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1. Iterative Hessian Sketch with Momentum

   https://doi.org/10.1109/ICASSP.2019.8682720  

   Ozaslan, Ibrahim Kurban; Pilanci, Mert; Arikan, Orhan (May 2019, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We propose a novel randomized linear least squares solver which is an improvement of Iterative Hessian Sketch and randomized preconditioning. In the proposed Momentum-IHS technique (M-IHS), Heavy Ball Method is used to accelerate the convergence of iterations. It is shown that for any full rank data matrix, rate of convergence depends on the ratio between the feature size and the sketch size. Unlike the Conjugate Gradient technique, the rate of convergence is unaffected by either the condition number or the eigenvalue spectrum of the data matrix. As demonstrated over many examples, the proposed M-IHS provides compatible performance with the state of the art randomized preconditioning methods such as LSRN or Blendenpik and yet, it provides a completely different perspective in the area of iterative solvers which can pave the way for future developments. 

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2. Exact Sketch-Based Read Mapping

   Schulz, Tizian; Medvedev, Paul (January 2023, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023))
3. Almost Linear Size Edit Distance Sketch

   https://doi.org/10.1145/3618260.3649783  

   Koucký, Michal; Saks, Michael E (June 2024, ACM)
4. ESKEMAP: exact sketch-based read mapping

   https://doi.org/10.1186/s13015-024-00261-7  

   Schulz, Tizian; Medvedev, Paul (December 2024, Algorithms for Molecular Biology)

   Abstract BackgroundGiven a sequencing read, the broad goal of read mapping is to find the location(s) in the reference genome that have a “similar sequence”. Traditionally, “similar sequence” was defined as having a high alignment score and read mappers were viewed as heuristic solutions to this well-defined problem. For sketch-based mappers, however, there has not been a problem formulation to capture what problem an exact sketch-based mapping algorithm should solve. Moreover, there is no sketch-based method that can find all possible mapping positions for a read above a certain score threshold. ResultsIn this paper, we formulate the problem of read mapping at the level of sequence sketches. We give an exact dynamic programming algorithm that finds all hits above a given similarity threshold. It runs in$$\mathcal {O} (|t| + |p| + \ell ^2)$$ $O\left(\right|t|+|p|+{\ell }^2)$time and$$\mathcal {O} (\ell \log \ell )$$ $O(\ell log\ell )$space, where |t| is the number of$$k$$ $k$-mers inside the sketch of the reference, |p| is the number of$$k$$ $k$-mers inside the read’s sketch and$$\ell$$ $\ell$is the number of times that$$k$$ $k$-mers from the pattern sketch occur in the sketch of the text. We evaluate our algorithm’s performance in mapping long reads to the T2T assembly of human chromosome Y, where ampliconic regions make it desirable to find all good mapping positions. For an equivalent level of precision as minimap2, the recall of our algorithm is 0.88, compared to only 0.76 of minimap2. 

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5. Open Vocabulary Semantic Scene Sketch Understanding

   Bourouis, Ahmed; Fan, Judith E; Gryaditskaya, Yulia (June 2024, Computer Vision Foundation)

   We study the underexplored but fundamental vision problem of machine understanding of abstract freehand scene sketches We introduce a sketch encoder that results in semantically- aware feature space, which we evaluate by testing its performance on a semantic sketch seg- mentation task. To train our model we rely only on the availability of bitmap sketches with their brief captions and do not require any pixel-level annotations. To obtain generalization to a large set of sketches and categories, we build on a vision transformer encoder pretrained with the CLIP model. We freeze the text encoder and perform visual-prompt tuning of the visual encoder branch while introducing a set of critical modifications. Firstly, we augment the classical key-query (k-q) self-attention blocks with value-value (v-v) self-attention blocks. Central to our model is a two-level hierarchical network design that enables efficient semantic disentanglement: The first level ensures holistic scene sketch encoding, and the second level focuses on individual categories. We, then, in the second level of the hierarchy, introduce a cross-attention between textual and visual branches. Our method outperforms zero-shot CLIP pixel accuracy of segmentation results by 37 points, reaching an accuracy of 85.5% on the FS-COCO sketch dataset. Finally, we conduct a user study that allows us to identify further improvements needed over our method to reconcile machine and human understanding of scene sketches. 

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