A Hopfieldian View-based Interpretation for Chain-of-Thought Reasoning

Lijie Hu, Liang Liu, Shu Yang, Xin Chen, Hongru Xiao, Mengdi Li, Pan Zhou, Muhammad Asif Ali, Di Wang·June 18, 2024

Summary

This collection of papers investigates the effectiveness of Chain-of-Thought (CoT) techniques in enhancing large language models' reasoning performance, particularly in zero-shot and few-shot learning. Researchers propose a Read-and-Control framework that decomposes CoT into concept modeling, simulation, and Hopfieldian analysis. The framework is applied to various datasets and tasks, such as arithmetic, commonsense, and symbolic reasoning, to understand CoT's inner workings, error localization, and reasoning path control. It reveals the importance of prompts and example-based approaches, while also addressing the lack of interpretability in CoT methods. The studies demonstrate improvements in model accuracy, interpretability, and the ability to correct reasoning errors, with a focus on enhancing the models' understanding and guiding their responses through controlled operations.

Key findings

13

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to investigate the effectiveness of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models. Specifically, it seeks to address why prompting the model with "let's think step by step" improves zero-shot CoT and why providing examples before questioning enhances few-shot CoT . This paper introduces a Read-and-Control approach based on the Hopfieldian view to analyze and control the accuracy of CoT, revealing the inner workings of CoT, identifying reasoning errors, and guiding correct reasoning paths through experiments on multiple datasets for various tasks . While the paper focuses on understanding and improving CoT methods, the problem itself is not entirely new, as previous studies have explored different aspects of reasoning enhancement in large language models .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis regarding the success of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models (LLMs) . The study delves into the reasons behind the effectiveness of CoT methods, particularly focusing on the impact of prompts like "let’s think step by step" in zero-shot CoT and providing examples before questioning in few-shot CoT . Through a top-down explainable analysis from the Hopfieldian view, the paper proposes a Read-and-Control approach to analyze and control the accuracy of CoT, aiming to decipher the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper proposes several new ideas, methods, and models related to Chain-of-Thought (CoT) techniques and large language models (LLMs) . One key proposal is the adoption of a Read-and-Control approach to analyze and control CoT accuracy, aiming to explain the success of CoT techniques in enhancing LLMs' reasoning performance . This approach involves prompting with "let's think step by step" to improve zero-shot CoT and providing examples before questioning to boost few-shot CoT .

Furthermore, the paper introduces an explainable framework to bridge the gap in understanding the key factors underlying the success of CoT techniques . This framework aims to reveal the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths through experiments on seven datasets for three tasks . Additionally, the paper explores the impact of Bayesian inference on LLMs, particularly in the context of in-context learning (ICL) . Bayesian inference is utilized to update the knowledge and beliefs of the network systematically with the acquisition of new information, enhancing the model's performance on complex reasoning tasks .

Moreover, the paper discusses efforts dedicated to exploring how LLMs can be utilized for more complex tasks such as commonsense and mathematical reasoning . Various studies have focused on improving the accuracy of CoT through efficient prompt design, process optimization, extra engine usage, and knowledge enhancement . These endeavors aim to enhance the reasoning capabilities of LLMs by identifying key factors or elements that contribute to the success of CoT techniques . The proposed framework in the paper offers several key characteristics and advantages compared to previous methods in the context of Chain-of-Thought (CoT) reasoning and large language models (LLMs) .

  1. Hopfieldian View and Read-and-Control Approach: The framework adopts a Hopfieldian view to explain cognition as transformations between representational spaces implemented by neural populations in response to stimuli. This view provides a natural setting to study LLMs and CoT reasoning . Additionally, the framework introduces a Read-and-Control approach to analyze and control CoT accuracy, enhancing the understanding of CoT techniques' impact on LLMs' reasoning performance .

  2. Interpretability and Explainable Framework: The framework emphasizes interpretability to identify potential risks and meet human requirements, offering a deeper understanding of LLMs . It provides an explainable framework that helps localize reasoning errors, guide correct reasoning paths, and enhance the transparency of CoT reasoning .

  3. Utility Evaluation and Performance Comparison: Through utility evaluation, the framework demonstrates the ability to guide and correct the reasoning direction of LLMs, leading to improved accuracy in reasoning tasks . The approach shows superior performance in zero-shot and few-shot CoT, surpassing baseline methods and enhancing the accuracy of reasoning by directing correct reasoning paths .

  4. Concept Modeling and Simulation: The framework incorporates Concept Modeling, highlighting how LLMs learn latent concepts during pre-training, and Concept Simulation, which uses prompts as stimuli to induce specific concepts, contributing to improved reasoning performance .

  5. Enhanced Reasoning Paths and Error Localization: By employing concept-level representation read operations to localize errors in CoT and control operations to rectify LLMs' reasoning paths, the framework enhances the accuracy of reasoning and provides intuitive and interpretable analysis for CoT reasoning .

Overall, the framework's unique characteristics, such as the Hopfieldian view, interpretability focus, utility evaluation, concept modeling, and error localization, offer significant advantages in understanding and improving CoT reasoning in LLMs compared to previous methods, contributing to enhanced reasoning performance and transparency in complex reasoning tasks.


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research studies exist in the field of Chain-of-Thought (CoT) reasoning and large language models (LLMs) . Noteworthy researchers in this area include Lijie Hu, Liang Liu, Shu Yang, Xin Chen, Hongru Xiao, Mengdi Li, Pan Zhou, Muhammad Asif Ali, and Di Wang . Additionally, other researchers such as Yiming Yang, Jamie Callan, Graham Neubig, and many more have contributed to this field .

The key to the solution mentioned in the paper is the adoption of a Read-and-Control approach to analyze and control the accuracy of CoT . This approach allows for a top-down explainable analysis from the Hopfieldian view, enabling the framework to decipher the inner workings of CoT, localize reasoning errors, and guide the correct reasoning path .


How were the experiments in the paper designed?

The experiments in the paper were designed by considering seven datasets for three different tasks: Arithmetic Reasoning, Commonsense Reasoning, and Symbolic Reasoning. For arithmetic reasoning, datasets such as GSM8K, SVAMP, and AQuA were selected. For commonsense reasoning, benchmarks like StrategyQA and CSQA were chosen. Symbolic reasoning tasks utilized datasets like Coin Flip and Random Letter . Three large language models (LLMs) were used as baselines for evaluation: Mistral-instruct-7B, LLamA-2-7B-chat, and LLamA-3-8B-instruct . The evaluation metrics employed accuracy measurements for all dataset benchmarks, and the answer extraction process followed the methodology outlined by Kojima et al. . The experiments utilized the last ten layers to control the reasoning direction of the LLMs and varied the number of stimulus samples based on different tasks. Additionally, different reading set sizes were employed, such as 128, 256, and 512 samples, with a threshold value of δ = 3.5. The experiments were conducted using float16 to load large models and employed a greedy search decoding strategy with a maximum of 512 new tokens for all datasets .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is comprised of 7 datasets covering 3 different tasks: Arithmetic Reasoning, Commonsense Reasoning, and Symbolic Reasoning. Specifically, the datasets include GSM8K, SVAMP, AQuA for arithmetic reasoning, strategyQA and CSQA for commonsense reasoning, and Coin Flip and Random Letter for symbolic reasoning . The availability of the code as open source is not explicitly mentioned in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The study delves into the success of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models (LLMs) by analyzing the impact of different CoT methods under various settings . Through a top-down explainable analysis from a Hopfieldian view, the authors propose a Read-and-Control approach to decipher the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths . Additionally, the experiments conducted on seven datasets for three different tasks demonstrate the effectiveness of the framework in controlling the accuracy of CoT and providing insights into the reasoning process of LLMs . The findings from the experiments align with the scientific hypotheses put forth in the paper, showcasing the utility and efficacy of the proposed CoT methods in improving reasoning performance .


What are the contributions of this paper?

The paper makes several key contributions:

  • It analyzes Chain-of-Thought (CoT) methods under different settings to explain why CoT achieves success in large language models (LLMs) .
  • It proposes a Read-and-Control approach based on the Hopfieldian view to control the accuracy of CoT and provide reasoning error localization .
  • Through extensive experiments on seven datasets for three different tasks, the paper demonstrates that their framework can decipher the inner workings of CoT, localize reasoning errors, and guide the model towards the correct reasoning path .

What work can be continued in depth?

Further research in the field of Chain-of-Thought (CoT) reasoning can be expanded in several directions based on the existing studies:

  • Exploring Complex Tasks: Researchers can delve deeper into how Large Language Models (LLMs) can be utilized for more complex tasks like commonsense and mathematical reasoning .
  • Enhancing CoT Accuracy: Efforts can be dedicated to improving the accuracy of CoT techniques through efficient prompt design, process optimization, extra engine usage, and knowledge enhancement .
  • Identifying Key Factors: Continued studies can focus on identifying the key factors or elements that contribute to enhancing the reasoning capabilities of LLMs through CoT techniques .
  • Error Localization and Control: Research can focus on employing concept-level representation read operations to localize errors in CoT and control operations to rectify LLMs' reasoning paths .
  • Experimental Evaluation: Conducting comprehensive experimental evaluations using different datasets across various tasks to offer faithful explanations with error localization and control for CoT .

Tables

1

Introduction
Background
Emergence of Chain-of-Thought (CoT) techniques in LLMs
Importance of reasoning in zero-shot and few-shot learning
Objective
To evaluate CoT effectiveness in reasoning performance
To propose the Read-and-Control framework
To analyze CoT's inner workings and error correction
Method
Data Collection
Selection of diverse datasets (arithmetic, commonsense, symbolic reasoning)
Collection of LLM responses with and without CoT techniques
Data Preprocessing
Standardization of tasks and prompts
Identifying CoT components in model outputs
Error annotation and categorization
Concept Modeling
Analysis of concept understanding in CoT
Comparison with non-CoT models
Simulation
Implementation of the Read-and-Control framework
Manipulation of reasoning paths through prompts and examples
Hopfieldian Analysis
Application of Hopfield networks to understand CoT dynamics
Identifying patterns and dependencies in reasoning steps
Experimental Setup
Zero-shot and few-shot learning experiments
Performance metrics (accuracy, F1 score, etc.)
Results and Analysis
Quantitative evaluation of CoT improvements
Error localization and correction analysis
Interpretability of reasoning paths
Discussion
Implications for model design and prompting strategies
Limitations and future directions of CoT methods
Conclusion
Summary of findings on CoT effectiveness
Contributions to the understanding of LLM reasoning
Recommendations for future research in the field
Basic info
papers
computation and language
human-computer interaction
machine learning
artificial intelligence
Advanced features
Insights
What are the key datasets and tasks the framework is applied to for analysis?
How does the Read-and-Control framework help in improving large language models' performance?
What is the proposed framework called that the researchers use for Chain-of-Thought techniques?
What is the primary focus of the research in the given text?

A Hopfieldian View-based Interpretation for Chain-of-Thought Reasoning

Lijie Hu, Liang Liu, Shu Yang, Xin Chen, Hongru Xiao, Mengdi Li, Pan Zhou, Muhammad Asif Ali, Di Wang·June 18, 2024

Summary

This collection of papers investigates the effectiveness of Chain-of-Thought (CoT) techniques in enhancing large language models' reasoning performance, particularly in zero-shot and few-shot learning. Researchers propose a Read-and-Control framework that decomposes CoT into concept modeling, simulation, and Hopfieldian analysis. The framework is applied to various datasets and tasks, such as arithmetic, commonsense, and symbolic reasoning, to understand CoT's inner workings, error localization, and reasoning path control. It reveals the importance of prompts and example-based approaches, while also addressing the lack of interpretability in CoT methods. The studies demonstrate improvements in model accuracy, interpretability, and the ability to correct reasoning errors, with a focus on enhancing the models' understanding and guiding their responses through controlled operations.
Mind map
Interpretability of reasoning paths
Error localization and correction analysis
Quantitative evaluation of CoT improvements
Identifying patterns and dependencies in reasoning steps
Application of Hopfield networks to understand CoT dynamics
Manipulation of reasoning paths through prompts and examples
Implementation of the Read-and-Control framework
Comparison with non-CoT models
Analysis of concept understanding in CoT
Limitations and future directions of CoT methods
Implications for model design and prompting strategies
Results and Analysis
Hopfieldian Analysis
Simulation
Concept Modeling
Collection of LLM responses with and without CoT techniques
Selection of diverse datasets (arithmetic, commonsense, symbolic reasoning)
To analyze CoT's inner workings and error correction
To propose the Read-and-Control framework
To evaluate CoT effectiveness in reasoning performance
Importance of reasoning in zero-shot and few-shot learning
Emergence of Chain-of-Thought (CoT) techniques in LLMs
Recommendations for future research in the field
Contributions to the understanding of LLM reasoning
Summary of findings on CoT effectiveness
Discussion
Experimental Setup
Data Preprocessing
Data Collection
Objective
Background
Conclusion
Method
Introduction
Outline
Introduction
Background
Emergence of Chain-of-Thought (CoT) techniques in LLMs
Importance of reasoning in zero-shot and few-shot learning
Objective
To evaluate CoT effectiveness in reasoning performance
To propose the Read-and-Control framework
To analyze CoT's inner workings and error correction
Method
Data Collection
Selection of diverse datasets (arithmetic, commonsense, symbolic reasoning)
Collection of LLM responses with and without CoT techniques
Data Preprocessing
Standardization of tasks and prompts
Identifying CoT components in model outputs
Error annotation and categorization
Concept Modeling
Analysis of concept understanding in CoT
Comparison with non-CoT models
Simulation
Implementation of the Read-and-Control framework
Manipulation of reasoning paths through prompts and examples
Hopfieldian Analysis
Application of Hopfield networks to understand CoT dynamics
Identifying patterns and dependencies in reasoning steps
Experimental Setup
Zero-shot and few-shot learning experiments
Performance metrics (accuracy, F1 score, etc.)
Results and Analysis
Quantitative evaluation of CoT improvements
Error localization and correction analysis
Interpretability of reasoning paths
Discussion
Implications for model design and prompting strategies
Limitations and future directions of CoT methods
Conclusion
Summary of findings on CoT effectiveness
Contributions to the understanding of LLM reasoning
Recommendations for future research in the field
Key findings
13

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to investigate the effectiveness of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models. Specifically, it seeks to address why prompting the model with "let's think step by step" improves zero-shot CoT and why providing examples before questioning enhances few-shot CoT . This paper introduces a Read-and-Control approach based on the Hopfieldian view to analyze and control the accuracy of CoT, revealing the inner workings of CoT, identifying reasoning errors, and guiding correct reasoning paths through experiments on multiple datasets for various tasks . While the paper focuses on understanding and improving CoT methods, the problem itself is not entirely new, as previous studies have explored different aspects of reasoning enhancement in large language models .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate the scientific hypothesis regarding the success of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models (LLMs) . The study delves into the reasons behind the effectiveness of CoT methods, particularly focusing on the impact of prompts like "let’s think step by step" in zero-shot CoT and providing examples before questioning in few-shot CoT . Through a top-down explainable analysis from the Hopfieldian view, the paper proposes a Read-and-Control approach to analyze and control the accuracy of CoT, aiming to decipher the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper proposes several new ideas, methods, and models related to Chain-of-Thought (CoT) techniques and large language models (LLMs) . One key proposal is the adoption of a Read-and-Control approach to analyze and control CoT accuracy, aiming to explain the success of CoT techniques in enhancing LLMs' reasoning performance . This approach involves prompting with "let's think step by step" to improve zero-shot CoT and providing examples before questioning to boost few-shot CoT .

Furthermore, the paper introduces an explainable framework to bridge the gap in understanding the key factors underlying the success of CoT techniques . This framework aims to reveal the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths through experiments on seven datasets for three tasks . Additionally, the paper explores the impact of Bayesian inference on LLMs, particularly in the context of in-context learning (ICL) . Bayesian inference is utilized to update the knowledge and beliefs of the network systematically with the acquisition of new information, enhancing the model's performance on complex reasoning tasks .

Moreover, the paper discusses efforts dedicated to exploring how LLMs can be utilized for more complex tasks such as commonsense and mathematical reasoning . Various studies have focused on improving the accuracy of CoT through efficient prompt design, process optimization, extra engine usage, and knowledge enhancement . These endeavors aim to enhance the reasoning capabilities of LLMs by identifying key factors or elements that contribute to the success of CoT techniques . The proposed framework in the paper offers several key characteristics and advantages compared to previous methods in the context of Chain-of-Thought (CoT) reasoning and large language models (LLMs) .

  1. Hopfieldian View and Read-and-Control Approach: The framework adopts a Hopfieldian view to explain cognition as transformations between representational spaces implemented by neural populations in response to stimuli. This view provides a natural setting to study LLMs and CoT reasoning . Additionally, the framework introduces a Read-and-Control approach to analyze and control CoT accuracy, enhancing the understanding of CoT techniques' impact on LLMs' reasoning performance .

  2. Interpretability and Explainable Framework: The framework emphasizes interpretability to identify potential risks and meet human requirements, offering a deeper understanding of LLMs . It provides an explainable framework that helps localize reasoning errors, guide correct reasoning paths, and enhance the transparency of CoT reasoning .

  3. Utility Evaluation and Performance Comparison: Through utility evaluation, the framework demonstrates the ability to guide and correct the reasoning direction of LLMs, leading to improved accuracy in reasoning tasks . The approach shows superior performance in zero-shot and few-shot CoT, surpassing baseline methods and enhancing the accuracy of reasoning by directing correct reasoning paths .

  4. Concept Modeling and Simulation: The framework incorporates Concept Modeling, highlighting how LLMs learn latent concepts during pre-training, and Concept Simulation, which uses prompts as stimuli to induce specific concepts, contributing to improved reasoning performance .

  5. Enhanced Reasoning Paths and Error Localization: By employing concept-level representation read operations to localize errors in CoT and control operations to rectify LLMs' reasoning paths, the framework enhances the accuracy of reasoning and provides intuitive and interpretable analysis for CoT reasoning .

Overall, the framework's unique characteristics, such as the Hopfieldian view, interpretability focus, utility evaluation, concept modeling, and error localization, offer significant advantages in understanding and improving CoT reasoning in LLMs compared to previous methods, contributing to enhanced reasoning performance and transparency in complex reasoning tasks.


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research studies exist in the field of Chain-of-Thought (CoT) reasoning and large language models (LLMs) . Noteworthy researchers in this area include Lijie Hu, Liang Liu, Shu Yang, Xin Chen, Hongru Xiao, Mengdi Li, Pan Zhou, Muhammad Asif Ali, and Di Wang . Additionally, other researchers such as Yiming Yang, Jamie Callan, Graham Neubig, and many more have contributed to this field .

The key to the solution mentioned in the paper is the adoption of a Read-and-Control approach to analyze and control the accuracy of CoT . This approach allows for a top-down explainable analysis from the Hopfieldian view, enabling the framework to decipher the inner workings of CoT, localize reasoning errors, and guide the correct reasoning path .


How were the experiments in the paper designed?

The experiments in the paper were designed by considering seven datasets for three different tasks: Arithmetic Reasoning, Commonsense Reasoning, and Symbolic Reasoning. For arithmetic reasoning, datasets such as GSM8K, SVAMP, and AQuA were selected. For commonsense reasoning, benchmarks like StrategyQA and CSQA were chosen. Symbolic reasoning tasks utilized datasets like Coin Flip and Random Letter . Three large language models (LLMs) were used as baselines for evaluation: Mistral-instruct-7B, LLamA-2-7B-chat, and LLamA-3-8B-instruct . The evaluation metrics employed accuracy measurements for all dataset benchmarks, and the answer extraction process followed the methodology outlined by Kojima et al. . The experiments utilized the last ten layers to control the reasoning direction of the LLMs and varied the number of stimulus samples based on different tasks. Additionally, different reading set sizes were employed, such as 128, 256, and 512 samples, with a threshold value of δ = 3.5. The experiments were conducted using float16 to load large models and employed a greedy search decoding strategy with a maximum of 512 new tokens for all datasets .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is comprised of 7 datasets covering 3 different tasks: Arithmetic Reasoning, Commonsense Reasoning, and Symbolic Reasoning. Specifically, the datasets include GSM8K, SVAMP, AQuA for arithmetic reasoning, strategyQA and CSQA for commonsense reasoning, and Coin Flip and Random Letter for symbolic reasoning . The availability of the code as open source is not explicitly mentioned in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The study delves into the success of Chain-of-Thought (CoT) techniques in enhancing the reasoning performance of large language models (LLMs) by analyzing the impact of different CoT methods under various settings . Through a top-down explainable analysis from a Hopfieldian view, the authors propose a Read-and-Control approach to decipher the inner workings of CoT, localize reasoning errors, and guide correct reasoning paths . Additionally, the experiments conducted on seven datasets for three different tasks demonstrate the effectiveness of the framework in controlling the accuracy of CoT and providing insights into the reasoning process of LLMs . The findings from the experiments align with the scientific hypotheses put forth in the paper, showcasing the utility and efficacy of the proposed CoT methods in improving reasoning performance .


What are the contributions of this paper?

The paper makes several key contributions:

  • It analyzes Chain-of-Thought (CoT) methods under different settings to explain why CoT achieves success in large language models (LLMs) .
  • It proposes a Read-and-Control approach based on the Hopfieldian view to control the accuracy of CoT and provide reasoning error localization .
  • Through extensive experiments on seven datasets for three different tasks, the paper demonstrates that their framework can decipher the inner workings of CoT, localize reasoning errors, and guide the model towards the correct reasoning path .

What work can be continued in depth?

Further research in the field of Chain-of-Thought (CoT) reasoning can be expanded in several directions based on the existing studies:

  • Exploring Complex Tasks: Researchers can delve deeper into how Large Language Models (LLMs) can be utilized for more complex tasks like commonsense and mathematical reasoning .
  • Enhancing CoT Accuracy: Efforts can be dedicated to improving the accuracy of CoT techniques through efficient prompt design, process optimization, extra engine usage, and knowledge enhancement .
  • Identifying Key Factors: Continued studies can focus on identifying the key factors or elements that contribute to enhancing the reasoning capabilities of LLMs through CoT techniques .
  • Error Localization and Control: Research can focus on employing concept-level representation read operations to localize errors in CoT and control operations to rectify LLMs' reasoning paths .
  • Experimental Evaluation: Conducting comprehensive experimental evaluations using different datasets across various tasks to offer faithful explanations with error localization and control for CoT .
Tables
1
Scan the QR code to ask more questions about the paper
© 2025 Powerdrill. All rights reserved.