arXiv subjects

Christopher J. MacLellan

Publications and source records attributed to Christopher J. MacLellan.

At least 19 recordsLinked to original sources

arXiv2026

Structure-Mapping-Guided Self-Explanation for Learning Mathematical Procedures

Worked examples are a powerful form of instruction, but learners must infer how the demonstrated steps were produced. A naive simulation of this self-explanation process can generate thousands of numerical explanations that reproduce one observed change without capturing its underlying procedure. We propose structure-mapping-guided self-explanation as a computational account of the cognitive biases that reduce search effort and make this inference tractable. The model represents mathematical expressions as typed relational structures and uses structure mapping to identify corresponding source and target regions. For each changed target value, the corresponding source region serves as an anchor: it guides abductive search toward structurally relevant values and operations before broader alternatives, yielding ordered, executable candidate procedures with inspectable source evidence. Across 70 mathematical transformations containing 120 changed numeric components, the model recovered every intended procedure. It returned the intended procedure before any other computation producing the same target value in 104 subproblems (86.7%), compared with a median of 32 (26.7%) across 100 unguided runs that tested candidate calculations in random order. Our proposed model also tested 93.8% fewer combinations of values and operations than unguided search before reaching the intended procedures. These results provide an efficient, interpretable account of how relational structure can guide procedural learning and a testable hypothesis about human self-explanation from worked examples.

cs.AI↗

arXiv2026

Diffusion Models and Concept Formation

Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a \emph{basic level} at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.

cs.AI↗

arXiv2026

When Should Users Check? Modeling Confirmation Frequency in Multi-Step Agentic AI Tasks

Existing AI agents typically execute multi-step tasks autonomously and only allow user confirmation at the end. During execution, users have little control, making the confirm-at-end approach brittle: a single error can cascade and force a complete restart. Confirming every step avoids such failures, but imposes tedious overhead. Balancing excessive interruptions against costly rollbacks remains an open challenge. We address this problem by modeling confirmation as a minimum time scheduling problem. We conducted a formative study with eight participants, which revealed a recurring Confirmation-Diagnosis-Correction-Redo (CDCR) pattern in how users monitor errors. Based on this pattern, we developed a decision-theoretic model to determine time-efficient confirmation point placement. We then evaluated our approach using a within-subjects study where 48 participants monitored AI agents and repaired their mistakes while executing tasks. Results show that 81 percent of participants preferred our intermediate confirmation approach over the confirm-at-end approach used by existing systems, and task completion time was reduced by 13.54 percent.

cs.HC↗

arXiv2026

Teaching AI Interactively: An Experience Report in Higher Education

Introductory artificial intelligence (AI) courses present significant learning challenges due to abstract concepts, mathematical complexity, and students' diverse technical backgrounds. This paper presents an experience report examining the redesign of in-class instructional time in a university-level Introduction to Artificial Intelligence course, inspired by CS Unplugged approaches. We redesigned the summer offering, integrating embodied, unplugged simulations, collaborative programming labs, and structured reflection to provide students with a first-person perspective on AI decision-making. We maintained identical assignments, exams, and assessments as the traditional lecture-based offering. We found that students in the redesigned course reported higher attendance, stronger agreement that assessments measured their understanding, and greater overall course effectiveness, despite no significant differences in self-reported learning. Post-course interviews indicate that unplugged simulations and collaboration fostered a safe, supportive learning environment that increased engagement and confidence with AI concepts. These results highlight the importance of in-class instructional design in improving students' learning experiences without compromising rigor.

cs.CY↗

arXiv2026

Trust Region Continual Learning as an Implicit Meta-Learner

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: \emph{trust region continual learning} that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly \emph{re-converges} to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

cs.LG↗

arXiv2026

Self-Consolidating Language Models: Continual Knowledge Incorporation from Context

Large language models (LLMs) increasingly receive information as streams of passages, conversations, and long-context workflows. While longer context windows expose more evidence, they do not ensure that useful information is preserved and reused. We study continual context consolidation: writing current context into model weights while limiting interference with previously consolidated information. We propose \textbf{S}elf-\textbf{Co}nsolidating \textbf{L}anguage Models (SCoL), a post-training framework in which, given current context, an LLM learns to generate textual update instructions specifying which of its own Transformer layers should be updated. Because committed updates change the model that later generates future selections, we train SCoL with meta-reinforcement learning over an evolving model state. We instantiate SCoL with supervised QA rewards on SQuAD knowledge incorporation and intrinsic likelihood-based rewards for LongBench v2 long-context consolidation. Across both settings, SCoL improves acquisition and retention over prompting, summarization, batch test-time training, and sequential finetuning baselines. Analysis of learned selection patterns shows that SCoL encourages the LLM to generate sparse update locations that align with layers of high Fisher information, suggesting that the model learns to route plasticity toward loss-sensitive regions while limiting interference. Moreover, SCoL transfers from shorter meta-training streams to longer LongBench v2 streams at evaluation, suggesting that our framework supports scalable streaming consolidation.

cs.CL↗

arXiv2026

Test-Time Compositional Generalization in Diffusion Models via Concept Discovery

Compositional generalization requires models to produce novel configurations from familiar parts. In diffusion models, prior compositional generation methods typically assume that the relevant concepts or conditioning signals are already available. We instead ask whether a pretrained diffusion model can discover query-specific concepts from the time-indexed scores it learns for the noisy marginals $p_t(x_t)$ and compose them at test time. Given a single out-of-distribution query, our method performs gradient ascent on $s_θ(x_t,t) \approx \nabla_{x_t}\log p_t(x_t)$ at multiple noising timesteps to recover local density modes, maps these modes into clean-space Gaussians, greedily selects relevant prototypes with a submodular likelihood objective, and combines them into a product-of-experts (PoE) teacher model with an analytic score. This teacher model can be sampled directly through classifier-free guidance or used to generate a sample pool for training a new class embedding and low-rank adapter. On held-out composition benchmarks built from ColorMNIST and CelebA, both the analytic PoE sampler and the low-rank adapted model outperform query-only and nearest trained-class baselines. These results suggest that the time-indexed score geometry of the diffusion model contains reusable density-mode concepts that support test-time compositional generation without a predefined concept library.

cs.LG↗

arXiv2026

Guidelines for Designing AI Technologies to Support Adult Learning

AI-powered educational technologies have demonstrated measurable benefits for learners, but their design and evaluation have largely centered on K-12 contexts. As a result, many AI-supported learning systems remain poorly aligned with the needs, constraints, and goals of adult learners. To better understand how AI systems function in adult education, this paper examines the deployment of several AI learning technologies developed within a multidisciplinary, national research institute in the United States focused on adult learning and online education. Drawing on longitudinal deployment data, we conducted a reflexive thematic analysis to identify recurring challenges and design considerations across systems. These insights were synthesized into a set of 19 design guidelines intended to inform future AI-supported adult learning technologies. We demonstrate the utility of these guidelines through a heuristic evaluation of the deployed systems. Lastly, we present a guideline exploration tool that aids in the ideation of technologies by connecting the guidelines to stakeholder statements surfaced in the analysis process.

cs.CY↗

arXiv2026

A Rational Account of Categorization Based on Information Theory

We present a new theory of categorization based on an information-theoretic rational analysis. To evaluate this theory, we investigate how well it can account for key findings from classic categorization experiments conducted by Hayes-Roth and Hayes-Roth (1977), Medin and Schaffer (1978), and Smith and Minda (1998). We find that it explains the human categorization behavior as well as (or better) than the independent cue and context models (Medin & Schaffer, 1978), the rational model of categorization (Anderson, 1991), and a hierarchical Dirichlet process model (Griffiths et al., 2007).

cs.AI↗

arXiv2026

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 CobwebTM, a low-parameter lifelong hierarchical topic model based on incremental probabilistic concept formation. By adapting the Cobweb algorithm to continuous document embeddings, CobwebTM constructs semantic hierarchies online, enabling unsupervised topic discovery, dynamic topic creation, and hierarchical organization without predefining the number of topics. Across diverse datasets, 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.

cs.CL↗

arXiv2026

AI Unplugged: Embodied Interactions for AI Literacy in Higher Education

As artificial intelligence (AI) becomes increasingly integrated into daily life, higher education must move beyond code-centric instruction to foster holistic AI literacy. We present a novel pedagogical approach that integrates embodied, unplugged activities into a university-level Introduction to AI course. Inspired by the effectiveness of CS Unplugged in K-12 education, our physical, collaborative activities gave students a first-person perspective on AI decision-making. Through interactive games modeling Search Algorithms, Markov Decision Processes, Q-learning, and Hidden Markov Models, students built an intuition for complex AI concepts and more easily transitioned to mathematical formalizations and code implementations. We present four unplugged AI activities, describe how to bridge from unplugged activities to plugged coding tasks, reflect on implementation challenges, and propose refinements. We suggest that unplugged activities can effectively bridge conceptual reasoning and technical skill-building in university-level AI education.

cs.CY↗

arXiv2026

Avoid Catastrophic Forgetting with Rank-1 Fisher from Diffusion Models

Catastrophic forgetting remains a central obstacle for continual learning in neural models. Popular approaches -- replay and elastic weight consolidation (EWC) -- have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation. In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data. We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient. Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction. We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift. On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is more than halved on ImageNet-1k. These results suggest that diffusion models admit an approximately rank-1 Fisher. With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift.

cs.LG↗

arXiv2026

Grounded Concreteness: Human-Like Concreteness Sensitivity in Vision-Language Models

Do vision--language models (VLMs) develop more human-like sensitivity to linguistic concreteness than text-only large language models (LLMs) when both are evaluated with text-only prompts? We study this question with a controlled comparison between matched Llama text backbones and their Llama Vision counterparts across multiple model scales, treating multimodal pretraining as an ablation on perceptual grounding rather than access to images at inference. We measure concreteness effects at three complementary levels: (i) output behavior, by relating question-level concreteness to QA accuracy; (ii) embedding geometry, by testing whether representations organize along a concreteness axis; and (iii) attention dynamics, by quantifying context reliance via attention-entropy measures. In addition, we elicit token-level concreteness ratings from models and evaluate alignment to human norm distributions, testing whether multimodal training yields more human-consistent judgments. Across benchmarks and scales, VLMs show larger gains on more concrete inputs, exhibit clearer concreteness-structured representations, produce ratings that better match human norms, and display systematically different attention patterns consistent with increased grounding.

cs.CL↗

arXiv2025

Deep Taxonomic Networks for Unsupervised Hierarchical Prototype Discovery

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to the number of classes and underutilize the rich prototype information available at intermediate hierarchical levels. We introduce deep taxonomic networks, a novel deep latent variable approach designed to bridge these gaps. Our method optimizes a large latent taxonomic hierarchy, specifically a complete binary tree structured mixture-of-Gaussian prior within a variational inference framework, to automatically discover taxonomic structures and associated prototype clusters directly from unlabeled data without assuming true label sizes. We analytically show that optimizing the ELBO of our method encourages the discovery of hierarchical relationships among prototypes. Empirically, our learned models demonstrate strong hierarchical clustering performance, outperforming baselines across diverse image classification datasets using our novel evaluation mechanism that leverages prototype clusters discovered at all hierarchical levels. Qualitative results further reveal that deep taxonomic networks discover rich and interpretable hierarchical taxonomies, capturing both coarse-grained semantic categories and fine-grained visual distinctions.

cs.CV↗

arXiv2025

Taxonomic Networks: A Representation for Neuro-Symbolic Pairing

We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which nodes represent hierarchically organized taxonomic concepts. Using this representation, we construct a novel neuro-symbolic pair and evaluate its performance. We show that our symbolic method learns taxonomic nets more efficiently with less data and compute, while the neural method finds higher-accuracy taxonomic nets when provided with greater resources. As a neuro-symbolic pair, these approaches can be used interchangeably based on situational needs, with seamless translation between them when necessary. This work lays the foundation for future systems that more fundamentally integrate neural and symbolic computation.

cs.AI↗

arXiv2025

Model Human Learners: Computational Models to Guide Instructional Design

Instructional designers face an overwhelming array of design choices, making it challenging to identify the most effective interventions. To address this issue, I propose the concept of a Model Human Learner, a unified computational model of learning that can aid designers in evaluating candidate interventions. This paper presents the first successful demonstration of this concept, showing that a computational model can accurately predict the outcomes of two human A/B experiments -- one testing a problem sequencing intervention and the other testing an item design intervention. It also demonstrates that such a model can generate learning curves without requiring human data and provide theoretical insights into why an instructional intervention is effective. These findings lay the groundwork for future Model Human Learners that integrate cognitive and learning theories to support instructional design across diverse tasks and interventions.

cs.HC↗

arXiv2025

TutorGym: A Testbed for Evaluating AI Agents as Tutors and Students

Recent improvements in large language model (LLM) performance on academic benchmarks, such as MATH and GSM8K, have emboldened their use as standalone tutors and as simulations of human learning. However, these new applications require more than evaluations of final solution generation. We introduce TutorGym to evaluate these applications more directly. TutorGym is a standard interface for testing artificial intelligence (AI) agents within existing intelligent tutoring systems (ITS) that have been tested and refined in classroom studies, including Cognitive Tutors (CTAT), Apprentice Tutors, and OATutors. TutorGym is more than a simple problem-solution benchmark, it situates AI agents within the interactive interfaces of existing ITSs. At each step of problem-solving, AI agents are asked what they would do as a tutor or as a learner. As tutors, AI agents are prompted to provide tutoring support -- such as generating examples, hints, and step-level correctness feedback -- which can be evaluated directly against the adaptive step-by-step support provided by existing ITSs. As students, agents directly learn from ITS instruction, and their mistakes and learning trajectories can be compared to student data. TutorGym establishes a common framework for training and evaluating diverse AI agents, including LLMs, computational models of learning, and reinforcement learning agents, within a growing suite of learning environments. Currently, TutorGym includes 223 different tutor domains. In an initial evaluation, we find that current LLMs are poor at tutoring -- none did better than chance at labeling incorrect actions, and next-step actions were correct only ~52-70% of the time -- but they could produce remarkably human-like learning curves when trained as students with in-context learning.

cs.AI↗

arXiv2025

Beyond Final Answers: Evaluating Large Language Models for Math Tutoring

Researchers have made notable progress in applying Large Language Models (LLMs) to solve math problems, as demonstrated through efforts like GSM8k, ProofNet, AlphaGeometry, and MathOdyssey. This progress has sparked interest in their potential use for tutoring students in mathematics. However, the reliability of LLMs in tutoring contexts -- where correctness and instructional quality are crucial -- remains underexplored. Moreover, LLM problem-solving capabilities may not necessarily translate into effective tutoring support for students. In this work, we present two novel approaches to evaluate the correctness and quality of LLMs in math tutoring contexts. The first approach uses an intelligent tutoring system for college algebra as a testbed to assess LLM problem-solving capabilities. We generate benchmark problems using the tutor, prompt a diverse set of LLMs to solve them, and compare the solutions to those generated by the tutor. The second approach evaluates LLM as tutors rather than problem solvers. We employ human evaluators, who act as students seeking tutoring support from each LLM. We then assess the quality and correctness of the support provided by the LLMs via a qualitative coding process. We applied these methods to evaluate several ChatGPT models, including 3.5 Turbo, 4, 4o, o1-mini, and o1-preview. Our findings show that when used as problem solvers, LLMs generate correct final answers for 85.5% of the college algebra problems tested. When employed interactively as tutors, 90% of LLM dialogues show high-quality instructional support; however, many contain errors -- only 56.6% are entirely correct. We conclude that, despite their potential, LLMs are not yet suitable as intelligent tutors for math without human oversight or additional mechanisms to ensure correctness and quality.

cs.HC↗