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.

A deployed question answering (QA) model can easily fail when the test data has a distribution shift compared to the training data. Robustness tuning (RT) methods have been widely studied to enhance model robustness against distribution shifts before model deployment. However, can we improve a model after deployment? To answer this question, we evaluate test-time adaptation (TTA) to improve a model after deployment. We first introduce COLDQA, a unified evaluation benchmark for robust QA against text corruption and changes in language and domain. We then evaluate previous TTA methods on COLDQA and compare them to RT methods. We also propose a novel TTA method called online imitation learning (OIL). Through extensive experiments, we find that TTA is comparable to RT methods, and applying TTA after RT can significantly boost the performance on COLDQA. Our proposed OIL improves TTA to be more robust to variation in hyper-parameters and test distributions over time.

One of the gnarliest challenges in reinforcement learning (RL) is exploration that scales to vast domains, where novelty-, or coverage-seeking behaviour falls short. Goal-directed, purposeful behaviours are able to overcome this, but rely on a good goal space. The core challenge in goal discovery is finding the right balance between generality (not hand-crafted) and tractability (useful, not too many). Our approach explicitly seeks the middle ground, enabling the human designer to specify a vast but meaningful proto-goal space, and an autonomous discovery process to refine this to a narrower space of controllable, reachable, novel, and relevant goals. The effectiveness of goal-conditioned exploration with the latter is then demonstrated in three challenging environments.

Training a team to complete a complex task via multi-agent reinforcement learning can be difficult due to challenges such as policy search in a large policy space, and non-stationarity caused by mutually adapting agents. To facilitate efficient learning of complex multi-agent tasks, we propose an approach which uses an expert-provided curriculum of simpler multi-agent sub-tasks. In each sub-task of the curriculum, a subset of the entire team is trained to acquire sub-task-specific policies. The sub-teams are then merged and transferred to the target task, where their policies are collectively fined tuned to solve the more complex target task. We present MEDoE, a flexible method which identifies situations in the target task where each agent can use its sub-task-specific skills, and uses this information to modulate hyperparameters for learning and exploration during the fine-tuning process. We compare MEDoE to multi-agent reinforcement learning baselines that train from scratch in the full task, and with na\"ive applications of standard multi-agent reinforcement learning techniques for fine-tuning. We show that MEDoE outperforms baselines which train from scratch or use na\"ive fine-tuning approaches, requiring significantly fewer total training timesteps to solve a range of complex teamwork tasks.

Online platforms often incentivize consumers to improve user engagement and platform revenue. Since different consumers might respond differently to incentives, individual-level budget allocation is an essential task in marketing campaigns. Recent advances in this field often address the budget allocation problem using a two-stage paradigm: the first stage estimates the individual-level treatment effects using causal inference algorithms, and the second stage invokes integer programming techniques to find the optimal budget allocation solution. Since the objectives of these two stages might not be perfectly aligned, such a two-stage paradigm could hurt the overall marketing effectiveness. In this paper, we propose a novel end-to-end framework to directly optimize the business goal under budget constraints. Our core idea is to construct a regularizer to represent the marketing goal and optimize it efficiently using gradient estimation techniques. As such, the obtained models can learn to maximize the marketing goal directly and precisely. We extensively evaluate our proposed method in both offline and online experiments, and experimental results demonstrate that our method outperforms current state-of-the-art methods. Our proposed method is currently deployed to allocate marketing budgets for hundreds of millions of users on a short video platform and achieves significant business goal improvements. Our code will be publicly available.

We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius norm of the Hessian matrix. This leads to a natural definition of smoothing splines on manifolds, which minimizes square error while optimizing a global curvature penalty. The existence and uniqueness of the solution is shown by applying the theory of reproducing kernel Hilbert spaces. The minimizer is expressed as a combination of Green's functions for the biharmonic operator, and 'linear' functions of everywhere vanishing Hessian. Furthermore, we utilize the Hessian estimation procedure from the Hessian Eigenmaps algorithm to approximate the spline loss when the true manifold is unknown. This yields a particularly simple quadratic optimization algorithm for smoothing response values without needing to fit the underlying manifold. Analysis of asymptotic error and robustness are given, as well as discussion of out-of-sample prediction methods and applications.

Specialised pre-trained language models are becoming more frequent in NLP since they can potentially outperform models trained on generic texts. BioBERT (Sanh et al., 2019) and BioClinicalBERT (Alsentzer et al., 2019) are two examples of such models that have shown promise in medical NLP tasks. Many of these models are overparametrised and resource-intensive, but thanks to techniques like Knowledge Distillation (KD), it is possible to create smaller versions that perform almost as well as their larger counterparts. In this work, we specifically focus on development of compact language models for processing clinical texts (i.e. We developed a number of efficient lightweight clinical transformers using knowledge distillation and continual learning, with the number of parameters ranging from 15 million to 65 million. These models performed comparably to larger models such as BioBERT and ClinicalBioBERT and significantly outperformed other compact models trained on general or biomedical data. Our extensive evaluation was done across several standard datasets and covered a wide range of clinical text-mining tasks, including Natural Language Inference, Relation Extraction, Named Entity Recognition, and Sequence Classification. To our knowledge, this is the first comprehensive study specifically focused on creating efficient and compact transformers for clinical NLP tasks. The models and code used in this study can be found on our Huggingface profile at https: //huggingface.co/nlpie and Github page at https://github.com/ Large language models pre-trained on generic texts serve as the foundation upon which most stateof-the-art NLP models are built. There is ample evidence that, for certain domains and downstream tasks, models that are pre-trained on specialised data outperform baselines that have only relied on generic texts (Sanh et al., 2019; Alsentzer et al., 2019; Beltagy et al., 2019; Nguyen et al., 2020; Chalkidis et al., 2020).

Sequence generation demonstrates promising performance in recent information extraction efforts, by incorporating large-scale pre-trained Seq2Seq models. This paper investigates the merits of employing sequence generation in relation extraction, finding that with relation names or synonyms as generation targets, their textual semantics and the correlation (in terms of word sequence pattern) among them affect model performance. We then propose Relation Extraction with Label Augmentation (RELA), a Seq2Seq model with automatic label augmentation for RE. By saying label augmentation, we mean prod semantically synonyms for each relation name as the generation target. Besides, we present an in-depth analysis of the Seq2Seq model's behavior when dealing with RE. Experimental results show that RELA achieves competitive results compared with previous methods on four RE datasets.

High-quality education is one of the keys to achieving a more sustainable world. In contrast to traditional face-to-face classroom education, online education enables us to record and research a large amount of learning data for offering intelligent educational services. Knowledge Tracing (KT), which aims to monitor students' evolving knowledge state in learning, is the fundamental task to support these intelligent services. In recent years, an increasing amount of research is focused on this emerging field and considerable progress has been made. In this survey, we categorize existing KT models from a technical perspective and investigate these models in a systematic manner. Subsequently, we review abundant variants of KT models that consider more strict learning assumptions from three phases: before, during, and after learning. To better facilitate researchers and practitioners working on this field, we open source two algorithm libraries: EduData for downloading and preprocessing KT-related datasets, and EduKTM with extensible and unified implementation of existing mainstream KT models. Moreover, the development of KT cannot be separated from its applications, therefore we further present typical KT applications in different scenarios. Finally, we discuss some potential directions for future research in this fast-growing field.

We revisit the classic problem of optimal subset selection in the online learning set-up. Assume that the set $[N]$ consists of $N$ distinct elements. On the $t$th round, an adversary chooses a monotone reward function $f_t: 2^{[N]} \to \mathbb{R}_+$ that assigns a non-negative reward to each subset of $[N].$ An online policy selects (perhaps randomly) a subset $S_t \subseteq [N]$ consisting of $k$ elements before the reward function $f_t$ for the $t$th round is revealed to the learner. As a consequence of its choice, the policy receives a reward of $f_t(S_t)$ on the $t$th round. Our goal is to design an online sequential subset selection policy to maximize the expected cumulative reward accumulated over a time horizon. In this connection, we propose an online learning policy called SCore (Subset Selection with Core) that solves the problem for a large class of reward functions. The proposed SCore policy is based on a new polyhedral characterization of the reward functions called $\alpha$-Core - a generalization of Core from the cooperative game theory literature. We establish a learning guarantee for the SCore policy in terms of a new performance metric called $\alpha$-augmented regret. In this new metric, the performance of the online policy is compared with an unrestricted offline benchmark that can select all $N$ elements at every round. We show that a large class of reward functions, including submodular, can be efficiently optimized with the SCore policy. We also extend the proposed policy to the optimistic learning set-up where the learner has access to additional untrusted hints regarding the reward functions. Finally, we conclude the paper with a list of open problems.