In this note we continue the work of Chon, as well as Mezzomo, Bedregal, and Santiago, by studying algebraic operations on fuzzy posets and bounded fuzzy lattices. We first prove that fuzzy posets are closed under finite direct products whenever the triangular norm realizing the product construction has no zero divisors. This result is then extended to the case of bounded fuzzy lattices. Some immediate consequences are then obtained within the setting of direct products realized by triangular norms with no nilpotent elements as well as strictly monotone and cancellative triangular norms. We then introduce a triangular norm based construction of ordinal products and similarly show that fuzzy posets are closed under ordinal products whenever the triangular norm realizing the product construction has no zero divisors.

As research and deployment of AI grows, the computational burden to support and sustain its progress inevitably does too. To train or fine-tune state-of-the-art models in NLP, computer vision, etc., some form of AI hardware acceleration is virtually a requirement. Recent large language models require considerable resources to train and deploy, resulting in significant energy usage, potential carbon emissions, and massive demand for GPUs and other hardware accelerators. However, this surge carries large implications for energy sustainability at the HPC/datacenter level. In this paper, we study the effects of power-capping GPUs at a research supercomputing center on GPU temperature and power draw; we show significant decreases in both temperature and power draw, reducing power consumption and potentially improving hardware life-span, with minimal impact on job performance. To our knowledge, our work is the first to conduct and make available a detailed analysis of the effects of GPU power-capping at the supercomputing scale. We hope our work will inspire HPCs/datacenters to further explore, evaluate, and communicate the impact of power-capping AI hardware accelerators for more sustainable AI.

Production high-performance computing (HPC) systems are adopting and integrating GPUs into their design to accommodate artificial intelligence (AI), machine learning, and data visualization workloads. To aid with the design and operations of new and existing GPU-based large-scale systems, we provide a detailed characterization of system operations, job characteristics, user behavior, and trends on a contemporary GPU-accelerated production HPC system. Our insights indicate that the pre-mature phases in modern AI workflow take up significant GPU hours while underutilizing GPUs, which opens up the opportunity for a multi-tier system. Finally, we provide various potential recommendations and areas for future investment for system architects, operators, and users.

This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$-norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.