Offline data selection and online self-refining generation, which enhance the data quality, are crucial steps in adapting large language models (LLMs) to specific downstream tasks. We tackle offline data selection and online self-refining generations through an optimization perspective. Specifically, bilevel data selection is used for offline data selection with respect to the validation dataset, and we treat online self-refining generation as a model adaptation step of selecting the model trained on current responses that best fits the validation data. Our framework offers a unified understanding of offline data selection and self-refining generation by assigning a learned data weight to each question and response, either explicitly or implicitly. For the first time, we theoretically demonstrate the effectiveness of the bilevel data selection framework and demonstrate its performance gains over unfiltered direct mixing baselines. By combining offline data with validation-weighted online generations, our method enhances fine-tuning performance. Experiments on quality enhancement and safety-aware LLM fine-tuning validate its effectiveness.

In professional basketball, the accurate prediction of scoring opportunities based on strategic decision-making is crucial for space and player evaluations. However, traditional models often face challenges in accounting for the complexities of off-ball movements, which are essential for accurate predictive performance. In this study, we propose two mathematical models to predict off-ball scoring opportunities in basketball, considering both pass-to-score and dribble-to-score movements: the Ball Movement for Off-ball Scoring (BMOS) and the Ball Intercept and Movement for Off-ball Scoring (BIMOS) models. The BMOS adapts principles from the Off-Ball Scoring Opportunities (OBSO) model, originally designed for soccer, to basketball, whereas the BIMOS also incorporates the likelihood of interception during ball movements. We evaluated these models using player tracking data from 630 NBA games in the 2015-2016 regular season, demonstrating that the BIMOS outperforms the BMOS in terms of scoring prediction accuracy. Thus, our models provide valuable insights for tactical analysis and player evaluation in basketball.

This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional data science. Modern techniques in algebraic geometry, approximation theory, computational harmonic analysis and extensions develop the first of its kind, a unified framework which allows for a simultaneous study of labeled and unlabeled near alignment data problems in of $\mathbb R^D$ with the near isometry extension problem for discrete and non-discrete subsets of $\mathbb R^D$ with certain geometries. In addition, the paper surveys related work on clustering, dimension reduction, manifold learning, vision as well as minimal energy partitions, discrepancy and min-max optimization. Numerous open problems are given.

Nature is an inhabitant for enormous number of species. All the species do perform complex activities with simple and elegant rules for their survival. The property of emergence of collective behavior is remarkably supporting their activities. One form of the collective behaviour is the swarm intelligence -- all agents poses same rules and capabilities. This equality along with local cooperation in the agents tremendously leads to achieving global results. Some of the swarm behaviours in the nature includes birds formations , fish school maneuverings, ants movement. Recently, one school of research has studied these behaviours and proposed artificial paradigms such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Glowworm Swarm Optimization (GSO) etc. Another school of research used these models and designed robotic platforms to detect (locate) multiple signal sources such as light, fire, plume, odour etc. Kinbots platform is one such recent experiment. In the same line of thought, this extended abstract presents the recently proposed butterfly inspired metaphor and corresponding simulations, ongoing experiments with outcomes.

TORONTO, ONTARIO, CANADA - 2015/03/29: The Bank of Montreal, or BMO Financial Group, is one of the ... [ ] Big Five banks in Canada. BMO Financial Group, the over 200 year old banking group also known as Bank of Montreal, is the 8th largest bank, by assets, in North America and one of the'Big Five' Canadian banks. After exploring intelligent automation for several years now, BMO is accelerating its robotic process automation (RPA) strategy. It is building on the strong foundation of RPA, machine learning, and AI to enable a future of digital and human workforce collaboration. These capabilities been evolving rapidly since 2017, when Randy Bean and I first wrote about BMO's work in the automation space.

Many firms today are introducing cognitive technologies to their organizations somewhat slowly. It's not that they don't believe the technologies are important, but rather that they have other, more pressing priorities, or that they need to prepare their environments for effective AI implementation. The Bank of Montreal is one organization that is moving steadily toward this objective. BMO Financial Group, widely known as BMO, is based in Toronto and is one of the "big five" Canadian banks, as well as one of the ten largest in North America. It has a sizable presence in the U.S., having acquired Harris Bank, Marshall & Ilsley, and the transportation finance operations of GE Capital.