The goal of learning to hash (L2H) is to derive data-dependent hash functions from a given data distribution to map data from the input space to a binary coding space. Despite the success of L2H, two observations have cast doubt on the source of its power, i.e., learning. First, a recent study shows that a version of locality-sensitive hashing without learning can achieve comparable accuracy to L2H methods with less time cost. Second, existing L2H methods are constrained to only three types of hash functions: thresholding, hyperspheres, and hyperplanes. In this paper, we identify Voronoi diagrams as a superior alternative for hashing, as they naturally possess three key properties, i.e., full space coverage, entropy maximization, and bit independence, that existing methods must acquire through complex learning. This insight leads us to propose Voronoi Diagram Encoded Hashing (VDeH), a simple and efficient no-learning approach. VDeH constructs hash functions directly from data-driven Voronoi partitions and leverages a simple encoding scheme to generate mutually independent binary bits. The no-learning and data-dependent nature of VDeH makes it an ideal and highly effective plug-and-play component for similarity search, not only in standard vector databases but also for complex data objects such as trajectories and graphs. For complex data objects, VDeH enables a straightforward two-stage process: an appropriate embedding method first maps the data into a vector space, after which VDeH efficiently generates binary hash codes to accelerate retrieval. Comprehensive experiments on multiple large-scale public benchmarks (consisting of databases of vectors, graphs, and trajectories) demonstrate that VDeH significantly outperforms state-of-the-art hashing methods in both retrieval accuracy and computational efficiency, establishing it as a versatile, efficient, and high-performance solution for similarity search across diverse data domains.
Background: Classifiers increasingly affect people's lives, necessitating their audit for fairness and accuracy on diverse populations. However, direct auditing is often not possible, due to a lack of access to the classifier or to suitable individual validation data. Objectives: This work aims to assess the fairness and accuracy of black-box classifiers using only population-level statistics, without requiring access to the classifier or individual predictions. Specifically, it introduces a method to lower-bound discrepancy of a classifier: a quantity that jointly captures inaccuracy and unfairness. Methods: We define a novel measure of unfairness based on the equalized odds fairness criterion, quantifying the fraction of the population on which a classifier deviates from ideal fair behavior. Using this measure, we develop a computationally efficient procedure for calculating the tightest possible lower bound on the classifier's discrepancy, using only aggregated rates of positive predictions and true positives across protected sub-populations. Results: Empirical evaluations confirm the tightness of the proposed lower bound in practical settings. The method demonstrated on several use cases, including estimating the reliability of voting polls and assessing the fairness of patient identification from internet search data. The code and data are available at https://github.com/sivansabato/bfa2. Conclusions: This work provides a practical and interpretable framework for auditing classifiers using population-level statistics. The proposed approach enables stakeholders to identify fairness and accuracy concerns in settings where traditional auditing is not feasible.
Background: Classical solvers for Boolean polynomial systems are usually based on the Conjunctive Normal Form (CNF) and the resolution calculus, or on the algebraic normal form (ANF) and the polynomial calculus, i.e., on Gr & ouml;bner basis methods. Here we develop a new solver which is based on the XOR-OR-AND normal form (XNF) and the XLIN proof system. XNF formulae allow compact encodings of XOR-rich problems, which, for instance, occur naturally in cryptography. Objectives: The paper has the following goals: lay a solid complexity-theoretic foundation for the new propositional logic proof system XLIN, devise XLIN-based conflict learning methods for formulae in XNF, create a variant of this framework optimized for practical efficiency, implement it in an actual solver called Xorricane, and finally apply this solver to benchmark suites consisting of random examples and cryptographic examples to prove its viability. Methods: As a first step, we show that the new propositional logic proof system XLIN is polynomially equivalent equivalent to the well-studied proof systems RES(circle plus) and SRES. It follows that there is an exponential separation between XLIN and the CNF-based resolution proof system RES. In the next step, we devise XLIN-based conflict-learning methods for formulae in XNF which are analogous to the CDCL methods of classical SAT solvers. Using Gau ss ian Constraint Propagation and a suitable version of conflict analysis, we obtain a conflict-driven framework CDXCL for XNF SAT-solving. To ensure practical efficiency, we also present a variant, called CDXCLlite, which uses a weaker propagation mechanism but retains the same learning method. Results: These theoretical advances result in Xorricane, an implementation of the latter XNF SAT-solving framework featuring novel lazy data structures. This implementation is compared to state-of-the-art algebraic and logic solving approaches on random and cryptographic benchmark suites. Although it still lacks several optimizations, it performs well on the benchmark problems and matches or outperforms modern CNF and CNF-XOR based SAT-solvers for XOR-rich problem instances. Conclusions: Solving Boolean polynomial systems, or equivalently, SAT-solving, based on the XNF and the XLIN proof system outperforms classical methods not only theoretically, but based on the new conflict-driven XNF clause learning methods developed here, it is possible to implement an XNF solver with good practical efficiency. The advantage of XNF-based SAT-solving is strongest for XOR-rich examples such as the ones derived from cryptographic attacks.
Adaptive Large Neighborhood Search (ALNS) is a meta-heuristic framework widely used to solve large-scale MAPF problems. It uses selection mechanisms such as the Roulette Wheel or Multi-Armed Bandit (MAB) policies, which adaptively learn to identify the most effective neighborhood (heuristic) at each iteration. A key assumption of these policies is that each heuristic's reward distribution (effectiveness) is stationary. However, the best heuristic can change during the search process. In this work, we address the inherent non-stationarity of neighborhood selection in ALNS-based MAPF solvers, where the reward distribution of the heuristic changes over time. We introduce DyMAB (Dynamic multi-armed bandit for neighborhood selection), a novel anytime algorithm that integrates a non-stationary multi-armed bandit (MAB) framework into ALNS. DyMAB leverages a windowed queue to track recent rewards, allowing for dynamic adaptation of neighborhood selection at each iteration. This ensures that the most effective heuristic is prioritized, improving overall search efficiency. We present a theoretical analysis showing that DyMAB achieves sub-linear regret under standard non-stationary bandit assumptions, offering formal performance guarantees. We benchmark DyMAB against a range of state-of-the-art anytime solvers across diverse MAPF scenarios, demonstrating that our method significantly enhances solution quality and scalability. In most cases, DyMAB achieves up to a 50% reduction in AUC and up to a 30% decrease in the Sum of Delays, highlighting its superiority in optimizing large-scale MAPF instances.
Multi-Agent Path Finding (MAPF) is a well-studied problem. In recent years, many derivations of MAPF-MAPF flavors-have been formulated and solved. Although some flavors only lift some assumptions present in MAPF, others result from combining two or more flavors. So far, no published work has focused specifically on these newly derived problems, which resulted in incomplete coverage of this area of MAPF, even if it enjoys significant research focus. We present a survey on MAPF flavors, in which we collected 48 existing MAPF-derived problems, categorized them, identified their key defining features, and mapped the relationships between them. The survey is designed to serve as a crossroads for both new and experienced researchers looking to obtain or update their knowledge about MAPF-adjacent problems and readers with such a problem looking for a solution or a reference method. The collected problems are therefore presented in a way that allows an interested reader to find and identify both new and related problems, learn about the state-of-the-art solution methods, and find literature that them in detail.
