Tootfinder

Adaptive Sketching Based Construction of H2 Matrices on GPUs
Wajih Halim Boukaram, Yang Liu, Pieter Ghysels, Xiaoye Sherry Li
https://arxiv.org/abs/2506.16759

Adaptive Sketching Based Construction of H2 Matrices on GPUs
We develop a novel linear-complexity bottom-up sketching-based algorithm for constructing a $H^2$ matrix, and present its high performance GPU implementation. The construction algorithm requires both a black-box sketching operator and an entry evaluation function. The novelty of our GPU approach centers around the design and implementation of the above two operations in batched mode on GPU with accommodation for variable-size data structures in a batch. The batch algorithms minimize the number …

User-Guided Force-Directed Graph Layout
Hasan Balci, Augustin Luna
https://arxiv.org/abs/2506.15860 https://arxiv.org/pdf/2506.15860

User-Guided Force-Directed Graph Layout
Visual analysis of relational data is essential for many real-world analytics tasks, with layout quality being key to interpretability. However, existing layout algorithms often require users to navigate complex parameters to express their intent. We present a user-guided force-directed layout approach that enables intuitive control through freehand sketching. Our method uses classical image analysis techniques to extract structural information from sketches, which is then used to generate posi…

Deterministic Lower Bounds for $k$-Edge Connectivity in the Distributed Sketching Model
Peter Robinson, Ming Ming Tan
https://arxiv.org/abs/2507.11257 http…

Deterministic Lower Bounds for $k$-Edge Connectivity in the Distributed Sketching Model
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the referee must decide whether the graph is $k$-edge connected by taking into account the received messages. We present the first lower bound for deciding a graph connectivity problem in this model with a deterministic algorithm. Concretely, we show that the …

A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems
Andrew J. Higgins, Erik G. Boman, Ichitaro Yamazaki
https://arxiv.org/abs/2508.14209

A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems
Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some $O(1)$ distortion factor with high probability. The most popular sketches in literature are the Gaussian sketch and the subsampled randomized Hadamard transform, while the CountSketch has lower complexity. Combining two sketches, known as multisketching, offers an inexpensive means of quickly reducing the dimension of a matrix by combining a CountSketch and Gaussian sketch.…

OddEEC: A New Sketch Technique for Error Estimating Coding
Huayi Wang, Jingfan Meng, Jun Xu
https://arxiv.org/abs/2508.11842 https://arxiv.org/pdf/2508.118…

OddEEC: A New Sketch Technique for Error Estimating Coding
Error estimating coding (EEC) is a standard technique for estimating the number of bit errors during packet transmission over wireless networks. In this paper, we propose OddEEC, a novel EEC scheme. OddEEC is a nontrivial adaptation of a data sketching technique named Odd Sketch to EEC, addressing new challenges therein by its bit sampling technique and maximum likelihood estimator. Our experiments show that OddEEC overall achieves comparable estimation accuracy as competing schemes such as gEE…

When topics of discourse prove difficult to approach, stories can help us on our way. This famed short story about a graceful city with an unexpected abberation helps me reflect on where I want to apply my capacity for writing, sketching and teaching.

https://axbom.com/omelas/

#DigitalEthics

Covering the Euclidean Plane by a Pair of Trees
Hung Le, Lazar Milenkovi\'c, Shay Solomon, Tianyi Zhang
https://arxiv.org/abs/2508.11507 https://arxiv.…

Covering the Euclidean Plane by a Pair of Trees
A {$t$-stretch tree cover} of a metric space $M = (X,δ)$, for a parameter $t \ge 1$, is a collection of trees such that every pair of points has a $t$-stretch path in one of the trees. Tree covers provide an important sketching tool that has found various applications over the years. The celebrated {Dumbbell Theorem} by Arya et al. [STOC'95] states that any set of points in the Euclidean plane admits a $(1+ε)$-stretch tree cover with $O_ε(1)$ trees. This result extends to any (constant) dime…

Mental Effort Estimation in Motion Exploration and Concept Generation Design Tasks using Inter-Band Relative Power Difference of EEG
G. Kalyan Ramana, Sumit Yempalle, Prasad S. Onkar
https://arxiv.org/abs/2508.10353

Mental Effort Estimation in Motion Exploration and Concept Generation Design Tasks using Inter-Band Relative Power Difference of EEG
Conceptual design is a cognitively complex task, especially in the engineering design of products having relative motion between components. Designers prefer sketching as a medium for conceptual design and use gestures and annotations to represent such relative motion. Literature suggests that static representations of motion in sketches may not achieve the intended functionality when realised, because it primarily depends on the designers' mental capabilities for motion simulation. Thus, it is…

A variable dimension sketching strategy for nonlinear least-squares
Stefania Bellavia, Greta Malaspina, Benedetta Morini
https://arxiv.org/abs/2506.03965 h…

A variable dimension sketching strategy for nonlinear least-squares
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its update: the first is based solely on the Armijo condition, the latter is based on information from the true Gauss-Newton model.…

Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
https://arxiv.org/abs/2506.05174 https://arxiv.org/pdf/2506.…

Norming Sets for Tensor and Polynomial Sketching
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a ne…

SongBloom: Coherent Song Generation via Interleaved Autoregressive Sketching and Diffusion Refinement
Chenyu Yang, Shuai Wang, Hangting Chen, Wei Tan, Jianwei Yu, Haizhou Li
https://arxiv.org/abs/2506.07634

SongBloom: Coherent Song Generation via Interleaved Autoregressive Sketching and Diffusion Refinement
Generating music with coherent structure, harmonious instrumental and vocal elements remains a significant challenge in song generation. Existing language models and diffusion-based methods often struggle to balance global coherence with local fidelity, resulting in outputs that lack musicality or suffer from incoherent progression and mismatched lyrics. This paper introduces $\textbf{SongBloom}$, a novel framework for full-length song generation that leverages an interleaved paradigm of autore…

This https://arxiv.org/abs/2505.24603 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches
Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient optimization, coded computing, and federated learning. This operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Renyi Differential Privacy (RDP), providing a refined pri…

On Sketching Trimmed Statistics
Honghao Lin, Hoai-An Nguyen, David P. Woodruff
https://arxiv.org/abs/2506.07342 https://arxiv.org/pdf…

On Sketching Trimmed Statistics
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed vector, which excludes the top and bottom $k$ frequencies. This is called the $F_p$ moment of the trimmed vector. Trimmed measures are used in robust estimation, as seen in the R programming language's `trim.var' function and the `trim' parameter in the mean fun…

Over the years i came more and more to the conclusion, that the Mindset of growing in sketching is the perennial thought:" this sketch is terrible. But i will finish it somehow and try again tomorrow" #beginnersmind #path

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Shiyuan Feng, Ying Feng, George Z. Li, Zhao Song, David P. Woodruff, Lichen Zhang
https://arxiv.org/abs/2506.05503

On Differential Privacy for Adaptively Solving Search Problems via Sketching
Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made without sacrificing the correctness of the responses. Although these works use differential privacy to show that for some problems it is possible to tolerate $T$ queries using $\widetilde{O}(\sqrt{T})$ copies of a data structure, such results only apply to numer…

Multipass Linear Sketches for Geometric LP-Type Problems
N. Efe \c{C}ekirge, William Gay, David P. Woodruff
https://arxiv.org/abs/2507.11484 https://

Multipass Linear Sketches for Geometric LP-Type Problems
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important applications in machine learning applications such as classification, bioinformatics, and noisy learning. We study LP-type problems in several streaming and distributed big data models, giving $\varepsilon$-approximation linear sketching algorithms with a focus on the h…

VeasyGuide: Personalized Visual Guidance for Low-vision Learners on Instructor Actions in Presentation Videos
Yotam Sechayk, Ariel Shamir, Amy Pavel, Takeo Igarashi
https://arxiv.org/abs/2507.21837

VeasyGuide: Personalized Visual Guidance for Low-vision Learners on Instructor Actions in Presentation Videos
Instructors often rely on visual actions such as pointing, marking, and sketching to convey information in educational presentation videos. These subtle visual cues often lack verbal descriptions, forcing low-vision (LV) learners to search for visual indicators or rely solely on audio, which can lead to missed information and increased cognitive load. To address this challenge, we conducted a co-design study with three LV participants and developed VeasyGuide, a tool that uses motion detection …

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
Haoran Guan, Yuwei Fan
https://arxiv.org/abs/2506.04208 https://

Rounding error analysis of randomized CholeskyQR2 for sparse matrices
This work focuses on rounding error analysis of randomized CholeskyQR2 (RCholeskyQR2) for sparse matrices. We form RCholeskyQR2 with CholeskyQR2 and matrix sketching in order to accelerate CholeskyQR2 and improve its applicability by compressing the input matrix $X \in \mathbb{R}^{m\times n}$. In many real-world applications, the input matrix $X$ is always sparse. In this work, we follow the model of sparse matrices proposed in \cite{CSparse} and provide an improved rounding error analysis of R…

Improved Analysis of Khatri-Rao Random Projections and Applications
Arvind K. Saibaba, Bhisham Dev Verma, Grey Ballard
https://arxiv.org/abs/2507.23207 https://

Improved Analysis of Khatri-Rao Random Projections and Applications
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard Gaussian random matrix, for which the theory is well developed. However, this approach has the drawback that the cost of generating and multiplying by the random matrix can be prohibitively expensive. Khatri-Rao random projections (KRPs), obtained by sketching …

This https://arxiv.org/abs/2502.13583 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fundamental Bias in Inverting Random Sampling Matrices with Application to Sub-sampled Newton
A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis using Johnson--Lindenstrauss and subspace embedding techniques. Recent studies have identified the issue of inversion bias -- the phenomenon that inverses of random sketches are not unbiased, despite the unbiasedness of the sketches themselves. This bias pres…