Despite the impressive capabilities of Large Language Models (LLMs) on various tasks, they still struggle with scenarios that involves complex reasoning and planning. Recent work proposed advanced prompting techniques and the necessity of fine-tuning with high-quality data to augment LLMs' reasoning abilities. However, these approaches are inherently constrained by data availability and quality. In light of this, self-correction and self-learning emerge as viable solutions, employing strategies that allow LLMs to refine their outputs and learn from self-assessed rewards. Yet, the efficacy of LLMs in self-refining its response, particularly in complex reasoning and planning task, remains dubious. In this paper, we introduce AlphaLLM for the self-improvements of LLMs, which integrates Monte Carlo Tree Search (MCTS) with LLMs to establish a self-improving loop, thereby enhancing the capabilities of LLMs without additional annotations. Drawing inspiration from the success of AlphaGo, AlphaLLM addresses the unique challenges of combining MCTS with LLM for self-improvement, including data scarcity, the vastness search spaces of language tasks, and the subjective nature of feedback in language tasks. AlphaLLM is comprised of prompt synthesis component, an efficient MCTS approach tailored for language tasks, and a trio of critic models for precise feedback. Our experimental results in mathematical reasoning tasks demonstrate that AlphaLLM significantly enhances the performance of LLMs without additional annotations, showing the potential for self-improvement in LLMs.
Training on large amounts of rationales (i.e., CoT Fine-tuning) is effective at improving the reasoning capabilities of large language models (LLMs). However, acquiring human-authored rationales or augmenting rationales from proprietary models is costly and not scalable. In this paper, we study the problem of whether LLMs could self-improve their reasoning capabilities. To this end, we propose Self-Explore, where the LLM is tasked to explore the first wrong step (i.e., the first pit) within the rationale and use such signals as fine-grained rewards for further improvement. On the GSM8K and MATH test set, Self-Explore achieves 11.57% and 2.89% improvement on average across three LLMs compared to supervised fine-tuning (SFT). Our code is available at https://github.com/hbin0701/Self-Explore.
Previous language model pre-training methods have uniformly applied a next-token prediction loss to all training tokens. Challenging this norm, we posit that "9l training". Our initial analysis examines token-level training dynamics of language model, revealing distinct loss patterns for different tokens. Leveraging these insights, we introduce a new language model called Rho-1. Unlike traditional LMs that learn to predict every next token in a corpus, Rho-1 employs Selective Language Modeling (SLM), which selectively trains on useful tokens that aligned with the desired distribution. This approach involves scoring pretraining tokens using a reference model, and then training the language model with a focused loss on tokens with higher scores. When continual pretraining on 15B OpenWebMath corpus, Rho-1 yields an absolute improvement in few-shot accuracy of up to 30% in 9 math tasks. After fine-tuning, Rho-1-1B and 7B achieved state-of-the-art results of 40.6% and 51.8% on MATH dataset, respectively - matching DeepSeekMath with only 3% of the pretraining tokens. Furthermore, when continual pretraining on 80B general tokens, Rho-1 achieves 6.8% average enhancement across 15 diverse tasks, increasing both efficiency and performance of the language model pre-training.
The leaderboard of Large Language Models (LLMs) in mathematical tasks has been continuously updated. However, the majority of evaluations focus solely on the final results, neglecting the quality of the intermediate steps. This oversight can mask underlying problems, such as logical errors or unnecessary steps in the reasoning process. To measure reasoning beyond final-answer accuracy, we introduce ReasonEval, a new methodology for evaluating the quality of reasoning steps. ReasonEval employs validity and redundancy to characterize the reasoning quality, as well as accompanying LLMs to assess them automatically. We explore different design options for the LLM-based evaluators and empirically demonstrate that ReasonEval, when instantiated with base models possessing strong mathematical knowledge and trained with high-quality labeled data, consistently outperforms baseline methods in the meta-evaluation datasets. We also highlight the strong generalization capabilities of ReasonEval. By utilizing ReasonEval to evaluate LLMs specialized in math, we find that an increase in final-answer accuracy does not necessarily guarantee an improvement in the overall quality of the reasoning steps for challenging mathematical problems. Additionally, we observe that ReasonEval can play a significant role in data selection. We open-source the best-performing model, meta-evaluation script, and all evaluation results to facilitate future research.
To advance the evaluation of multimodal math reasoning in large multimodal models (LMMs), this paper introduces a novel benchmark, MM-MATH. MM-MATH consists of 5,929 open-ended middle school math problems with visual contexts, with fine-grained classification across difficulty, grade level, and knowledge points. Unlike existing benchmarks relying on binary answer comparison, MM-MATH incorporates both outcome and process evaluations. Process evaluation employs LMM-as-a-judge to automatically analyze solution steps, identifying and categorizing errors into specific error types. Extensive evaluation of ten models on MM-MATH reveals significant challenges for existing LMMs, highlighting their limited utilization of visual information and struggles with higher-difficulty problems. The best-performing model achieves only 31% accuracy on MM-MATH, compared to 82% for humans. This highlights the challenging nature of our benchmark for existing models and the significant gap between the multimodal reasoning capabilities of current models and humans. Our process evaluation reveals that diagram misinterpretation is the most common error, accounting for more than half of the total error cases, underscoring the need for improved image comprehension in multimodal reasoning.
Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in \textbf{advanced mathematical problems requiring complex, multi-step logical reasoning}. To enhance their inferential capabilities, current research has delved into \textit{prompting engineering}, exemplified by methodologies such as the Tree of Thought and Graph of Thought. Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability. In response to these limitations, this paper introduces the \textit{Multi-Agent System for conditional Mining} (\textbf{MACM}) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts. With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from $\mathbf{54.68\%} \text{ to } \mathbf{76.73\%}$. The code is available in \url{https://github.com/bin123apple/MACM}.
Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\footnote{\url{https://chatglm.cn}}, an online serving LLM. Related evaluation dataset and scripts are released at \url{https://github.com/THUDM/ChatGLM-Math}.
This work presents BAdam, an optimization method that leverages the block coordinate descent (BCD) framework with Adam's update rule. BAdam offers a memory efficient approach to the full parameter finetuning of large language models. We conduct a theoretical convergence analysis for BAdam in the deterministic case. Experimentally, we apply BAdam to finetune the Llama 3-8B and Llama 3-70B models using a single RTX3090-24GB GPU and 4 A100-80GB GPUs, respectively. The results confirm BAdam's efficiency in terms of memory usage, running time, and optimization capability. Furthermore, the downstream performance evaluation based on MT-bench and math benchmarks shows that BAdam outperforms existing memory efficient baselines such as LoRA. It also demonstrates that BAdam can achieve comparable or even superior performance compared to Adam. Finally, the ablation study using SGD's update rule illustrates the suitability of BCD for finetuning LLMs. Our code can be easily integrated into any PyTorch-based codebase and is available at https://github.com/Ledzy/BAdam.
This paper explores the efficacy of large language models (LLMs) for Persian. While ChatGPT and consequent LLMs have shown remarkable performance in English, their efficiency for more low-resource languages remains an open question. We present the first comprehensive benchmarking study of LLMs across diverse Persian language tasks. Our primary focus is on GPT-3.5-turbo, but we also include GPT-4 and OpenChat-3.5 to provide a more holistic evaluation. Our assessment encompasses a diverse set of tasks categorized into classic, reasoning, and knowledge-based domains. To enable a thorough comparison, we evaluate LLMs against existing task-specific fine-tuned models. Given the limited availability of Persian datasets for reasoning tasks, we introduce two new benchmarks: one based on elementary school math questions and another derived from the entrance exams for 7th and 10th grades. Our findings reveal that while LLMs, especially GPT-4, excel in tasks requiring reasoning abilities and a broad understanding of general knowledge, they often lag behind smaller pre-trained models fine-tuned specifically for particular tasks. Additionally, we observe improved performance when test sets are translated to English before inputting them into GPT-3.5. These results highlight the significant potential for enhancing LLM performance in the Persian language. This is particularly noteworthy due to the unique attributes of Persian, including its distinct alphabet and writing styles.
Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this study, we adopted a two-step approach for investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our Case analysis indicates that while the GPT-4 can generate relevant responses in certain instances, it does not consistently answer all questions accurately. This paper explores the current limitations of LLMs in navigating complex mathematical problem-solving. Through case analysis, we shed light on the gaps in LLM capabilities within mathematics, thereby setting the stage for future research and advancements in AI-driven mathematical reasoning. We make our code and findings publicly available for research: \url{https://github.com/gipplab/LLM-Investig-MathStackExchange}
Multiple-choice questions (MCQs) are ubiquitous in almost all levels of education since they are easy to administer, grade, and are a reliable format in assessments and practices. One of the most important aspects of MCQs is the distractors, i.e., incorrect options that are designed to target common errors or misconceptions among real students. To date, the task of crafting high-quality distractors largely remains a labor and time-intensive process for teachers and learning content designers, which has limited scalability. In this work, we study the task of automated distractor generation in the domain of math MCQs and explore a wide variety of large language model (LLM)-based approaches, from in-context learning to fine-tuning. We conduct extensive experiments using a real-world math MCQ dataset and find that although LLMs can generate some mathematically valid distractors, they are less adept at anticipating common errors or misconceptions among real students.
Current Large Language Models (LLMs), even those tuned for safety and alignment, are susceptible to jailbreaking. Some have found that just further fine-tuning an aligned model with benign data (i.e., data without harmful content) surprisingly leads to substantial degradation in safety. We delve into the data-centric aspects of why benign fine-tuning inadvertently contributes to jailbreaking. First, we represent fine-tuning data through two lenses: representation and gradient spaces. Additionally, we propose a bi-directional anchoring method that, during the selection process, prioritizes data points that are close to harmful examples and far from benign ones. Our approach effectively identifies subsets of benign data that are more likely to degrade the model's safety after fine-tuning. Training on just 100 of these seemingly benign datapoints surprisingly leads to the fine-tuned model affirmatively responding to >70% of tested harmful requests, compared to <20% after fine-tuning on randomly selected data. We also observe that the selected data frequently appear as lists, bullet points, or math questions, indicating a systematic pattern in fine-tuning data that contributes to jailbreaking.
Large language models (LLMs) have shown promising abilities of in-context learning (ICL), adapting swiftly to new tasks with only few-shot demonstrations. However, current few-shot methods heavily depend on high-quality, query-specific demos, which are often lacking. When faced with out-of-demonstration (OOD) queries, methods that rely on hand-crafted demos or external retrievers might fail. To bridge the gap between limited demos and OOD queries, we propose Self-Demos, a novel prompting method that elicits the inherent generalizability in LLMs by query-aware demo generation. The generated demos strategically interpolate between existing demos and the given query, transforming the query from OOD to ID. To evaluate the effectiveness of our approach, we manually constructed OOD-Toolset, a dataset in the tool-using scenario with over 300 real-world APIs and 1000 instances, each consisting of three tool-use cases as demos and an OOD query. Thorough experiments on our dataset and two public math benchmarks have shown that our method can outperform state-of-the-art baselines in the OOD setting. Moreover, we conduct a range of analyses to validate Self-Demos's generalization and provide more insights.
Brain encoding with neuroimaging data is an established analysis aimed at predicting human brain activity directly from complex stimuli features such as movie frames. Typically, these features are the latent space representation from an artificial neural network, and the stimuli are image, audio, or text inputs. Ridge regression is a popular prediction model for brain encoding due to its good out-of-sample generalization performance. However, training a ridge regression model can be highly time-consuming when dealing with large-scale deep functional magnetic resonance imaging (fMRI) datasets that include many space-time samples of brain activity. This paper evaluates different parallelization techniques to reduce the training time of brain encoding with ridge regression on the CNeuroMod Friends dataset, one of the largest deep fMRI resource currently available. With multi-threading, our results show that the Intel Math Kernel Library (MKL) significantly outperforms the OpenBLAS library, being 1.9 times faster using 32 threads on a single machine. We then evaluated the Dask multi-CPU implementation of ridge regression readily available in scikit-learn (MultiOutput), and we proposed a new "batch" version of Dask parallelization, motivated by a time complexity analysis. In line with our theoretical analysis, MultiOutput parallelization was found to be impractical, i.e., slower than multi-threading on a single machine. In contrast, the Batch-MultiOutput regression scaled well across compute nodes and threads, providing speed-ups of up to 33 times with 8 compute nodes and 32 threads compared to a single-threaded scikit-learn execution. Batch parallelization using Dask thus emerges as a scalable approach for brain encoding with ridge regression on high-performance computing systems using scikit-learn and large fMRI datasets.
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational errors in their reasoning steps and answers. In this paper, we leverage the fact that if the training corpus of LLMs contained sufficiently many examples of formal mathematics (e.g. in Isabelle, a formal theorem proving environment), they can be prompted to translate i.e. autoformalize informal mathematical statements into formal Isabelle code -- which can be verified automatically for internal consistency. This provides a mechanism to automatically reject solutions whose formalized versions are inconsistent within themselves or with the formalized problem statement. We evaluate our method on GSM8K, MATH and MultiArith datasets and demonstrate that our approach provides a consistently better heuristic than vanilla majority voting -- the previously best method to identify correct answers, by more than 12% on GSM8K. In our experiments it improves results consistently across all datasets and LLM model sizes. The code can be found at https://github.com/jinpz/dtv.
In the context of online education, designing an automatic solver for geometric problems has been considered a crucial step towards general math Artificial Intelligence (AI), empowered by natural language understanding and traditional logical inference. In most instances, problems are addressed by adding auxiliary components such as lines or points. However, adding auxiliary components automatically is challenging due to the complexity in selecting suitable auxiliary components especially when pivotal decisions have to be made. The state-of-the-art performance has been achieved by exhausting all possible strategies from the category library to identify the one with the maximum likelihood. However, an extensive strategy search have to be applied to trade accuracy for ef-ficiency. To add auxiliary components automatically and efficiently, we present deep reinforcement learning framework based on the language model, such as BERT. We firstly apply the graph attention mechanism to reduce the strategy searching space, called AttnStrategy, which only focus on the conclusion-related components. Meanwhile, a novel algorithm, named Automatically Adding Auxiliary Components using Reinforcement Learning framework (A3C-RL), is proposed by forcing an agent to select top strategies, which incorporates the AttnStrategy and BERT as the memory components. Results from extensive experiments show that the proposed A3C-RL algorithm can substantially enhance the average precision by 32.7% compared to the traditional MCTS. In addition, the A3C-RL algorithm outperforms humans on the geometric questions from the annual University Entrance Mathematical Examination of China.
Large language models (LLMs) have become increasingly capable, but their development often requires substantial computational resources. While model merging has emerged as a cost-effective promising approach for creating new models by combining existing ones, it currently relies on human intuition and domain knowledge, limiting its potential. Here, we propose an evolutionary approach that overcomes this limitation by automatically discovering effective combinations of diverse open-source models, harnessing their collective intelligence without requiring extensive additional training data or compute. Our approach operates in both parameter space and data flow space, allowing for optimization beyond just the weights of the individual models. This approach even facilitates cross-domain merging, generating models like a Japanese LLM with Math reasoning capabilities. Surprisingly, our Japanese Math LLM achieved state-of-the-art performance on a variety of established Japanese LLM benchmarks, even surpassing models with significantly more parameters, despite not being explicitly trained for such tasks. Furthermore, a culturally-aware Japanese VLM generated through our approach demonstrates its effectiveness in describing Japanese culture-specific content, outperforming previous Japanese VLMs. This work not only contributes new state-of-the-art models back to the open-source community, but also introduces a new paradigm for automated model composition, paving the way for exploring alternative, efficient approaches to foundation model development.
Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I$^3$C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I$^3$C with few-shot reasoning. We develop I$^3$C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I$^3$C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I$^3$C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.
Edge intelligence enables resource-demanding Deep Neural Network (DNN) inference without transferring original data, addressing concerns about data privacy in consumer Internet of Things (IoT) devices. For privacy-sensitive applications, deploying models in hardware-isolated trusted execution environments (TEEs) becomes essential. However, the limited secure memory in TEEs poses challenges for deploying DNN inference, and alternative techniques like model partitioning and offloading introduce performance degradation and security issues. In this paper, we present a novel approach for advanced model deployment in TrustZone that ensures comprehensive privacy preservation during model inference. We design a memory-efficient management method to support memory-demanding inference in TEEs. By adjusting the memory priority, we effectively mitigate memory leakage risks and memory overlap conflicts, resulting in 32 lines of code alterations in the trusted operating system. Additionally, we leverage two tiny libraries: S-Tinylib (2,538 LoCs), a tiny deep learning library, and Tinylibm (827 LoCs), a tiny math library, to support efficient inference in TEEs. We implemented a prototype on Raspberry Pi 3B+ and evaluated it using three well-known lightweight DNN models. The experimental results demonstrate that our design significantly improves inference speed by 3.13 times and reduces power consumption by over 66.5% compared to non-memory optimization method in TEEs.
This paper investigates the question of what makes math word problems (MWPs) in English challenging for large language models (LLMs). We conduct an in-depth analysis of the key linguistic and mathematical characteristics of MWPs. In addition, we train feature-based classifiers to better understand the impact of each feature on the overall difficulty of MWPs for prominent LLMs and investigate whether this helps predict how well LLMs fare against specific categories of MWPs.