Exploiting large language models (LLMs) to tackle reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex logical problems, characterized by plenty of premises within the prompt and requiring multi-hop reasoning. In particular, the reasoning capabilities of LLMs are brittle to disorder and distractibility. In this work, we first examine the mechanism from the perspective of information flow and reveal that LLMs exhibit failure patterns akin to human-like cognitive biases when dealing with disordered and irrelevant content in reasoning tasks. However, in contrast to LLMs, disordered and irrelevant content does not significantly decrease human performance, as humans have a propensity to distill the most relevant information and systematically organize their thoughts, aiding them in responding to questions. Stem from that, we further propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to identify the most pertinent information while eliminating redundancy efficiently. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized context, the reasoning abilities of LLMs can be better elicited. Extensive experimental results on several popular logical benchmarks (ProofWriter, PrOntoQA, PrOntoQA-OOD, and FOLIO) and math benchmark (DI-GSM) show that COP significantly outperforms previous state-of-the-art methods.
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.
Large language models (LLMs) have revolutionized zero-shot task performance, mitigating the need for task-specific annotations while enhancing task generalizability. Despite its advancements, current methods using trigger phrases such as "Let's think step by step" remain limited. This study introduces PRomPTed, an approach that optimizes the zero-shot prompts for individual task instances following an innovative manner of "LLMs in the loop". Our comprehensive evaluation across 13 datasets and 10 task types based on GPT-4 reveals that PRomPTed significantly outperforms both the naive zero-shot approaches and a strong baseline (i.e., "Output Refinement") which refines the task output instead of the input prompt. Our experimental results also confirmed the generalization of this advantage to the relatively weaker GPT-3.5. Even more intriguingly, we found that leveraging GPT-3.5 to rewrite prompts for the stronger GPT-4 not only matches but occasionally exceeds the efficacy of using GPT-4 as the prompt rewriter. Our research thus presents a huge value in not only enhancing zero-shot LLM performance but also potentially enabling supervising LLMs with their weaker counterparts, a capability attracting much interest recently. Finally, our additional experiments confirm the generalization of the advantages to open-source LLMs such as Mistral 7B and Mixtral 8x7B.
As of September 2023, ChatGPT correctly answers "what is 7+8" with 15, but when asked "7+8=15, True or False" it responds with "False". This inconsistency between generating and validating an answer is prevalent in language models (LMs) and erodes trust. In this paper, we propose a framework for measuring the consistency between generation and validation (which we call generator-validator consistency, or GV-consistency), finding that even GPT-4, a state-of-the-art LM, is GV-consistent only 76% of the time. To improve the consistency of LMs, we propose to finetune on the filtered generator and validator responses that are GV-consistent, and call this approach consistency fine-tuning. We find that this approach improves GV-consistency of Alpaca-30B from 60% to 93%, and the improvement extrapolates to unseen tasks and domains (e.g., GV-consistency for positive style transfers extrapolates to unseen styles like humor). In addition to improving consistency, consistency fine-tuning improves both generator quality and validator accuracy without using any labeled data. Evaluated across 6 tasks, including math questions, knowledge-intensive QA, and instruction following, our method improves the generator quality by 16% and the validator accuracy by 6.3% across all tasks.
Chain-of-thought (CoT) prompting for language models demonstrates impressive performance across reasoning tasks, but typically needs labeled exemplars of the reasoning process. In this work, we introduce a new prompting approach, analogical prompting, designed to automatically guide the reasoning process of large language models. Inspired by analogical reasoning, a cognitive process in which humans draw from relevant past experiences to tackle new problems, our approach prompts language models to self-generate relevant exemplars or knowledge in the context, before proceeding to solve the given problem. This method presents several advantages: it obviates the need for labeling or retrieving exemplars, offering generality and convenience; it can also tailor the generated exemplars and knowledge to each problem, offering adaptability. Experimental results show that our approach outperforms 0-shot CoT and manual few-shot CoT in a variety of reasoning tasks, including math problem solving in GSM8K and MATH, code generation in Codeforces, and other reasoning tasks in BIG-Bench.
Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive problem-solving skills in many tasks and domains, but their ability in mathematical reasoning in visual contexts has not been systematically studied. To bridge this gap, we present MathVista, a benchmark designed to combine challenges from diverse mathematical and visual tasks. It consists of 6,141 examples, derived from 28 existing multimodal datasets involving mathematics and 3 newly created datasets (i.e., IQTest, FunctionQA, and PaperQA). Completing these tasks requires fine-grained, deep visual understanding and compositional reasoning, which all state-of-the-art foundation models find challenging. With MathVista, we have conducted a comprehensive, quantitative evaluation of 12 prominent foundation models. The best-performing GPT-4V model achieves an overall accuracy of 49.9%, substantially outperforming Bard, the second-best performer, by 15.1%. Our in-depth analysis reveals that the superiority of GPT-4V is mainly attributed to its enhanced visual perception and mathematical reasoning. However, GPT-4V still falls short of human performance by 10.4%, as it often struggles to understand complex figures and perform rigorous reasoning. This significant gap underscores the critical role that MathVista will play in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. We further explore the new ability of self-verification, the application of self-consistency, and the interactive chatbot capabilities of GPT-4V, highlighting its promising potential for future research. The project is available at https://mathvista.github.io/.
In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic multi-modal understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training model, which employs contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in the low data regime scenarios where available data is limited. Code and model are available at: https://github.com/deep-symbolic-mathematics/Multimodal-Math-Pretraining
Recent studies show that collaborating multiple large language model (LLM) powered agents is a promising way for task solving. However, current approaches are constrained by using a fixed number of agents and static communication structures. In this work, we propose automatically selecting a team of agents from candidates to collaborate in a dynamic communication structure toward different tasks and domains. Specifically, we build a framework named Dynamic LLM-Powered Agent Network ($\textbf{DyLAN}$) for LLM-powered agent collaboration, operating a two-stage paradigm: (1) Team Optimization and (2) Task Solving. During the first stage, we utilize an $\textit{agent selection}$ algorithm, based on an unsupervised metric called $\textit{Agent Importance Score}$, enabling the selection of best agents according to their contributions in a preliminary trial, oriented to the given task. Then, in the second stage, the selected agents collaborate dynamically according to the query. Empirically, we demonstrate that DyLAN outperforms strong baselines in code generation, decision-making, general reasoning, and arithmetic reasoning tasks with moderate computational cost. On specific subjects in MMLU, selecting a team of agents in the team optimization stage improves accuracy by up to 25.0% in DyLAN.
While forward reasoning (i.e., find the answer given the question) has been explored extensively in recent literature, backward reasoning is relatively unexplored. We examine the backward reasoning capabilities of LLMs on Math Word Problems (MWPs): given a mathematical question and its answer, with some details omitted from the question, can LLMs effectively retrieve the missing information? On modifying three benchmark datasets for this task, to evaluate this task: GSM8k, SVAMP, and MultiArith, we find a significant drop in the accuracy of models on this task compared to forward reasoning across SOTA LLMs (GPT4, GPT3.5, PaLM-2, and LLaMa). Motivated by the fact backward reasoning can be seen as the ''inverse'' of forward reasoning, we propose variations of three different forward reasoning strategies to improve performance. Rephrase reformulates the given problem into a forward reasoning problem, PAL-Tools combines the idea of Program-Aided LLMs to produce a set of equations that can be solved by an external solver, and Check your Work exploits the availability of natural verifier of high accuracy in the forward direction, interleaving solving and verification steps. Finally, realizing that each of our base methods correctly solves a different set of problems, we propose a novel Bayesian formulation for creating an ensemble over the base methods to further boost the accuracy. Extensive experimentation demonstrates successive improvement in the performance of LLMs on the backward reasoning task, using our strategies, with our ensemble-based method resulting in significant performance gains compared to the SOTA forward reasoning strategies we adapt.
Large Language Models, such as Generative Pre-trained Transformer 3 (aka. GPT-3), have been developed to understand language through the analysis of extensive text data, allowing them to identify patterns and connections between words. While LLMs have demonstrated impressive performance across various text-related tasks, they encounter challenges in tasks associated with reasoning. To address this challenge, Chain of Thought(CoT) prompting method has been proposed as a means to enhance LLMs' proficiency in complex reasoning tasks like solving math word problems and answering questions based on logical argumentative reasoning. The primary aim of this research is to assess how well four language models can grade reflective essays of third-year medical students. The assessment will specifically target the evaluation of critical thinking skills using CoT prompting. The research will provide the following contributions; to introduce and educate on the process of instructing models to evaluate reflective essays from a dataset they have not been previously trained on; to illustrate the use of CoT prompting as an instructional approach for training large models to carry out particular tasks. Our results suggest that among all the models, Llama-7b performs the least effectively, displaying the highest mean squared error. Conversely, ChatGPT emerges as the superior model, boasting a higher Cohen kappa score value of 0.53. Lastly, it's important to note that the selected models do prioritise user privacy by allowing users to delete their own conducted conversations.
Recently, large language models (LLMs), especially those that are pretrained on code, have demonstrated strong capabilities in generating programs from natural language inputs in a few-shot or even zero-shot manner. Despite promising results, there is a notable lack of a comprehensive evaluation of these models language-to-code generation capabilities. Existing studies often focus on specific tasks, model architectures, or learning paradigms, leading to a fragmented understanding of the overall landscape. In this work, we present L2CEval, a systematic evaluation of the language-to-code generation capabilities of LLMs on 7 tasks across the domain spectrum of semantic parsing, math reasoning and Python programming, analyzing the factors that potentially affect their performance, such as model size, pretraining data, instruction tuning, and different prompting methods. In addition to assessing model performance, we measure confidence calibration for the models and conduct human evaluations of the output programs. This enables us to identify and analyze the typical failure modes across various tasks and models. L2CEval offers a comprehensive understanding of the capabilities and limitations of LLMs in language-to-code generation. We also release the evaluation framework and all model outputs, hoping to lay the groundwork for further future research in this domain.
Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging mathematical problems by seamlessly integrating natural language reasoning with the utilization of external tools (e.g., computation libraries and symbolic solvers), thereby amalgamating the analytical prowess of language and the computational efficiency of tools. To train ToRA, we curate interactive tool-use trajectories on mathematical datasets, apply imitation learning on the annotations, and propose output space shaping to further refine models' reasoning behavior. As a result, ToRA models significantly outperform open-source models on 10 mathematical reasoning datasets across all scales with 13%-19% absolute improvements on average. Notably, ToRA-7B reaches 44.6% on the competition-level dataset MATH, surpassing the best open-source model WizardMath-70B by 22% absolute. ToRA-Code-34B is also the first open-source model that achieves an accuracy exceeding 50% on MATH, which significantly outperforms GPT-4's CoT result, and is competitive with GPT-4 solving problems with programs. Additionally, we conduct a comprehensive analysis of the benefits and remaining challenges of tool interaction for mathematical reasoning, providing valuable insights for future research.
In the era of digital communication, memes have become a potent medium for conveying ideas, humor, and cultural references. This paper introduces the “Mathematical Mathematics Memes Dataset”, a comprehensive collection of over 10,000 math-related memes sourced from the “Mathematical Mathematics Memes” Facebook group. These memes offer a unique perspective on the intersection of mathematics and humor. We discuss the dataset's origins, content, and potential applications, including meme generation, abusive meme detection, and text extraction for popularity prediction. This dataset serves as a valuable resource for researchers and meme enthusiasts interested in exploring the realm of mathematical memes.
Large language models (LLMs) have revolutionized the field of artificial intelligence, enabling natural language processing tasks that were previously thought to be exclusive to humans. In this work, we introduce Qwen, the first installment of our large language model series. Qwen is a comprehensive language model series that encompasses distinct models with varying parameter counts. It includes Qwen, the base pretrained language models, and Qwen-Chat, the chat models finetuned with human alignment techniques. The base language models consistently demonstrate superior performance across a multitude of downstream tasks, and the chat models, particularly those trained using Reinforcement Learning from Human Feedback (RLHF), are highly competitive. The chat models possess advanced tool-use and planning capabilities for creating agent applications, showcasing impressive performance even when compared to bigger models on complex tasks like utilizing a code interpreter. Furthermore, we have developed coding-specialized models, Code-Qwen and Code-Qwen-Chat, as well as mathematics-focused models, Math-Qwen-Chat, which are built upon base language models. These models demonstrate significantly improved performance in comparison with open-source models, and slightly fall behind the proprietary models.
Recent developments in large language models (LLMs) have shown promise in enhancing the capabilities of natural language processing (NLP). Despite these successes, there remains a dearth of research dedicated to the NLP problem-solving abilities of LLMs. To fill the gap in this area, we present a unique benchmarking dataset, NLPBench, comprising 378 college-level NLP questions spanning various NLP topics sourced from Yale University's prior final exams. NLPBench includes questions with context, in which multiple sub-questions share the same public information, and diverse question types, including multiple choice, short answer, and math. Our evaluation, centered on LLMs such as GPT-3.5/4, PaLM-2, and LLAMA-2, incorporates advanced prompting strategies like the chain-of-thought (CoT) and tree-of-thought (ToT). Our study reveals that the effectiveness of the advanced prompting strategies can be inconsistent, occasionally damaging LLM performance, especially in smaller models like the LLAMA-2 (13b). Furthermore, our manual assessment illuminated specific shortcomings in LLMs' scientific problem-solving skills, with weaknesses in logical decomposition and reasoning notably affecting results.
To measure bias, we encourage teams to consider using AUC Gap: the absolute difference between the highest and lowest test AUC for subgroups (e.g., gender, race, SES, prior knowledge). It is agnostic to the AI/ML algorithm used and it captures the disparity in model performance for any number of subgroups, which enables non-binary fairness assessments such as for intersectional identity groups. The teams use a wide range of AI/ML models in pursuit of a common goal of doubling math achievement in low-income middle schools. Ensuring that the models, which are trained on datasets collected in many different contexts, do not introduce or amplify biases is important for achieving the goal. We offer here a versatile and easy-to-compute measure of model bias for all the teams in order to create a common benchmark and an analytical basis for sharing what strategies have worked for different teams.
Large Language Models (LLMs) still struggle with natural language reasoning tasks. Motivated by the society of minds (Minsky, 1988), we propose ReConcile, a multi-model multi-agent framework designed as a round table conference among diverse LLM agents. ReConcile enhances collaborative reasoning between LLM agents via multiple rounds of discussion, learning to convince other agents to improve their answers, and employing a confidence-weighted voting mechanism that leads to a better consensus. In each round, ReConcile initiates discussion between agents via a 'discussion prompt' that consists of (a) grouped answers and explanations generated by each agent in the previous round, (b) their confidence scores, and (c) demonstrations of answer-rectifying human explanations, used for convincing other agents. Experiments on seven benchmarks demonstrate that ReConcile significantly improves LLMs' reasoning -- both individually and as a team -- surpassing prior single-agent and multi-agent baselines by up to 11.4% and even outperforming GPT-4 on three datasets. ReConcile also flexibly incorporates different combinations of agents, including API-based, open-source, and domain-specific models, leading to an 8% improvement on MATH. Finally, we analyze the individual components of ReConcile, demonstrating that the diversity originating from different models is critical to its superior performance. Code: https://github.com/dinobby/ReConcile
Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.
Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the self-describing program, the comment-describing program, and the non-describing program. Furthermore, we investigate the impact of programming language on program CoTs, comparing Python and Wolfram Language. Through extensive experiments on GSM8K, MATHQA, and SVAMP, we find that program CoTs often have superior effectiveness in math problem solving. Notably, the best performing combination with 30B parameters beats GPT-3.5-turbo by a significant margin. The results show that self-describing program offers greater diversity and thus can generally achieve higher performance. We also find that Python is a better choice of language than Wolfram for program CoTs. The experimental results provide a valuable guideline for future CoT designs that take into account both programming language and coding style for further advancements. Our datasets and code are publicly available.
How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic reasoning, natural language understanding, and instruction following tasks. Our approach prompts a language model to generate full Python programs that define functions over data structures which contain natural language representations of structured knowledge. A Python interpreter then executes the generated code and prints the output. Despite using a task-general prompt, we find that this approach can improve upon strong baselines across a range of different tasks including math and symbolic reasoning, text classification, question answering, and instruction following. We found that the generated programs are interpretable since they outline the exact reasoning process followed by the program interpreter.