Language Models (LMs) have demonstrated impressive capabilities in solving complex reasoning tasks, particularly when prompted to generate intermediate explanations. However, it remains an open question whether these intermediate reasoning traces represent a dynamic, evolving thought process or merely reflect sophisticated pattern recognition acquired during large scale pre training. Drawing inspiration from human cognition, where reasoning unfolds incrementally as new information is assimilated and internal models are continuously updated, we propose to delve deeper into the mental model of various LMs. We propose a new way to assess the mental modeling of LMs, where they are provided with problem details gradually, allowing each new piece of data to build upon and refine the model's internal representation of the task. We systematically compare this step by step mental modeling strategy with traditional full prompt methods across both text only and vision and text modalities. Experiments on the MathWorld dataset across different model sizes and problem complexities confirm that both text-based LLMs and multimodal LMs struggle to create mental representations, questioning how their internal cognitive processes work.

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

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.

Language models can solve complex reasoning tasks better by learning to generate rationales for their predictions. Often these models know how to solve a task but their auto-regressive decoding nature leads to incorrect results if they start incorrectly. We observe that smaller models in particular when corrected, can solve a task that they would have otherwise struggled with. We demonstrate this phenomenon by using a larger model to guide smaller models, which leads to significantly improved performance (up to +24 points on the GSM8K dataset by 7B models). To assist smaller models in initiating the starting step, we propose QuestCoT, where a smaller model first asks itself how to start, before proceeding with a chain of reasoning. On various multistep mathematical reasoning datasets over multiple smaller models, we show that getting the right start can lead to significant performance gains across all models (gains of up to +6 points on GSM8K, +9 on SVAMP, +5 on ASDiv, and +7 on MultiArith).

Accurately gauging the confidence level of Large Language Models' (LLMs) predictions is pivotal for their reliable application. However, LLMs are often uncalibrated inherently and elude conventional calibration techniques due to their proprietary nature and massive scale. In this work, we explore the potential of deriving confidence from the distribution of multiple randomly sampled model generations, via three measures of consistency. We perform an extensive evaluation across various open and closed-source models on nine reasoning datasets. Results show that consistency-based calibration methods outperform existing post-hoc approaches. Meanwhile, we find that factors such as intermediate explanations, model scaling, and larger sample sizes enhance calibration, while instruction-tuning makes calibration more difficult. Moreover, confidence scores obtained from consistency have the potential to enhance model performance. Finally, we offer practical guidance on choosing suitable consistency metrics for calibration, tailored to the characteristics of various LMs.

Large Language Models (LLMs) have demonstrated proficiency in their reasoning abilities, yet their large size presents scalability challenges and limits any further customization. In contrast, compact models offer customized training but often fall short in solving complex reasoning tasks. This study focuses on distilling the LLMs' decomposition skills into compact models using offline reinforcement learning. We leverage the advancements in the LLM's capabilities to provide feedback and generate a specialized task-specific dataset for training compact models. These models not only excel at straightforward tasks such as summarization and sentiment analysis but, with adept prompting, demonstrate proficiency in handling reasoning tasks that demand mathematical and logical abilities (Huang & Chang, 2022). Notably, Chain-of-Thoughts (CoT) prompting (Wei et al., 2022) and its variations (Kojima et al., 2022; Wang et al., 2022) have proven to be promising and relatively simple techniques for enhancing LLMs' reasoning capabilities. Within the realm of complex reasoning, the ability to decompose intricate questions into a set of simpler sub-questions represents a crucial and understudied component (Shridhar et al., 2022). While existing works predominantly focus on end-to-end solutions for reasoning (Zhou et al., 2022; Lyu et al., 2023), the specific aspect of breaking down complex questions into simpler components has received limited attention. The creation of specialized datasets and benchmarks is integral to advancing the field of Deep Learning (Guss et al., 2019; Vinyals et al., 2019; Fu et al., 2020; Kurenkov et al., 2023). This work addresses the gap in understanding and exploration of the reasoning subquestioning process by providing a dataset and baselines for further research in this direction. Compounding the challenge is the computational overhead associated with large model sizes, making reasoning tasks computationally expensive and time-consuming when tuning models. Concurrently, approaches similar to Chain-of-Thoughts (CoT) may incur expenses, given that models with superior reasoning abilities are not available for free. In response, distilling distinct components of the reasoning process into smaller models emerges as a promising avenue for research.

Large language models (LLMs) can improve their accuracy on various tasks through iteratively refining and revising their output based on feedback. We observe that these revisions can introduce errors, in which case it is better to roll back to a previous result. Further, revisions are typically homogeneous: they use the same reasoning method that produced the initial answer, which may not correct errors. To enable exploration in this space, we present SCREWS, a modular framework for reasoning with revisions. It is comprised of three main modules: Sampling, Conditional Resampling, and Selection, each consisting of sub-modules that can be hand-selected per task. We show that SCREWS not only unifies several previous approaches under a common framework, but also reveals several novel strategies for identifying improved reasoning chains. We evaluate our framework with state-of-the-art LLMs (ChatGPT and GPT-4) on a diverse set of reasoning tasks and uncover useful new reasoning strategies for each: arithmetic word problems, multi-hop question answering, and code debugging. Heterogeneous revision strategies prove to be important, as does selection between original and revised candidates.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Step-by-step reasoning approaches like chain of thought (CoT) have proved to be very effective in inducing reasoning capabilities in large language models. However, the success of the CoT approach is fundamentally tied to the model size, and billion parameter-scale models are often needed to get CoT to work. In this paper, we propose a knowledge distillation approach that leverages the step-by-step CoT reasoning capabilities of larger models and distills these abilities into smaller models. In this work, we propose an alternative reasoning scheme, Socratic CoT, that learns a decomposition of the original problem into a sequence of subproblems and uses it to guide the intermediate reasoning steps. We use Socratic CoT to train a combination of two small distilled models: a problem decomposer and a subproblem solver. In practice, given a new problem, the two distilled models work in sync to decompose and solve complex problems. On multiple reasoning datasets (GSM8K, StrategyQA, and SVAMP), our proposed distillation strategies boosts the performance of smaller models over 70% compared to the baselines. Finally, we investigate when Socratic CoT is an effective alternative to CoT, demonstrating cases where a much smaller model (GPT-2 large) can outperform a 10X larger model (GPT-3 6B). Our code is available here: https://github.com/kumar-shridhar/Distiiling-LM