# Understanding Reasoning Ability of Language Models From the Perspective of Reasoning Paths Aggregation

arXiv: https://arxiv.org/abs/2402.03268 · HTML: https://mlsanity.com/paper/2402.03268/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 43)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)

## Built on by (most cited first, 22 of 22)

- [Generalization v.s. Memorization: Tracing Language Models' Capabilities Back to Pretraining Data](https://mlsanity.com/paper/2407.14985/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Disentangling Memory and Reasoning Ability in Large Language Models](https://mlsanity.com/paper/2411.13504/) (2024)
- [Towards a Theoretical Understanding of the 'Reversal Curse' via Training Dynamics](https://mlsanity.com/paper/2405.04669/) (2024)
- [On Linear Representations and Pretraining Data Frequency in Language Models](https://mlsanity.com/paper/2504.12459/) (2025)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism](https://mlsanity.com/paper/2405.15302/) (2024)
- [Learning from Diverse Reasoning Paths with Routing and Collaboration](https://mlsanity.com/paper/2508.16861/) (2025)
- [Emergent Slow Thinking in LLMs as Inverse Tree Freezing](https://mlsanity.com/paper/2509.23629/) (2025)
- [On the Empirical Complexity of Reasoning and Planning in LLMs](https://mlsanity.com/paper/2404.11041/) (2024)
- [A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search](https://mlsanity.com/paper/2507.00004/) (2025)
- [Finding the Minimal Parameter Budget for Implicit Reasoning: A Data Complexity Driven Scaling Law for Language Models](https://mlsanity.com/paper/2504.03635/) (2025)
- [Efficient Knowledge Probing of Large Language Models by Adapting Pre-trained Embeddings](https://mlsanity.com/paper/2508.06030/) (2025)
- [Achilles' Heel of Mamba: Essential difficulties of the Mamba architecture demonstrated by synthetic data](https://mlsanity.com/paper/2509.17514/) (2025)
- [From Chains to DAGs: Probing the Graph Structure of Reasoning in LLMs](https://mlsanity.com/paper/2601.17593/) (2026)
- [Scalable Complexity Control Facilitates Reasoning Ability of LLMs](https://mlsanity.com/paper/2505.23013/) (2025)
- [Shortcut Solutions Learned by Transformers Impair Continual Compositional Reasoning](https://mlsanity.com/paper/2605.05495/) (2026)
- [SPARK: Self-Play with Asymmetric Reward from Knowledge Graphs](https://mlsanity.com/paper/2605.05546/) (2026)
- [The Periodic Table of LLM Reasoning: A Structured Survey of Reasoning Paradigms, Methods, and Failure Modes](https://mlsanity.com/paper/2606.11470/) (2026)
- [Leveraging Trajectory Graphs for Pre-Execution Error Diagnosis in Agentic LLM Systems](https://mlsanity.com/paper/2607.27443/) (2026)

## Abstract (arXiv)

Pre-trained language models (LMs) are able to perform complex reasoning without explicit fine-tuning. To understand how pre-training with a next-token prediction objective contributes to the emergence of such reasoning capability, we propose that we can view an LM as deriving new conclusions by aggregating indirect reasoning paths seen at pre-training time. We found this perspective effective in two important cases of reasoning: logic reasoning with knowledge graphs (KGs) and chain-of-thought (CoT) reasoning. More specifically, we formalize the reasoning paths as random walk paths on the knowledge/reasoning graphs. Analyses of learned LM distributions suggest that a weighted sum of relevant random walk path probabilities is a reasonable way to explain how LMs reason. Experiments and analysis on multiple KG and CoT datasets reveal the effect of training on random walk paths and suggest that augmenting unlabeled random walk reasoning paths can improve real-world multi-step reasoning performance. code: https://github.com/WANGXinyiLinda/LM_random_walk