Evaluating Performance of Large Language Models on Numerical Reasoning Tasks

Published on 2025-11-12 • Avichala Research

Evaluating Performance of Large Language Models on Numerical Reasoning Tasks

Abstract: This paper investigates the performance of Large Language Models (LLMs) across a diverse suite of numerical reasoning tasks, highlighting their strengths and weaknesses. Through systematic experimentation on benchmarks like GSM8K, MATH500, and AIME25, the research identifies key factors influencing accuracy and reveals significant variability in LLM performance depending on task complexity, prompting investigations into the underlying mechanisms driving their numerical abilities. The study employs a comprehensive set of evaluation metrics and hyperparameter configurations, shedding light on optimal model configurations for numerical problem-solving.

Problem Statement: Large Language Models have demonstrated remarkable capabilities in various natural language tasks, but their ability to perform accurate numerical reasoning remains a significant challenge. The ability to translate natural language descriptions of mathematical problems into executable code or to directly perform calculations is critical for numerous real-world applications – from automated financial analysis and scientific modeling to interactive educational tools. The paper addresses the crucial need to quantify and understand the limitations of current LLMs in tackling numerical reasoning, focusing on the discrepancies observed across different problem types and benchmarks. The lack of systematic evaluation across diverse datasets hinders the development of more robust and reliable AI systems for quantitative tasks.

Methodology: The research utilizes a battery of standard numerical reasoning datasets, representing a range of difficulty levels. The core datasets include: GSM8K (a grade school math dataset), MATH500 (a higher-level arithmetic benchmark), AIME25 (Advanced Math Competition exam questions), and OlympiadBench (covering international math competitions). Crucially, the study employs a range of LLMs including models with varying parameter counts (0.6B, 1.7B, and 1.77B) and employs multiple prompting strategies (Standard, AlwaysThink, TaH, TaH+), focusing on the impact of "reasoning" or "thinking-out-loud" techniques. The researchers implemented a set of evaluation metrics including accuracy, and FLOPs (floating point operations per second) to assess computational efficiency. The paper extensively explores different architectural choices, such as LoRA (Low-Rank Adaptation) and dynamic decision-making approaches (Underthink, Overthink) to investigate how model structure and training methods influence performance. The experiments controlled for hyperparameter values – learning rate (4e-5), maximum gradient norm (0.2), training epochs (5), global batch size (128), and a cosine annealing learning rate scheduler with a minimum learning rate ratio of 0.1. This systematic approach allowed for a robust comparison of model configurations. A novel "token-only oracle" was tested in addition to standard oracle approaches.

Findings & Results: The results demonstrate substantial variability in LLM performance across the datasets. The models exhibited the highest accuracy on the MATH500 dataset, particularly with the “AlwaysThink” prompting strategy, achieving an average accuracy of around 74.4% across iterations. However, performance sharply declined on the more complex GSM8K dataset, with accuracy hovering around 52.8% on average. The inclusion of “TaH” and “TaH+” prompting strategies did not drastically improve performance, suggesting that simply requesting the model to “think-out-loud” without an underlying architectural adaptation didn’t lead to significant gains. The use of the token-only oracle demonstrated a significant reduction in accuracy compared to the standard oracle, highlighting the need for more sophisticated mechanisms to translate natural language into numerical operations. The models also exhibited a clear dependence on model size – larger models (1.77B) generally performed better than smaller models, but at a substantial computational cost as measured by FLOPs. Iteration number had a pronounced effect, with the model generally improving its accuracy over multiple iterations. Notably, the models exhibited a tendency towards “underthinking” (incorrectly choosing simpler solutions) and "overthinking" (excessive complexity).

Limitations: This study does not fully address the underlying mechanisms driving LLM numerical reasoning. While the experiment explored prompt engineering and model architectures, a deeper analysis of attention patterns, internal representations, and the interaction between language and numerical computation remains limited. The focus on specific prompting strategies also doesn’t fully capture the potential of more advanced reasoning frameworks or symbolic AI integration. Furthermore, the sample size and scope of the benchmark datasets restrict the generalizability of the findings to all numerical tasks. The paper also doesn’t delve deeply into the potential biases inherent in the training data that might be influencing the model’s responses. The effect of specialized numerical datasets and their effect on model optimization needs to be addressed.

Future Work & Outlook: Future research should focus on developing more interpretable LLMs for numerical reasoning, incorporating symbolic AI techniques to enhance reasoning capabilities, and expanding the benchmark datasets to include a wider range of problem types. Exploring methods for incorporating external tools and calculators into the LLM architecture is a critical direction. Research into more robust and efficient training methodologies, potentially leveraging reinforcement learning and curriculum learning, is also warranted. Further investigation into the alignment between LLM internal representations and human mathematical intuition is paramount. Finally, the field needs to move beyond simply measuring accuracy and explore metrics that capture the quality and justification of the solutions provided by LLMs.

Avichala Commentary: This work represents a crucial step in understanding the nascent capabilities of LLMs in quantitative domains. It’s a reminder that impressive natural language generation doesn’t automatically translate to proficiency in math. This research aligns with the broader evolution of AI agents, moving beyond passively responding to prompts towards truly reasoning and problem-solving. The variability in performance underscores the need for AI systems that are not just fluent in language, but deeply understand the logic and structure of mathematical thought. The research offers valuable insights for the design of more sophisticated AI agents capable of tackling complex, real-world problems involving numerical data – particularly relevant as we increasingly rely on AI to assist in scientific discovery, financial modeling, and data-driven decision making. The study lays the foundation for future research in the development of agents that can learn and adapt to different mathematical domains with increasing efficiency and robustness.

Link to the Arxiv: https://arxiv.org/abs/2511.08577v1.pdf