Multivariate time series forecasting (MTSF) endeavors to predict future observations given historical data, playing a crucial role in time series data management systems. With advancements in large language models (LLMs), recent studies employ textual prompt tuning to infuse the knowledge of LLMs into MTSF. However, the deployment of LLMs often suffers from low efficiency during the inference phase. To address this problem, we introduce TimeKD, an efficient MTSF framework that leverages the calibrated language models and privileged knowledge distillation. TimeKD aims to generate high-quality future representations from the proposed cross-modality teacher model and cultivate an effective student model. The cross-modality teacher model adopts calibrated language models (CLMs) with ground truth prompts, motivated by the paradigm of Learning Under Privileged Information (LUPI). In addition, we design a subtractive cross attention (SCA) mechanism to refine these representations. To cultivate an effective student model, we propose an innovative privileged knowledge distillation (PKD) mechanism including correlation and feature distillation. PKD enables the student to replicate the teacher's behavior while minimizing their output discrepancy. Extensive experiments on real data offer insight into the effectiveness, efficiency, and scalability of the proposed TimeKD.

Neurosymbolic approaches integrating large language models with formal reasoning have recently achieved human-level performance on mathematics competition problems in algebra, geometry and number theory. In comparison, combinatorics remains a challenging domain, characterized by a lack of appropriate benchmarks and theorem libraries. To address this gap, we introduce CombiBench, a comprehensive benchmark comprising 100 combinatorial problems, each formalized in Lean~4 and paired with its corresponding informal statement. The problem set covers a wide spectrum of difficulty levels, ranging from middle school to IMO and university level, and span over ten combinatorial topics. CombiBench is suitable for testing IMO solving capabilities since it includes all IMO combinatorial problems since 2000 (except IMO 2004 P3 as its statement contain an images). Furthermore, we provide a comprehensive and standardized evaluation framework, dubbed Fine-Eval (for $\textbf{F}$ill-in-the-blank $\textbf{in}$ L$\textbf{e}$an Evaluation), for formal mathematics. It accommodates not only proof-based problems but also, for the first time, the evaluation of fill-in-the-blank questions. Using Fine-Eval as the evaluation method and Kimina Lean Server as the backend, we benchmark several LLMs on CombiBench and observe that their capabilities for formally solving combinatorial problems remain limited. Among all models tested (none of which has been trained for this particular task), Kimina-Prover attains the best results, solving 7 problems (out of 100) under both ``with solution'' and ``without solution'' scenarios. We open source the benchmark dataset alongside with the code of the proposed evaluation method at https://github.com/MoonshotAI/CombiBench/.

Online Resource Allocation problem is a central problem in many areas of Computer Science, Operations Research, and Economics. In this problem, we sequentially receive $n$ stochastic requests for $m$ kinds of shared resources, where each request can be satisfied in multiple ways, consuming different amounts of resources and generating different values. The goal is to achieve a $(1-ε)$-approximation to the hindsight optimum, where $ε>0$ is a small constant, assuming each resource has a large budget. In this paper, we investigate the learnability and robustness of online resource allocation. Our primary contribution is a novel Exponential Pricing algorithm with the following properties: 1. It requires only a \emph{single sample} from each of the $n$ request distributions to achieve a $(1-ε)$-approximation for online resource allocation with large budgets. Such an algorithm was previously unknown, even with access to polynomially many samples, as prior work either assumed full distributional knowledge or was limited to i.i.d.\,or random-order arrivals. 2. It is robust to corruptions in the outliers model and the value augmentation model. Specifically, it maintains its $(1 - ε)$-approximation guarantee under both these robustness models, resolving the open question posed in Argue, Gupta, Molinaro, and Singla (SODA'22). 3. It operates as a simple item-pricing algorithm that ensures incentive compatibility. The intuition behind our Exponential Pricing algorithm is that the price of a resource should adjust exponentially as it is overused or underused. It differs from conventional approaches that use an online learning algorithm for item pricing. This departure guarantees that the algorithm will never run out of any resource, but loses the usual no-regret properties of online learning algorithms, necessitating a new analytical approach.

Ensuring the safe and efficient operation of CAVs relies heavily on the software framework used. A software framework needs to ensure real-time properties, reliable communication, and efficient resource utilization. Furthermore, a software framework needs to enable seamless transition between testing stages, from simulation to small-scale to full-scale experiments. In this paper, we survey prominent software frameworks used for in-vehicle and inter-vehicle communication in CAVs. We analyze these frameworks regarding opportunities and challenges, such as their real-time properties and transitioning capabilities. Additionally, we delve into the tooling requirements necessary for addressing the associated challenges. We illustrate the practical implications of these challenges through case studies focusing on critical areas such as perception, motion planning, and control. Furthermore, we identify research gaps in the field, highlighting areas where further investigation is needed to advance the development and deployment of safe and efficient CAV systems.

Human education transcends mere knowledge transfer, it relies on co-adaptation dynamics -- the mutual adjustment of teaching and learning strategies between agents. Despite its centrality, computational models of co-adaptive teacher-student interactions (T-SI) remain underdeveloped. We argue that this gap impedes Educational Science in testing and scaling contextual insights across diverse settings, and limits the potential of Machine Learning systems, which struggle to emulate and adaptively support human learning processes. To address this, we present a computational T-SI model that integrates contextual insights on human education into a testable framework. We use the model to evaluate diverse T-SI strategies in a realistic synthetic classroom setting, simulating student groups with unequal access to sensory information. Results show that strategies incorporating co-adaptation principles (e.g., bidirectional agency) outperform unilateral approaches (i.e., where only the teacher or the student is active), improving the learning outcomes for all learning types. Beyond the testing and scaling of context-dependent educational insights, our model enables hypothesis generation in controlled yet adaptable environments. This work bridges non-computational theories of human education with scalable, inclusive AI in Education systems, providing a foundation for equitable technologies that dynamically adapt to learner needs.

This study proposes a novel artificial protozoa optimizer (APO) that is inspired by protozoa in nature. The APO mimics the survival mechanisms of protozoa by simulating their foraging, dormancy, and reproductive behaviors. The APO was mathematically modeled and implemented to perform the optimization processes of metaheuristic algorithms. The performance of the APO was verified via experimental simulations and compared with 32 state-of-the-art algorithms. Wilcoxon signed-rank test was performed for pairwise comparisons of the proposed APO with the state-of-the-art algorithms, and Friedman test was used for multiple comparisons. First, the APO was tested using 12 functions of the 2022 IEEE Congress on Evolutionary Computation benchmark. Considering practicality, the proposed APO was used to solve five popular engineering design problems in a continuous space with constraints. Moreover, the APO was applied to solve a multilevel image segmentation task in a discrete space with constraints. The experiments confirmed that the APO could provide highly competitive results for optimization problems. The source codes of Artificial Protozoa Optimizer are publicly available at https://seyedalimirjalili.com/projects and https://ww2.mathworks.cn/matlabcentral/fileexchange/162656-artificial-protozoa-optimizer.

We rigorously analyse fully-trained neural networks of arbitrary depth in the Bayesian optimal setting in the so-called proportional scaling regime where the number of training samples and width of the input and all inner layers diverge proportionally. We prove an information-theoretic equivalence between the Bayesian deep neural network model trained from data generated by a teacher with matching architecture, and a simpler model of optimal inference in a generalized linear model. This equivalence enables us to compute the optimal generalization error for deep neural networks in this regime. We thus prove the "deep Gaussian equivalence principle" conjectured in Cui et al. (2023) (arXiv:2302.00375). Our result highlights that in order to escape this "trivialisation" of deep neural networks (in the sense of reduction to a linear model) happening in the strongly overparametrized proportional regime, models trained from much more data have to be considered.

Diffusion models is a popular computational tool to generate new data samples. It utilizes a forward diffusion process that add noise to the data distribution and then use a reverse process to remove noises to produce samples from the data distribution. However, when the empirical data distribution consists of $n$ data point, using the empirical diffusion model will necessarily produce one of the existing data points. This is often referred to as the memorization effect, which is usually resolved by sophisticated machine learning procedures in the current literature. This work shows that the memorization problem can be resolved by a simple inertia update step at the end of the empirical diffusion model simulation. Our inertial diffusion model requires only the empirical diffusion model score function and it does not require any further training. We show that choosing the inertia diffusion model sample distribution is an $O\left(n^{-\frac{2}{d+4}}\right)$ Wasserstein-1 approximation of a data distribution lying on a $C^2$ manifold of dimension $d$. Since this estimate is significant smaller the Wasserstein1 distance between population and empirical distributions, it rigorously shows the inertial diffusion model produces new data samples. Remarkably, this upper bound is completely free of the ambient space dimension, since there is no training involved. Our analysis utilizes the fact that the inertial diffusion model samples are approximately distributed as the Gaussian kernel density estimator on the manifold. This reveals an interesting connection between diffusion model and manifold learning.

Free play is a fundamental aspect of early childhood education, supporting children's cognitive, social, emotional, and motor development. However, assessing children's development during free play poses significant challenges due to the unstructured and spontaneous nature of the activity. Traditional assessment methods often rely on direct observations by teachers, parents, or researchers, which may fail to capture comprehensive insights from free play and provide timely feedback to educators. This study proposes an innovative approach combining Large Language Models (LLMs) with learning analytics to analyze children's self-narratives of their play experiences. The LLM identifies developmental abilities, while performance scores across different play settings are calculated using learning analytics techniques. We collected 2,224 play narratives from 29 children in a kindergarten, covering four distinct play areas over one semester. According to the evaluation results from eight professionals, the LLM-based approach achieved high accuracy in identifying cognitive, motor, and social abilities, with accuracy exceeding 90% in most domains. Moreover, significant differences in developmental outcomes were observed across play settings, highlighting each area's unique contributions to specific abilities. These findings confirm that the proposed approach is effective in identifying children's development across various free play settings. This study demonstrates the potential of integrating LLMs and learning analytics to provide child-centered insights into developmental trajectories, offering educators valuable data to support personalized learning and enhance early childhood education practices.

This paper presents a survey of Abstract Meaning Representation (AMR), a semantic representation framework that captures the meaning of sentences through a graph-based structure. AMR represents sentences as rooted, directed acyclic graphs, where nodes correspond to concepts and edges denote relationships, effectively encoding the meaning of complex sentences. This survey investigates AMR and its extensions, focusing on AMR capabilities. It then explores the parsing (text-to-AMR) and generation (AMR-to-text) tasks by showing traditional, current, and possible futures approaches. It also reviews various applications of AMR including text generation, text classification, and information extraction and information seeking. By analyzing recent developments and challenges in the field, this survey provides insights into future directions for research and the potential impact of AMR on enhancing machine understanding of human language.