Per-Competency Bayesian Knowledge Tracing

We introduce the Unified Neural Variational Measurement of Proficiency (UNVaMP) architecture, a knowledge tracing method that integrates observed student-item interactions with internal memory to produce evolving latent representations of student knowledge. These representations support accurate predictions of future responses while enabling explicit control over the smoothness of estimated learning trajectories. UNVaMP can be configured as either a purely neural model or a hybrid model that predicts responses through an interpretable measurement function over the latent space. We show that a pure neural configuration (UNVaMP-MLP) achieves the strongest predictive performance among compared models on three out of four datasets. Meanwhile, a hybrid configuration (UNVaMP-MIRT, using a 1PL MIRT measurement function) lags only slightly behind UNVaMP-MLP, indicating that the predictive cost of interpretability is modest. Beyond predictive accuracy, UNVaMP provides the following: a principled mechanism for controlling volatility when estimating student latent variables, quantification of uncertainty over student knowledge state estimates, and flexible input specification that supports heterogeneous student-item interaction features. In addition, the hybrid UNVaMP-MIRT configuration generates interpretable moment-in-time student knowledge state estimates. Using an experimental dataset, we show that auxiliary inputs induce structured changes in the predictive behavior of UNVaMP-MIRT, consistent with sensitivity to underlying structure beyond response correctness. Furthermore, through a simulation study, we show that UNVaMP yields well-behaved knowledge state estimates under controlled measurement conditions. In total, these results indicate that UNVaMP is both useful for real-world education systems and capable of recovering underlying structure from student-item interactions.

Knowledge tracing (KT) aims to predict students' future performance by modeling their evolving knowledge states from historical interactions. Existing KT methods usually treat the raw interaction sequence as a unified behavioral process, overlooking the phase-specific nature of learning behaviors. Our preliminary observations show that students are more likely to correctly answer previously failed knowledge concepts after sufficient practice, suggesting a transition from ability-building to proficiency-oriented learning. Motivated by this, we propose Phase-Aware Knowledge Tracing (PAKT), a KT framework that decomposes student interactions into ability and proficiency phases based on the tailored decomposition mechanism. To effectively exploit the decomposed sequences, we design a multi-branch Transformer with a type-aware readout module to jointly capture phase-specific and holistic knowledge states. We further provide a causal analysis to reveal the confounding bias caused by entangling complex learning behaviors in phase-agnostic KT models. Extensive experiments on six public benchmarks demonstrate that our method consistently outperforms representative baselines, with a maximum AUC gain of 1.33% and an average gain of 0.82%.

Recent research has increasingly focused on understanding how Transformers store and process knowledge, as well as how this knowledge can be edited. Research work in this area is often conducted in two phases: first, phenomena are explored on individual samples. Then, when results appear promising, more statistically robust experiments follow. To support the first phase, we propose KnowledgeDebugger, a GUI-based exploration tool for knowledge localization and editing in Transformers. Our tool - inspired by LM-Debugger - offers no-code access to the methods in EasyEdit, a widely used library of state-of-the-art Knowledge Editing approaches. We demonstrate the tool's effectiveness through case studies of recent findings in this field.

Knowledge Tracing (KT) is important for personalized education but traditionally suffers from two key limitations: a reliance on shallow ID-based representations that neglect semantic depth and a restriction to single-granularity mastery estimation that overlooks hierarchical knowledge dependencies. To address these challenges, we propose MOSAIC (Multi-granularity Online Semantic AI for Collaborative Knowledge), a novel framework that orchestrates LLM-driven semantic alignment with sequential modeling. Unlike methods that use LLMs solely as predictors, MOSAIC leverages a frozen LLM to generate dynamic, context-aware embeddings and hierarchical prediction prompts, explicitly capturing collaborative signals and peer interactions. Furthermore, we introduce a cross-granularity consistency objective that jointly regularizes mastery estimation across concept, topic-cluster, and global proficiency levels. Extensive experiments on ASSISTments, EdNet, and a newly collected large-scale MOOC dataset demonstrate that MOSAIC establishes new state-of-the-art results. Specifically, our method achieves AUC improvements of up to 3.4% and Accuracy gains of up to 2.5 % across all benchmarks. Notably, MOSAIC exhibits superior robustness in collaboration-rich environments and long-sequence scenarios (AUC 0.862 on MOOC), offering both high predictive precision and semantically grounded interpretability.

Assessing financial literacy during gameplay without disrupting the learning experience remains a key challenge in serious games for education. We present the Agentic BKT pipeline, a multi-agent large language model architecture for stealth assessment of financial competencies from open-ended gameplay events. The pipeline processes events from a 2D platformer serious game aligned with the OECD/INFE financial literacy framework through four phases: (1) the game captures every player decision as a structured event log; (2) an LLM event classifier labels each action on a four-point rubric validated against three domain experts (Fleiss kappa = 0.624, substantial agreement); (3) four domain-specific agents specializing in risk mitigation, investing, spending, and credit management perform session-level reasoning over behavioral trajectories, feeding per-competency Bayesian Knowledge Tracing that estimates mastery within each domain; and (4) an expert judge agent synthesizes the domain-level estimates into an overall mastery score. Evaluated with 193 K-12 participants across 264 game sessions, the Agentic BKT pipeline yields mastery estimates significantly correlated with learning gain (r = 0.276, p = 0.0001) and post-test scores (r = 0.333, p < 0.0001) while showing no correlation with pre-test scores, providing both convergent and discriminant validity. The multi-agent approach approximately triples the predictive validity of a single-LLM baseline (r = 0.095, not significant) in this study, demonstrating that domain decomposition and session-level reasoning play a central role in capturing the multidimensional nature of financial literacy from gameplay

Deployed knowledge-tracing models are typically frozen after training, yet systematic per-item logit bias arises, from limited per-item expressivity in backbone architectures and from post-deployment shifts in item properties, degrading prediction quality. Global post-hoc calibrators such as Platt scaling, temperature scaling, and isotonic regression improve probability estimates but leave discriminative ability, as measured by AUC, unchanged. This AUC invariance is a structural consequence of monotone score-only transforms; recovering the stranded discrimination requires conditioning on item identity. We propose SLC (State-space Logit Correction), which converts binary observations to Gaussian pseudo-observations via Laplace/IRLS, applies empirical-Bayes shrinkage through a Kalman smoother, and fits an offset-Platt link. The state-space formulation also yields a detectability bound that characterizes the Bernoulli information floor, explaining why temporal tracking provides no benefit at current data densities. Across four datasets, five backbones, and three seeds, SLC improves AUC on all four datasets and NLL on three, with the advantage concentrating on sparse items. Cross-domain controls suggest that the same phenomenon can arise beyond education when the deployed backbone leaves entity-level bias.

Introductory programming instruction relies on hands-on practice and short learning activities to support mastery of foundational concepts. Although many such learning resources exist, organizing and linking these items in instructionally meaningful ways is challenging without time-intensive expert curation. This study investigates the use of pattern-based Knowledge Components (KCs) to automatically identify code-based learning resources targeting similar concepts. In our approach, pattern-based KCs are extracted from each code sample, and related activities are identified by measuring similarity between the KC sets associated with each activity. By leveraging alignment at the level of semantically important programming patterns, this method supports contextually appropriate and pedagogically useful recommendations. We evaluate our approach on an expert-organized corpus of introductory Python materials in which instructors grouped items into bundles based on conceptual similarity. Results show that our pattern-based KC approach retrieves resources that align with this expert organization, and outperformed representative KC- and embedding-based baselines across standard ranking evaluations. Overall, the framework supports targeted, concept-oriented guidance for programming learners and can help instructors organize, bundle, and recommend instructional content at scale.

Agentic reinforcement learning (RL) has proven effective for training LLM-based agents with external tool-use capabilities. However, we identify that agentic RL training induces increasing redundant tool calls and blurs the model's intrinsic knowledge boundary, where the model fails to distinguish when tools are needed versus when parametric knowledge suffices. Existing solutions based on reward shaping create coarse-grained optimization targets that tend to incentivize indiscriminate tool-call suppression, leading to reward hacking. In this paper, we propose AKBE (Agentic Knowledge Boundary Enhancement), an on-policy method that dynamically probes the model's intrinsic knowledge boundary through dual-path (with-tool and no-tool) rollouts during training. We define the knowledge boundary as the per-instance determination of whether tools are required and the minimum tool calls necessary. By comparing correctness across paths, AKBE categorizes trajectories and constructs targeted supervisory signals that guide efficient tool-use patterns for each question. These signals are integrated seamlessly into the agentic RL training loop. Experiments on seven QA benchmarks demonstrate that AKBE improves task accuracy by +1.85 on average and reduces tool calls by 18% over standard agentic RL, yielding 25% higher tool productivity without any accuracy-efficiency trade-off. Further analysis suggests its plug-and-play compatibility across different RL algorithms and the mechanism of each signal category. Our code is available at https://github.com/CuSO4-Chen/AKBE.

Recent research in educational data mining, especially knowledge tracing, has focused on predicting learners' future knowledge states to support adaptive instruction. However, in many real-world educational settings, learning data are often available only as single-time-point assessments without temporal information, making existing time-series-based approaches difficult to apply. In this paper, we propose a novel framework for predicting future skill acquisition using only snapshot data. Specifically, we address the problem of predicting the next skill to be acquired from skill mastery patterns estimated by cognitive diagnostic models (CDMs). In the absence of temporal information, we exploit inclusion relations among learners' skill sets to induce a pseudo-temporal ordering, interpreting expanding skill sets as a proxy for learning progression. To efficiently approximate unobserved acquisition paths, we introduce a neural model that captures latent skill acquisition dynamics through expected skill increments. Experiments on both synthetic and real-world datasets demonstrate that the proposed method consistently outperforms baseline approaches, with particularly strong advantages as the skill space becomes larger. These results indicate that meaningful skill acquisition patterns can be inferred from snapshot data alone, providing a practical framework for adaptive learning support in data-constrained educational environments.

Knowledge Tracing (KT) models students' knowledge states based on learning interactions to predict performance. While deep learning-based KT models have boosted predictive accuracy, most models rely on deterministic vector embeddings and opaque latent state transitions, limiting interpretability regarding how specific past behaviors influence predictions. To address this limitation, we propose Probabilistic Logical Knowledge Tracing (PLKT), an interpretable KT framework that formulates prediction as a goal-conditioned evidence reasoning process over historical learning behaviors. Instead of representing knowledge states as deterministic vector embeddings, PLKT employs robust Beta-distributed probabilistic embeddings to represent student knowledge states. This probabilistic foundation allows us to model the uncertainty of historical behaviors and perform explicit logical operations (e.g., conjunction), constructing transparent reasoning paths that reveal how specific past interactions contribute to the prediction. Extensive experiments show that PLKT outperforms state-of-the-art KT methods while achieving superior interpretability. Our code is available at https://anonymous.4open.science/r/PLKT-D3CE/.

The emerging collaborative information-based knowledge tracing (KT) has been a promising way to enhance modeling of learners' knowledge states. The core idea is to extract the collaborative information from interaction sequences of other learners to assist the prediction on the target one. Despite effectiveness, existing methods are built on the raw interaction sequences with tailored modules, which inevitably limits their capacity in deeply capturing learning behavioral patterns and generalization. To this end, we propose a general meta-behavioral pattern-aware framework (MBP-KT) for KT. Specifically, MBP-KT introduces a novel meta-behavioral sequence construction to transform the raw interaction sequences into the combinations of different meta-behavioral patterns. In this way, the learning behavioral patterns of learners can be effectively preserved. Then, MBP-KT develops a parameter-free module to extract the global collaborative representations from the constructed meta-behavioral sequences. Moreover, MBP-KT provides general injection strategies to introduce the extracted global collaborative information into various downstream KT models, ensuring the universality of the collaborative information. Extensive results on real-world datasets demonstrate that MBP-KT can consistently boosts the performance of a wide range of KT models.

Knowledge Tracing (KT) is fundamental to intelligent education systems, yet relies on educational logs that are selectively observed. The non-random nature of exercise recommendations and student choices inevitably induces severe selection bias. Most existing KT methods neglect this issue, training on observed logs using standard empirical risk, which yields biased mastery estimates and accumulates errors in subsequent recommendations. To address this, we introduce a doubly robust (DR) formulation for KT that integrates a propensity model with an error imputation model, theoretically guaranteeing unbiasedness if either model is accurate. Beyond unbiasedness, in the sequential setting of KT, we identify that the estimator's performance is compromised by variance-dependent stochastic deviations that accumulate over time, thereby causing training instability and limiting performance. To mitigate this, we derive a generalization bound that explicitly characterizes the impact of estimator variance and identifies temporal smoothness as a key factor in controlling it. Building on these theoretical insights, we propose the Temporal Smoothness Doubly Robust (TSDR) framework. TSDR jointly optimizes the KT predictor and the imputation model with a smoothness regularizer, effectively reducing variance while preserving the unbiasedness guarantee of DR. Experiments on multiple real-world benchmarks demonstrate that TSDR consistently enhances various state-of-the-art KT backbones, underscoring the vital role of principled bias correction in KT.

Programming Knowledge Tracing (PKT) has recently advanced through hybrid approaches that integrate attention-based feature modeling for code representation with RNN-based sequential prediction. While these models report strong empirical performance, their reliability can be sensitive to subtle implementation and experimental design choices. This study revisits representative PKT models and shows that reported gains can be substantially influenced by model configuration and sequence construction practices. We identify issues in attention dimension settings that affect performance estimates, and demonstrate that improper ordering of student attempts, such as ignoring ServerTimestamp, can violate temporal causality and lead to overly optimistic results. To ensure consistent evaluation, hyperparameters are selected via grid search guided by a single designated fold and then fixed uniformly across all folds during cross-validation. We further analyze the role of assignment-wise characteristics and systematically explore the impact of maximum sequence length. Using this protocol, we re-evaluate PKT models on the CodeWorkout dataset. Our results show that, under controlled and consistent settings, the performance gap between attention-enhanced models and standard DKT is significantly reduced, and increased architectural complexity does not consistently translate into superior performance. Beyond individual model comparisons, this work provides practical guidance for reliable and comparable evaluation in programming knowledge tracing.

Recent advances in large language models (LLMs) have led to the development of AI-powered tutoring systems that provide interactive support via dialogue. To enable these tutoring systems to provide personalized support, it is essential to assess student performance at each turn, motivating knowledge tracing (KT) in dialogue settings. However, existing dialogue-based KT approaches often ignore question difficulty modeling and rely on opaque latent representations from LLMs, hindering accurate and interpretable prediction. In this work, we propose an interpretable difficulty-aware conversational KT framework built upon LLMs, which explicitly models students' abilities and the difficulty of tutor-posed tasks at each turn. The framework incorporates the original textual question and the next tutor-posed task to estimate the student's knowledge state and the difficulty of the upcoming turn. Furthermore, it integrates Item Response Theory to map LLM's outputs into student ability and question difficulty parameters, enabling interpretable prediction of student performance grounded in cognitive theories of learning. We evaluate the framework on two tutor-student dialogue datasets. Both quantitative and qualitative results show that our framework outperforms existing KT baselines, meanwhile generating interpretable outputs consistent with cognitive theory.

Educational Question Generation (EQG) aims to synthesize customized exercise questions that enhance student learning. An effective EQG system should ideally personalize questions for each student by modeling the student's knowledge state and generating questions that provide the greatest learning benefit. However, few existing EQG approaches are able to achieve such fine-grained personalization. In this paper, we explore how EQG can benefit from knowledge tracing (KT), which models students' knowledge states based on historical performance and predicts future performance. We propose KT4EQG, a personalized EQG framework that generates effective questions for individual students under the guidance of a KT model. Specifically, KT4EQG seeks to maximize a student's potential improvement in overall knowledge mastery by leveraging the KT model to select the most suitable knowledge concept for the student to practice. An LLM-based question generator is then trained to produce a question faithfully grounded in the selected concept. Experimental results on XES3G5M and MOOCRadar show that KT4EQG consistently generates more effective questions than methods with limited or no personalization.

We study how large language models recall relational knowledge during text generation, with a focus on identifying latent representations suitable for relation classification via linear probes. Prior work shows how attention heads and MLPs interact to resolve subject, predicate, and object, but it remains unclear which representations support faithful linear relation classification and why some relation types are easier to capture linearly than others. We systematically evaluate different latent representations derived from attention head and MLP contributions, showing that per-head attention contributions to the residual stream are comparatively strong features for linear relation classification. Feature attribution analyses of the trained probes, as well as characteristics of the different relation types, reveal clear correlations between probe accuracy and relation specificity, entity connectedness, and how distributed the signal on which the probe relies is across attention heads. Finally, we show how token-level feature attribution of probe predictions can be used to reveal probe behavior in further detail.

Knowledge Tracing (KT) aims to model student's knowledge state and predict future performance to enable personalized learning in Intelligent Tutoring Systems. However, traditional KT methods face fundamental limitations in explainability, as they rely solely on the response correctness, neglecting the rich information embedded in students' problem-solving processes. To address this gap, we propose Knowledge Tracing Leveraging Problem-Solving Process (KT-PSP), which incorporates students' problem-solving processes to capture the multidimensional aspects of mathematical proficiency. We also introduce KT-PSP-25, a new dataset specifically designed for KT-PSP. Building on this, we present StatusKT, a KT framework that employs a teacher-student-teacher three-stage LLM pipeline to extract students' Mathematical Proficiency (MP) as intermediate representation. In this pipeline, the teacher LLM first extracts problem-specific proficiency indicators, then a student LLM generates responses based on the student's solution process, and a teacher LLM evaluates these responses to determine mastery of each indicator. The experimental results on KT-PSP-25 demonstrate that StatusKT improves the prediction performance of existing KT methods. Moreover, StatusKT provides interpretable explanations for its predictions by explicitly modeling students' mathematical proficiency. Code is available \href{https://github.com/jungyangpark/KT-PSP-25}{here}.