Token-by-Token Regeneration and Domain Biases: A Benchmark of LLMs on Advanced Mathematical Problem-Solving

• URL: http://arxiv.org/abs/2501.17084v1
• Date: Tue, 28 Jan 2025 17:11:36 GMT
• Title: Token-by-Token Regeneration and Domain Biases: A Benchmark of LLMs on Advanced Mathematical Problem-Solving
• Authors: Evgenii Evstafev,
• Abstract summary: This study evalu-ates 10 large language models (LLMs) with 7 to 8 billion parameters using the MATH dataset. The focus is on their ability to generate executable Python code as a step in their reasoning process, involving over 9,450 code executions.
• Score: 0.0
• License:
• Abstract: Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8 billion parameters using 945 competition-level problems from the MATH dataset. The focus is on their ability to generate executable Python code as a step in their reasoning process, involving over 9,450 code executions. The research introduces an evaluation framework using mistral-large-2411 to rate answers on a 5-point scale, which helps address inconsistencies in mathematical notation. It also examines the impact of regenerating output token-by-token on refining results. The findings reveal a significant 34.5% per-formance gap between the top commercial model (gpt-4o-mini, scoring 83.7%) and the least effective open-source model (open-codestral-mamba:v0.1, scoring 49.2%). This disparity is especially noticeable in complex areas like Number Theory. While token-by-token regeneration slightly improved accuracy (+0.8%) for the model llama3.1:8b, it also reduced code execution time by 36.7%, highlighting a trade-off between efficiency and precision. The study also noted a consistent trend where harder problems correlated with lower accuracy across all models. Despite using controlled execution environments, less than 1% of the generated code was unsafe, and 3.17% of problems remained unsolved after 10 attempts, suggesting that hybrid reasoning methods may be beneficial.

Related papers

• Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs [76.43407125275202]
  o1-like models can emulate human-like long-time thinking during inference. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models. We propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy.
  arXiv  Detail & Related papers  (2024-12-30T18:55:12Z)
• Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability [53.51560766150442]
  Critical tokens are elements within reasoning trajectories that significantly influence incorrect outcomes. We present a novel framework for identifying these tokens through rollout sampling. We show that identifying and replacing critical tokens significantly improves model accuracy.
  arXiv  Detail & Related papers  (2024-11-29T18:58:22Z)
• Preference Optimization for Reasoning with Pseudo Feedback [100.62603571434167]
  We introduce a novel approach to generate pseudo feedback for reasoning tasks by framing the labeling of solutions as an evaluation against associated test cases. We conduct experiments on both mathematical reasoning and coding tasks using pseudo feedback for preference optimization, and observe improvements across both tasks.
  arXiv  Detail & Related papers  (2024-11-25T12:44:02Z)
• Subtle Errors Matter: Preference Learning via Error-injected Self-editing [59.405145971637204]
  We propose a novel preference learning framework called eRror-Injected Self-Editing (RISE) RISE injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. Experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.
  arXiv  Detail & Related papers  (2024-10-09T07:43:38Z)
• Uncovering Weaknesses in Neural Code Generation [21.552898575210534]
  We assess the quality of generated code using match-based and execution-based metrics, then conduct thematic analysis to develop a taxonomy of nine types of weaknesses. In the CoNaLa dataset, inaccurate prompts are a notable problem, causing all large models to fail in 26.84% of cases. Missing pivotal semantics is a pervasive issue across benchmarks, with one or more large models omitting key semantics in 65.78% of CoNaLa tasks. All models struggle with proper API usage, a challenge amplified by vague or complex prompts.
  arXiv  Detail & Related papers  (2024-07-13T07:31:43Z)
• Common 7B Language Models Already Possess Strong Math Capabilities [61.61442513067561]
  This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities. The potential for extensive scaling is constrained by the scarcity of publicly available math questions.
  arXiv  Detail & Related papers  (2024-03-07T18:00:40Z)
• DeepCode AI Fix: Fixing Security Vulnerabilities with Large Language Models [3.1690235522182104]
  Large language models (LLMs) are increasingly used to solve various programming tasks. We show that the task is difficult as it requires the model to learn long-range code relationships. We propose a technique to address these challenges with a new approach for querying and fine-tuning LLMs.
  arXiv  Detail & Related papers  (2024-02-19T18:35:40Z)
• Orca-Math: Unlocking the potential of SLMs in Grade School Math [10.206509967833664]
  A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Our approach has the following key elements: A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data.
  arXiv  Detail & Related papers  (2024-02-16T23:44:38Z)
• Cumulative Reasoning with Large Language Models [12.267474250936123]
  Cumulative Reasoning (CR) is a novel approach that utilizes language models cumulatively and iteratively. We demonstrate CR's superiority through several complex reasoning tasks. CR sets new state-of-the-art on the MATH dataset.
  arXiv  Detail & Related papers  (2023-08-08T16:18:20Z)
• Code Detection for Hardware Acceleration Using Large Language Models [0.0]
  This work presents the first analysis of code detection using large language models (LLMs) We propose both a preliminary, naive prompt and a novel prompting strategy for code detection. Results reveal that conventional prompting achieves great precision but poor accuracy (68.8%, 22.3%, and 79.2% for GEMM, convolution, and FFT, respectively) due to a high number of false positives. Our novel prompting strategy substantially reduces false positives, resulting in excellent overall accuracy (91.1%, 97.9%, and 99.7%, respectively)
  arXiv  Detail & Related papers  (2023-07-19T17:21:58Z)
• PAL: Program-aided Language Models [112.94785609781503]
  We present Program-Aided Language models (PaL) to understand natural language problems. PaL offloads the solution step to a programmatic runtime such as a Python interpreter. We set new state-of-the-art results in all 12 benchmarks.
  arXiv  Detail & Related papers  (2022-11-18T18:56:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.