It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence the complexity of the dataset at hand. A great variety of dimension estimators have been developed to find the intrinsic dimension of the data but there is little guidance on how to reliably use these estimators. This survey reviews a wide range of dimension estimation methods, categorising them by the geometric information they exploit: tangential estimators which detect a local affine structure; parametric estimators which rely on dimension-dependent probability distributions; and estimators which use topological or metric invariants. The paper evaluates the performance of these methods, as well as investigating varying responses to curvature and noise. Key issues addressed include robustness to hyperparameter selection, sample size requirements, accuracy in high dimensions, precision, and performance on non-linear geometries. In identifying the best hyperparameters for benchmark datasets, overfitting is frequent, indicating that many estimators may not generalise well beyond the datasets on which they have been tested.

Academic programs are increasingly recognizing the importance of personal and professional skills and their critical role alongside technical expertise in preparing students for future success in diverse career paths. With this growing demand comes the need for scalable systems to measure, evaluate, and develop these skills. Situational Judgment Tests (SJTs) offer one potential avenue for measuring these skills in a standardized and reliable way, but open-response SJTs have traditionally relied on trained human raters for evaluation, presenting operational challenges to delivering SJTs at scale. Past attempts at developing NLP-based scoring systems for SJTs have fallen short due to issues with construct validity of these systems. In this article, we explore a novel approach to extracting construct-relevant features from SJT responses using large language models (LLMs). We use the Casper SJT to demonstrate the efficacy of this approach. This study sets the foundation for future developments in automated scoring for personal and professional skills.

Effective storytelling relies on a delicate balance between meeting the reader's prior expectations and introducing unexpected developments. In the domain of detective fiction, this tension is known as fair play, which includes the implicit agreement between the writer and the reader as to the range of possible resolutions the mystery story may have. In this work, we present a probabilistic framework for detective fiction that allows us to define desired qualities. Using this framework, we formally define fair play and design appropriate metrics for it. Stemming from these definitions is an inherent tension between the coherence of the story, which measures how much it ``makes sense'', and the surprise it induces. We validate the framework by applying it to LLM-generated detective stories. This domain is appealing since we have an abundance of data, we can sample from the distribution generating the story, and the story-writing capabilities of LLMs are interesting in their own right. Results show that while LLM-generated stories may be unpredictable, they generally fail to balance the trade-off between surprise and fair play, which greatly contributes to their poor quality.

Large Language Models (LLMs) have demonstrated considerable potential in improving coding education by providing support for code writing, explanation, and debugging. However, existing LLM-based approaches generally fail to assess students' abilities, design learning plans, provide personalized material aligned with individual learning goals, and enable interactive learning. Current work mostly uses single LLM agents, which limits their ability to understand complex code repositories and schedule step-by-step tutoring. Recent research has shown that multi-agent LLMs can collaborate to solve complicated problems in various domains like software engineering, but their potential in the field of education remains unexplored. In this work, we introduce CodeEdu, an innovative multi-agent collaborative platform that combines LLMs with tool use to provide proactive and personalized education in coding. Unlike static pipelines, CodeEdu dynamically allocates agents and tasks to meet student needs. Various agents in CodeEdu undertake certain functions specifically, including task planning, personalized material generation, real-time QA, step-by-step tutoring, code execution, debugging, and learning report generation, facilitated with extensive external tools to improve task efficiency. Automated evaluations reveal that CodeEdu substantially enhances students' coding performance.

Large language models (LLMs) have demonstrated state-of-the-art performance across a wide range of natural language processing tasks. However, high-performing models are typically accessible only via APIs, incurring substantial inference costs. Cascade methods address this by initially employing a cheaper model and escalating to a stronger one only when necessary. Nevertheless, existing cascade approaches struggle to select a reliable representative response and assess the overall reliability of free-form outputs, as they rely on exact text matching. To overcome these limitations, we propose Keyword-inspired Cascade (KiC), a novel framework for cost-efficient free-form text generation. KiC identifies the most representative answer among multiple outputs from a weaker model and evaluates the semantic alignment of other responses with it. Based on the degree of alignment, KiC determines whether to accept the weaker model's output or escalate to a stronger model. Experiments on three free-form text generation benchmarks show that KiC achieves 97.53 percent of GPT-4's accuracy while reducing API costs by 28.81 percent on average, and even outperforms GPT-4 in a specific benchmark.

This paper presents a scalable and adaptive control framework for legged robots that integrates Iterative Learning Control (ILC) with a biologically inspired torque library (TL), analogous to muscle memory. The proposed method addresses key challenges in robotic locomotion, including accurate trajectory tracking under unmodeled dynamics and external disturbances. By leveraging the repetitive nature of periodic gaits and extending ILC to nonperiodic tasks, the framework enhances accuracy and generalization across diverse locomotion scenarios. The control architecture is data-enabled, combining a physics-based model derived from hybrid-system trajectory optimization with real-time learning to compensate for model uncertainties and external disturbances. A central contribution is the development of a generalized TL that stores learned control profiles and enables rapid adaptation to changes in speed, terrain, and gravitational conditions-eliminating the need for repeated learning and significantly reducing online computation. The approach is validated on the bipedal robot Cassie and the quadrupedal robot A1 through extensive simulations and hardware experiments. Results demonstrate that the proposed framework reduces joint tracking errors by up to 85% within a few seconds and enables reliable execution of both periodic and nonperiodic gaits, including slope traversal and terrain adaptation. Compared to state-of-the-art whole-body controllers, the learned skills eliminate the need for online computation during execution and achieve control update rates exceeding 30x those of existing methods. These findings highlight the effectiveness of integrating ILC with torque memory as a highly data-efficient and practical solution for legged locomotion in unstructured and dynamic environments.

Model tracing and constraint-based modeling are two approaches to diagnose student input in stepwise tasks. Model tracing supports identifying consecutive problem-solving steps taken by a student, whereas constraint-based modeling supports student input diagnosis even when several steps are combined into one step. We propose an approach that merges both paradigms. By defining constraints as properties that a student input has in common with a step of a strategy, it is possible to provide a diagnosis when a student deviates from a strategy even when the student combines several steps. In this study we explore the design of a system for multistep strategy diagnoses, and evaluate these diagnoses. As a proof of concept, we generate diagnoses for an existing dataset containing steps students take when solving quadratic equations (n=2136). To compare with human diagnoses, two teachers coded a random sample of deviations (n=70) and applications of the strategy (n=70). Results show that that the system diagnosis aligned with the teacher coding in all of the 140 student steps.

Many intelligent tutoring systems can support a student in solving a stepwise task. When a student combines several steps in one step, the number of possible paths connecting consecutive inputs may be very large. This combinatorial explosion makes error diagnosis hard. Using a final answer to diagnose a combination of steps can mitigate the combinatorial explosion, because there are generally fewer possible (erroneous) final answers than (erroneous) solution paths. An intermediate input for a task can be diagnosed by automatically completing it according to the task solution strategy and diagnosing this solution. This study explores the potential of automated error diagnosis based on a final answer. We investigate the design of a service that provides a buggy rule diagnosis when a student combines several steps. To validate the approach, we apply the service to an existing dataset (n=1939) of unique student steps when solving quadratic equations, which could not be diagnosed by a buggy rule service that tries to connect consecutive inputs with a single rule. Results show that final answer evaluation can diagnose 29,4% of these steps. Moreover, a comparison of the generated diagnoses with teacher diagnoses on a subset (n=115) shows that the diagnoses align in 97% of the cases. These results can be considered a basis for further exploration of the approach.

The integration of agential artificial intelligence into socioeconomic systems requires us to reexamine the evolutionary processes that describe changes in our economic institutions. This article synthesizes three frameworks: multi-level selection theory, Aoki's view of firms as computational processes, and Ostrom's design principles for robust institutions. We develop a framework where selection operates concurrently across organizational levels, firms implement distributed inference via game-theoretic architectures, and Ostrom-style rules evolve as alignment mechanisms that address AI-related risks. This synthesis yields a multi-level Price equation expressed over nested games, providing quantitative metrics for how selection and governance co-determine economic outcomes. We examine connections to Acemoglu's work on inclusive institutions, analyze how institutional structures shape AI deployment, and demonstrate the framework's explanatory power via case studies. We conclude by proposing a set of design principles that operationalize alignment between humans and AI across institutional layers, enabling scalable, adaptive, and inclusive governance of agential AI systems. We conclude with practical policy recommendations and further research to extend these principles into real-world implementation.

The advent of neural machine translation (NMT) has revolutionized cross-lingual communication, yet preserving stylistic nuances remains a significant challenge. While existing approaches often require parallel corpora for style preservation, we introduce Babel, a novel framework that enhances stylistic fidelity in NMT using only monolingual corpora. Babel employs two key components: (1) a style detector based on contextual embeddings that identifies stylistic disparities between source and target texts, and (2) a diffusion-based style applicator that rectifies stylistic inconsistencies while maintaining semantic integrity. Our framework integrates with existing NMT systems as a post-processing module, enabling style-aware translation without requiring architectural modifications or parallel stylistic data. Extensive experiments on five diverse domains (law, literature, scientific writing, medicine, and educational content) demonstrate Babel's effectiveness: it identifies stylistic inconsistencies with 88.21% precision and improves stylistic preservation by 150% while maintaining a high semantic similarity score of 0.92. Human evaluation confirms that translations refined by Babel better preserve source text style while maintaining fluency and adequacy.