Navigating the Helpfulness-Truthfulness Trade-Off with Uncertainty-Aware Instruction Fine-Tuning

Instruction Fine-tuning (IFT) can enhance the helpfulness of Large Language Models (LLMs), but it may lower their truthfulness. This trade-off arises because IFT steers LLMs to generate responses with long-tail knowledge that is not well covered during pre-training, leading to more informative but less truthful answers when generalizing to unseen tasks. In this paper, we empirically demonstrate this helpfulness-truthfulness trade-off in IFT and propose $\textbf{UNIT}$, a novel IFT paradigm to address it. UNIT teaches LLMs to recognize their uncertainty and explicitly reflect it at the end of their responses. Experimental results show that UNIT-tuned models maintain their helpfulness while distinguishing between certain and uncertain claims, thereby reducing hallucinations.

Grammar Control in Dialogue Response Generation for Language Learning Chatbots

Chatbots based on large language models offer cheap conversation practice opportunities for language learners. However, they are hard to control for linguistic forms that correspond to learners' current needs, such as grammar. We control grammar in chatbot conversation practice by grounding a dialogue response generation model in a pedagogical repository of grammar skills. We also explore how this control helps learners to produce specific grammar. We comprehensively evaluate prompting, fine-tuning, and decoding strategies for grammar-controlled dialogue response generation. Strategically decoding Llama3 outperforms GPT-3.5 when tolerating minor response quality losses. Our simulation predicts grammar-controlled responses to support grammar acquisition adapted to learner proficiency. Existing language learning chatbots and research on second language acquisition benefit from these affordances. Code available on GitHub.

Investigating the Zone of Proximal Development of Language Models for In-Context Learning

In this paper, we introduce a learning analytics framework to analyze the in-context learning (ICL) behavior of large language models (LLMs) through the lens of the Zone of Proximal Development (ZPD), an established theory in educational psychology. ZPD delineates the space between what a learner is capable of doing unsupported and what the learner cannot do even with support. We adapt this concept to ICL, measuring the ZPD of LLMs based on model performance on individual examples with and without ICL. Furthermore, we propose an item response theory (IRT) model to predict the distribution of zones for LLMs. Our findings reveal a series of intricate and multifaceted behaviors of ICL, providing new insights into understanding and leveraging this technique. Finally, we demonstrate how our framework can enhance LLM in both inference and fine-tuning scenarios: (1) By predicting a model's zone of proximal development, we selectively apply ICL to queries that are most likely to benefit from demonstrations, achieving a better balance between inference cost and performance; (2) We propose a human-like curriculum for fine-tuning, which prioritizes examples within the model's ZPD. The curriculum results in improved performance, and we explain its effectiveness through an analysis of the training dynamics of LLMs.

How to Select Datapoints for Efficient Human Evaluation of NLG Models?

Human evaluation is the gold-standard for evaluating text generation models. It is also expensive, and to fit budgetary constraints, a random subset of the test data is often chosen in practice. The randomly selected data may not accurately represent test performance, making this approach economically inefficient for model comparison. Thus, in this work, we develop a suite of selectors to get the most informative datapoints for human evaluation while taking the evaluation costs into account. We show that selectors based on variance in automated metric scores, diversity in model outputs, or Item Response Theory outperform random selection. We further develop an approach to distill these selectors to the scenario where the model outputs are not yet available. In particular, we introduce source-based estimators, which predict item usefulness for human evaluation just based on the source texts. We demonstrate the efficacy of our selectors in two common NLG tasks, machine translation and summarization, and show that up to only ~50% of the test data is needed to produce the same evaluation result as the entire data. Our implementations are published in the subset2evaluate package.

Likelihood as a Performance Gauge for Retrieval-Augmented Generation

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

SIKeD: Self-guided Iterative Knowledge Distillation for mathematical reasoning

Large Language Models (LLMs) can transfer their reasoning skills to smaller models by teaching them to generate the intermediate reasoning process required to solve multistep reasoning tasks. While LLMs can accurately solve reasoning tasks through a variety of strategies, even without fine-tuning, smaller models are not expressive enough to fit the LLMs distribution on all strategies when distilled and tend to prioritize one strategy over the others. This reliance on one strategy poses a challenge for smaller models when attempting to solve reasoning tasks that may be difficult with their preferred strategy. To address this, we propose a distillation method SIKeD (Self-guided Iterative Knowledge Distillation for mathematical reasoning), where the LLM teaches the smaller model to approach a task using different strategies and the smaller model uses its self-generated on-policy outputs to choose the most suitable strategy for the given task. The training continues in a self-guided iterative manner, where for each training iteration, a decision is made on how to combine the LLM data with the self-generated outputs. Unlike traditional distillation methods, SIKeD allows the smaller model to learn which strategy is suitable for a given task while continuously learning to solve a task using different strategies. Our experiments on various mathematical reasoning datasets show that SIKeD significantly outperforms traditional distillation techniques across smaller models of different sizes. Our code is available at: https://github.com/kumar-shridhar/SIKeD

SMART: Self-learning Meta-strategy Agent for Reasoning Tasks

Tasks requiring deductive reasoning, especially those involving multiple steps, often demand adaptive strategies such as intermediate generation of rationales or programs, as no single approach is universally optimal. While Language Models (LMs) can enhance their outputs through iterative self-refinement and strategy adjustments, they frequently fail to apply the most effective strategy in their first attempt. This inefficiency raises the question: Can LMs learn to select the optimal strategy in the first attempt, without a need for refinement? To address this challenge, we introduce SMART (Self-learning Meta-strategy Agent for Reasoning Tasks), a novel framework that enables LMs to autonomously learn and select the most effective strategies for various reasoning tasks. We model the strategy selection process as a Markov Decision Process and leverage reinforcement learning-driven continuous self-improvement to allow the model to find the suitable strategy to solve a given task. Unlike traditional self-refinement methods that rely on multiple inference passes or external feedback, SMART allows an LM to internalize the outcomes of its own reasoning processes and adjust its strategy accordingly, aiming for correct solutions on the first attempt. Our experiments across various reasoning datasets and with different model architectures demonstrate that SMART significantly enhances the ability of models to choose optimal strategies without external guidance (+15 points on the GSM8K dataset). By achieving higher accuracy with a single inference pass, SMART not only improves performance but also reduces computational costs for refinement-based strategies, paving the way for more efficient and intelligent reasoning in LMs.

Efficiently Computing Susceptibility to Context in Language Models

One strength of modern language models is their ability to incorporate information from a user-input context when answering queries. However, they are not equally sensitive to the subtle changes to that context. To quantify this, Du et al. (2024) gives an information-theoretic metric to measure such sensitivity. Their metric, susceptibility, is defined as the degree to which contexts can influence a model's response to a query at a distributional level. However, exactly computing susceptibility is difficult and, thus, Du et al. (2024) falls back on a Monte Carlo approximation. Due to the large number of samples required, the Monte Carlo approximation is inefficient in practice. As a faster alternative, we propose Fisher susceptibility, an efficient method to estimate the susceptibility based on Fisher information. Empirically, we validate that Fisher susceptibility is comparable to Monte Carlo estimated susceptibility across a diverse set of query domains despite its being $70\times$ faster. Exploiting the improved efficiency, we apply Fisher susceptibility to analyze factors affecting the susceptibility of language models. We observe that larger models are as susceptible as smaller ones.

MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs

Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to problems that are more complex than the ones on which they have been trained. Empirical investigations of such questions are impeded by two major flaws of current evaluations: (i) much of the evaluation data is contaminated, in the sense that it has already been seen during training, and (ii) benchmark datasets do not capture how problem proofs may be arbitrarily complex in various ways. As a step towards addressing these issues, we present a framework for evaluating LLMs on problems that have arbitrarily complex arithmetic proofs, called MathGAP. MathGAP generates problems that follow fixed proof specifications -- along with chain-of-thought reasoning annotations -- enabling systematic studies on generalization with respect to arithmetic proof complexity. We apply MathGAP to analyze how in-context learning interacts with generalization to problems that have more complex proofs. We find that among the models tested, most show a significant decrease in performance as proofs get deeper and wider. This effect is more pronounced in complex, nonlinear proof structures, which are challenging even for GPT-4o. Surprisingly, providing in-context examples from the same distribution as the test set is not always beneficial for performance. In particular, zero-shot prompting as well as demonstrating a diverse range of examples that are less complex than the test data sometimes yield similar or higher accuracies.

LLM-based Cognitive Models of Students with Misconceptions

Accurately modeling student cognition is crucial for developing effective AI-driven educational technologies. A key challenge is creating realistic student models that satisfy two essential properties: (1) accurately replicating specific misconceptions, and (2) correctly solving problems where these misconceptions are not applicable. This dual requirement reflects the complex nature of student understanding, where misconceptions coexist with correct knowledge. This paper investigates whether Large Language Models (LLMs) can be instruction-tuned to meet this dual requirement and effectively simulate student thinking in algebra. We introduce MalAlgoPy, a novel Python library that generates datasets reflecting authentic student solution patterns through a graph-based representation of algebraic problem-solving. Utilizing MalAlgoPy, we define and examine Cognitive Student Models (CSMs) - LLMs instruction tuned to faithfully emulate realistic student behavior. Our findings reveal that LLMs trained on misconception examples can efficiently learn to replicate errors. However, the training diminishes the model's ability to solve problems correctly, particularly for problem types where the misconceptions are not applicable, thus failing to satisfy second property of CSMs. We demonstrate that by carefully calibrating the ratio of correct to misconception examples in the training data - sometimes as low as 0.25 - it is possible to develop CSMs that satisfy both properties. Our insights enhance our understanding of AI-based student models and pave the way for effective adaptive learning systems.