While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.
Closed-source agents suffer from several issues such as a lack of affordability, transparency, and reproducibility, particularly on complex interactive tasks. This motivates the development of open-source alternatives. We introduce LUMOS, one of the first frameworks for training open-source LLM-based agents. LUMOS features a learnable, unified, and modular architecture with a planning module that learns high-level subgoal generation, and a grounding module trained to translate these into actions using various tools in the execution module. The design allows for modular upgrades and wider applicability to diverse interactive tasks. To foster generalizable agent learning, we collect large-scale, unified, and high-quality training annotations derived from diverse ground-truth reasoning rationales across various complex interactive tasks. On 9 datasets, LUMOS exhibits several key advantages: (1) LUMOS excels multiple larger open-source agents on the held-out datasets (unused for training) for each task type. LUMOS even surpasses GPT agents on QA and web tasks; (2) LUMOS outperforms open-source agents produced by chain-of-thoughts and unmodularized integrated training; and (3) LUMOS effectively generalizes to unseen tasks, outperforming 33B-scale agents and domain-specific agents.
Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.
Recent works have showcased the ability of LLMs to embody diverse personas in their responses, exemplified by prompts like 'You are Yoda. Explain the Theory of Relativity.' While this ability allows personalization of LLMs and enables human behavior simulation, its effect on LLMs' capabilities remains unclear. To fill this gap, we present the first extensive study of the unintended side-effects of persona assignment on the ability of LLMs to perform basic reasoning tasks. Our study covers 24 reasoning datasets, 4 LLMs, and 19 diverse personas (e.g. an Asian person) spanning 5 socio-demographic groups. Our experiments unveil that LLMs harbor deep rooted bias against various socio-demographics underneath a veneer of fairness. While they overtly reject stereotypes when explicitly asked ('Are Black people less skilled at mathematics?'), they manifest stereotypical and erroneous presumptions when asked to answer questions while adopting a persona. These can be observed as abstentions in responses, e.g., 'As a Black person, I can't answer this question as it requires math knowledge', and generally result in a substantial performance drop. Our experiments with ChatGPT-3.5 show that this bias is ubiquitous - 80% of our personas demonstrate bias; it is significant - some datasets show performance drops of 70%+; and can be especially harmful for certain groups - some personas suffer statistically significant drops on 80%+ of the datasets. Overall, all 4 LLMs exhibit this bias to varying extents, with GPT-4-Turbo showing the least but still a problematic amount of bias (evident in 42% of the personas). Further analysis shows that these persona-induced errors can be hard-to-discern and hard-to-avoid. Our findings serve as a cautionary tale that the practice of assigning personas to LLMs - a trend on the rise - can surface their deep-rooted biases and have unforeseeable and detrimental side-effects.
Large Language Models (LLMs) are smart but forgetful. Recent studies, (e.g., (Bubeck et al., 2023)) on modern LLMs have shown that they are capable of performing amazing tasks typically necessitating human-level intelligence. However, unlike humans, frozen LLMs do not improve over time; they neither acquire new knowledge nor learn from their successes or failures. Some approaches to improving the intelligence of LLMs include fine-tuning models based on problem-solving performance (Zelikman et al., 2022), and building bigger and more sophisticated models (Bubeck et al., 2023). However, these methods have the drawback of requiring substantial data and computational resources to retrain existing models. In this paper, we explore the use of Retrieval Augmented Generation, also known as RAG (Lewis et al., 2021) to improve problem-solving performance. We propose ARM-RAG (Auxiliary Rationale Memory for Retrieval Augmented Generation), a system that learns from its successes without incurring high training costs. We demonstrate that the storage and subsequent retrieval of reasoning chains have a positive influence on performance in grade-school math problems.
While transformer models exhibit strong capabilities on linguistic tasks, their complex architectures make them difficult to interpret. Recent work has aimed to reverse engineer transformer models into human-readable representations called circuits that implement algorithmic functions. We extend this research by analyzing and comparing circuits for similar sequence continuation tasks, which include increasing sequences of Arabic numerals, number words, and months. By applying circuit interpretability analysis, we identify a key sub-circuit in both GPT-2 Small and Llama-2-7B responsible for detecting sequence members and for predicting the next member in a sequence. Our analysis reveals that semantically related sequences rely on shared circuit subgraphs with analogous roles. Additionally, we show that this sub-circuit has effects on various math-related prompts, such as on intervaled circuits, Spanish number word and months continuation, and natural language word problems. Overall, documenting shared computational structures enables better model behavior predictions, identification of errors, and safer editing procedures. This mechanistic understanding of transformers is a critical step towards building more robust, aligned, and interpretable language models.
To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.
Solving math word problems depends on how to articulate the problems, the lens through which models view human linguistic expressions. Real-world settings count on such a method even more due to the diverse practices of the same mathematical operations. Earlier works constrain available thinking processes by limited prediction strategies without considering their significance in acquiring mathematical knowledge. We introduce Attention-based THought Expansion Network Architecture (ATHENA) to tackle the challenges of real-world practices by mimicking human thought expansion mechanisms in the form of neural network propagation. A thought expansion recurrently generates the candidates carrying the thoughts of possible math expressions driven from the previous step and yields reasonable thoughts by selecting the valid pathways to the goal. Our experiments show that ATHENA achieves a new state-of-the-art stage toward the ideal model that is compelling in variant questions even when the informativeness in training examples is restricted.
Large Language Models (LLMs) have achieved tremendous progress, yet they still often struggle with challenging reasoning problems. Current approaches address this challenge by sampling or searching detailed and low-level reasoning chains. However, these methods are still limited in their exploration capabilities, making it challenging for correct solutions to stand out in the huge solution space. In this work, we unleash LLMs' creative potential for exploring multiple diverse problem solving strategies by framing an LLM as a hierarchical policy via in-context learning. This policy comprises of a visionary leader that proposes multiple diverse high-level problem-solving tactics as hints, accompanied by a follower that executes detailed problem-solving processes following each of the high-level instruction. The follower uses each of the leader's directives as a guide and samples multiple reasoning chains to tackle the problem, generating a solution group for each leader proposal. Additionally, we propose an effective and efficient tournament-based approach to select among these explored solution groups to reach the final answer. Our approach produces meaningful and inspiring hints, enhances problem-solving strategy exploration, and improves the final answer accuracy on challenging problems in the MATH dataset. Code will be released at https://github.com/lz1oceani/LLM-As-Hierarchical-Policy.
Existing research predominantly focuses on developing powerful language learning models (LLMs) for mathematical reasoning within monolingual languages, with few explorations in preserving efficacy in a multilingual context. To bridge this gap, this paper pioneers exploring and training powerful Multilingual Math Reasoning (xMR) LLMs. Firstly, by utilizing translation, we construct the first multilingual math reasoning instruction dataset, MGSM8KInstruct, encompassing ten distinct languages, thus addressing the issue of training data scarcity in xMR tasks. Based on the collected dataset, we propose different training strategies to build powerful xMR LLMs, named MathOctopus, notably outperform conventional open-source LLMs and exhibit superiority over ChatGPT in few-shot scenarios. Notably, MathOctopus-13B reaches 47.6% accuracy which exceeds ChatGPT 46.3% on MGSM testset. Beyond remarkable results, we unearth several pivotal observations and insights from extensive experiments: (1) When extending the rejection sampling strategy to the multilingual context, it proves effective for model performances, albeit limited. (2) Employing parallel corpora for math Supervised Fine-Tuning (SFT) across multiple languages not only significantly enhances model performance multilingually but also elevates their monolingual performance. This indicates that crafting multilingual corpora can be regarded as a vital strategy for enhancing model performance in a specific language, especially in mathematical reasoning tasks. For instance, MathOctopus-7B improves its counterparts that trained on English from 42.2% to 50.8% on GSM8K testset. Codes are available at https://github.com/microsoft/MathOctopus.
Large language models (LLMs) recently exhibited remarkable reasoning capabilities on solving math problems. To further improve their reasoning capabilities, this work explores whether LLMs can LEarn from MistAkes (LEMA), akin to the human learning process. Consider a human student who failed to solve a math problem, he will learn from what mistake he has made and how to correct it. Mimicking this error-driven learning process, LEMA incorporates mistake-correction data pairs during fine-tuning LLMs. Specifically, we first collect inaccurate reasoning paths from various LLMs, and then employ GPT-4 as a ''corrector'' to identify the mistake step, explain the reason for the mistake, correct the mistake and generate the final answer. In addition, we apply a correction-centric evolution strategy that effectively expands the question set for generating correction data. Experiments across various LLMs and reasoning tasks show that LEMA effectively improves CoT-alone fine-tuning. Our further ablations shed light on the non-homogeneous effectiveness between CoT data and correction data. These results suggest a significant potential for LLMs to improve through learning from their mistakes. Our code, models and prompts are publicly available at https://github.com/microsoft/LEMA.
Previous work adopts large language models (LLMs) as evaluators to evaluate natural language process (NLP) tasks. However, certain shortcomings, e.g., fairness, scope, and accuracy, persist for current LLM evaluators. To analyze whether LLMs can serve as reliable alternatives to humans, we examine the fine-grained alignment between LLM evaluators and human annotators, particularly in understanding the target evaluation tasks and conducting evaluations that meet diverse criteria. This paper explores both conventional tasks (e.g., story generation) and alignment tasks (e.g., math reasoning), each with different evaluation criteria. Our analysis shows that 1) LLM evaluators can generate unnecessary criteria or omit crucial criteria, resulting in a slight deviation from the experts. 2) LLM evaluators excel in general criteria, such as fluency, but face challenges with complex criteria, such as numerical reasoning. We also find that LLM-pre-drafting before human evaluation can help reduce the impact of human subjectivity and minimize annotation outliers in pure human evaluation, leading to more objective evaluation.
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in formalizing mathematics, and discovering connections between different mathematical areas, to name a few. While prior work has leveraged computers for exhaustive mathematical proof search, recent efforts based on large language models (LLMs) aspire to position computing platforms as co-contributors in the mathematical research process. Despite their current limitations in logic and mathematical tasks, there is growing interest in melding theorem proving systems with foundation models. This work investigates the applicability of LLMs in formalizing advanced mathematical concepts and proposes a framework that can critically review and check mathematical reasoning in research papers. Given the noted reasoning shortcomings of LLMs, our approach synergizes the capabilities of proof assistants, specifically PVS, with LLMs, enabling a bridge between textual descriptions in academic papers and formal specifications in PVS. By harnessing the PVS environment, coupled with data ingestion and conversion mechanisms, we envision an automated process, called \emph{math-PVS}, to extract and formalize mathematical theorems from research papers, offering an innovative tool for academic review and discovery.
In this paper, we evaluate different abilities of GPT-4V including visual understanding, language understanding, visual puzzle solving, and understanding of other modalities such as depth, thermal, video, and audio. To estimate GPT-4V's performance, we manually construct 656 test instances and carefully evaluate the results of GPT-4V. The highlights of our findings are as follows: (1) GPT-4V exhibits impressive performance on English visual-centric benchmarks but fails to recognize simple Chinese texts in the images; (2) GPT-4V shows inconsistent refusal behavior when answering questions related to sensitive traits such as gender, race, and age; (3) GPT-4V obtains worse results than GPT-4 (API) on language understanding tasks including general language understanding benchmarks and visual commonsense knowledge evaluation benchmarks; (4) Few-shot prompting can improve GPT-4V's performance on both visual understanding and language understanding; (5) GPT-4V struggles to find the nuances between two similar images and solve the easy math picture puzzles; (6) GPT-4V shows non-trivial performance on the tasks of similar modalities to image, such as video and thermal. Our experimental results reveal the ability and limitations of GPT-4V and we hope our paper can provide some insights into the application and research of GPT-4V.
Math Word Problems (MWP) aims to automatically solve mathematical questions given in texts. Previous studies tend to design complex models to capture additional information in the original text so as to enable the model to gain more comprehensive features. In this paper, we turn our attention in the opposite direction, and work on how to discard redundant features containing spurious correlations for MWP. To this end, we design an Expression Syntax Information Bottleneck method for MWP (called ESIB) based on variational information bottleneck, which extracts essential features of expression syntax tree while filtering latent-specific redundancy containing syntax-irrelevant features. The key idea of ESIB is to encourage multiple models to predict the same expression syntax tree for different problem representations of the same problem by mutual learning so as to capture consistent information of expression syntax tree and discard latent-specific redundancy. To improve the generalization ability of the model and generate more diverse expressions, we design a self-distillation loss to encourage the model to rely more on the expression syntax information in the latent space. Experimental results on two large-scale benchmarks show that our model not only achieves state-of-the-art results but also generates more diverse solutions. The code is available.
Natural Language Processing (NLP) is poised to substantially influence the world. However, significant progress comes hand-in-hand with substantial risks. Addressing them requires broad engagement with various fields of study. Yet, little empirical work examines the state of such engagement (past or current). In this paper, we quantify the degree of influence between 23 fields of study and NLP (on each other). We analyzed ~77k NLP papers, ~3.1m citations from NLP papers to other papers, and ~1.8m citations from other papers to NLP papers. We show that, unlike most fields, the cross-field engagement of NLP, measured by our proposed Citation Field Diversity Index (CFDI), has declined from 0.58 in 1980 to 0.31 in 2022 (an all-time low). In addition, we find that NLP has grown more insular -- citing increasingly more NLP papers and having fewer papers that act as bridges between fields. NLP citations are dominated by computer science; Less than 8% of NLP citations are to linguistics, and less than 3% are to math and psychology. These findings underscore NLP's urgent need to reflect on its engagement with various fields.
As large language models (LLMs) have shown effectiveness with different prompting methods, such as Chain of Thought, Program of Thought, we find that these methods have formed a great complementarity to each other on math reasoning tasks. In this work, we propose XoT, an integrated problem solving framework by prompting LLMs with diverse reasoning thoughts. For each question, XoT always begins with selecting the most suitable method then executes each method iteratively. Within each iteration, XoT actively checks the validity of the generated answer and incorporates the feedback from external executors, allowing it to dynamically switch among different prompting methods. Through extensive experiments on 10 popular math reasoning datasets, we demonstrate the effectiveness of our proposed approach and thoroughly analyze the strengths of each module. Moreover, empirical results suggest that our framework is orthogonal to recent work that makes improvements on single reasoning methods and can further generalise to logical reasoning domain. By allowing method switching, XoT provides a fresh perspective on the collaborative integration of diverse reasoning thoughts in a unified framework. The code is available at https://github.com/tengxiaoliu/XoT.
The self-improving ability of large language models (LLMs), enabled by prompting them to analyze and revise their own outputs, has garnered significant interest in recent research. However, this ability has been shown to be absent and difficult to learn for smaller models, thus widening the performance gap between state-of-the-art LLMs and more cost-effective and faster ones. To reduce this gap, we introduce TriPosT, a training algorithm that endows smaller models with such self-improvement ability, and show that our approach can improve a LLaMA-7b's performance on math and reasoning tasks by up to 7.13%. In contrast to prior work, we achieve this by using the smaller model to interact with LLMs to collect feedback and improvements on its own generations. We then replay this experience to train the small model. Our experiments on four math and reasoning datasets show that the interactive experience of learning from and correcting its own mistakes is crucial for small models to improve their performance.
Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of subgoal-based methods, we propose a novel framework called \textbf{SE}quential sub\textbf{G}oal \textbf{O}ptimization (SEGO) to enhance LLMs' ability to solve mathematical problems. By establishing a connection between the subgoal breakdown process and the probability of solving problems, SEGO aims to identify better subgoals with theoretical guarantees. Addressing the challenge of identifying suitable subgoals in a large solution space, our framework generates problem-specific subgoals and adjusts them according to carefully designed criteria. Incorporating these optimized subgoals into the policy model training leads to significant improvements in problem-solving performance. We validate SEGO's efficacy through experiments on two benchmarks, GSM8K and MATH, where our approach outperforms existing methods, highlighting the potential of SEGO in AI-driven mathematical problem-solving. Data and code associated with this paper will be available at https://github.com/zhaoxlpku/SEGO
With the recent rise of widely successful deep learning models, there is emerging interest among professionals in various math and science communities to see and evaluate the state-of-the-art models' abilities to collaborate on finding or solving problems that often require creativity and thus brainstorming. While a significant chasm still exists between current human-machine intellectual collaborations and the resolution of complex math and science problems, such as the six unsolved Millennium Prize Problems, our initial investigation into this matter reveals a promising step towards bridging the divide. This is due to the recent advancements in Large Language Models (LLMs). More specifically, we conduct comprehensive case studies to explore both the capabilities and limitations of the current state-of-the-art LLM, notably GPT-4, in collective brainstorming with humans.