## Scatter Plot: Chain of Thought Accuracy vs. Answer Only Accuracy for Various Tasks ### Overview The image is a scatter plot comparing the accuracy of "Chain of Thought" (CoT) and "Answer Only" (AO) approaches for different language models (InstructGPT, Codex, and PaLM 540B) across a range of tasks. The x-axis represents the accuracy difference (CoT - AO), and the y-axis lists the tasks. Each data point represents the accuracy difference for a specific model and task. ### Components/Axes * **X-axis:** "Chain of Thought Accuracy - Answer Only Accuracy". The scale ranges from -20 to 60, with tick marks at -20, -10, 0, 10, 20, 30, 40, 50, and 60. * **Y-axis:** List of tasks. The tasks are: * Boolean Expressionsλ * Causal Judgement * Date Understanding * Disambiguation QA * Dyck Languagesλ * Formal Fallacies * Geometric Shapesλ * Hyperbaton * Logical Deductionλ (avg) * Movie Recommendation * Multi Step Arithmeticλ [Two] * Navigateλ * Object Countingλ * Penguins in a Table * Reasoning about Colored Objects * Ruin Names * Salient Translation Error Detection * Snarks * Sports Understanding * Temporal Sequencesλ * Tracking Shuffled Objectsλ (avg) * Web of Liesλ * Word Sortingλ * NLP Task (avg) * Algorithmic Taskλ (avg) * All Tasks (avg) * **Legend:** Located in the bottom-right corner. * Blue: InstructGPT (CoT) - InstructGPT (AO) * Orange: Codex (CoT) - Codex (AO) * Green: PaLM 540B (CoT) - PaLM 540B (AO) * **Vertical Lines:** * Dashed Black Line: Located at approximately x = 0. * Dashed Green Line: Located at approximately x = 15. * Dashed Gray Lines: Located at approximately x = 18 and x = 20. ### Detailed Analysis * **InstructGPT (CoT - AO) - Blue:** * Generally, the blue data points are clustered towards the right side of the plot, indicating that InstructGPT benefits from the Chain of Thought approach for most tasks. * Specific points: * Boolean Expressionsλ: ~35 * Causal Judgement: ~25 * Date Understanding: ~30 * Disambiguation QA: ~40 * Dyck Languagesλ: ~35 * Formal Fallacies: ~30 * Geometric Shapesλ: ~35 * Hyperbaton: ~40 * Logical Deductionλ (avg): ~35 * Movie Recommendation: ~35 * Multi Step Arithmeticλ [Two]: ~35 * Navigateλ: ~40 * Object Countingλ: ~40 * Penguins in a Table: ~30 * Reasoning about Colored Objects: ~35 * Ruin Names: ~35 * Salient Translation Error Detection: ~35 * Snarks: ~40 * Sports Understanding: ~40 * Temporal Sequencesλ: ~40 * Tracking Shuffled Objectsλ (avg): ~40 * Web of Liesλ: ~40 * Word Sortingλ: ~35 * NLP Task (avg): ~35 * Algorithmic Taskλ (avg): ~35 * All Tasks (avg): ~35 * **Codex (CoT - AO) - Orange:** * The orange data points are more scattered, with some tasks showing a benefit from CoT and others showing little to no difference or even a slight decrease in accuracy. * Specific points: * Boolean Expressionsλ: ~-5 * Causal Judgement: ~10 * Date Understanding: ~10 * Disambiguation QA: ~10 * Dyck Languagesλ: ~10 * Formal Fallacies: ~10 * Geometric Shapesλ: ~10 * Hyperbaton: ~10 * Logical Deductionλ (avg): ~10 * Movie Recommendation: ~10 * Multi Step Arithmeticλ [Two]: ~10 * Navigateλ: ~10 * Object Countingλ: ~10 * Penguins in a Table: ~10 * Reasoning about Colored Objects: ~10 * Ruin Names: ~10 * Salient Translation Error Detection: ~10 * Snarks: ~10 * Sports Understanding: ~10 * Temporal Sequencesλ: ~10 * Tracking Shuffled Objectsλ (avg): ~10 * Web of Liesλ: ~10 * Word Sortingλ: ~10 * NLP Task (avg): ~10 * Algorithmic Taskλ (avg): ~10 * All Tasks (avg): ~10 * **PaLM 540B (CoT - AO) - Green:** * The green data points are generally clustered between 0 and 20, suggesting a modest benefit from CoT for PaLM 540B. * Specific points: * Boolean Expressionsλ: ~10 * Causal Judgement: ~10 * Date Understanding: ~10 * Disambiguation QA: ~10 * Dyck Languagesλ: ~10 * Formal Fallacies: ~10 * Geometric Shapesλ: ~10 * Hyperbaton: ~10 * Logical Deductionλ (avg): ~10 * Movie Recommendation: ~10 * Multi Step Arithmeticλ [Two]: ~10 * Navigateλ: ~10 * Object Countingλ: ~10 * Penguins in a Table: ~10 * Reasoning about Colored Objects: ~10 * Ruin Names: ~10 * Salient Translation Error Detection: ~10 * Snarks: ~10 * Sports Understanding: ~10 * Temporal Sequencesλ: ~10 * Tracking Shuffled Objectsλ (avg): ~10 * Web of Liesλ: ~10 * Word Sortingλ: ~10 * NLP Task (avg): ~10 * Algorithmic Taskλ (avg): ~10 * All Tasks (avg): ~10 ### Key Observations * InstructGPT consistently benefits from the Chain of Thought approach across all tasks. * Codex shows mixed results, with some tasks benefiting from CoT and others not. * PaLM 540B shows a moderate benefit from CoT, generally less pronounced than InstructGPT. * The "All Tasks (avg)" data points for each model reflect the general trend observed for the individual tasks. ### Interpretation The data suggests that the effectiveness of the Chain of Thought approach varies significantly depending on the language model and the specific task. InstructGPT appears to be the most sensitive to the benefits of CoT, while Codex shows more task-dependent performance. PaLM 540B exhibits a more consistent, albeit less dramatic, improvement with CoT. The vertical lines could represent thresholds or benchmarks for acceptable accuracy differences. The dashed black line at 0 indicates the point where CoT and AO have equal accuracy. The other lines may represent target accuracy improvements or significant performance differences. The tasks themselves likely vary in complexity and the degree to which they benefit from explicit reasoning steps. Tasks with a higher "λ" symbol may be more amenable to the Chain of Thought approach. Further investigation into the nature of these tasks and the internal mechanisms of each language model would be needed to fully explain the observed differences.

\n ## Scatter Plot: Chain of Thought Accuracy vs. Answer Only Accuracy ### Overview The image presents a scatter plot comparing the performance of different language models (InstructGPT, Codex, and PaLM 540B) on various reasoning tasks. The x-axis represents the Chain of Thought (CoT) accuracy, and the y-axis represents the Answer Only (AO) accuracy. Each point on the plot represents a specific task, and the color of the point indicates the model used. A vertical dashed line at x=10 separates negative and positive CoT accuracy. ### Components/Axes * **X-axis Title:** Chain of Thought Accuracy - Answer Only Accuracy * **Y-axis Title:** (Implicitly) Accuracy (Scale ranges from -20 to 60) * **Tasks (Y-axis Labels):** * Boolean Expressions * Causal Judgment * Date Understanding * Disambiguation * Dyck Languages * Formal Fallacies * Geometric Shapes * Hyperbaton * Logical Deduction-(avg) * Movie Recommendation * Multi Step Arithmetic-(Two) * Navigator * Object Counting * Penguins in a Table * Reasoning about Colored Objects * Ruin Names * Salient Translation Error Detection * Snarks * Sports Understanding * Temporal Sequences * Tracking Shuffled Objects (avg) * Web of Lies * Word Sorting * NLP Task * Algorithmic Task * All Tasks (avg) * **Legend:** * InstructGPT (CoT) - Orange circles * InstructGPT (AO) - Blue circles * Codex (CoT) - Orange squares * Codex (AO) - Blue squares * PaLM 540B (CoT) - Green circles * PaLM 540B (AO) - Green squares ### Detailed Analysis The plot shows the accuracy of each model on each task using two methods: Chain of Thought (CoT) and Answer Only (AO). **InstructGPT:** * **CoT (Orange circles):** Generally exhibits higher accuracy than AO, especially for tasks with positive CoT accuracy. The trend is generally upward, with accuracy increasing as CoT accuracy increases. * Boolean Expressions: ~50 * Causal Judgment: ~20 * Date Understanding: ~10 * Disambiguation: ~10 * Dyck Languages: ~10 * Formal Fallacies: ~10 * Geometric Shapes: ~10 * Hyperbaton: ~10 * Logical Deduction-(avg): ~40 * Movie Recommendation: ~20 * Multi Step Arithmetic-(Two): ~50 * Navigator: ~10 * Object Counting: ~10 * Penguins in a Table: ~20 * Reasoning about Colored Objects: ~10 * Ruin Names: ~10 * Salient Translation Error Detection: ~10 * Snarks: ~10 * Sports Understanding: ~10 * Temporal Sequences: ~10 * Tracking Shuffled Objects (avg): ~10 * Web of Lies: ~10 * Word Sorting: ~10 * NLP Task: ~10 * Algorithmic Task: ~10 * All Tasks (avg): ~20 * **AO (Blue circles):** Accuracy is generally lower and more consistent across tasks, hovering around 10. **Codex:** * **CoT (Orange squares):** Shows a similar trend to InstructGPT CoT, with higher accuracy than AO. * Boolean Expressions: ~10 * Causal Judgment: ~10 * Date Understanding: ~10 * Disambiguation: ~10 * Dyck Languages: ~10 * Formal Fallacies: ~10 * Geometric Shapes: ~10 * Hyperbaton: ~10 * Logical Deduction-(avg): ~10 * Movie Recommendation: ~10 * Multi Step Arithmetic-(Two): ~10 * Navigator: ~10 * Object Counting: ~10 * Penguins in a Table: ~10 * Reasoning about Colored Objects: ~10 * Ruin Names: ~10 * Salient Translation Error Detection: ~10 * Snarks: ~10 * Sports Understanding: ~10 * Temporal Sequences: ~10 * Tracking Shuffled Objects (avg): ~10 * Web of Lies: ~10 * Word Sorting: ~10 * NLP Task: ~10 * Algorithmic Task: ~10 * All Tasks (avg): ~10 * **AO (Blue squares):** Accuracy is generally lower and more consistent across tasks, hovering around 10. **PaLM 540B:** * **CoT (Green circles):** Shows a wide range of accuracy, with some tasks exhibiting high accuracy and others low accuracy. * Boolean Expressions: ~0 * Causal Judgment: ~0 * Date Understanding: ~0 * Disambiguation: ~0 * Dyck Languages: ~0 * Formal Fallacies: ~0 * Geometric Shapes: ~0 * Hyperbaton: ~0 * Logical Deduction-(avg): ~0 * Movie Recommendation: ~0 * Multi Step Arithmetic-(Two): ~0 * Navigator: ~0 * Object Counting: ~0 * Penguins in a Table: ~0 * Reasoning about Colored Objects: ~0 * Ruin Names: ~0 * Salient Translation Error Detection: ~0 * Snarks: ~0 * Sports Understanding: ~0 * Temporal Sequences: ~0 * Tracking Shuffled Objects (avg): ~0 * Web of Lies: ~0 * Word Sorting: ~0 * NLP Task: ~0 * Algorithmic Task: ~0 * All Tasks (avg): ~0 * **AO (Green squares):** Accuracy is generally lower and more consistent across tasks, hovering around 10. ### Key Observations * CoT generally improves accuracy for InstructGPT and Codex. * PaLM 540B shows a wider variance in CoT accuracy, with some tasks performing well and others poorly. * The vertical dashed line at x=10 highlights tasks where CoT provides a significant accuracy boost. * The "All Tasks (avg)" point suggests that InstructGPT performs best overall with CoT, followed by Codex, and then PaLM 540B. ### Interpretation The data suggests that Chain of Thought prompting is a beneficial technique for improving the reasoning capabilities of language models, particularly InstructGPT and Codex. The significant difference in accuracy between CoT and AO for many tasks indicates that the models benefit from being able to articulate their reasoning process. PaLM 540B's performance is more variable, suggesting that its ability to leverage CoT may be more task-dependent. The plot provides a comparative analysis of the models' strengths and weaknesses on different reasoning tasks, offering insights into their underlying capabilities and limitations. The negative CoT accuracy for some tasks with PaLM 540B suggests that CoT may sometimes hinder performance, potentially due to the model generating misleading or incorrect reasoning steps. The consistent low AO accuracy across all models suggests that direct answer prediction is less reliable for these complex reasoning tasks.

## Heatmap: Chain of Thought Accuracy ### Overview The heatmap displays the accuracy of various AI models in answering questions based on a given Chain of Thought (CoT) approach. The x-axis represents the accuracy of the CoT approach, while the y-axis represents the accuracy of different AI models. The color intensity indicates the level of accuracy, with darker colors representing higher accuracy. ### Components/Axes - **X-Axis**: Chain of Thought Accuracy - Answer Only Accuracy - **Y-Axis**: AI Models - **Legend**: - **Blue**: CoT (CoT) - **Orange**: CoT (CoT) - **Green**: CoT (CoT) - **Red**: CoT (CoT) ### Detailed Analysis or ### Content Details The heatmap shows that the CoT approach generally leads to higher accuracy across all AI models. The CoT (CoT) model consistently outperforms the other models, with the highest accuracy observed in the CoT (CoT) model. The CoT (CoT) model also shows a slight improvement in accuracy as the CoT approach becomes more complex. ### Key Observations - The CoT (CoT) model consistently outperforms the other models. - The CoT (CoT) model shows a slight improvement in accuracy as the CoT approach becomes more complex. - There is a noticeable difference in accuracy between the CoT (CoT) model and the other models. ### Interpretation The heatmap suggests that the CoT approach is a more effective method for answering questions based on a given Chain of Thought approach. The CoT (CoT) model consistently outperforms the other models, indicating that it is a more reliable method for answering questions. The slight improvement in accuracy as the CoT approach becomes more complex suggests that the CoT approach can be further refined to improve its accuracy.

## Scatter Plot: Chain of Thought vs. Answer Only Accuracy Across Tasks ### Overview The image is a scatter plot comparing the performance of three AI models (InstructGPT, Codex, PaLM 540B) on 20+ reasoning tasks. The x-axis measures the difference between Chain of Thought (CoT) and Answer Only (AO) accuracies, while the y-axis lists specific tasks. Three colored data series represent the models, with vertical lines marking accuracy thresholds. ### Components/Axes - **X-axis**: "Chain of Thought Accuracy - Answer Only Accuracy" (range: -20 to 60, increments of 10) - **Y-axis**: Tasks (e.g., Boolean Expressions, Causal Judgement, Sports Understanding) - **Legend**: - Blue: InstructGPT (CoT) - InstructGPT (AO) - Orange: Codex (CoT) - Codex (AO) - Green: PaLM 540B (CoT) - PaLM 540B (AO) - **Vertical Lines**: Dashed lines at x=0, 10, 20, 30, 40, 50, 60 ### Detailed Analysis 1. **Task Distribution**: - Tasks cluster across the y-axis, with "All Tasks (avg)" at the bottom. - High-performing tasks (e.g., "Geometric Shapes") show PaLM 540B (green) dots near x=30-40. - Low-performing tasks (e.g., "Ruin Names") have InstructGPT (blue) near x=5-10. 2. **Model Performance**: - **PaLM 540B (green)**: Consistently rightmost dots (x=15-45), indicating higher CoT-AO accuracy. - **Codex (orange)**: Middle-range performance (x=5-25), with outliers like "Penguins in a Table" at x=10. - **InstructGPT (blue)**: Leftmost dots (x=-5 to 15), often overlapping with Codex. 3. **Thresholds**: - Vertical lines at x=0 (baseline), 10, 20, etc., suggest performance benchmarks. - Most PaLM 540B dots exceed x=10, while InstructGPT rarely crosses x=10. ### Key Observations - **PaLM 540B Dominance**: Outperforms others in most tasks, especially "All Tasks (avg)" (x≈40). - **Codex Variability**: Mixed results, with some tasks (e.g., "Tracking Shuffled Objects") near x=20. - **InstructGPT Limitations**: Struggles with complex reasoning (e.g., "Dyck Languages" at x≈5). - **Negative Values**: Rare (e.g., "Ruin Names" for InstructGPT at x≈-5), indicating AO > CoT. ### Interpretation The data demonstrates that **PaLM 540B** excels in CoT reasoning across diverse tasks, likely due to its scale and training. **Codex** shows moderate performance, while **InstructGPT** lags, particularly in multi-step or abstract tasks. The vertical lines may represent industry benchmarks, with PaLM 540B surpassing them in most cases. Outliers like "Penguins in a Table" (Codex at x=10) suggest task-specific strengths. The negative values for InstructGPT highlight potential overfitting to AO patterns. This aligns with prior research on model scaling and reasoning capabilities.