Personalized Worked Example Generation from Student Code Submissions using Pattern-based Knowledge Components

Adaptive programming practice often relies on fixed libraries of worked examples and practice problems, which require substantial authoring effort and may not correspond well to the logical errors and partial solutions students produce while writing code. As a result, students may receive learning content that does not directly address the concepts they are working to understand, while instructors must either invest additional effort in expanding content libraries or accept a coarse level of personalization. We present an approach for knowledge-component (KC) guided educational content generation using pattern-based KCs extracted from student code. Given a problem statement and student submissions, our pipeline extracts recurring structural KC patterns from students' code through AST-based analysis and uses them to condition a generative model. In this study, we apply this approach to worked example generation, and compare baseline and KC-conditioned outputs through expert evaluation. Results suggest that KC-conditioned generation improves topical focus and relevance to learners' underlying logical errors, providing evidence that KC-based steering of generative models can support personalized learning at scale.

Who Defines "Best"? Towards Interactive, User-Defined Evaluation of LLM Leaderboards

LLM leaderboards are widely used to compare models and guide deployment decisions. However, leaderboard rankings are shaped by evaluation priorities set by benchmark designers, rather than by the diverse goals and constraints of actual users and organizations. A single aggregate score often obscures how models behave across different prompt types and compositions. In this work, we conduct an in-depth analysis of the dataset used in the LMArena (formerly Chatbot Arena) benchmark and investigate this evaluation challenge by designing an interactive visualization interface as a design probe. Our analysis reveals that the dataset is heavily skewed toward certain topics, that model rankings vary across prompt slices, and that preference-based judgments are used in ways that blur their intended scope. Building on this analysis, we introduce a visualization interface that allows users to define their own evaluation priorities by selecting and weighting prompt slices and to explore how rankings change accordingly. A qualitative study suggests that this interactive approach improves transparency and supports more context-specific model evaluation, pointing toward alternative ways to design and use LLM leaderboards.

Domain-Filtered Knowledge Graphs from Sparse Autoencoder Features

Sparse autoencoders (SAEs) extract millions of interpretable features from a language model, but flat feature inventories aren't very useful on their own. Domain concepts get mixed with generic and weakly grounded features, while related ideas are scattered across many units, and there's no way to understand relationships between features. We address this by first constructing a strict domain-specific concept universe from a large SAE inventory using contrastive activations and a multi-stage filtering process. Next, we build two aligned graph views on the filtered set: a co-occurrence graph for corpus-level conceptual structure, organized at multiple levels of granularity, and a transcoder-based mechanism graph that links source-layer and target-layer features through sparse latent pathways. Automated edge labeling then turns these graph views into readable knowledge graphs rather than unlabeled layouts. In a case study on a biology textbook, these graphs recover coherent chapter and subchapter-level structure, reveal concepts that bridge neighboring topics, and transform messy sentence-level activity containing thousands of features into compact, readable views that illustrate the model's local activity. Taken together, this reframes a flat SAE inventory as an internal knowledge graph that converts feature-level interpretability into a global map of model knowledge and enables audits of reasoning faithfulness.

Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm

K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear manifolds. Traditional KPC or fuzzy KPC models demonstrate a pronounced susceptibility to outliers, as they presuppose that the projection distance between data points and the plane normal vector adheres to the L2 distance. Meanwhile, the assumption of infinitely extending clusters adversely affects clustering performance. To solve these problems, this paper proposed a new robust fuzzy local k-plane clustering (RFLkPC) method that combines the mixture distance of hinge loss and L1 norm. The RFLkPC model assumes that each plane cluster is bounded to a finite area, which can flexibly and robustly handle plane clustering tasks with outliers or not. The corresponding model and optimization algorithms of RFLkPC were provided. Compared to other related models on this topic, a large number of experiments verify the efficiency of RFLkPC on simulated data and real data. The source code for the proposed RFLkPC method is publicly available at https://github.com/xuelin-xie/RFLkPC.

Personalized Benchmarking: Evaluating LLMs by Individual Preferences

With the rise in capabilities of large language models (LLMs) and their deployment in real-world tasks, evaluating LLM alignment with human preferences has become an important challenge. Current benchmarks average preferences across all users to compute aggregate ratings, overlooking individual user preferences when establishing model rankings. Since users have varying preferences in different contexts, we call for personalized LLM benchmarks that rank models according to individual needs. We compute personalized model rankings using ELO ratings and Bradley-Terry coefficients for 115 active Chatbot Arena users and analyze how user query characteristics (topics and writing style) relate to LLM ranking variations. We demonstrate that individual rankings of LLM models diverge dramatically from aggregate LLM rankings, with Bradley-Terry correlations averaging only $ρ= 0.04$ (57\% of users show near-zero or negative correlation) and ELO ratings showing moderate correlation ($ρ= 0.43$). Through topic modeling and style analysis, we find users exhibit substantial heterogeneity in topical interests and communication styles, influencing their model preferences. We further show that a compact combination of topic and style features provides a useful feature space for predicting user-specific model rankings. Our results provide strong quantitative evidence that aggregate benchmarks fail to capture individual preferences for most users, and highlight the importance of developing personalized benchmarks that rank LLM models according to individual user preferences.

CobwebTM: Probabilistic Concept Formation for Lifelong and Hierarchical Topic Modeling

Topic modeling seeks to uncover latent semantic structure in text corpora with minimal supervision. Neural approaches achieve strong performance but require extensive tuning and struggle with lifelong learning due to catastrophic forgetting and fixed capacity, while classical probabilistic models lack flexibility and adaptability to streaming data. We introduce \textsc{CobwebTM}, a low-parameter lifelong hierarchical topic model based on incremental probabilistic concept formation. By adapting the Cobweb algorithm to continuous document embeddings, \textsc{CobwebTM} constructs semantic hierarchies online, enabling unsupervised topic discovery, dynamic topic creation, and hierarchical organization without predefining the number of topics. Across diverse datasets, \textsc{CobwebTM} achieves strong topic coherence, stable topics over time, and high-quality hierarchies, demonstrating that incremental symbolic concept formation combined with pretrained representations is an efficient approach to topic modeling.

Measuring Opinion Bias and Sycophancy via LLM-based Coercion

Large language models increasingly shape the information people consume: they are embedded in search, consulted for professional advice, deployed as agents, and used as a first stop for questions about policy, ethics, health, and politics. When such a model silently holds a position on a contested topic, that position propagates at scale into users' decisions. Eliciting a model's positions is harder than it first appears: contemporary assistants answer direct opinion questions with evasive disclaimers, and the same model may concede the opposite position once the user starts arguing one side. We propose a method, released as the open-source llm-bias-bench, for discovering the opinions an LLM actually holds on contested topics under conditions that resemble real multi-turn interaction. The method pairs two complementary free-form probes. Direct probing asks for the model's opinion across five turns of escalating pressure from a simulated user. Indirect probing never asks for an opinion and engages the model in argumentative debate, letting bias leak through how it concedes, resists, or counter-argues. Three user personas (neutral, agree, disagree) collapse into a nine-way behavioral classification that separates persona-independent positions from persona-dependent sycophancy, and an auditable LLM judge produces verdicts with textual evidence. The first instantiation ships 38 topics in Brazilian Portuguese across values, scientific consensus, philosophy, and economic policy. Applied to 13 assistants, the method surfaces findings of practical interest: argumentative debate triggers sycophancy 2-3x more than direct questioning (median 50% to 79%); models that look opinionated under direct questioning often collapse into mirroring under sustained arguments; and attacker capability matters mainly when an existing opinion must be dislodged, not when the assistant starts neutral.

Probably Approximately Consensus: On the Learning Theory of Finding Common Ground

A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements provided by users and should incorporate the relative salience of particular topics. We address this issue by modelling consensus as an interval in a one-dimensional opinion space derived from potentially high-dimensional data via embedding and dimensionality reduction. We define an objective that maximizes expected agreement within a hypothesis interval where the expectation is over an underlying distribution of issues, implicitly taking into account their salience. We propose an efficient Empirical Risk Minimization (ERM) algorithm and establish PAC-learning guarantees. Our initial experiments demonstrate the performance of our algorithm and examine more efficient approaches to identifying optimal consensus regions. We find that through selectively querying users on an existing sample of statements, we can reduce the number of queries needed to a practical number.

From Similarity to Structure: Training-free LLM Context Compression with Hybrid Graph Priors

Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches typically rely on trained compressors, dense retrieval-style selection, or heuristic trimming, and they often struggle to jointly preserve task relevance, topic coverage, and cross-sentence coherence under a strict token budget. To address this, we propose a training-free and model-agnostic compression framework that selects a compact set of sentences guided by structural graph priors. Our method constructs a sparse hybrid sentence graph that combines mutual k-NN semantic edges with short-range sequential edges, extracts a topic skeleton via clustering, and ranks sentences using an interpretable score that integrates task relevance, cluster representativeness, bridge centrality, and a cycle coverage cue. A budgeted greedy selection with redundancy suppression then produces a readable compressed context in original order. Experimental results on four datasets show that our approach is competitive with strong extractive and abstractive baselines, demonstrating larger gains on long-document benchmarks.

Mix and Match: Context Pairing for Scalable Topic-Controlled Educational Summarisation

Topic-controlled summarisation enables users to generate summaries focused on specific aspects of source documents. This paper investigates a data augmentation strategy for training small language models (sLMs) to perform topic-controlled summarisation. We propose a pairwise data augmentation method that combines contexts from different documents to create contrastive training examples, enabling models to learn the relationship between topics and summaries more effectively. Using the SciTLDR dataset enriched with Wikipedia-derived topics, we systematically evaluate how augmentation scale affects model performance. Results show consistent improvements in win rate and semantic alignment as the augmentation scale increases, while the amount of real training data remains fixed. Consequently, a T5-base model trained with our augmentation approach achieves competitive performance relative to larger models, despite using significantly fewer parameters and substantially fewer real training examples.