Search for: All records

Data compression is a powerful solution for addressing big data challenges in database and data management. In scientific data compression for vector fields, preserving topological information is essential for accurate analysis and visualization. The topological skeleton, a fundamental component of vector field topology, consists of critical points and their connectivity, known as separatrices. While previous work has focused on preserving critical points in error-controlled lossy compression, little attention has been given to preserving separatrices, which are equally important. In this work, we introduce TspSZ, an efficient error-bounded lossy compression framework designed to preserve both critical points and separatrices. Our key contributions are threefold: First, we propose TspSZ, a topological-skeleton-preserving lossy compression framework that integrates two algorithms. This allows existing critical-point-preserving compressors to also retain separatrices, significantly enhancing their ability to preserve topological structures. Second, we optimize TspSZ for efficiency through tailored improvements and parallelization. Specifically, we introduce a new error control mechanism to achieve high compression ratios and implement a shared-memory parallelization strategy to boost compression throughput. Third, we evaluate TspSZ against state-of-the-art lossy and lossless compressors using four real-world scientific datasets. Experimental results show that TspSZ achieves compression ratios of up to 7.7 times while effectively preserving the topological skeleton. This ensures efficient storage and transmission of scientific data without compromising topological integrity. 

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: (1) The “atomic” small-scale structure contains “crystals” whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man:woman::king:queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently performed with linear discriminant analysis. (2) The “brain” intermediate-scale structure has significant spatial modularity; for example, math and code features form a “lobe” akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. (3) The “galaxy”-scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer. 

This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the discrepancies in topology between original and decompressed datasets could potentially result in erroneous interpretations or even incorrect scientific conclusions. In this paper, we focus on preserving Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting the precise reconstruction of minimum/maximum labels induced by the integral line of each vertex. The key is to derive a series of edits during compression time; the edits are applied to the decompressed data, leading to an accurate reconstruction of segmentations while keeping the error within the prescribed error bound. To this end, we developed a workflow to fix extrema and integral lines alternatively until convergence within finite iterations; we accelerate each workflow component with shared-memory/GPU parallelism to make the performance practical for coupling with compressors. We demonstrate use cases with fluid dynamics, ocean, and cosmology application datasets with a significant acceleration with an NVIDIA A100 GPU. 

Machine learning with artificial neural networks has recently transformed many scientific fields by introducing new data analysis and information processing techniques. Despite these advancements, efficient implementation of machine learning on conventional computers remains challenging due to speed and power constraints. Optical computing schemes have quickly emerged as the leading candidate for replacing their electronic counterparts as the backbone for artificial neural networks. Some early integrated photonic neural network (IPNN) techniques have already been fast-tracked to industrial technologies. This review article focuses on the next generation of optical neural networks (ONNs), which can perform machine learning algorithms directly in free space. We have aptly named this class of neural network model the free space optical neural network (FSONN). We systematically compare FSONNs, IPNNs, and the traditional machine learning models with regard to their fundamental principles, forward propagation model, and training process. We survey several broad classes of FSONNs and categorize them based on the technology used in their hidden layers. These technologies include 3D printed layers, dielectric and plasmonic metasurface layers, and spatial light modulators. Finally, we summarize the current state of FSONN research and provide a roadmap for its future development.