Solving symbolic mathematics has always been of in the arena of human ingenuity that needs compositional reasoning and recurrence. However, recent studies have shown that large-scale language models such as transformers are universal and surprisingly can be trained as a sequence-to-sequence task to solve complex mathematical equations. These large transformer models need humongous amounts of training data to generalize to unseen symbolic mathematics problems. In this paper, we present a sample efficient way of solving the symbolic tasks by first pretraining the transformer model with language translation and then fine-tuning the pretrained transformer model to solve the downstream task of symbolic mathematics. We achieve comparable accuracy on the integration task with our pretrained model while using around $1.5$ orders of magnitude less number of training samples with respect to the state-of-the-art deep learning for symbolic mathematics. The test accuracy on differential equation tasks is considerably lower comparing with integration as they need higher order recursions that are not present in language translations. We pretrain our model with different pairs of language translations. Our results show language bias in solving symbolic mathematics tasks. Finally, we study the robustness of the fine-tuned model on symbolic math tasks against distribution shift, and our approach generalizes better in distribution shift scenarios for the function integration.

Creating labeled training sets has become one of the major roadblocks in machine learning. To address this, recent Weak Supervision (WS) frameworks synthesize training labels from multiple potentially noisy supervision sources. However, existing frameworks are restricted to supervision sources that share the same output space as the target task. To extend the scope of usable sources, we formulate Weak Indirect Supervision (WIS), a new research problem for automatically synthesizing training labels based on indirect supervision sources that have different output label spaces. To overcome the challenge of mismatched output spaces, we develop a probabilistic modeling approach, PLRM, which uses user-provided label relations to model and leverage indirect supervision sources. Moreover, we provide a theoretically-principled test of the distinguishability of PLRM for unseen labels, along with an generalization bound. On both image and text classification tasks as well as an industrial advertising application, we demonstrate the advantages of PLRM by outperforming baselines by a margin of 2%-9%.

Machine learning models based on the aggregated outputs of submodels, either at the activation or prediction levels, lead to strong performance. We study the interplay of two popular classes of such models: ensembles of neural networks and sparse mixture of experts (sparse MoEs). First, we show that these two approaches have complementary features whose combination is beneficial. Then, we present partitioned batch ensembles, an efficient ensemble of sparse MoEs that takes the best of both classes of models. Extensive experiments on fine-tuned vision transformers demonstrate the accuracy, log-likelihood, few-shot learning, robustness, and uncertainty calibration improvements of our approach over several challenging baselines. Partitioned batch ensembles not only scale to models with up to 2.7B parameters, but also provide larger performance gains for larger models.

Principal component analysis (PCA) has been widely used as an effective technique for feature extraction and dimension reduction. In the High Dimension Low Sample Size (HDLSS) setting, one may prefer modified principal components, with penalized loadings, and automated penalty selection by implementing model selection among these different models with varying penalties. The earlier work [1, 2] has proposed penalized PCA, indicating the feasibility of model selection in $L_2$- penalized PCA through the solution path of Ridge regression, however, it is extremely time-consuming because of the intensive calculation of matrix inverse. In this paper, we propose a fast model selection method for penalized PCA, named Approximated Gradient Flow (AgFlow), which lowers the computation complexity through incorporating the implicit regularization effect introduced by (stochastic) gradient flow [3, 4] and obtains the complete solution path of $L_2$-penalized PCA under varying $L_2$-regularization. We perform extensive experiments on real-world datasets. AgFlow outperforms existing methods (Oja [5], Power [6], and Shamir [7] and the vanilla Ridge estimators) in terms of computation costs.

What is learning? 20$^{st}$ century formalizations of learning theory -- which precipitated revolutions in artificial intelligence -- focus primarily on $\mathit{in-distribution}$ learning, that is, learning under the assumption that the training data are sampled from the same distribution as the evaluation distribution. This assumption renders these theories inadequate for characterizing 21$^{st}$ century real world data problems, which are typically characterized by evaluation distributions that differ from the training data distributions (referred to as out-of-distribution learning). We therefore make a small change to existing formal definitions of learnability by relaxing that assumption. We then introduce $\mathbf{learning\ efficiency}$ (LE) to quantify the amount a learner is able to leverage data for a given problem, regardless of whether it is an in- or out-of-distribution problem. We then define and prove the relationship between generalized notions of learnability, and show how this framework is sufficiently general to characterize transfer, multitask, meta, continual, and lifelong learning. We hope this unification helps bridge the gap between empirical practice and theoretical guidance in real world problems. Finally, because biological learning continues to outperform machine learning algorithms on certain OOD challenges, we discuss the limitations of this framework vis-\'a-vis its ability to formalize biological learning, suggesting multiple avenues for future research.

In high-income Asian nations, such as Japan and Singapore, babies born today can expect to live into their ninth decade or beyond. Advances in medical science and technology promise to lengthen our lifespans even further. In fact, Asia's'silver generation' – the cohort of people aged over 60 – is due to triple between 2010 and 2050, reaching close to 1.3 billion people. But as more of us enter our silver years, many will encounter new challenges. Aging-related chronic diseases, like diabetes, heart disease, and some types of cancer, are impacting lives across Asia and putting enormous pressure on our already under-resourced healthcare sectors.

Alphabet subsidiary Wing has launched a pilot program that will have its drones fly products from the rooftops of shopping centers. In fact, it has already started the program in its biggest market, Logan, Australia. The subsidiary has teamed up with Australian retail property group, Vicinity Centres, to test the new model at Logan's Grand Plaza, where Wing's drones have been flying orders to customers from businesses directly below their launching pad. Wing has been operating in Logan over the past two years, but up until now, businesses have had to co-locate their products at the company's delivery facility. This is the first time the subsidiary is conducting deliveries from participating merchants' existing location instead.

The last words that Liviana Sulzer spoke, 18 months ago, were very much in character: "Now it's time for a song." This was often how she felt, living as she did inside a toddler movie-musical, where even just a spilled cup of milk could get her up onto a chair, twirling with her arms out wide and singing as loud as she could manage: We just spilled our milk … It was messy on the table, and then we cleaned it up … And noooow it's aaaaall cleeeaaaned up! When the song was over, she'd bend toward her brothers, ages 6 and 1, in a deep and gracious bow. It was May 2020--a week before Livie's fourth birthday--and the kids were playing in the yard. Throughout the Sulzers' quiet neighborhood in Austin, Texas, the Persian silk trees had begun to bloom in pink-tipped puffs. There were flowers in their backyard, too. Livie had a favorite one, purple and about as tall as she was. Iris and, trapped at home by the COVID-19 shutdown, she'd made a game of scooting over to it in her push-car and spilling all her problems. But the loneliest phase of the pandemic, with its makeshift games and spotty child care, was nearly over. Things were getting back to normal. A nanny had started just over a week before, and Livie's mother, Lindsay--a bioengineer and expert in regenerative medicine--was headed to the office for her first day back at work, at a local cell-therapy start-up. Livie's father, James, an assistant professor at the University of Texas at Austin who specializes in rehabilitation robotics, was grading papers in the walk-in closet that he'd turned into a home office. He'd asked his graduate students to propose studies or devices that might one day help a patient recover from a nervous-system injury. The sky was clear and calm and sunny. Livie stood near the center of the yard, 30 feet below the overhanging branches of a pecan tree. Her two brothers were nearby.

The Royal Bahamas Police Force (RBPF) could be on the verge of making another leap in the fight against crime in The Bahamas, with high-level meetings taking place this week with potential vendors and stakeholders in public safety artificial intelligence technology. During a welcome and oath-swearing ceremony for nearly 100 new police recruits, Commissioner of Police Paul Rolle told the men and women that his executive team was present with the exceptions of two assistant commissioner's, including Assistant Commissioner Zhavargo Dames, "who's representing me in another meeting trying to get some technology, additional technology for the Royal Bahamas Police Force". When contacted for specifics, Rolle told Eyewitness News: "We are doing some exploration with artificial intelligence." He did not expound on what area the AI technology could be used in or what it could potentially achieve in its use in The Bahamas. The use of AI in law enforcement is not uncommon in other jurisdictions with significant advances in recent years.

Tissue awareness has a great demand to improve surgical accuracy in minimally invasive procedures. In arthroscopy, it is one of the challenging tasks due to surgical sites exhibit limited features and textures. Moreover, arthroscopic surgical video shows high intra-class variations. Arthroscopic videos are recorded with endoscope known as arthroscope which records tissue structures at proximity, therefore, frames contain minimal joint structure. As consequences, fully conventional network-based segmentation model suffers from long- and short- term dependency problems. In this study, we present a densely connected shape aware multi-scale segmentation model which captures multi-scale features and integrates shape features to achieve tissue-tool segmentations. The model has been evaluated with three distinct datasets. Moreover, with the publicly available polyp dataset our proposed model achieved 5.09 % accuracy improvement.