Neuro-Symbolic Data Generation for Math Reasoning
A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts.
Code (0)
등록된 구현이 없습니다.
Tasks
DiversityMathMathematical ReasoningSimilar Papers 제목 키워드 기반
SymCode: A Neurosymbolic Approach to Mathematical Reasoning via Verifiable Code Generation
Large Language Models (LLMs) often struggle with complex mathematical reasoning, where prose-based generation leads to unverified and arithmetically unsound solutions. Current prompting strategies like Chain of Thought s…
Mathematical ReasoningLogical FallaciesCode GenerationOntology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge
Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investig…
Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the avail…
Mathematical ReasoningImproving Rule-based Reasoning in LLMs via Neurosymbolic Representations
Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly tasks that involve precise rule following, as often found in mathematical reasoning tasks. This paper introduces …
Mathematical ReasoningVERAFI: Verified Agentic Financial Intelligence through Neurosymbolic Policy Generation
Financial AI systems suffer from a critical blind spot: while Retrieval-Augmented Generation (RAG) excels at finding relevant documents, language models still generate calculation errors and regulatory violations during …