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文章背景与核心概要

一阶概念合成（First-order concept synthesis）旨在推断出一个能够在一系列有限关系结构中一致分类带标签对象的公式。尽管可以对单个候选公式进行精确评估，但量化一阶公式庞大的搜索空间仍然带来了巨大的挑战。此外，大语言模型（LLMs）生成的公式往往在语义上很有前景，但实际上存在瑕疵。

为了解决这一问题，“假设前沿”（Hypothesis Frontier）提出了一种验证器引导的神经符号框架，旨在实现以下目标： * 评估与保留： 针对每个训练对象测试大语言模型生成的每个公式，在迭代轮次中保留最强的已验证假设。 * 引导生成： 利用最佳假设中剩余的错误来指导后续的生成轮次。 * 修复与简化： 应用符号处理来修复无效公式（同时锚定于大语言模型假设），并在不改变任何训练预测的情况下压缩训练有效公式。

在相同的模型、问题集和大语言模型轮次预算下，“假设前沿”比传统的重复原始提示词生成解决了多得多的问题，证明了精确的符号推理能够有效增强问题求解能力和公式压缩能力。

Hypothesis Frontier: Verifier Guided LLM and Symbolic Search for First-Order Induction

Hypothesis Frontier: Verifier Guided LLM and Symbolic Search for First-Order Induction

Authors: Serafim Batzoglou
Published: August 11, 2026
Primary Subject: Artificial Intelligence (cs.AI)
arXiv ID: arXiv:2608.10843

Authors: Serafim Batzoglou
Published: August 11, 2026
Primary Subject: Artificial Intelligence (cs.AI)
arXiv ID: arXiv:2608.10843

📌 Summary

📌 Summary

First-order concept synthesis involves inferring a single formula that consistently classifies labeled objects across multiple finite relational structures. While individual candidates can be evaluated precisely, the vast search space of quantified first-order formulas presents a significant challenge. Furthermore, Large Language Models (LLMs) often generate formulas that are semantically promising yet flawed.

First-order concept synthesis involves inferring a single formula that consistently classifies labeled objects across multiple finite relational structures. While individual candidates can be evaluated precisely, the vast search space of quantified first-order formulas presents a significant challenge. Furthermore, Large Language Models (LLMs) often generate formulas that are semantically promising yet flawed.

To address this, Hypothesis Frontier introduces a verifier-guided neurosymbolic framework designed to: * Evaluate and Retain: Test each LLM-generated formula against every training object, keeping the strongest verified hypothesis across iterative rounds. * Guide Generation: Utilize remaining errors from the best hypothesis to steer subsequent generation rounds. * Repair and Simplify: Apply symbolic processing to fix invalid formulas (while remaining anchored to the LLM hypothesis) and compress train-valid formulas without altering any training predictions.

To address this, Hypothesis Frontier introduces a verifier-guided neurosymbolic framework designed to: * Evaluate and Retain: Test each LLM-generated formula against every training object, keeping the strongest verified hypothesis across iterative rounds. * Guide Generation: Utilize remaining errors from the best hypothesis to steer subsequent generation rounds. * Repair and Simplify: Apply symbolic processing to fix invalid formulas (while remaining anchored to the LLM hypothesis) and compress train-valid formulas without altering any training predictions.

Under identical models, problem sets, and LLM-round budgets, Hypothesis Frontier solves significantly more problems than traditional repeated original-prompt generation, proving that exact symbolic reasoning effectively enhances both problem-solving capability and formula compression.

Under identical models, problem sets, and LLM-round budgets, Hypothesis Frontier solves significantly more problems than traditional repeated original-prompt generation, proving that exact symbolic reasoning effectively enhances both problem-solving capability and formula compression.

🗂️ Submission History

🗂️ Submission History

  • [v1] Tue, 11 Aug 2026 12:13:35 UTC (129 KB)
  • [v1] Tue, 11 Aug 2026 12:13:35 UTC (129 KB)