Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between inductive and deductive reasoning, leading to a blending of the two. This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning? While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored. To investigate into the true inductive reasoning capabilities of LLMs, we propose a novel framework, SolverLearner. This framework enables LLMs to learn the underlying function (i.e., $y = f_w(x)$), that maps input data points $(x)$ to their corresponding output values $(y)$, using only in-context examples. By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner. Our observations reveal that LLMs demonstrate remarkable inductive reasoning capabilities through SolverLearner, achieving near-perfect performance with ACC of 1 in most cases. Surprisingly, despite their strong inductive reasoning abilities, LLMs tend to relatively lack deductive reasoning capabilities, particularly in tasks involving ``counterfactual'' reasoning.

翻译：推理包含两种典型类型：演绎推理与归纳推理。尽管针对大语言模型推理能力的研究已相当广泛，但多数研究未能严格区分归纳与演绎推理，导致二者相互混淆。这引发了一个根本性问题：在大语言模型的推理过程中，演绎推理与归纳推理何者更具挑战性？虽然大语言模型的演绎推理能力（即遵循推理任务指令的能力）已受到广泛关注，但其真正的归纳推理能力在很大程度上仍未被探索。为深入探究大语言模型真实的归纳推理能力，我们提出了一个新颖的框架——SolverLearner。该框架使大语言模型能够仅通过上下文示例学习从输入数据点$(x)$到对应输出值$(y)$的映射关系（即$y = f_w(x)$）。通过聚焦归纳推理并将其与基于大语言模型的演绎推理相分离，我们得以借助SolverLearner以纯粹形式隔离并研究大语言模型的归纳推理。我们的观察表明，大语言模型通过SolverLearner展现出卓越的归纳推理能力，在多数情况下达到接近完美的表现（准确率ACC为1）。令人惊讶的是，尽管大语言模型具备强大的归纳推理能力，但其演绎推理能力相对欠缺，尤其在涉及"反事实"推理的任务中表现明显。