Local Prompt Optimization

In recent years, the use of prompts to guide the output of Large Language Models have increased dramatically. However, even the best of experts struggle to choose the correct words to stitch up a prompt for the desired task. To solve this, LLM driven prompt optimization emerged as an important problem. Existing prompt optimization methods optimize a prompt globally, where in all the prompt tokens have to be optimized over a large vocabulary while solving a complex task. The large optimization space (tokens) leads to insufficient guidance for a better prompt. In this work, we introduce Local Prompt Optimization (LPO) that integrates with any general automatic prompt engineering method. We identify the optimization tokens in a prompt and nudge the LLM to focus only on those tokens in its optimization step. We observe remarkable performance improvements on Math Reasoning (GSM8k and MultiArith) and BIG-bench Hard benchmarks across various automatic prompt engineering methods. Further, we show that LPO converges to the optimal prompt faster than global methods.

Exploring the Hidden Reasoning Process of Large Language Models by Misleading Them

Large language models (LLMs) and Vision language models (VLMs) have been able to perform various forms of reasoning tasks in a wide range of scenarios, but are they truly engaging in task abstraction and rule-based reasoning beyond mere memorization and pattern matching? To answer this question, we propose a novel experimental approach, Misleading Fine-Tuning (MisFT), to examine whether LLMs/VLMs perform abstract reasoning by altering their original understanding of fundamental rules. In particular, by constructing a dataset with math expressions that contradict correct operation principles, we fine-tune the model to learn those contradictory rules and assess its generalization ability on different test domains. Through a series of experiments, we find that current LLMs/VLMs are capable of effectively applying contradictory rules to solve practical math word problems and math expressions represented by images, implying the presence of an internal mechanism that abstracts before reasoning.

Large Language Models in Numberland: A Quick Test of Their Numerical Reasoning Abilities

An essential element of human mathematical reasoning is our number sense -- an abstract understanding of numbers and their relationships -- which allows us to solve problems involving vast number spaces using limited computational resources. Mathematical reasoning of Large Language Models (LLMs) is often tested on high-level problems (such as Olympiad challenges, geometry, word problems, and puzzles), but their low-level number sense remains less explored. We introduce "Numberland," a 100-problem test to evaluate the numerical reasoning abilities of LLM-based agents. The tasks -- basic operations, advanced calculations (e.g., exponentiation, complex numbers), prime number checks, and the 24 game -- aim to test elementary skills and their integration in solving complex and uncertain problems. We evaluated five LLM-based agents: OpenAI's o1 and o1-mini, Google Gemini, Microsoft Copilot, and Anthropic Claude. They scored 74-95% on the first three tasks that allow deterministic steps to solutions. In the 24 game, which needs trial-and-error search, performance dropped to 10-73%. We tested the top 24 solver (o1 with 73% accuracy) on 25 harder problems, and its score fell to 27%, confirming search as a bottleneck. These results, along with the types of mistakes, suggest a fragile number of LLMs, which is a bit surprising given their prowess in challenging benchmarks. The limits of LLM numerical reasoning highlight the scope of simple, targeted tests to evaluate and explain LLM math skills to ensure safe use.

QuestBench: Can LLMs ask the right question to acquire information in reasoning tasks?

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

DiffSampling: Enhancing Diversity and Accuracy in Neural Text Generation

Despite their increasing performance, large language models still tend to reproduce training data, generate several repetitions, and focus on the most common grammatical structures and words. A possible cause is the decoding strategy adopted: the most common ones either consider only the most probable tokens, reducing output diversity, or increase the likelihood of unlikely tokens at the cost of output accuracy and correctness. In this paper, we propose a family of three new decoding methods by leveraging a mathematical analysis of the token probability distribution. In particular, the difference between consecutive, sorted probabilities can be used to avoid incorrect tokens and increase the chance of low-probable but accurate words. Experiments concerning math problem solving, extreme summarization, and the divergent association task show that our approach consistently performs at least as well as current alternatives in terms of quality and diversity.

A Diversity-Enhanced Knowledge Distillation Model for Practical Math Word Problem Solving

Math Word Problem (MWP) solving is a critical task in natural language processing, has garnered significant research interest in recent years. Various recent studies heavily rely on Seq2Seq models and their extensions (e.g., Seq2Tree and Graph2Tree) to generate mathematical equations. While effective, these models struggle to generate diverse but counterpart solution equations, limiting their generalization across various math problem scenarios. In this paper, we introduce a novel Diversity-enhanced Knowledge Distillation (DivKD) model for practical MWP solving. Our approach proposes an adaptive diversity distillation method, in which a student model learns diverse equations by selectively transferring high-quality knowledge from a teacher model. Additionally, we design a diversity prior-enhanced student model to better capture the diversity distribution of equations by incorporating a conditional variational auto-encoder. Extensive experiments on {four} MWP benchmark datasets demonstrate that our approach achieves higher answer accuracy than strong baselines while maintaining high efficiency for practical applications.

Empowering Bengali Education with AI: Solving Bengali Math Word Problems through Transformer Models

Mathematical word problems (MWPs) involve the task of converting textual descriptions into mathematical equations. This poses a significant challenge in natural language processing, particularly for low-resource languages such as Bengali. This paper addresses this challenge by developing an innovative approach to solving Bengali MWPs using transformer-based models, including Basic Transformer, mT5, BanglaT5, and mBART50. To support this effort, the "PatiGonit" dataset was introduced, containing 10,000 Bengali math problems, and these models were fine-tuned to translate the word problems into equations accurately. The evaluation revealed that the mT5 model achieved the highest accuracy of 97.30%, demonstrating the effectiveness of transformer models in this domain. This research marks a significant step forward in Bengali natural language processing, offering valuable methodologies and resources for educational AI tools. By improving math education, it also supports the development of advanced problem-solving skills for Bengali-speaking students.

Mathematical Reasoning in Large Language Models: Assessing Logical and Arithmetic Errors across Wide Numerical Ranges

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods only compare model outputs to ground-truth answers, obscuring insights into reasoning processes. To address these limitations, we introduce GSM-Ranges, a dataset generator derived from GSM8K that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales. Additionally, we propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy. Our experiments with various models reveal a significant increase in logical error rates-up to 14 percentage points-as numerical complexity rises, demonstrating a general weakness in reasoning with out-of-distribution numerical values. Moreover, while models demonstrate high accuracy on standalone arithmetic tasks, their performance deteriorates substantially when computations are embedded within word problems. These findings provide a comprehensive evaluation of LLMs' mathematical reasoning capabilities and inform future research directions for improving numerical generalization in language models.

Template-Driven LLM-Paraphrased Framework for Tabular Math Word Problem Generation

Solving tabular math word problems (TMWPs) has become a critical role in evaluating the mathematical reasoning ability of large language models (LLMs), where large-scale TMWP samples are commonly required for LLM fine-tuning. Since the collection of high-quality TMWP datasets is costly and time-consuming, recent research has concentrated on automatic TMWP generation. However, current generated samples usually suffer from issues of either correctness or diversity. In this paper, we propose a Template-driven LLM-paraphrased (TeLL) framework for generating high-quality TMWP samples with diverse backgrounds and accurate tables, questions, answers, and solutions. To this end, we first extract templates from existing real samples to generate initial problems, ensuring correctness. Then, we adopt an LLM to extend templates and paraphrase problems, obtaining diverse TMWP samples. Furthermore, we find the reasoning annotation is important for solving TMWPs. Therefore, we propose to enrich each solution with illustrative reasoning steps. Through the proposed framework, we construct a high-quality dataset TabMWP-TeLL by adhering to the question types in the TabMWP dataset, and we conduct extensive experiments on a variety of LLMs to demonstrate the effectiveness of TabMWP-TeLL in improving TMWP solving performance. The code and data of this paper are available at: https://github.com/Jason8Kang/TELL.

ArithmAttack: Evaluating Robustness of LLMs to Noisy Context in Math Problem Solving

While Large Language Models (LLMs) have shown impressive capabilities in math problem-solving tasks, their robustness to noisy inputs is not well-studied. In this work, we propose ArithmAttack to examine how robust the LLMs are when they encounter noisy prompts that contain extra noise in the form of punctuation marks. While being easy to implement, ArithmAttack does not cause any information loss since words are not added or deleted from the context. We evaluate the robustness of seven LLMs, including LLama3, Mistral, and Mathstral, on noisy GSM8K and MultiArith datasets. Our experiments suggest that all the studied models show vulnerability to such noise, with more noise leading to poorer performances.