Knowledge concept tagging for questions plays a crucial role in contemporary intelligent educational applications, including learning progress diagnosis, practice question recommendations, and course content organization. Traditionally, these annotations have been conducted manually with help from pedagogical experts, as the task requires not only a strong semantic understanding of both question stems and knowledge definitions but also deep insights into connecting question-solving logic with corresponding knowledge concepts. In this paper, we explore automating the tagging task using Large Language Models (LLMs), in response to the inability of prior manual methods to meet the rapidly growing demand for concept tagging in questions posed by advanced educational applications. Moreover, the zero/few-shot learning capability of LLMs makes them well-suited for application in educational scenarios, which often face challenges in collecting large-scale, expertise-annotated datasets. By conducting extensive experiments with a variety of representative LLMs, we demonstrate that LLMs are a promising tool for concept tagging in math questions. Furthermore, through case studies examining the results from different LLMs, we draw some empirical conclusions about the key factors for success in applying LLMs to the automatic concept tagging task.
In this paper, we present a challenging code reasoning task: vulnerability detection. Large Language Models (LLMs) have shown promising results in natural-language and math reasoning, but state-of-the-art (SOTA) models reported only 54.5% Balanced Accuracy in our vulnerability detection evaluation, even those models pre-trained on large amounts of source code. Our error analysis on LLM responses shows that the models struggle to reason about the code semantics relevant to identifying vulnerabilities, especially subtle semantic differences caused by small textual changes. We explored prominent models and training settings to understand their effects on vulnerability detection performance -- including better prompts, larger models, more pre-training data, and fine-tuning -- but none led to significant improvements. This raises the question of whether simply scaling training data and model size will allow us to "solve" complex code reasoning tasks like vulnerability detection, or if a fundamental shift in modeling and training techniques is required. We also explored adding domain knowledge to prompts; although it helped certain models understand some code semantics, vulnerability detection requires multi-step reasoning, and these models still failed in steps, such as reasoning about variable relations. Our results suggest that new models, new training methods, or more execution-specific pretraining data may be needed to conquer vulnerability detection. We speculate that auto-regressive pre-training on source code may not effectively extract code semantics, especially on the current pretraining mixtures, in which execution data is scarce. Success on vulnerability detection as a code reasoning task can benefit many areas of software engineering such as debugging, test input generation, and program repair. Our code and data are available at https://doi.org/10.6084/m9.figshare.27368025.
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.
The prediction of student performance and the analysis of students' learning behavior play an important role in enhancing online courses. By analysing a massive amount of clickstream data that captures student behavior, educators can gain valuable insights into the factors that influence academic outcomes and identify areas of improvement in courses. In this study, we developed ClickTree, a tree-based methodology, to predict student performance in mathematical assignments based on students' clickstream data. We extracted a set of features, including problem-level, assignment-level and student-level features, from the extensive clickstream data and trained a CatBoost tree to predict whether a student successfully answers a problem in an assignment. The developed method achieved an AUC of 0.78844 in the Educational Data Mining Cup 2023 and ranked second in the competition. Furthermore, our results indicate that students encounter more difficulties in the problem types that they must select a subset of answers from a given set as well as problem subjects of Algebra II. Additionally, students who performed well in answering end-unit assignment problems engaged more with in-unit assignments and answered more problems correctly, while those who struggled had higher tutoring request rate. The proposed method can be utilized to improve students' learning experiences, and the above insights can be integrated into mathematical courses to enhance students' learning outcomes.
This paper explores the use of large language models (LLMs) to score and explain short-answer assessments in K-12 science. While existing methods can score more structured math and computer science assessments, they often do not provide explanations for the scores. Our study focuses on employing GPT-4 for automated assessment in middle school Earth Science, combining few-shot and active learning with chain-of-thought reasoning. Using a human-in-the-loop approach, we successfully score and provide meaningful explanations for formative assessment responses. A systematic analysis of our method's pros and cons sheds light on the potential for human-in-the-loop techniques to enhance automated grading for open-ended science assessments.
Addressing the challenge of high annotation costs in solving Math Word Problems (MWPs) through full supervision with intermediate equations, recent works have proposed weakly supervised task settings that rely solely on the final answer as a supervised signal. Existing leading approaches typically employ various search techniques to infer intermediate equations, but cannot ensure their semantic consistency with natural language descriptions. The rise of Large Language Models (LLMs) like ChatGPT has opened up new possibilities for addressing MWPs directly. However, the computational demands of LLMs make them less than ideal for use in settings where resources are tight. In light of these challenges, we introduce an innovative two-stage framework that adeptly transfers mathematical Expertise from large to tiny language models. In \emph{Distillation Stage}, we propose a series of extraction processes that satisfy the properties of MWPs to distill mathematical knowledge from LLMs to construct problem-equation pairs required for supervised training. In \emph{Refinement Stage}, Due to Knowledge distilling method cannot guarantee the full utilization of all data, we further utilize the unsuccessfully searched data effectively by Knowledge Refine method. Finally, We train a small model using distilled data generated through two-stage methods. As our method fully leverages the semantic understanding capabilities during the searching 'problem-equation' pair, it demonstrates significantly improved performance on the Math23K and Weak12K datasets compared to existing small model methods, while maintaining a much lower computational cost than ChatGPT.
The remarkable progress of Multi-modal Large Language Models (MLLMs) has garnered unparalleled attention, due to their superior performance in visual contexts. However, their capabilities in visual math problem-solving remain insufficiently evaluated and understood. We investigate current benchmarks to incorporate excessive visual content within textual questions, which potentially assist MLLMs in deducing answers without truly interpreting the input diagrams. To this end, we introduce MathVerse, an all-around visual math benchmark designed for an equitable and in-depth evaluation of MLLMs. We meticulously collect 2,612 high-quality, multi-subject math problems with diagrams from publicly available sources. Each problem is then transformed by human annotators into six distinct versions, each offering varying degrees of information content in multi-modality, contributing to 15K test samples in total. This approach allows MathVerse to comprehensively assess whether and how much MLLMs can truly understand the visual diagrams for mathematical reasoning. In addition, we propose a Chain-of-Thought (CoT) evaluation strategy for a fine-grained assessment of the output answers. Rather than naively judging True or False, we employ GPT-4(V) to adaptively extract crucial reasoning steps, and then score each step with detailed error analysis, which can reveal the intermediate CoT reasoning quality by MLLMs. We hope the MathVerse benchmark may provide unique insights to guide the future development of MLLMs. Project page: https://mathverse-cuhk.github.io
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.
In this paper, we present Paramanu-Ayn, a collection of legal language models trained exclusively on Indian legal case documents. This 97-million-parameter Auto-Regressive (AR) decoder-only model was pretrained from scratch with a context size of 8192 on a single GPU for just 185 hours, achieving an efficient MFU of 41.35. We also developed a legal domain specialized BPE tokenizer. We evaluated our model using perplexity and zero-shot tasks: case judgment prediction with explanation and abstractive case summarization. Paramanu-Ayn outperformed Llama-2 7B and Gemini-Pro in case judgment prediction with explanation task on test accuracy by nearly 2 percentage points, despite being 72 times smaller. In zero-shot abstractive summarization, it surpassed decoder-only LLMs generating fixed-length summaries (5000 tokens) by over 10 percentage points in BLEU and METEOR metrics, and by nearly 4 percentage points in BERTScore. Further evaluations on zero-shot commonsense and mathematical benchmarks showed that Paramanu-Ayn excelled despite being trained exclusively on legal documents, outperforming Llama-1, Llama-2, and Falcon on AGIEVAL-AQuA-RAT and AGIEVAL-SAT-Math tasks. We also instruction-tuned our model on 10,763 diverse legal tasks, including legal clause generation, legal drafting, case summarization, etc. The Paramanu-Ayn-instruct model scored above 8 out of 10 in clarity, relevance, completeness, and legal reasoning metrics by GPT-3.5-Turbo. We found that our models, were able to learn drafting knowledge and generalize to draft legal contracts and legal clauses with limited instruction-tuning. Hence, we conclude that for a strong domain-specialized generative language model (such as legal), domain specialized pretraining from scratch is more cost effective, environmentally friendly, and remains competitive with larger models or even better than adapting LLMs for legal domain tasks.
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.
An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.
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.
As an important part of genetic algorithms (GAs), mutation operators is widely used in evolutionary algorithms to solve $\mathcal{NP}$-hard problems because it can increase the population diversity of individual. Due to limitations in mathematical tools, the mutation probability of the mutation operator is primarily empirically set in practical applications. In this paper, we propose a novel reduction method for the 0-1 knapsack problem(0-1 KP) and an improved mutation operator (IMO) based on the assumption $\mathcal{NP}\neq\mathcal{P}$, along with the utilization of linear relaxation techniques and a recent result by Dey et al. (Math. Prog., pp 569-587, 2022). We employ this method to calculate an upper bound of the mutation probability in general instances of the 0-1 KP, and construct an instance where the mutation probability does not tend towards 0 as the problem size increases. Finally, we prove that the probability of the IMO hitting the optimal solution within only a single iteration in large-scale instances is superior to that of the traditional mutation operator.
We introduce Sabi\'a-2, a family of large language models trained on Portuguese texts. The models are evaluated on a diverse range of exams, including entry-level tests for Brazilian universities, professional certification exams, and graduate-level exams for various disciplines such as accounting, economics, engineering, law and medicine. Our results reveal that our best model so far, Sabi\'a-2 Medium, matches or surpasses GPT-4's performance in 23 out of 64 exams and outperforms GPT-3.5 in 58 out of 64 exams. Notably, specialization has a significant impact on a model's performance without the need to increase its size, allowing us to offer Sabi\'a-2 Medium at a price per token that is 10 times cheaper than GPT-4. Finally, we identified that math and coding are key abilities that need improvement.
Calibration, which establishes the correlation between accuracy and model confidence, is important for LLM development. We design three off-the-shelf calibration methods based on self-consistency (Wang et al., 2022) for math reasoning tasks. Evaluation on two popular benchmarks (GSM8K and MathQA) using strong open-source LLMs (Mistral and LLaMA2), our methods better bridge model confidence and accuracy than existing methods based on p(True) (Kadavath et al., 2022) or logit (Kadavath et al., 2022).
Current language models have demonstrated their capability to develop basic reasoning, but struggle in more complicated reasoning tasks that require a combination of atomic skills, such as math word problem requiring skills like arithmetic and unit conversion. Previous methods either do not improve the inherent atomic skills of models or not attempt to generalize the atomic skills to complex reasoning tasks. In this paper, we first propose a probing framework to investigate whether the atomic skill can spontaneously generalize to complex reasoning tasks. Then, we introduce a hierarchical curriculum learning training strategy to achieve better skill generalization. In our experiments, we find that atomic skills can not spontaneously generalize to compositional tasks. By leveraging hierarchical curriculum learning, we successfully induce generalization, significantly improve the performance of open-source LMs on complex reasoning tasks. Promisingly, the skill generalization exhibit effective in cross-dataset and cross-domain scenarios. Complex reasoning can also help enhance atomic skills. Our findings offer valuable guidance for designing better training strategies for complex reasoning tasks.
Current AI alignment methodologies rely on human-provided demonstrations or judgments, and the learned capabilities of AI systems would be upper-bounded by human capabilities as a result. This raises a challenging research question: How can we keep improving the systems when their capabilities have surpassed the levels of humans? This paper answers this question in the context of tackling hard reasoning tasks (e.g., level 4-5 MATH problems) via learning from human annotations on easier tasks (e.g., level 1-3 MATH problems), which we term as easy-to-hard generalization. Our key insight is that an evaluator (reward model) trained on supervisions for easier tasks can be effectively used for scoring candidate solutions of harder tasks and hence facilitating easy-to-hard generalization over different levels of tasks. Based on this insight, we propose a novel approach to scalable alignment, which firstly trains the (process-supervised) reward models on easy problems (e.g., level 1-3), and then uses them to evaluate the performance of policy models on hard problems. We show that such easy-to-hard generalization from evaluators can enable easy-to-hard generalizations in generators either through re-ranking or reinforcement learning (RL). Notably, our process-supervised 7b RL model and 34b model (reranking@1024) achieves an accuracy of 34.0% and 52.5% on MATH500, respectively, despite only using human supervision on easy problems. Our approach suggests a promising path toward AI systems that advance beyond the frontier of human supervision.
Large vision-language models (LVLMs), designed to interpret and respond to human instructions, occasionally generate hallucinated or harmful content due to inappropriate instructions. This study uses linear probing to shed light on the hidden knowledge at the output layers of LVLMs. We demonstrate that the logit distributions of the first tokens contain sufficient information to determine whether to respond to the instructions, including recognizing unanswerable visual questions, defending against jailbreaking attacks, and identifying deceptive questions. Such hidden knowledge is gradually lost in logits of subsequent tokens during response generation. Then, we illustrate a simple decoding strategy at the generation of the first token, effectively improving the generated content. In experiments, we find a few interesting insights: First, the CLIP model already contains a strong signal for solving these tasks, which indicates potential bias in the existing datasets. Second, we observe performance improvement by utilizing the first logit distributions on three additional tasks, including indicating uncertainty in math solving, mitigating hallucination, and image classification. Last, with the same training data, simply finetuning LVLMs improves models' performance but is still inferior to linear probing on these tasks.
Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.