Regressive Side Effects of Training Language Models to Mimic Student Misconceptions

This paper presents a novel exploration into the regressive side effects of training Large Language Models (LLMs) to mimic student misconceptions for personalized education. We highlight the problem that as LLMs are trained to more accurately mimic student misconceptions, there is a compromise in the factual integrity and reasoning ability of the models. Our work involved training an LLM on a student-tutor dialogue dataset to predict student responses. The results demonstrated a decrease in the model's performance across multiple benchmark datasets, including the ARC reasoning challenge and TruthfulQA, which evaluates the truthfulness of model's generated responses. Furthermore, the HaluEval Dial dataset, used for hallucination detection, and MemoTrap, a memory-based task dataset, also reported a decline in the model accuracy. To combat these side effects, we introduced a "hallucination token" technique. This token, appended at the beginning of each student response during training, instructs the model to switch between mimicking student misconceptions and providing factually accurate responses. Despite the significant improvement across all datasets, the technique does not completely restore the LLM's baseline performance, indicating the need for further research in this area. This paper contributes to the ongoing discussion on the use of LLMs for student modeling, emphasizing the need for a balance between personalized education and factual accuracy.

Automated Long Answer Grading with RiceChem Dataset

We introduce a new area of study in the field of educational Natural Language Processing: Automated Long Answer Grading (ALAG). Distinguishing itself from Automated Short Answer Grading (ASAG) and Automated Essay Grading (AEG), ALAG presents unique challenges due to the complexity and multifaceted nature of fact-based long answers. To study ALAG, we introduce RiceChem, a dataset derived from a college chemistry course, featuring real student responses to long-answer questions with an average word count notably higher than typical ASAG datasets. We propose a novel approach to ALAG by formulating it as a rubric entailment problem, employing natural language inference models to verify whether each criterion, represented by a rubric item, is addressed in the student's response. This formulation enables the effective use of MNLI for transfer learning, significantly improving the performance of models on the RiceChem dataset. We demonstrate the importance of rubric-based formulation in ALAG, showcasing its superiority over traditional score-based approaches in capturing the nuances of student responses. We also investigate the performance of models in cold start scenarios, providing valuable insights into the practical deployment considerations in educational settings. Lastly, we benchmark state-of-the-art open-sourced Large Language Models (LLMs) on RiceChem and compare their results to GPT models, highlighting the increased complexity of ALAG compared to ASAG. Despite leveraging the benefits of a rubric-based approach and transfer learning from MNLI, the lower performance of LLMs on RiceChem underscores the significant difficulty posed by the ALAG task. With this work, we offer a fresh perspective on grading long, fact-based answers and introduce a new dataset to stimulate further research in this important area. Code: \url{https://github.com/luffycodes/Automated-Long-Answer-Grading}.

Marking: Visual Grading with Highlighting Errors and Annotating Missing Bits

In this paper, we introduce "Marking", a novel grading task that enhances automated grading systems by performing an in-depth analysis of student responses and providing students with visual highlights. Unlike traditional systems that provide binary scores, "marking" identifies and categorizes segments of the student response as correct, incorrect, or irrelevant and detects omissions from gold answers. We introduce a new dataset meticulously curated by Subject Matter Experts specifically for this task. We frame "Marking" as an extension of the Natural Language Inference (NLI) task, which is extensively explored in the field of Natural Language Processing. The gold answer and the student response play the roles of premise and hypothesis in NLI, respectively. We subsequently train language models to identify entailment, contradiction, and neutrality from student response, akin to NLI, and with the added dimension of identifying omissions from gold answers. Our experimental setup involves the use of transformer models, specifically BERT and RoBERTa, and an intelligent training step using the e-SNLI dataset. We present extensive baseline results highlighting the complexity of the "Marking" task, which sets a clear trajectory for the upcoming study. Our work not only opens up new avenues for research in AI-powered educational assessment tools, but also provides a valuable benchmark for the AI in education community to engage with and improve upon in the future. The code and dataset can be found at https://github.com/luffycodes/marking.

PIDformer: Transformer Meets Control Theory

In this work, we address two main shortcomings of transformer architectures: input corruption and rank collapse in their output representation. We unveil self-attention as an autonomous state-space model that inherently promotes smoothness in its solutions, leading to lower-rank outputs and diminished representation capacity. Moreover, the steady-state solution of the model is sensitive to input perturbations. We incorporate a Proportional-Integral-Derivative (PID) closed-loop feedback control system with a reference point into the model to improve robustness and representation capacity. This integration aims to preserve high-frequency details while bolstering model stability, rendering it more noise-resilient. The resulting controlled state-space model is theoretically proven robust and adept at addressing the rank collapse. Motivated by this control framework, we derive a novel class of transformers, PID-controlled Transformer (PIDformer), aimed at improving robustness and mitigating the rank-collapse issue inherent in softmax transformers. We empirically evaluate the model for advantages and robustness against baseline transformers across various practical tasks, including object classification, image segmentation, and language modeling.

Pedagogical Alignment of Large Language Models

In this paper, we introduce the novel concept of pedagogically aligned Large Language Models (LLMs) that signifies a transformative shift in the application of LLMs within educational contexts. Rather than providing direct responses to user queries, pedagogically-aligned LLMs function as scaffolding tools, breaking complex problems into manageable subproblems and guiding students towards the final answer through constructive feedback and hints. The objective is to equip learners with problem-solving strategies that deepen their understanding and internalization of the subject matter. Previous research in this field has primarily applied the supervised finetuning approach without framing the objective as an alignment problem, hence not employing reinforcement learning through human feedback (RLHF) methods. This study reinterprets the narrative by viewing the task through the lens of alignment and demonstrates how RLHF methods emerge naturally as a superior alternative for aligning LLM behaviour. Building on this perspective, we propose a novel approach for constructing a reward dataset specifically designed for the pedagogical alignment of LLMs. We apply three state-of-the-art RLHF algorithms and find that they outperform SFT significantly. Our qualitative analyses across model differences and hyperparameter sensitivity further validate the superiority of RLHF over SFT. Also, our study sheds light on the potential of online feedback for enhancing the performance of pedagogically-aligned LLMs, thus providing valuable insights for the advancement of these models in educational settings.

[Re] The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Non-Gaussian Observation Models

Kalman filters provide a straightforward and interpretable means to estimate hidden or latent variables, and have found numerous applications in control, robotics, signal processing, and machine learning. One such application is neural decoding for neuroprostheses. In 2020, Burkhart et al. thoroughly evaluated their new version of the Kalman filter that leverages Bayes' theorem to improve filter performance for highly non-linear or non-Gaussian observation models. This work provides an open-source Python alternative to the authors' MATLAB algorithm. Specifically, we reproduce their most salient results for neuroscientific contexts and further examine the efficacy of their filter using multiple random seeds and previously unused trials from the authors' dataset. All experiments were performed offline on a single computer.

Mitigating Over-smoothing in Transformers via Regularized Nonlocal Functionals

Transformers have achieved remarkable success in a wide range of natural language processing and computer vision applications. However, the representation capacity of a deep transformer model is degraded due to the over-smoothing issue in which the token representations become identical when the model's depth grows. In this work, we show that self-attention layers in transformers minimize a functional which promotes smoothness, thereby causing token uniformity. We then propose a novel regularizer that penalizes the norm of the difference between the smooth output tokens from self-attention and the input tokens to preserve the fidelity of the tokens. Minimizing the resulting regularized energy functional, we derive the Neural Transformer with a Regularized Nonlocal Functional (NeuTRENO), a novel class of transformer models that can mitigate the over-smoothing issue. We empirically demonstrate the advantages of NeuTRENO over the baseline transformers and state-of-the-art methods in reducing the over-smoothing of token representations on various practical tasks, including object classification, image segmentation, and language modeling.

Novice Learner and Expert Tutor: Evaluating Math Reasoning Abilities of Large Language Models with Misconceptions

We propose novel evaluations for mathematical reasoning capabilities of Large Language Models (LLMs) based on mathematical misconceptions. Our primary approach is to simulate LLMs as a novice learner and an expert tutor, aiming to identify the incorrect answer to math question resulted from a specific misconception and to recognize the misconception(s) behind an incorrect answer, respectively. Contrary to traditional LLMs-based mathematical evaluations that focus on answering math questions correctly, our approach takes inspirations from principles in educational learning sciences. We explicitly ask LLMs to mimic a novice learner by answering questions in a specific incorrect manner based on incomplete knowledge; and to mimic an expert tutor by identifying misconception(s) corresponding to an incorrect answer to a question. Using simple grade-school math problems, our experiments reveal that, while LLMs can easily answer these questions correctly, they struggle to identify 1) the incorrect answer corresponding to specific incomplete knowledge (misconceptions); 2) the misconceptions that explain particular incorrect answers. Our study indicates new opportunities for enhancing LLMs' math reasoning capabilities, especially on developing robust student simulation and expert tutoring models in the educational applications such as intelligent tutoring systems.

Implicit Neural Representations and the Algebra of Complex Wavelets

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Code Soliloquies for Accurate Calculations in Large Language Models

High-quality conversational datasets are integral to the successful development of Intelligent Tutoring Systems (ITS) that employ a Large Language Model (LLM) backend. These datasets, when used to fine-tune the LLM backend, significantly enhance the quality of interactions between students and ITS. A common strategy for developing these datasets involves generating synthetic student-teacher dialogues using advanced GPT-4 models. However, challenges arise when these dialogues demand complex calculations, common in subjects like physics. Despite its advanced capabilities, GPT-4's performance falls short in reliably handling even simple multiplication tasks, marking a significant limitation in its utility for these subjects. To address these challenges, this paper introduces an innovative stateful prompt design. Our approach generates a mock conversation between a student and a tutorbot, both roles simulated by GPT-4. Each student response triggers a soliloquy (an inner monologue) in the GPT-tutorbot, which assesses whether its response would necessitate calculations. If so, it proceeds to script the required code in Python and then uses the resulting output to construct its response to the student. Our approach notably enhances the quality of synthetic conversation datasets, especially for subjects that are calculation-intensive. Our findings show that our Higgs model -- a LLaMA finetuned with datasets generated through our novel stateful prompt design -- proficiently utilizes Python for computations. Consequently, finetuning with our datasets enriched with code soliloquies enhances not just the accuracy but also the computational reliability of Higgs' responses.