Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

However, a closer examination reveals inconsistencies that challenge this optimistic view. Consider this straightforward question: “The day the US was established is in a leap year or a normal year?” When prompted with the CoT prefix, the modern LLM Gemini responded: “The United States was established in 1776. 1776 is divisible by 4, but it’s not a century year, so it’s a leap year. Therefore, the day the US was established was in a normal year.” This response exemplifies a concerning pattern: the model correctly recites the leap year rule and articulates intermediate reasoning steps, yet produces a logically inconsistent conclusion (i.e., asserting 1776 is both a leap year and a normal year). Such inconsistencies suggest that there is a distinction between human-like inference and CoT reasoning.

An expanding body of analyses reveals that LLMs tend to rely on surface-level semantics and clues rather than logical procedures (Bentham et al., 2024; Chen et al., 2025b; Lanham et al., 2023). LLMs construct superficial chains of logic based on learned token associations, often failing on tasks that deviate from commonsense heuristics or familiar templates (Tang et al., 2023). In the reasoning process, performance degrades sharply when irrelevant clauses are introduced, which indicates that models cannot grasp the underlying logic (Mirzadeh et al., 2024). This fragility becomes even more apparent when models are tested on more complex tasks, where they frequently produce incoherent solutions and fail to follow consistent reasoning paths (Shojaee et al., 2025). Collectively, these pioneering works deepen the skepticism surrounding the true nature of CoT reasoning.

In light of this line of research, we question the CoT reasoning by proposing an alternative lens through data distribution and further investigating why and when it fails. We hypothesize that CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. As such, its effectiveness is inherently limited by the nature and extent of the distribution discrepancy between training data and the test queries. Guided by this data distribution lens, we dissect CoT reasoning via three dimensions: (i) task—To what extent CoT reasoning can handle tasks that involve transformations or previously unseen task structures. (2) length—how CoT reasoning generalizes to chains with length different from that of training data; and (3) format—how sensitive CoT reasoning is to surface-level query form variations. To evaluate each aspect, we introduce DataAlchemy, a controlled and isolated experiment that allows us to train LLMs from scratch and systematically probe them under various distribution shifts.

Our findings reveal that CoT reasoning works effectively when applied to in-distribution or near in-distribution data but becomes fragile and prone to failure even under moderate distribution shifts. In some cases, LLMs generate fluent yet logically inconsistent reasoning steps. The results suggest that what appears to be structured reasoning can be a mirage, emerging from memorized or interpolated patterns in the training data rather than logical inference. These insights carry important implications for both practitioners and researchers. For practitioners, our results highlight the risk of relying on CoT as a plug-and-play solution for reasoning tasks and caution against equating CoT-style output with human thinking. For researchers, the results underscore the ongoing challenge of achieving reasoning that is both faithful and generalizable, motivating the need to develop models that can move beyond surface-level pattern recognition to exhibit deeper inferential competence.

2.2. Discussion on Illusion of LLM Reasoning

While Chain-of-Thought prompting has led to impressive gains on complex reasoning tasks, a growing body of work has started questioning the nature of these gains. One major line of research highlights the fragility of CoT reasoning. Minor and semantically irrelevant perturbations such as distractor phrases or altered symbolic forms can cause significant performance drops in state-of-the-art models (Mirzadeh et al., 2024; Tang et al., 2023). Models often incorporate such irrelevant details into their reasoning, revealing a lack of sensitivity to salient information. Other studies show that models prioritize the surface form of reasoning over logical soundness; in some cases, longer but flawed reasoning paths yield better final answers than shorter, correct ones (Bentham et al., 2024). Similarly, performance does not scale with problem complexity as expected—models may overthink easy problems and give up on harder ones (Shojaee et al., 2025). Another critical concern is the faithfulness of the reasoning process. Intervention-based studies reveal that final answers often remain unchanged even when intermediate steps are falsified or omitted (Lanham et al., 2023), a phenomenon dubbed the illusion of transparency (Bentham et al., 2024; Chen et al., 2025b). Together, these findings suggest that LLMs are not principled reasoners but rather sophisticated simulators of reasoning-like text. However, a systematic understanding of why and when CoT reasoning fails is still a mystery.

Building on this data distribution perspective, we identify three critical dimensions along which distributional shifts can occur, each revealing different aspects of CoT’s pattern-matching nature: ➊ Task generalization examines how well CoT transfers across different types of reasoning tasks. Novel tasks may have unique elements and underlying logical structure, which introduces distributional shifts that challenge the model’s ability to apply learned reasoning patterns. ➋ Length generalization investigates CoT’s robustness to reasoning chains of varying lengths. Since training data typically contains reasoning sequences within a certain length range, test cases requiring substantially longer or shorter reasoning chains represent a form of distributional shift along the sequence length dimension. This length discrepancy could result from the reasoning step or the text-dependent solution space. ➌ Format generalization explores how sensitive CoT is to variations in prompt formulation and structure. Due to various reasons (e.g., sophistical training data or diverse background of users), it is challenging for LLM practitioners to design a golden prompt to elicit knowledge suitable for the current case. Their detailed definition and implementation are given in subsequent sections.

Each dimension provides a unique lens for understanding the boundaries of CoT’s effectiveness and the mechanisms underlying its apparent reasoning capabilities. By systematically varying these dimensions in controlled experimental settings, we can empirically validate our hypothesis that CoT performance degrades predictably as distributional discrepancy increases, thereby revealing its fundamental nature as a pattern-matching rather than reasoning system.