Abstract--T ask-oriented knowledge graphs (KGs) enable AIpowered learning assistant systems to automatically generate high-quality multiple-choice questions (MCQs). Y et converting unstructured educational materials, such as lecture notes and slides, into KGs that capture key pedagogical content remains difficult. We propose a framework for knowledge graph construction and refinement grounded in rate-distortion (RD) theory and optimal transport geometry. In the framework, lecture content is modeled as a metric-measure space, capturing semantic and relational structure, while candidate KGs are aligned using Fused Gromov-Wasserstein (FGW) couplings to quantify semantic distortion. The rate term, expressed via the size of KG, reflects complexity and compactness. Refinement operators (add, merge, split, remove, rewire) minimize the rate-distortion Lagrangian, yielding compact, information-preserving KGs. Our prototype applied to data science lectures yields interpretable RD curves and shows that MCQs generated from refined KGs consistently surpass those from raw notes on fifteen quality criteria. This study establishes a principled foundation for information-theoretic KG optimization in personalized and AI-assisted education. An AI-powered learning assistant (AILA) system [1] can automatically generate educational questions such as multiple choice questions (MCQs) from teaching materials including lecture notes and slides [2], [3]. Recent research demonstrates that integrating knowledge graphs (KGs) with large language models (LLMs) significantly improves the factual accuracy, explainability, and reasoning capabilities of LLM-powered answers [4], [5].

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing kernel Hilbert spaces (RKHS), and Hilbert-Schmidt operators, emphasizing their role in statistical estimation and representation of probability measures. Classical concepts such as covariance, regression, and information measures are revisited through the lens of Hilbert space geometry. We also introduce kernel density estimation, kernel embeddings of distributions, and the Maximum Mean Discrepancy (MMD). The exposition is designed to serve as a foundation for more advanced topics, including Gaussian processes, kernel Bayesian inference, and functional analytic approaches to modern machine learning.

Large Language Models (LLMs) are increasingly integrated into educational applications. However, they remain vulnerable to jailbreak and fine-tuning attacks, which can compromise safety alignment and lead to harmful outputs. Existing studies mainly focus on general safety evaluations, with limited attention to the unique safety requirements of educational scenarios. To address this gap, we construct EduHarm, a benchmark containing safe-unsafe instruction pairs across five representative educational scenarios, enabling systematic safety evaluation of educational LLMs. Furthermore, we propose a three-stage shield framework (TSSF) for educational LLMs that simultaneously mitigates both jailbreak and fine-tuning attacks. First, safety-aware attention realignment redirects attention toward critical unsafe tokens, thereby restoring the harmfulness feature that discriminates between unsafe and safe inputs. Second, layer-wise safety judgment identifies harmfulness features by aggregating safety cues across multiple layers to detect unsafe instructions. Finally, defense-driven dual routing separates safe and unsafe queries, ensuring normal processing for benign inputs and guarded responses for harmful ones. Extensive experiments across eight jailbreak attack strategies demonstrate that TSSF effectively strengthens safety while preventing over-refusal of benign queries. Evaluations on three fine-tuning attack datasets further show that it consistently achieves robust defense against harmful queries while maintaining preserving utility gains from benign fine-tuning.

Adaptive learning often diagnoses precisely yet intervenes weakly, yielding help that is mistimed or misaligned. This study presents evidence supporting an instructor-governed feedback loop that converts concept-level assessment evidence into vetted micro-interventions. The adaptive learning algorithm contains three safeguards: adequacy as a hard guarantee of gap closure, attention as a budgeted constraint for time and redundancy, and diversity as protection against overfitting to a single resource. We formalize intervention assignment as a binary integer program with constraints for coverage, time, difficulty windows informed by ability estimates, prerequisites encoded by a concept matrix, and anti-redundancy enforced through diversity. Greedy selection serves low-richness and tight-latency regimes, gradient-based relaxation serves rich repositories, and a hybrid method transitions along a richness-latency frontier. In simulation and in an introductory physics deployment with one thousand two hundred four students, both solvers achieved full skill coverage for essentially all learners within bounded watch time. The gradient-based method reduced redundant coverage by approximately twelve percentage points relative to greedy and harmonized difficulty across slates, while greedy delivered comparable adequacy with lower computational cost in scarce settings. Slack variables localized missing content and supported targeted curation, sustaining sufficiency across subgroups. The result is a tractable and auditable controller that closes the diagnostic-pedagogical loop and delivers equitable, load-aware personalization at classroom scale.

Real-time voice interfaces using multimodal Generative AI (GenAI) can potentially address the accessibility needs of novice programmers with disabilities (e.g., related to vision). Yet, little is known about how novices interact with GenAI tools and their feedback quality in the form of audio output. This paper analyzes audio dialogues from nine 9th-grade students using a voice-enabled tutor (powered by OpenAI's Realtime API) in an authentic classroom setting while learning Python. We examined the students' voice prompts and AI's responses (1210 messages) by using qualitative coding. We also gathered students' perceptions via the Partner Modeling Questionnaire. The GenAI Voice Tutor primarily offered feedback on mistakes and next steps, but its correctness was limited (71.4% correct out of 416 feedback outputs). Quality issues were observed, particularly when the AI attempted to utter programming code elements. Students used the GenAI voice tutor primarily for debugging. They perceived it as competent, only somewhat human-like, and flexible. The present study is the first to explore the interaction dynamics of real-time voice GenAI tutors and novice programmers, informing future educational tool design and potentially addressing accessibility needs of diverse learners.

As AI systems become more capable, deceptive behaviors can undermine evaluation and mislead users at deployment. Recent work has shown that lie detectors can accurately classify deceptive behavior, but they are not typically used in the training pipeline due to concerns around contamination and objective hacking. We examine these concerns by incorporating a lie detector into the labelling step of LLM post-training and evaluating whether the learned policy is genuinely more honest, or instead learns to fool the lie detector while remaining deceptive. Using DolusChat, a novel 65k-example dataset with paired truthful/deceptive responses, we identify three key factors that determine the honesty of learned policies: amount of exploration during preference learning, lie detector accuracy, and KL regularization strength. We find that preference learning with lie detectors and GRPO can lead to policies which evade lie detectors, with deception rates of over 85\%. However, if the lie detector true positive rate (TPR) or KL regularization is sufficiently high, GRPO learns honest policies. In contrast, off-policy algorithms (DPO) consistently lead to deception rates under 25\% for realistic TPRs. Our results illustrate a more complex picture than previously assumed: depending on the context, lie-detector-enhanced training can be a powerful tool for scalable oversight, or a counterproductive method encouraging undetectable misalignment.

Data Driven Classroom Interviews (DDCIs) are an interviewing technique that is facilitated by recent technological developments in the learning analytics community. DDCIs are short, targeted interviews that allow researchers to contextualize students' interactions with a digital learning environment (e.g., intelligent tutoring systems or educational games) while minimizing the amount of time that the researcher interrupts that learning experience, and focusing researcher time on the events they most want to focus on DDCIs are facilitated by a research tool called the Quick Red Fox (QRF)--an open-source server-client Android app that optimizes researcher time by directing interviewers to users that have just displayed an interesting behavior (previously defined by the research team). QRF integrates with existing student modeling technologies (e.g., behavior-sensing, affect-sensing, detection of self-regulated learning) to alert researchers to key moments in a learner's experience. This manual documents the tech while providing training on the processes involved in developing triggers and interview techniques; it also suggests methods of analyses.

Adaptive exercise recommendation (ER) aims to choose the next activity that matches a learner's evolving Zone of Proximal Development (ZPD). We present KUL-Rec, a biologically inspired ER system that couples a fast Hebbian memory with slow replay-based consolidation to enable continual, few-shot personalization from sparse interactions. The model operates in an embedding space, allowing a single architecture to handle both tabular knowledge-tracing logs and open-ended short-answer text. We align evaluation with tutoring needs using bidirectional ranking and rank-sensitive metrics (nDCG, Recall@K). Across ten public datasets, KUL-Rec improves macro nDCG (0.316 vs. 0.265 for the strongest baseline) and Recall@10 (0.305 vs. 0.211), while achieving low inference latency and an $\approx99$\% reduction in peak GPU memory relative to a competitive graph-based model. In a 13-week graduate course, KUL-Rec personalized weekly short-answer quizzes generated by a retrieval-augmented pipeline and the personalized quizzes were associated with lower perceived difficulty and higher helpfulness (p < .05). An embedding robustness audit highlights that encoder choice affects semantic alignment, motivating routine audits when deploying open-response assessment. Together, these results indicate that Hebbian replay with bounded consolidation offers a practical path to real-time, interpretable ER that scales across data modalities and classroom settings.

Solving Inductive Logic Programming (ILP) problems with neural networks is a key challenge in Neural-Symbolic Ar- tificial Intelligence (AI). While most research has focused on designing novel network architectures for individual prob- lems, less effort has been devoted to exploring new learning paradigms involving a sequence of problems. In this work, we investigate lifelong learning ILP, which leverages the com- positional and transferable nature of logic rules for efficient learning of new problems. We introduce a compositional framework, demonstrating how logic rules acquired from ear- lier tasks can be efficiently reused in subsequent ones, leading to improved scalability and performance. We formalize our approach and empirically evaluate it on sequences of tasks. Experimental results validate the feasibility and advantages of this paradigm, opening new directions for continual learn- ing in Neural-Symbolic AI.

Classical analyses of gradient descent (GD) define a stability threshold based on the largest eigenvalue of the loss Hessian, often termed sharpness. When the learning rate lies below this threshold, training is stable and the loss decreases monotonically. Yet, modern deep networks often achieve their best performance beyond this regime. We demonstrate that such instabilities induce an implicit bias in GD, driving parameters toward flatter regions of the loss landscape and thereby improving generalization. The key mechanism is the Rotational Polarity of Eigenvectors (RPE), a geometric phenomenon in which the leading eigenvectors of the Hessian rotate during training instabilities. These rotations, which increase with learning rates, promote exploration and provably lead to flatter minima. This theoretical framework extends to stochastic GD, where instability-driven flattening persists and its empirical effects outweigh minibatch noise. Finally, we show that restoring instabilities in Adam further improves generalization. Together, these results establish and understand the constructive role of training instabilities in deep learning.