Exploring Automated Distractor Generation for Math Multiple-choice Questions via Large Language Models

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in assessments and practices. One of the most important aspects of MCQs is the distractors, i.e., incorrect options that are designed to target common errors or misconceptions among real students. To date, the task of crafting high-quality distractors largely remains a labor and time-intensive process for teachers and learning content designers, which has limited scalability. In this work, we study the task of automated distractor generation in the domain of math MCQs and explore a wide variety of large language model (LLM)-based approaches, from in-context learning to fine-tuning. We conduct extensive experiments using a real-world math MCQ dataset and find that although LLMs can generate some mathematically valid distractors, they are less adept at anticipating common errors or misconceptions among real students.

Fundamental Benefit of Alternating Updates in Minimax Optimization

The Gradient Descent-Ascent (GDA) algorithm, designed to solve minimax optimization problems, takes the descent and ascent steps either simultaneously (Sim-GDA) or alternately (Alt-GDA). While Alt-GDA is commonly observed to converge faster, the performance gap between the two is not yet well understood theoretically, especially in terms of global convergence rates. To address this theory-practice gap, we present fine-grained convergence analyses of both algorithms for strongly-convex-strongly-concave and Lipschitz-gradient objectives. Our new iteration complexity upper bound of Alt-GDA is strictly smaller than the lower bound of Sim-GDA; i.e., Alt-GDA is provably faster. Moreover, we propose Alternating-Extrapolation GDA (Alex-GDA), a general algorithmic framework that subsumes Sim-GDA and Alt-GDA, for which the main idea is to alternately take gradients from extrapolations of the iterates. We show that Alex-GDA satisfies a smaller iteration complexity bound, identical to that of the Extra-gradient method, while requiring less gradient computations. We also prove that Alex-GDA enjoys linear convergence for bilinear problems, for which both Sim-GDA and Alt-GDA fail to converge at all.

Fair Sampling in Diffusion Models through Switching Mechanism

Diffusion models have shown their effectiveness in generation tasks by well-approximating the underlying probability distribution. However, diffusion models are known to suffer from an amplified inherent bias from the training data in terms of fairness. While the sampling process of diffusion models can be controlled by conditional guidance, previous works have attempted to find empirical guidance to achieve quantitative fairness. To address this limitation, we propose a fairness-aware sampling method called \textit{attribute switching} mechanism for diffusion models. Without additional training, the proposed sampling can obfuscate sensitive attributes in generated data without relying on classifiers. We mathematically prove and experimentally demonstrate the effectiveness of the proposed method on two key aspects: (i) the generation of fair data and (ii) the preservation of the utility of the generated data.

Attention Mechanism for Lithium-Ion Battery Lifespan Prediction: Temporal and Cyclic Attention

Accurately predicting the lifespan of lithium-ion batteries (LIBs) is pivotal for optimizing usage and preventing accidents. Previous studies in constructing prediction models often relied on inputs challenging to measure in real-time operations and failed to capture intra-cycle and inter-cycle data patterns, essential features for accurate predictions, comprehensively. In this study, we employ attention mechanisms (AM) to develop data-driven models for predicting LIB lifespan using easily measurable inputs such as voltage, current, temperature, and capacity data. The developed model integrates recurrent neural network (RNN) and convolutional neural network (CNN) components, featuring two types of attention mechanisms: temporal attention (TA) and cyclic attention (CA). The inclusion of TA aims to identify important time steps within each cycle by scoring the hidden states of the RNN, whereas CA strives to capture key features of inter-cycle correlations through self-attention (SA). This enhances model accuracy and elucidates critical features in the input data. To validate our method, we apply it to publicly available cycling data consisting of three batches of cycling modes. The calculated TA scores highlight the rest phase as a key characteristic distinguishing LIB data among different batches. Additionally, CA scores reveal variations in the importance of cycles across batches. By leveraging CA scores, we explore the potential to reduce the number of cycles in the input data. The single-head and multi-head attentions enable us to decrease the input dimension from 100 to 50 and 30 cycles, respectively.

Exploring Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learning

Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in both assessments and practices. An important aspect of MCQs is the distractors, i.e., incorrect options that are designed to target specific misconceptions or insufficient knowledge among students. To date, the task of crafting high-quality distractors has largely remained a labor-intensive process for teachers and learning content designers, which has limited scalability. In this work, we explore the task of automated distractor and corresponding feedback message generation in math MCQs using large language models. We establish a formulation of these two tasks and propose a simple, in-context learning-based solution. Moreover, we explore using two non-standard metrics to evaluate the quality of the generated distractors and feedback messages. We conduct extensive experiments on these tasks using a real-world MCQ dataset that contains student response information. Our findings suggest that there is a lot of room for improvement in automated distractor and feedback generation. We also outline several directions for future work

Knowledge Graph-Augmented Korean Generative Commonsense Reasoning

Generative commonsense reasoning refers to the task of generating acceptable and logical assumptions about everyday situations based on commonsense understanding. By utilizing an existing dataset such as Korean CommonGen, language generation models can learn commonsense reasoning specific to the Korean language. However, language models often fail to consider the relationships between concepts and the deep knowledge inherent to concepts. To address these limitations, we propose a method to utilize the Korean knowledge graph data for text generation. Our experimental result shows that the proposed method can enhance the efficiency of Korean commonsense inference, thereby underlining the significance of employing supplementary data.

Differentially Private Sharpness-Aware Training

Training deep learning models with differential privacy (DP) results in a degradation of performance. The training dynamics of models with DP show a significant difference from standard training, whereas understanding the geometric properties of private learning remains largely unexplored. In this paper, we investigate sharpness, a key factor in achieving better generalization, in private learning. We show that flat minima can help reduce the negative effects of per-example gradient clipping and the addition of Gaussian noise. We then verify the effectiveness of Sharpness-Aware Minimization (SAM) for seeking flat minima in private learning. However, we also discover that SAM is detrimental to the privacy budget and computational time due to its two-step optimization. Thus, we propose a new sharpness-aware training method that mitigates the privacy-optimization trade-off. Our experimental results demonstrate that the proposed method improves the performance of deep learning models with DP from both scratch and fine-tuning. Code is available at https://github.com/jinseongP/DPSAT.

A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing

In this paper, we take a preliminary step towards solving the problem of causal discovery in knowledge tracing, i.e., finding the underlying causal relationship among different skills from real-world student response data. This problem is important since it can potentially help us understand the causal relationship between different skills without extensive A/B testing, which can potentially help educators to design better curricula according to skill prerequisite information. Specifically, we propose a conceptual solution, a novel causal gated recurrent unit (GRU) module in a modified deep knowledge tracing model, which uses i) a learnable permutation matrix for causal ordering among skills and ii) an optionally learnable lower-triangular matrix for causal structure among skills. We also detail how to learn the model parameters in an end-to-end, differentiable way. Our solution placed among the top entries in Task 3 of the NeurIPS 2022 Challenge on Causal Insights for Learning Paths in Education. We detail preliminary experiments as evaluated on the challenge's public leaderboard since the ground truth causal structure has not been publicly released, making detailed local evaluation impossible.

SmartPhone: Exploring Keyword Mnemonic with Auto-generated Verbal and Visual Cues

In second language vocabulary learning, existing works have primarily focused on either the learning interface or scheduling personalized retrieval practices to maximize memory retention. However, the learning content, i.e., the information presented on flashcards, has mostly remained constant. Keyword mnemonic is a notable learning strategy that relates new vocabulary to existing knowledge by building an acoustic and imagery link using a keyword that sounds alike. Beyond that, producing verbal and visual cues associated with the keyword to facilitate building these links requires a manual process and is not scalable. In this paper, we explore an opportunity to use large language models to automatically generate verbal and visual cues for keyword mnemonics. Our approach, an end-to-end pipeline for auto-generating verbal and visual cues, can automatically generate highly memorable cues. We investigate the effectiveness of our approach via a human participant experiment by comparing it with manually generated cues.