The recent progress in large language models (LLMs), especially the invention of chain-of-thought prompting, has made it possible to automatically answer questions by stepwise reasoning. However, when faced with more complicated problems that require non-linear thinking, even the strongest LLMs make mistakes. To address this, we explore whether LLMs are able to recognize errors in their own step-by-step reasoning, without resorting to external resources. To this end, we propose SelfCheck, a general-purpose zero-shot verification schema for recognizing such errors. We then use the results of these checks to improve question-answering performance by conducting weighted voting on multiple solutions to the question. We test SelfCheck on three datasets (GSM8K, MathQA, and MATH) and find that it successfully recognizes errors and, in turn, increases final answer accuracies.
We introduce Augmented Math, a machine learning-based approach to authoring AR explorable explanations by augmenting static math textbooks without programming. To augment a static document, our system first extracts mathematical formulas and figures from a given document using optical character recognition (OCR) and computer vision. By binding and manipulating these extracted contents, the user can see the interactive animation overlaid onto the document through mobile AR interfaces. This empowers non-technical users, such as teachers or students, to transform existing math textbooks and handouts into on-demand and personalized explorable explanations. To design our system, we first analyzed existing explorable math explanations to identify common design strategies. Based on the findings, we developed a set of augmentation techniques that can be automatically generated based on the extracted content, which are 1) dynamic values, 2) interactive figures, 3) relationship highlights, 4) concrete examples, and 5) step-by-step hints. To evaluate our system, we conduct two user studies: preliminary user testing and expert interviews. The study results confirm that our system allows more engaging experiences for learning math concepts.
GPT-3.5 and GPT-4 are the two most widely used large language model (LLM) services. However, when and how these models are updated over time is opaque. Here, we evaluate the March 2023 and June 2023 versions of GPT-3.5 and GPT-4 on several diverse tasks: 1) math problems, 2) sensitive/dangerous questions, 3) opinion surveys, 4) multi-hop knowledge-intensive questions, 5) generating code, 6) US Medical License tests, and 7) visual reasoning. We find that the performance and behavior of both GPT-3.5 and GPT-4 can vary greatly over time. For example, GPT-4 (March 2023) was reasonable at identifying prime vs. composite numbers (84% accuracy) but GPT-4 (June 2023) was poor on these same questions (51% accuracy). This is partly explained by a drop in GPT-4's amenity to follow chain-of-thought prompting. Interestingly, GPT-3.5 was much better in June than in March in this task. GPT-4 became less willing to answer sensitive questions and opinion survey questions in June than in March. GPT-4 performed better at multi-hop questions in June than in March, while GPT-3.5's performance dropped on this task. Both GPT-4 and GPT-3.5 had more formatting mistakes in code generation in June than in March. We provide evidence that GPT-4's ability to follow user instructions has decreased over time, which is one common factor behind the many behavior drifts. Overall, our findings show that the behavior of the "same" LLM service can change substantially in a relatively short amount of time, highlighting the need for continuous monitoring of LLMs.
When to solve math problems, most language models take a sampling strategy to predict next word according conditional probabilities. In the math reasoning step, it may generate wrong answer. Considering math problems are deterministic, we propose a mixed policy exploration approach to solve math problems with reinforcement learning. In peculiar, we propose a two level token exploration policy: the abstract level explores next token with probability and the second level is deterministic. Specifically, the abstract level policy will decide whether the token is operator or operand with probability sampling, while the second level is deterministic to select next token with the highest score in a greedy way. We test our method on GSM8K dataset with GPT-2 model, and demonstrate more than $2\%$ performance gain. Our implementation is available at https://github.com/vividitytech/math_lm_rl.
The art of mathematical reasoning stands as a fundamental pillar of intellectual progress and is a central catalyst in cultivating human ingenuity. Researchers have recently published a plethora of works centered around the task of solving Math Word Problems (MWP) $-$ a crucial stride towards general AI. These existing models are susceptible to dependency on shallow heuristics and spurious correlations to derive the solution expressions. In order to ameliorate this issue, in this paper, we propose a framework for MWP solvers based on the generation of linguistic variants of the problem text. The approach involves solving each of the variant problems and electing the predicted expression with the majority of the votes. We use DeBERTa (Decoding-enhanced BERT with disentangled attention) as the encoder to leverage its rich textual representations and enhanced mask decoder to construct the solution expressions. Furthermore, we introduce a challenging dataset, $\mathrm{P\small{ARA}\normalsize{MAWPS}}$, consisting of paraphrased, adversarial, and inverse variants of selectively sampled MWPs from the benchmark $\mathrm{M\small{AWPS}}$ dataset. We extensively experiment on this dataset along with other benchmark datasets using some baseline MWP solver models. We show that training on linguistic variants of problem statements and voting on candidate predictions improve the mathematical reasoning and robustness of the model. We make our code and data publicly available.
Recently, Multimodal Large Language Model (MLLM) represented by GPT-4V has been a new rising research hotspot, which uses powerful Large Language Models (LLMs) as a brain to perform multimodal tasks. The surprising emergent capabilities of MLLM, such as writing stories based on images and OCR-free math reasoning, are rare in traditional multimodal methods, suggesting a potential path to artificial general intelligence. To this end, both academia and industry have endeavored to develop MLLMs that can compete with or even better than GPT-4V, pushing the limit of research at a surprising speed. In this paper, we aim to trace and summarize the recent progress of MLLMs. First of all, we present the basic formulation of MLLM and delineate its related concepts, including architecture, training strategy and data, as well as evaluation. Then, we introduce research topics about how MLLMs can be extended to support more granularity, modalities, languages, and scenarios. We continue with multimodal hallucination and extended techniques, including Multimodal ICL (M-ICL), Multimodal CoT (M-CoT), and LLM-Aided Visual Reasoning (LAVR). To conclude the paper, we discuss existing challenges and point out promising research directions. In light of the fact that the era of MLLM has only just begun, we will keep updating this survey and hope it can inspire more research. An associated GitHub link collecting the latest papers is available at https://github.com/BradyFU/Awesome-Multimodal-Large-Language-Models.
ChatGPT sets a new record with the fastest-growing user base, as a chatbot powered by a large language model (LLM). While it demonstrates state-of-the-art capabilities in a variety of language-generation tasks, it also raises widespread public concerns regarding its societal impact. In this paper, we investigated public attitudes towards ChatGPT by applying natural language processing techniques such as sentiment analysis and topic modeling to Twitter data from December 5, 2022 to June 10, 2023. Our sentiment analysis result indicates that the overall sentiment was largely neutral to positive, and negative sentiments were decreasing over time. Our topic model reveals that the most popular topics discussed were Education, Bard, Search Engines, OpenAI, Marketing, and Cybersecurity, but the ranking varies by month. We also analyzed the occupations of Twitter users and found that those with occupations in arts and entertainment tweeted aboutChatGPT most frequently. Additionally, people tended to tweet about topics relevant to their occupation. For instance, Cybersecurity is the most discussed topic among those with occupations related to computer and math, and Education is the most discussed topic among those in academic and research. Overall, our exploratory study provides insights into the public perception of ChatGPT, which could be valuable to both the general public and developers of this technology.
Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP solver to better understand same problems which may typically be formulated in diverse ways. However most existing works exploit the shortcut learning to train MWP solvers simply based on samples with a single question. In lack of diverse questions, these methods merely learn shallow heuristics. In this paper, we make a first attempt to solve MWPs by generating diverse yet consistent questions/equations. Given a typical MWP including the scenario description, question, and equation (i.e., answer), we first generate multiple consistent equations via a group of heuristic rules. We then feed them to a question generator together with the scenario to obtain the corresponding diverse questions, forming a new MWP with a variety of questions and equations. Finally we engage a data filter to remove those unreasonable MWPs, keeping the high-quality augmented ones. To evaluate the ability of learning by analogy for an MWP solver, we generate a new MWP dataset (called DiverseMath23K) with diverse questions by extending the current benchmark Math23K. Extensive experimental results demonstrate that our proposed method can generate high-quality diverse questions with corresponding equations, further leading to performance improvement on Diverse-Math23K. The code and dataset is available at: https://github.com/zhouzihao501/DiverseMWP
Lectures are a learning experience for both students and teachers. Students learn from teachers about the subject material, while teachers learn from students about how to refine their instruction. However, online student feedback is unstructured and abundant, making it challenging for teachers to learn and improve. We take a step towards tackling this challenge. First, we contribute a dataset for studying this problem: SIGHT is a large dataset of 288 math lecture transcripts and 15,784 comments collected from the Massachusetts Institute of Technology OpenCourseWare (MIT OCW) YouTube channel. Second, we develop a rubric for categorizing feedback types using qualitative analysis. Qualitative analysis methods are powerful in uncovering domain-specific insights, however they are costly to apply to large data sources. To overcome this challenge, we propose a set of best practices for using large language models (LLMs) to cheaply classify the comments at scale. We observe a striking correlation between the model's and humans' annotation: Categories with consistent human annotations (>$0.9$ inter-rater reliability, IRR) also display higher human-model agreement (>$0.7$), while categories with less consistent human annotations ($0.7$-$0.8$ IRR) correspondingly demonstrate lower human-model agreement ($0.3$-$0.5$). These techniques uncover useful student feedback from thousands of comments, costing around $\$0.002$ per comment. We conclude by discussing exciting future directions on using online student feedback and improving automated annotation techniques for qualitative research.
The increasing reliance on Large Language Models (LLMs) across academia and industry necessitates a comprehensive understanding of their robustness to prompts. In response to this vital need, we introduce PromptRobust, a robustness benchmark designed to measure LLMs' resilience to adversarial prompts. This study uses a plethora of adversarial textual attacks targeting prompts across multiple levels: character, word, sentence, and semantic. The adversarial prompts, crafted to mimic plausible user errors like typos or synonyms, aim to evaluate how slight deviations can affect LLM outcomes while maintaining semantic integrity. These prompts are then employed in diverse tasks including sentiment analysis, natural language inference, reading comprehension, machine translation, and math problem-solving. Our study generates 4,788 adversarial prompts, meticulously evaluated over 8 tasks and 13 datasets. Our findings demonstrate that contemporary LLMs are not robust to adversarial prompts. Furthermore, we present a comprehensive analysis to understand the mystery behind prompt robustness and its transferability. We then offer insightful robustness analysis and pragmatic recommendations for prompt composition, beneficial to both researchers and everyday users.
Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.
Coaching, which involves classroom observation and expert feedback, is a widespread and fundamental part of teacher training. However, the majority of teachers do not have access to consistent, high quality coaching due to limited resources and access to expertise. We explore whether generative AI could become a cost-effective complement to expert feedback by serving as an automated teacher coach. In doing so, we propose three teacher coaching tasks for generative AI: (A) scoring transcript segments based on classroom observation instruments, (B) identifying highlights and missed opportunities for good instructional strategies, and (C) providing actionable suggestions for eliciting more student reasoning. We recruit expert math teachers to evaluate the zero-shot performance of ChatGPT on each of these tasks for elementary math classroom transcripts. Our results reveal that ChatGPT generates responses that are relevant to improving instruction, but they are often not novel or insightful. For example, 82% of the model's suggestions point to places in the transcript where the teacher is already implementing that suggestion. Our work highlights the challenges of producing insightful, novel and truthful feedback for teachers while paving the way for future research to address these obstacles and improve the capacity of generative AI to coach teachers.
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.
Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. LLMs, with their generalized ability, are used as a foundation model to build AI agents for different tasks. In this paper, we study the effectiveness of utilizing LLM agents to solve math problems through conversations. We propose MathChat, a conversational problem-solving framework designed for math problems. MathChat consists of an LLM agent and a user proxy agent which is responsible for tool execution and additional guidance. This synergy facilitates a collaborative problem-solving process, where the agents engage in a dialogue to solve the problems. We perform evaluation on difficult high school competition problems from the MATH dataset. Utilizing Python, we show that MathChat can further improve previous tool-using prompting methods by 6%.
Large language models (LLMs) have transformed numerous AI applications. On-device LLM is becoming increasingly important: running LLMs locally on edge devices can reduce the cloud computing cost and protect users' privacy. However, the astronomical model size and the limited hardware resource pose significant deployment challenges. We propose Activation-aware Weight Quantization (AWQ), a hardware-friendly approach for LLM low-bit weight-only quantization. AWQ finds that not all weights in an LLM are equally important. Protecting only 1% salient weights can greatly reduce quantization error. To identify salient weight channels, we should refer to the activation distribution, not weights. To avoid the hardware-inefficient mix-precision quantization, we mathematically derive that scaling up the salient channels can reduce the quantization error. AWQ employs an equivalent transformation to scale the salient weight channels to protect them. The scale is determined by collecting the activation statistics offline. AWQ does not rely on any backpropagation or reconstruction, so it generalizes to different domains and modalities without overfitting the calibration set. AWQ outperforms existing work on various language modeling and domain-specific benchmarks (coding and math). Thanks to better generalization, it achieves excellent quantization performance for instruction-tuned LMs and, for the first time, multi-modal LMs. Alongside AWQ, we implement TinyChat, an efficient and flexible inference framework tailored for 4-bit on-device LLM/VLMs. With kernel fusion and platform-aware weight packing, TinyChat offers more than 3x speedup over the Huggingface FP16 implementation on both desktop and mobile GPUs. It also democratizes the deployment of the 70B Llama-2 model on mobile GPUs.
In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can turn either to outcome supervision, which provides feedback for a final result, or process supervision, which provides feedback for each intermediate reasoning step. Given the importance of training reliable models, and given the high cost of human feedback, it is important to carefully compare the both methods. Recent work has already begun this comparison, but many questions still remain. We conduct our own investigation, finding that process supervision significantly outperforms outcome supervision for training models to solve problems from the challenging MATH dataset. Our process-supervised model solves 78% of problems from a representative subset of the MATH test set. Additionally, we show that active learning significantly improves the efficacy of process supervision. To support related research, we also release PRM800K, the complete dataset of 800,000 step-level human feedback labels used to train our best reward model.
Chain-of-thought (CoT) prompting with large language models has proven effective in numerous natural language processing tasks, but designing prompts that generalize well to diverse problem types can be challenging, especially in the context of math word problem (MWP) solving. Additionally, it is common to have a large amount of training data that have a better diversity coverage but CoT annotations are not available, which limits the use of supervised learning techniques. To address these issues, we investigate two approaches to leverage the training data in a few-shot prompting scenario: dynamic program prompting and program distillation. Our approach is largely inspired by Gao et al., (2022), where they proposed to replace the CoT with the programs as the intermediate reasoning step. Such a prompting strategy allows us to accurately verify the answer correctness through program execution in MWP solving. Our dynamic program prompting involves annotating the training data by sampling correct programs from a large language model, while program distillation involves adapting a smaller model to the program-annotated training data. Our experiments on three standard MWP datasets demonstrate the effectiveness of these approaches, yielding significant improvements over previous baselines for prompting and fine-tuning. Our results suggest that leveraging a large amount of training data can improve the generalization ability of prompts and boost the performance of fine-tuned small models in MWP solving.
The temporal aspect is a significant dimension of our reality. We notice the challenge that large language models (LLMs) face when engaging in temporal reasoning. Our preliminary experiments show that methods involving the generation of intermediate reasoning steps, such as chain-of-thought and program-aided language models, do not consistently boost the performance of complex temporal question-answering tasks. This limitation can be attributed to the LLMs' inadequate understanding of temporal information. To address this problem, we propose TempLogic, a novel framework designed specifically for temporal question-answering tasks across three levels of reasoning. TempLogic incorporates retrieval-guided context distillation, temporal data extraction, and tailor-made logic reasoning. Extensive experiments and analysis demonstrate the effectiveness of our framework in solving intricate time-bound reasoning tasks.
Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the initial decisions, causing errors in early steps to accumulate and impact the final answers. In contrast, humans adopt recursive thinking when tackling complex reasoning problems, i.e., iteratively breaking the original problem into approachable sub-problems and aggregating their answers to resolve the original one. Inspired by the human cognitive process, we propose SOCRATIC QUESTIONING, a divide-and-conquer style algorithm that mimics the recursive thinking process. Specifically, SOCRATIC QUESTIONING leverages large language models to raise and answer sub-questions until collecting enough information to tackle the original question. Unlike CoT, SOCRATIC QUESTIONING explicitly navigates the thinking space, stimulates effective recursive thinking, and is more robust towards errors in the thinking process. Extensive experiments on several complex reasoning tasks, including MMLU, MATH, LogiQA, and visual question-answering demonstrate significant performance improvements over the state-of-the-art prompting methods, such as CoT, and Tree-of-Thought. The qualitative analysis clearly shows that the intermediate reasoning steps elicited by SOCRATIC QUESTIONING are similar to humans' recursively thinking process of complex reasoning problems.
In the context of multi-step reasoning, e.g., with chain-of-thought, language models (LMs) can easily assign a high likelihood to incorrect steps. As a result, decoding strategies that optimize for solution likelihood often yield incorrect solutions. To address this issue, we propose Guiding chain-of-thought ReAsoning with a CorrectnEss Discriminator (GRACE), a stepwise decoding approach that steers the decoding process towards producing correct reasoning steps. GRACE employs a discriminator trained with a contrastive loss over correct and incorrect steps, which is used during decoding to score next-step candidates based on their correctness. Importantly, GRACE only requires sampling from the LM, without the need for LM training or fine-tuning. Using models from FLAN-T5 and LLaMA families, we evaluate GRACE over four math and two symbolic reasoning tasks, where it exhibits substantial performance gains compared to greedy decoding, verifiers, and self-consistency in most settings. When further combined with self-consistency, GRACE outperforms all the baselines by sizeable margins. Human and LLM evaluations over GSM8K show that GRACE not only improves the final answer accuracy but also the correctness of the intermediate reasoning. Our implementation can be accessed at \url{https://github.com/mukhal/grace}.