphs generated by approximate nearest neighbor algorithms, strategically prioritizing promising documents for reranking based on document similarity. Experimental results demonstrate substantial performance improvements across multiple benchmarks: 3.5 points on BRIGHT, 2.9 on FollowIR, and 5.1 on M-BEIR, all within a constrained reranker budget of 100 documents. Our analysis suggests that, given a fixed pair of embedding and reranker models, strategically selecting documents to rerank can significantly improve retrieval accuracy under limited reranker budget.

cs.IR↗

arXiv2025

In-Place Updates of a Graph Index for Streaming Approximate Nearest Neighbor Search

Indices for approximate nearest neighbor search (ANNS) are a basic component for information retrieval and widely used in database, search, recommendation and RAG systems. In these scenarios, documents or other objects are inserted into and deleted from the working set at a high rate, requiring a stream of updates to the vector index. Algorithms based on proximity graph indices are the most efficient indices for ANNS, winning many benchmark competitions. However, it is challenging to update such graph index at a high rate, while supporting stable recall after many updates. Since the graph is singly-linked, deletions are hard because there is no fast way to find in-neighbors of a deleted vertex. Therefore, to update the graph, state-of-the-art algorithms such as FreshDiskANN accumulate deletions in a batch and periodically consolidate, removing edges to deleted vertices and modifying the graph to ensure recall stability. In this paper, we present IP-DiskANN (InPlaceUpdate-DiskANN), the first algorithm to avoid batch consolidation by efficiently processing each insertion and deletion in-place. Our experiments using standard benchmarks show that IP-DiskANN has stable recall over various lengthy update patterns in both high-recall and low-recall regimes. Further, its query throughput and update speed are better than using the batch consolidation algorithm and HNSW.

cs.IR↗

arXiv2025

Graph-Based Algorithms for Diverse Similarity Search

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report data points that are closest to a given query, it has long been noted (Carbonell and Goldstein, 1998) that without additional constraints the reported answers can be redundant and/or duplicative. This issue is typically addressed in two stages: in the first stage, the algorithm retrieves a (large) number $r$ of points closest to the query, while in the second stage, the $r$ points are post-processed and a small subset is selected to maximize the desired diversity objective. Although popular, this method suffers from a fundamental efficiency bottleneck, as the set of points retrieved in the first stage often needs to be much larger than the final output. In this paper we present provably efficient algorithms for approximate nearest neighbor search with diversity constraints that bypass this two stage process. Our algorithms are based on popular graph-based methods, which allows us to "piggy-back" on the existing efficient implementations. These are the first graph-based algorithms for nearest neighbor search with diversity constraints. For data sets with low intrinsic dimension, our data structures report a diverse set of $k$ points approximately closest to the query, in time that only depends on $k$ and $\log \Delta$, where $\Delta$ is the ratio of the diameter to the closest pair distance in the data set. This bound is qualitatively similar to the best known bounds for standard (non-diverse) graph-based algorithms. Our experiments show that the search time of our algorithms is substantially lower than that using the standard two-stage approach.

cs.DS↗

arXiv2024

Statistical-Computational Trade-offs for Density Estimation

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that is ``close'' to $q$. Recently~\cite{aamand2023data} gave the first and only known result that achieves sublinear bounds in {\em both} the sampling complexity and the query time while preserving polynomial data structure space. However, their improvement over linear samples and time is only by subpolynomial factors. Our main result is a lower bound showing that, for a broad class of data structures, their bounds cannot be significantly improved. In particular, if an algorithm uses $O(n/\log^c k)$ samples for some constant $c>0$ and polynomial space, then the query time of the data structure must be at least $k^{1-O(1)/\log \log k}$, i.e., close to linear in the number of distributions $k$. This is a novel \emph{statistical-computational} trade-off for density estimation, demonstrating that any data structure must use close to a linear number of samples or take close to linear query time. The lower bound holds even in the realizable case where $q=p_i$ for some $i$, and when the distributions are flat (specifically, all distributions are uniform over half of the domain $[n]$). We also give a simple data structure for our lower bound instance with asymptotically matching upper bounds. Experiments show that the data structure is quite efficient in practice.

cs.DS↗

arXiv2024

SparseCL: Sparse Contrastive Learning for Contradiction Retrieval

Contradiction retrieval refers to identifying and extracting documents that explicitly disagree with or refute the content of a query, which is important to many downstream applications like fact checking and data cleaning. To retrieve contradiction argument to the query from large document corpora, existing methods such as similarity search and crossencoder models exhibit significant limitations. The former struggles to capture the essence of contradiction due to its inherent nature of favoring similarity, while the latter suffers from computational inefficiency, especially when the size of corpora is large. To address these challenges, we introduce a novel approach: SparseCL that leverages specially trained sentence embeddings designed to preserve subtle, contradictory nuances between sentences. Our method utilizes a combined metric of cosine similarity and a sparsity function to efficiently identify and retrieve documents that contradict a given query. This approach dramatically enhances the speed of contradiction detection by reducing the need for exhaustive document comparisons to simple vector calculations. We validate our model using the Arguana dataset, a benchmark dataset specifically geared towards contradiction retrieval, as well as synthetic contradictions generated from the MSMARCO and HotpotQA datasets using GPT-4. Our experiments demonstrate the efficacy of our approach not only in contradiction retrieval with more than 30% accuracy improvements on MSMARCO and HotpotQA across different model architectures but also in applications such as cleaning corrupted corpora to restore high-quality QA retrieval. This paper outlines a promising direction for improving the accuracy and efficiency of contradiction retrieval in large-scale text corpora.

cs.CL↗

arXiv2024

A Bi-metric Framework for Fast Similarity Search

We propose a new "bi-metric" framework for designing nearest neighbor data structures. Our framework assumes two dissimilarity functions: a ground-truth metric that is accurate but expensive to compute, and a proxy metric that is cheaper but less accurate. In both theory and practice, we show how to construct data structures using only the proxy metric such that the query procedure achieves the accuracy of the expensive metric, while only using a limited number of calls to both metrics. Our theoretical results instantiate this framework for two popular nearest neighbor search algorithms: DiskANN and Cover Tree. In both cases we show that, as long as the proxy metric used to construct the data structure approximates the ground-truth metric up to a bounded factor, our data structure achieves arbitrarily good approximation guarantees with respect to the ground-truth metric. On the empirical side, we apply the framework to the text retrieval problem with two dissimilarity functions evaluated by ML models with vastly different computational costs. We observe that for almost all data sets in the MTEB benchmark, our approach achieves a considerably better accuracy-efficiency tradeoff than the alternatives, such as re-ranking.

cs.IR↗

arXiv2023

Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations

Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing" version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic" dimension. For the other data structure variants studied, including DiskANN with "fast preprocessing", HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a "reasonable" accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least $0.1 n$ steps on instances of size $n$ before it encounters any of the $5$ nearest neighbors of the query.

cs.DS↗

arXiv2023

A Universal Discriminator for Zero-Shot Generalization

Generative modeling has been the dominant approach for large-scale pretraining and zero-shot generalization. In this work, we challenge this convention by showing that discriminative approaches perform substantially better than generative ones on a large number of NLP tasks. Technically, we train a single discriminator to predict whether a text sample comes from the true data distribution, similar to GANs. Since many NLP tasks can be formulated as selecting from a few options, we use this discriminator to predict the concatenation of input and which option has the highest probability of coming from the true data distribution. This simple formulation achieves state-of-the-art zero-shot results on the T0 benchmark, outperforming T0 by 16.0\%, 7.8\%, and 11.5\% respectively on different scales. In the finetuning setting, our approach also achieves new state-of-the-art results on a wide range of NLP tasks, with only 1/4 parameters of previous methods. Meanwhile, our approach requires minimal prompting efforts, which largely improves robustness and is essential for real-world applications. Furthermore, we also jointly train a generalized UD in combination with generative tasks, which maintains its advantage on discriminative tasks and simultaneously works on generative tasks.

cs.CL↗

arXiv2021

Embeddings and labeling schemes for A*

A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics have been handcrafted by domain experts. However, over the last few years, there has been a growing interest in learning heuristic functions. Such learned heuristics estimate the distance between given nodes based on "features" of those nodes. In this paper we formalize and initiate the study of such feature-based heuristics. In particular, we consider heuristics induced by norm embeddings and distance labeling schemes, and provide lower bounds for the tradeoffs between the number of dimensions or bits used to represent each graph node, and the running time of the A* algorithm. We also show that, under natural assumptions, our lower bounds are almost optimal.

cs.CG↗

arXiv2021

Fine-Grained Gap-Dependent Bounds for Tabular MDPs via Adaptive Multi-Step Bootstrap

This paper presents a new model-free algorithm for episodic finite-horizon Markov Decision Processes (MDP), Adaptive Multi-step Bootstrap (AMB), which enjoys a stronger gap-dependent regret bound. The first innovation is to estimate the optimal $Q$-function by combining an optimistic bootstrap with an adaptive multi-step Monte Carlo rollout. The second innovation is to select the action with the largest confidence interval length among admissible actions that are not dominated by any other actions. We show when each state has a unique optimal action, AMB achieves a gap-dependent regret bound that only scales with the sum of the inverse of the sub-optimality gaps. In contrast, Simchowitz and Jamieson (2019) showed all upper-confidence-bound (UCB) algorithms suffer an additional $Ω\left(\frac{S}{Δ_{min}}\right)$ regret due to over-exploration where $Δ_{min}$ is the minimum sub-optimality gap and $S$ is the number of states. We further show that for general MDPs, AMB suffers an additional $\frac{|Z_{mul}|}{Δ_{min}}$ regret, where $Z_{mul}$ is the set of state-action pairs $(s,a)$'s satisfying $a$ is a non-unique optimal action for $s$. We complement our upper bound with a lower bound showing the dependency on $\frac{|Z_{mul}|}{Δ_{min}}$ is unavoidable for any consistent algorithm. This lower bound also implies a separation between reinforcement learning and contextual bandits.

cs.LG↗

arXiv2021

Simple Combinatorial Algorithms for Combinatorial Bandits: Corruptions and Approximations

We consider the stochastic combinatorial semi-bandit problem with adversarial corruptions. We provide a simple combinatorial algorithm that can achieve a regret of $\tilde{O}\left(C+d^2K/Δ_{min}\right)$ where $C$ is the total amount of corruptions, $d$ is the maximal number of arms one can play in each round, $K$ is the number of arms. If one selects only one arm in each round, we achieves a regret of $\tilde{O}\left(C+\sum_{Δ_i>0}(1/Δ_i)\right)$. Our algorithm is combinatorial and improves on the previous combinatorial algorithm by [Gupta et al., COLT2019] (their bound is $\tilde{O}\left(KC+\sum_{Δ_i>0}(1/Δ_i)\right)$), and almost matches the best known bounds obtained by [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] (up to logarithmic factor). Note that the algorithms in [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] require one to solve complex convex programs while our algorithm is combinatorial, very easy to implement, requires weaker assumptions and has very low oracle complexity and running time. We also study the setting where we only get access to an approximation oracle for the stochastic combinatorial semi-bandit problem. Our algorithm achieves an (approximation) regret bound of $\tilde{O}\left(d\sqrt{KT}\right)$. Our algorithm is very simple, only worse than the best known regret bound by $\sqrt{d}$, and has much lower oracle complexity than previous work.

cs.LG↗