mlsanityData to 14 Oct 2026

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

arXiv 2405.15302 ↗First posted 24 May 2024cs.AI cs.CL cs.LGcited by 15

On the map: LLM reasoning → Prompting and chain-of-thought reasoning

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.

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.

Builds on

54 of 70 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024How to think step-by-step: A mechanistic understanding of chain-of-thought reasoning28 Feb
  2. 2024Chain of Thought Empowers Transformers to Solve Inherently Serial Problems20 Feb
  3. 2022Large Language Models are Zero-Shot Reasoners24 May

Other references · 51

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  3. 2020Language Models are Few-Shot Learnerscited by 32,419
  4. 2022Locating and Editing Factual Associations in GPTcited by 2,691
  5. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  6. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,165
  7. 2022In-context Learning and Induction Headscited by 964
  8. 2019Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Prunedcited by 856
  9. 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 724
  10. 2022A Survey on In-context Learningcited by 721
  11. 2022What Can Transformers Learn In-Context? A Case Study of Simple Function Classescited by 715
  12. 2019On Exact Computation with an Infinitely Wide Neural Netcited by 573
38 more
  1. 2019Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networkscited by 566
  2. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
  3. 2021Transformers Can Do Bayesian Inferencecited by 360
  4. 2022Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thoughtcited by 337
  5. 2018Generating Wikipedia by Summarizing Long Sequencescited by 335
  6. 2019Revealing the Dark Secrets of BERTcited by 301
  7. 2019A Multiscale Visualization of Attention in the Transformer Modelcited by 292
  8. 2020Transformers as Soft Reasoners over Languagecited by 270
  9. 2023Label Words are Anchors: An Information Flow Perspective for Understanding In-Context Learningcited by 236
  10. 2023Localizing Model Behavior with Path Patchingcited by 195
  11. 2018A Convergence Analysis of Gradient Descent for Deep Linear Neural Networkscited by 184
  12. 2024Do Large Language Models Latently Perform Multi-Hop Reasoning?cited by 169
  13. 2019CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Textcited by 162
  14. 2023Birth of a Transformer: A Memory Viewpointcited by 161
  15. 2023The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reductioncited by 123
  16. 2023The mechanistic basis of data dependence and abrupt learning in an in-context classification taskcited by 118
  17. 2024The Evolution of Statistical Induction Heads: In-Context Learning Markov Chainscited by 118
  18. 2024How Transformers Learn Causal Structure with Gradient Descentcited by 118
  19. 2023Circuit Component Reuse Across Tasks in Transformer Language Modelscited by 108
  20. 2023How do Language Models Bind Entities in Context?cited by 108
  21. 2024Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalizationcited by 79
  22. 2023How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representationscited by 75
  23. 2024Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimalitycited by 74
  24. 2021On the Validity of Modeling SGD with Stochastic Differential Equations (SDEs)cited by 73
  25. 2022StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Textscited by 68
  26. 2020Phase diagram for two-layer ReLU neural networks at infinite-width limitcited by 67
  27. 2024Mechanistic Design and Scaling of Hybrid Architecturescited by 59
  28. 2020Implicit Regularization of Random Feature Modelscited by 54
  29. 2024A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Taskcited by 49
  30. 2024Understanding and Patching Compositional Reasoning in LLMscited by 46
  31. 2021Pointer Value Retrieval: A new benchmark for understanding the limits of neural network generalizationcited by 29
  32. 2023When can transformers reason with abstract symbols?cited by 24
  33. 2024Understanding Reasoning Ability of Language Models From the Perspective of Reasoning Paths Aggregationcited by 22
  34. 2024What Can Transformer Learn with Varying Depth? Case Studies on Sequence Learning Taskscited by 19
  35. 2022Empirical Phase Diagram for Three-layer Neural Networks with Infinite Widthcited by 17
  36. 2022Learning to Reason with Neural Networks: Generalization, Unseen Data and Boolean Measurescited by 17
  37. 2022Multi-Step Deductive Reasoning Over Natural Language: An Empirical Study on Out-of-Distribution Generalisationcited by 15
  38. 2022LogicInference: A New Dataset for Teaching Logical Inference to seq2seq Modelscited by 12

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 6; 2026: 3.

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  1. 2024Transformers Provably Solve Parity Efficiently with Chain of Thoughtcited by 50
  2. 2024Reasoning Circuits in Language Models: A Mechanistic Interpretation of Syllogistic Inferencecited by 29
  3. 2024From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiencycited by 29
  4. 2024Out-of-distribution generalization via composition: a lens through induction heads in Transformerscited by 28
  5. 2025Complexity Control Facilitates Reasoning-Based Compositional Generalization in Transformerscited by 20
  6. 2024A Implies B: Circuit Analysis in LLMs for Propositional Logical Reasoningcited by 15
  7. 2025An Analysis for Reasoning Bias of Language Models with Small Initializationcited by 13
  8. 2024Exact Conversion of In-Context Learning to Model Weights in Linearized-Attention Transformerscited by 7
  9. 2025Punctuation and Predicates in Language Modelscited by 5
  10. 2025Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Trainingcited by 3
  11. 2025Nature's Insight: A Novel Framework and Comprehensive Analysis of Agentic Reasoning Through the Lens of Neurosciencecited by 3
  12. 2026Invariant Learning Dynamics of Transformers in Inductive Reasoning Taskscited by 2
3 more
  1. 2026Scaling Reasoning Hop Exposes Weaknesses: Demystifying and Improving Hop Generalization in Large Language Modelscited by 1
  2. 2026DenseSteer: Steering Small Language Models towards Dense Math Reasoningcited by 1
  3. 2025Limit Analysis for Symbolic Multi-step Reasoning Tasks with Information Propagation Rules Based on Transformerscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Opening the Black Box: A Survey on the Mechanisms of Multi-Step Reasoning in Large Language Models
  2. 2023Towards a Mechanistic Interpretation of Multi-Step Reasoning Capabilities of Language Models
  3. 2024LLMs Faithfully and Iteratively Compute Answers During CoT: A Systematic Analysis With Multi-step Arithmetics
  4. 2026Revealing Algorithmic Deductive Circuits for Logical Reasoning
  5. 2025Analyzing the Power of Chain of Thought through Memorization Capabilities
  6. 2025Advancing Reasoning in Large Language Models: Promising Methods and Approaches
  7. 2025Mechanistic Unveiling of Transformer Circuits: Self-Influence as a Key to Model Reasoning
  8. 2025Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning