We consider a decision maker allocating one unit of renewable and divisible resource in each period on a number of arms. The arms have unknown and random rewards whose means are proportional to the allocated resource and whose variances are proportional to an order $b$ of the allocated resource. In particular, if the decision maker allocates resource $A_i$ to arm $i$ in a period, then the reward $Y_i$ is$Y_i(A_i)=A_i \mu_i+A_i^b \xi_{i}$, where $\mu_i$ is the unknown mean and the noise $\xi_{i}$ is independent and sub-Gaussian. When the order $b$ ranges from 0 to 1, the framework smoothly bridges the standard stochastic multi-armed bandit and online learning with full feedback. We design two algorithms that attain the optimal gap-dependent and gap-independent regret bounds for $b\in [0,1]$, and demonstrate a phase transition at $b=1/2$. The theoretical results hinge on a novel concentration inequality we have developed that bounds a linear combination of sub-Gaussian random variables whose weights are fractional, adapted to the filtration, and monotonic.

Self-training is an important technique for solving semi-supervised learning problems. It leverages unlabeled data by generating pseudo-labels and combining them with a limited labeled dataset for training. The effectiveness of self-training heavily relies on the accuracy of these pseudo-labels. In this paper, we introduce doubly robust self-training, a novel semi-supervised algorithm that provably balances between two extremes. When the pseudo-labels are entirely incorrect, our method reduces to a training process solely using labeled data. Conversely, when the pseudo-labels are completely accurate, our method transforms into a training process utilizing all pseudo-labeled data and labeled data, thus increasing the effective sample size. Through empirical evaluations on both the ImageNet dataset for image classification and the nuScenes autonomous driving dataset for 3D object detection, we demonstrate the superiority of the doubly robust loss over the standard self-training baseline.

LinkedIn is adding a new, AI-powered perk for its premium subscribers: a built-in job coach that uses AI and LinkedIn data to help job seekers find, research and apply for roles. The new feature arrives as the company announced its user base has grown to 1 billion members as it looks to ramp up its investment in AI-driven features. The Microsoft-owned company has increasingly been experimenting with AI features for its paying members. Earlier this year, it introduced the ability to use generative AI to write better profile descriptions and messages to hiring managers. But the latest AI perks aim to provide an even more personalized experience.

Providing consistent, individualized feedback to teachers on their instruction can improve student learning outcomes. Such feedback can especially benefit novice instructors who teach on online platforms and have limited access to instructional training. To build scalable measures of instruction, we fine-tune RoBERTa and GPT models to identify five instructional talk moves inspired by accountable talk theory: adding on, connecting, eliciting, probing and revoicing students' ideas. We fine-tune these models on a newly annotated dataset of 2500 instructor utterances derived from transcripts of small group instruction in an online computer science course, Code in Place. Although we find that GPT-3 consistently outperforms RoBERTa in terms of precision, its recall varies significantly. We correlate the instructors' use of each talk move with indicators of student engagement and satisfaction, including students' section attendance, section ratings, and assignment completion rates. We find that using talk moves generally correlates positively with student outcomes, and connecting student ideas has the largest positive impact. These results corroborate previous research on the effectiveness of accountable talk moves and provide exciting avenues for using these models to provide instructors with useful, scalable feedback.

There have been recent advances in computer-based recognition of isolated, citation-form signs from video. There are many challenges for such a task, not least the naturally occurring inter- and intra- signer synchronic variation in sign production, including sociolinguistic variation in the realization of certain signs. However, there are several significant factors that make recognition of signs from continuous signing an even more difficult problem. This article presents an overview of such challenges, based in part on findings from a large corpus of linguistically annotated video data for American Sign Language (ASL). Some linguistic regularities in the structure of signs that can boost handshape and sign recognition are also discussed.

Domain generalization asks for models trained over a set of training environments to generalize well in unseen test environments. Recently, a series of algorithms such as Invariant Risk Minimization (IRM) have been proposed for domain generalization. However, Rosenfeld et al. (2021) shows that in a simple linear data model, even if non-convexity issues are ignored, IRM and its extensions cannot generalize to unseen environments with less than $d_s+1$ training environments, where $d_s$ is the dimension of the spurious-feature subspace. In this work, we propose Invariant-feature Subspace Recovery (ISR): a new class of algorithms to achieve provable domain generalization across the settings of classification and regression problems. First, in the binary classification setup of Rosenfeld et al. (2021), we show that our first algorithm, ISR-Mean, can identify the subspace spanned by invariant features from the first-order moments of the class-conditional distributions, and achieve provable domain generalization with $d_s+1$ training environments. Our second algorithm, ISR-Cov, further reduces the required number of training environments to $O(1)$ using the information of second-order moments. Notably, unlike IRM, our algorithms bypass non-convexity issues and enjoy global convergence guarantees. Next, we extend ISR-Mean to the more general setting of multi-class classification and propose ISR-Multiclass, which leverages class information and provably recovers the invariant-feature subspace with $\lceil d_s/k\rceil+1$ training environments for $k$-class classification. Finally, for regression problems, we propose ISR-Regression that can identify the invariant-feature subspace with $d_s+1$ training environments. Empirically, we demonstrate the superior performance of our ISRs on synthetic benchmarks. Further, ISR can be used as post-processing methods for feature extractors such as neural nets.

In the year since OpenAI released ChatGPT, high school teacher Vicki Davis has been rethinking every single assignment she gives her students. Davis, a computer science teacher at Sherwood Christian Academy in Georgia, was well-positioned to be an early adopter of the technology. She's also the IT director at the school and helped put together an AI policy in March: the school opted to allow the use of AI tools for specific projects so long as students discussed it with their teachers and cited the tool. In Davis' mind, there were good and bad uses of AI, and ignoring its growing popularity was not going to help students unlock the productive uses or understand its dangers. "It's actually changed how I design my projects because there are some times I want my students to use AI, and then there are times I don't want them to," Davis said.

Teachers themselves are exploring the potential of this rapidly developing technology, too. Jonathan Wharmby, who teaches computer science at Cardinal Heenan Catholic High School in Liverpool, uses AI to help with planning and creating resources, such as multiple choice questions - but said there were issues.

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation capacities of ANNs (including a calculus for ANNs), optimization theory (including Kurdyka-{\L}ojasiewicz inequalities), and generalization errors. In the last part of the book some deep learning approximation methods for PDEs are reviewed including physics-informed neural networks (PINNs) and deep Galerkin methods. We hope that this book will be useful for students and scientists who do not yet have any background in deep learning at all and would like to gain a solid foundation as well as for practitioners who would like to obtain a firmer mathematical understanding of the objects and methods considered in deep learning.

This study offers a complete analysis of ChatGPT's mathematics abilities in responding to multiple-choice questions for the Vietnamese National High School Graduation Examination (VNHSGE) on a range of subjects and difficulty levels. The dataset included 250 questions divided into four levels: knowledge (K), comprehension (C), application (A), and high application (H), and it included ten themes that covered diverse mathematical concepts. The outcomes demonstrate that ChatGPT's performance varies depending on the difficulty level and subject. It performed best on questions at Level (K), with an accuracy rate of $83\%$; but, as the difficulty level rose, it scored poorly, with an accuracy rate of $10\%$. The study has also shown that ChatGPT significantly succeeds in providing responses to questions on subjects including exponential and logarithmic functions, geometric progression, and arithmetic progression. The study found that ChatGPT had difficulty correctly answering questions on topics including derivatives and applications, spatial geometry, and Oxyz spatial calculus. Additionally, this study contrasted ChatGPT outcomes with Vietnamese students in VNHSGE and in other math competitions. ChatGPT dominated in the SAT Math competition with a success rate of $70\%$, followed by VNHSGE mathematics ($58.8\%)$. However, its success rates were lower on other exams, such as AP Statistics, the GRE Quantitative, AMC 10, AMC 12, and AP Calculus BC. These results suggest that ChatGPT has the potential to be an effective teaching tool for mathematics, but more work is needed to enhance its handling of graphical data and address the challenges presented by questions that are getting more challenging.