Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD has only been recently studied, yet is important due to the growing need for uncertainty quantification. We investigate two computationally cheap resampling-based methods to construct confidence intervals for SGD solutions. One uses multiple, but few, SGDs in parallel via resampling with replacement from the data, and another operates this in an online fashion. Our methods can be regarded as enhancements of established bootstrap schemes to substantially reduce the computation effort in terms of resampling requirements, while at the same time bypassing the intricate mixing conditions in existing batching methods. We achieve these via a recent so-called cheap bootstrap idea and Berry-Esseen-type bound for SGD.

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Although prohibitively large, such matrices are often approximately low rank. We propose an algorithm that exploits this structure to obtain a low rank decomposition of any matrix $\mathbf{A}$ as $\mathbf{A} \approx \mathbf{L}\mathbf{R}$, where $\mathbf{L}$ and $\mathbf{R}$ are the low rank factors. The total number of elements in $\mathbf{L}$ and $\mathbf{R}$ can be significantly less than that in $\mathbf{A}$. Furthermore, the entries of $\mathbf{L}$ and $\mathbf{R}$ are quantized to low precision formats $--$ compressing $\mathbf{A}$ by giving us a low rank and low precision factorization. Our algorithm first computes an approximate basis of the range space of $\mathbf{A}$ by randomly sketching its columns, followed by a quantization of the vectors constituting this basis. It then computes approximate projections of the columns of $\mathbf{A}$ onto this quantized basis. We derive upper bounds on the approximation error of our algorithm, and analyze the impact of target rank and quantization bit-budget. The tradeoff between compression ratio and approximation accuracy allows for flexibility in choosing these parameters based on specific application requirements. We empirically demonstrate the efficacy of our algorithm in image compression, nearest neighbor classification of image and text embeddings, and compressing the layers of LlaMa-$7$b. Our results illustrate that we can achieve compression ratios as aggressive as one bit per matrix coordinate, all while surpassing or maintaining the performance of traditional compression techniques.

In the ongoing court battle between Google and the U.S. Justice Department over whether the company has violated an antitrust law, the stakes are high. The outcome of the 10-week trial, which will be decided by U.S. District Judge Amit Mehta, could fundamentally change the way people search the internet and reduce revenue for the company that has the most common search engine for online users. The civil antitrust lawsuit is the first to go to trial in a series of cases targeting other big tech companies like Meta and Amazon. But this particular suit, brought forward by the Justice Department and eleven other states, alleges that Google illegally monopolizes search engine services--spending billions to do so-- making it the default company through which advertising companies and website publishers purchase and sell ads. "The question is whether [Google] is entrenching its monopoly and closing off avenues for competitors to try to develop a competitive search engine," says Eleanor Fox, professor at New York University School of Law.

CyberGuy explains how Walmart is using artificial intelligence to enhance the shopping experience. You might be tempted to buy products on Amazon that have glowing reviews and high ratings. After all, who doesn't want to get the best deal possible? Before you click that "buy now" button, you might want to take a closer look at those reviews. Because, as it turns out, not all of them are genuine.

Writing in the Sunday Telegraph over the weekend, he said: "A short stretch of a few months inside isn't enough time to rehabilitate criminals, but is more than enough to dislocate them from the family, work and home connections that keep them from crime.

House Armed Services Committee holds hearing on the Department of Defense using AI. The AI revolution started by ChatGPT continues to accelerate, with machine learning showing up in everything from ecommerce to tractors. And while the applications continue to explode, it's becoming clear that AI can help smaller players compete by harnessing their data in the same way industrial behemoths have for decades. In warfare, AI is giving a similar edge to smaller, tech-savvy militaries – for good and ill. Decision-making: Generative AI tools like ChatGPT, Bard or Midjourney use internet data to train a model so it can predict how to complete tasks like writing a line of computer code or creating a new painting in Picasso's style.

The U.S. will take steps to prevent American chipmakers from selling products to China that circumvent government restrictions, a U.S. official said, as part of the Biden administration's upcoming actions to block more AI chip exports. The new rules will be added to sweeping U.S. restrictions on shipments of advanced chips and chipmaking equipment to China unveiled last October. The updates are expected this week, other people familiar with the matter said, though such timetables often slip. The new rules will block some AI chips that fall just under current technical parameters while demanding companies report shipments of others, said the official, who provided information on condition of anonymity.

Are you the type who turns on GPS navigation no matter where you're headed, or do you just wing it? You might know where you're going, but Google Maps, Apple Maps and Waze have a few slick tools beyond plain old directions. These hidden hacks let you find the best gas prices along your route, avoid leaving a digital track, change the robotic-like navigator voice to something fun and help you find your way around mega malls and airports. Are you the type who turns on GPS navigation no matter where you're headed, or do you just wing it? You might know where you're going, but Google Maps, Apple Maps and Waze have a few slick tools beyond plain old directions Want to sneak your way to a place without leaving digital tracks?

Most contributions on Few-Shot Object Detection (FSOD) evaluate their methods on natural images only, yet the transferability of the announced performance is not guaranteed for applications on other kinds of images. We demonstrate this with an in-depth analysis of existing FSOD methods on aerial images and observed a large performance gap compared to natural images. Small objects, more numerous in aerial images, are the cause for the apparent performance gap between natural and aerial images. As a consequence, we improve FSOD performance on small objects with a carefully designed attention mechanism. In addition, we also propose a scale-adaptive box similarity criterion, that improves the training and evaluation of FSOD methods, particularly for small objects. We also contribute to generic FSOD with two distinct approaches based on metric learning and fine-tuning. Impressive results are achieved with the fine-tuning method, which encourages tackling more complex scenarios such as Cross-Domain FSOD. We conduct preliminary experiments in this direction and obtain promising results. Finally, we address the deployment of the detection models inside COSE's systems. Detection must be done in real-time in extremely large images (more than 100 megapixels), with limited computation power. Leveraging existing optimization tools such as TensorRT, we successfully tackle this engineering challenge.

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional primary solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics (SINDy) framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly.