randomized sketching

This work addresses the challenge of efficiently processing high-throughput matrix streams under stringent resource constraints, where existing approaches suffer from poor update efficiency due to frequent cubic-time matrix decompositions under tight error bounds. The authors propose AeroSketch, a framework that leverages randomized numerical linear algebra (RandNLA) to construct compact matrix sketches suitable for persistent, sliding-window, and distributed streaming settings. AeroSketch is the first method to simultaneously achieve optimal communication and space complexity while reducing the per-update time complexity from cubic to quadratic, thereby attaining near-optimal (within logarithmic factors) update performance. Experimental results on both synthetic and real-world datasets demonstrate that AeroSketch significantly improves throughput while maintaining comparable approximation accuracy and optimal resource consumption.

This work addresses the fundamental limitations of conventional linear sketching methods in data stream scenarios, where achieving a balance among reconstruction accuracy, computational efficiency, and real-time performance remains challenging due to information gaps caused by loss of orthogonal components. To overcome this, we propose FLORE—the first unsupervised generative sketching framework that incorporates a generative prior, enabling high-fidelity signal recovery without requiring ground-truth training data. By synergistically integrating generative modeling, linear sketching, and a lightweight recovery algorithm, FLORE achieves high-quality reconstruction while reducing recovery error by up to three orders of magnitude and accelerating computation by up to 100× compared to existing learning-based approaches.

Cardinality sketches (e.g., MinHash, linear sketches) exhibit strong statistical guarantees under random queries but suffer severe security degradation under adaptive querying—posing critical risks in privacy-sensitive interactive systems. Method: We propose the first generic attack framework against union-compatible sketches, leveraging adaptive interactions to exploit structural vulnerabilities. Contribution/Results: We prove that any union-compatible sketch can be compromised with only Õ(k⁴) adaptive queries while degrading estimation accuracy. For monotonic or linear sketches, we construct tight attacks achieving the optimal Õ(k²) query complexity and establish a matching Ω(k²) information-theoretic lower bound. Our work unifies and strengthens prior analyses of statistical queries and MinHash security, providing the first systematic characterization of adaptive security thresholds for cardinality sketches. These results yield foundational theoretical guidance for the secure deployment of sketches in adaptive, privacy-critical applications.

This paper addresses streaming computation of four fundamental geometric problems over dynamic point sets in high-dimensional Euclidean space: diameter approximation, farthest neighbor queries, minimum enclosing ball (MEB), and core-set construction. We propose the first deterministic streaming algorithm, built upon geometric pruning and hierarchical grid sampling, integrated with structural analysis of farthest-point pairs and core-set theory. Our algorithm achieves a (√2 + ε)-approximation guarantee while reducing space complexity to O(ε⁻² log(1/ε)), improving upon the prior SODA 2010 state-of-the-art by a factor of ε⁻¹. We further establish a tight Ω(ε⁻¹) lower bound on space, proving asymptotic optimality of our complexity. Crucially, a single unified framework supports all four query types, enhancing both space efficiency and theoretical completeness for geometric streaming.

This paper studies average-distortion sketching in metric spaces: designing compact sketches of points that simultaneously (i) never underestimate pairwise distances under any fixed distribution, and (ii) approximate their expected distance within a multiplicative factor. We formally introduce this notion—breaking the inherent lower bounds of worst-case sketching. Our method combines randomized ℓₚ-projection, a data-dependent variant of locality-sensitive hashing (LSH), and probabilistic far-point certificates. For the metric space ([Δ]ᵈ, ℓₚ), it achieves c-approximation for any constant c > 1, with bit complexity poly(2^{p/c} · log(dΔ)). Consequently, we reduce the approximation ratio of ℓₚ nearest-neighbor search from prior O(p) to any constant c, while improving space complexity to n^{O(p/c)}.

This work addresses the high communication overhead and lack of efficient parallel strategies in sketching with random dense matrices in distributed-memory environments. It establishes, for the first time, a communication complexity lower bound for this problem, revealing that zero communication is achievable when using a small number of processors, and extends this theoretical insight to the Nyström approximation setting. Building on these results, the authors propose a novel parallel algorithm whose communication cost matches the established lower bound. Implemented on CPU/GPU heterogeneous supercomputing platforms, the method demonstrates excellent strong and weak scalability, with empirical communication costs approaching the theoretical limit, thereby confirming its efficiency and practicality.

This work addresses the tail latency bottleneck in large-scale distributed computing caused by slow or unresponsive nodes by proposing a novel framework that integrates coded computation with randomized numerical linear algebra. By systematically combining polynomial codes and random sketching techniques for the first time, and incorporating a probabilistic compression mechanism, the approach significantly enhances computational efficiency while preserving fault tolerance. The method effectively reduces both communication and computational overhead in high-dimensional machine learning tasks, accelerating model training without compromising robustness. This solution offers a theoretically rigorous and practically efficient paradigm for distributed optimization.

This work addresses a key limitation in traditional linear sketching methods for streaming data statistics, which rely on the strong assumption that each hash bucket contains only a single key—thereby constraining space efficiency. To overcome this, the authors propose a novel approach that stores randomized linear combinations of multiple keys within each bucket and reconstructs key-value pairs during recovery by solving a sparse linear system. This design effectively relaxes the single-key-per-bucket constraint, achieving substantially improved space efficiency with only a modest increase in computational overhead. Experimental results demonstrate that the proposed method significantly reduces memory consumption while markedly enhancing space utilization for streaming data statistics.

This work systematically investigates the robustness of streaming algorithms under adversarial adaptive inputs, where future data depend on prior algorithmic outputs—a setting in which classical sketching and streaming methods fail to guarantee correctness. By integrating differential privacy, cryptographic techniques, and linear sketching theory, we develop novel robust algorithms for both insertion-only and turnstile (insertion-deletion) streams. We uncover deep connections between adversarial robustness, differential privacy, and cryptography, and delineate the feasibility boundaries for fundamental tasks such as norm estimation, frequency moment approximation, and heavy-hitter detection under adaptive adversaries. Our results establish that achieving robustness often necessitates polynomial space or high-dimensional sketches, revealing inherent limitations, while also providing efficient solutions for frequency-based statistics and outlining promising directions for future research.

This work resolves the long-standing open question of whether efficient turnstile streaming algorithms for polynomial-length streams are essentially equivalent to linear sketching. By introducing tools from Fourier analysis and additive combinatorics, we establish this equivalence in the practical turnstile model for the first time: any turnstile algorithm using space $S$ can be simulated by a linear sketch requiring only $O(S)$ linear measurements, with total space $O(S \log S)$. Our approach abandons the traditional transition-graph machinery, enabling efficient reconstruction of the final vector via a linear sketch. This yields new lower bounds and, under a natural smoothness assumption, leads to a compact sketch with bounded entries and total space merely $O(S)$.