# Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism

arXiv: https://arxiv.org/abs/2405.15302 · HTML: https://mlsanity.com/paper/2405.15302/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 54 of its 70 references that are in the map.
- First posted on arXiv 24 May 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Revealing the Dark Secrets of BERT](https://mlsanity.com/paper/1908.08593/) (2019)
- [A Multiscale Visualization of Attention in the Transformer Model](https://mlsanity.com/paper/1906.05714/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Label Words are Anchors: An Information Flow Perspective for Understanding In-Context Learning](https://mlsanity.com/paper/2305.14160/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks](https://mlsanity.com/paper/1810.02281/) (2018)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)
- [Birth of a Transformer: A Memory Viewpoint](https://mlsanity.com/paper/2306.00802/) (2023)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [The mechanistic basis of data dependence and abrupt learning in an in-context classification task](https://mlsanity.com/paper/2312.03002/) (2023)

## Built on by (most cited first, 15 of 15)

- [Transformers Provably Solve Parity Efficiently with Chain of Thought](https://mlsanity.com/paper/2410.08633/) (2024)
- [Reasoning Circuits in Language Models: A Mechanistic Interpretation of Syllogistic Inference](https://mlsanity.com/paper/2408.08590/) (2024)
- [From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiency](https://mlsanity.com/paper/2410.05459/) (2024)
- [Out-of-distribution generalization via composition: a lens through induction heads in Transformers](https://mlsanity.com/paper/2408.09503/) (2024)
- [Complexity Control Facilitates Reasoning-Based Compositional Generalization in Transformers](https://mlsanity.com/paper/2501.08537/) (2025)
- [A Implies B: Circuit Analysis in LLMs for Propositional Logical Reasoning](https://mlsanity.com/paper/2411.04105/) (2024)
- [An Analysis for Reasoning Bias of Language Models with Small Initialization](https://mlsanity.com/paper/2502.04375/) (2025)
- [Exact Conversion of In-Context Learning to Model Weights in Linearized-Attention Transformers](https://mlsanity.com/paper/2406.02847/) (2024)
- [Punctuation and Predicates in Language Models](https://mlsanity.com/paper/2508.14067/) (2025)
- [Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Training](https://mlsanity.com/paper/2502.17800/) (2025)
- [Nature's Insight: A Novel Framework and Comprehensive Analysis of Agentic Reasoning Through the Lens of Neuroscience](https://mlsanity.com/paper/2505.05515/) (2025)
- [Invariant Learning Dynamics of Transformers in Inductive Reasoning Tasks](https://mlsanity.com/paper/2607.11875/) (2026)
- [Scaling Reasoning Hop Exposes Weaknesses: Demystifying and Improving Hop Generalization in Large Language Models](https://mlsanity.com/paper/2601.21214/) (2026)
- [DenseSteer: Steering Small Language Models towards Dense Math Reasoning](https://mlsanity.com/paper/2605.29247/) (2026)
- [Limit Analysis for Symbolic Multi-step Reasoning Tasks with Information Propagation Rules Based on Transformers](https://mlsanity.com/paper/2509.23178/) (2025)

## Abstract (arXiv)

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capability. In this study, we constructed a symbolic multi-step reasoning task to investigate the information propagation mechanisms in Transformer models when solving the task through direct answering and Chain-of-Thought (CoT) reasoning. We introduced the concept of buffer mechanism: the model stores various information in distinct buffers and selectively extracts it through the query-key matrix. We proposed a random matrix-based algorithm to enhance the model's reasoning ability. This algorithm introduces only 132 trainable parameters, yet leads to significant performance improvements on 7 multi-step reasoning datasets, including PrOntoQA, LogicAsker, and LogicInference. These findings provide new insights into understanding the large language models.