## Heatmap: Task Accuracy vs. Prompt Type ### Overview The image is a heatmap displaying the accuracy (in percentage) of different tasks when using different prompt types: AO, CoT, and CoT (Invalid). The tasks are listed on the vertical axis, and the prompt types are listed on the horizontal axis. The color intensity represents the accuracy percentage, with red indicating high accuracy and blue indicating low accuracy. ### Components/Axes * **Title:** Accuracy (%) * **X-Axis Title:** Prompt Type * **X-Axis Labels:** AO, CoT, CoT (Invalid) * **Y-Axis Title:** Task * **Y-Axis Labels:** boolean\_expressions, causal\_judgement, date\_understanding, disambiguation\_qa, dyck\_languages, formal\_fallacies, geometric\_shapes, hyperbaton, logical\_deduction\_five\_objects, logical\_deduction\_seven\_objects, logical\_deduction\_three\_objects, movie\_recommendation, multistep\_arithmetic\_two, navigate, object\_counting, penguins\_in\_a\_table, reasoning\_about\_colored\_objects, ruin\_names, salient\_translation\_error\_detection, snarks, sports\_understanding, temporal\_sequences, tracking\_shuffled\_objects\_five\_objects, tracking\_shuffled\_objects\_seven\_objects, tracking\_shuffled\_objects\_three\_objects, web\_of\_lies, word\_sorting * **Colorbar (Right Side):** * 100 (Red) * 80 * 60 * 40 * 20 * 0 (Blue) ### Detailed Analysis Here's a breakdown of the accuracy for each task across the different prompt types: * **boolean\_expressions:** AO: 88.0%, CoT: 93.6%, CoT (Invalid): 52.9% * **causal\_judgement:** AO: 65.8%, CoT: 57.2%, CoT (Invalid): 52.9% * **date\_understanding:** AO: 60.4%, CoT: 87.6%, CoT (Invalid): 84.8% * **disambiguation\_qa:** AO: 67.2%, CoT: 76.0%, CoT (Invalid): 53.6% * **dyck\_languages:** AO: 45.2%, CoT: 51.2%, CoT (Invalid): 34.0% * **formal\_fallacies:** AO: 55.2%, CoT: 21.6%, CoT (Invalid): 54.4% * **geometric\_shapes:** AO: 31.2%, CoT: 55.6%, CoT (Invalid): 53.6% * **hyperbaton:** AO: 64.0%, CoT: 59.6%, CoT (Invalid): 58.4% * **logical\_deduction\_five\_objects:** AO: 31.2%, CoT: 52.4%, CoT (Invalid): 51.2% * **logical\_deduction\_seven\_objects:** AO: 29.2%, CoT: 12.4%, CoT (Invalid): 34.4% * **logical\_deduction\_three\_objects:** AO: 54.8%, CoT: 86.4%, CoT (Invalid): 70.0% * **movie\_recommendation:** AO: 85.6%, CoT: 90.8%, CoT (Invalid): 90.0% * **multistep\_arithmetic\_two:** AO: 0.4%, CoT: 46.4%, CoT (Invalid): 22.0% * **navigate:** AO: 42.8%, CoT: 96.0%, CoT (Invalid): 90.8% * **object\_counting:** AO: 46.0%, CoT: 93.2%, CoT (Invalid): 15.2% * **penguins\_in\_a\_table:** AO: 64.4%, CoT: 78.8%, CoT (Invalid): 65.8% * **reasoning\_about\_colored\_objects:** AO: 66.4%, CoT: 91.2%, CoT (Invalid): 82.8% * **ruin\_names:** AO: 75.2%, CoT: 68.0%, CoT (Invalid): 60.8% * **salient\_translation\_error\_detection:** AO: 61.6%, CoT: 57.6%, CoT (Invalid): 55.6% * **snarks:** AO: 59.0%, CoT: 60.1%, CoT (Invalid): 64.0% * **sports\_understanding:** AO: 71.0%, CoT: 98.4%, CoT (Invalid): 52.4% * **temporal\_sequences:** AO: 80.4%, CoT: 97.2%, CoT (Invalid): 92.8% * **tracking\_shuffled\_objects\_five\_objects:** AO: 15.6%, CoT: 74.0%, CoT (Invalid): 84.4% * **tracking\_shuffled\_objects\_seven\_objects:** AO: 0.0%, CoT: 0.0%, CoT (Invalid): 76.0% * **tracking\_shuffled\_objects\_three\_objects:** AO: 36.0%, CoT: 76.8%, CoT (Invalid): 66.4% * **web\_of\_lies:** AO: 51.2%, CoT: 94.4%, CoT (Invalid): 56.0% * **word\_sorting:** AO: 0.0%, CoT: 0.0%, CoT (Invalid): 20.8% ### Key Observations * **CoT (Chain of Thought) Prompting generally improves accuracy:** For most tasks, the CoT prompt type (both valid and invalid) yields higher accuracy compared to the AO prompt type. * **Multistep Arithmetic is uniquely bad with AO:** The "multistep\_arithmetic\_two" task has extremely low accuracy with the AO prompt (0.4%), but improves significantly with CoT (46.4%) and CoT (Invalid) (22.0%). * **Tracking Shuffled Objects is uniquely bad with AO and CoT:** The "tracking\_shuffled\_objects\_seven\_objects" task has 0.0% accuracy with both AO and CoT, but improves significantly with CoT (Invalid) (76.0%). * **CoT (Invalid) can sometimes outperform CoT:** In some cases, the "CoT (Invalid)" prompt performs better than the "CoT" prompt, suggesting that even flawed reasoning chains can be beneficial. * **Some tasks are consistently high-performing:** "movie\_recommendation" and "temporal\_sequences" consistently show high accuracy across all prompt types. ### Interpretation The heatmap illustrates the impact of different prompting strategies on the accuracy of various tasks. The Chain of Thought (CoT) prompting method generally enhances performance, likely by enabling the model to break down complex problems into smaller, more manageable steps. However, the "CoT (Invalid)" results suggest that even imperfect reasoning chains can lead to improved outcomes compared to direct prompting (AO). The significant accuracy boost observed for "multistep\_arithmetic\_two" and "tracking\_shuffled\_objects\_seven\_objects" with CoT prompting highlights the importance of structured reasoning for tasks that require multiple steps or complex logic. The fact that "CoT (Invalid)" sometimes outperforms "CoT" indicates that the mere presence of a reasoning chain, even if flawed, can be more beneficial than no reasoning at all. The consistent high performance of tasks like "movie\_recommendation" and "temporal\_sequences" suggests that these tasks are inherently easier for the model, regardless of the prompting strategy used. Conversely, tasks like "dyck\_languages" and "logical\_deduction\_seven\_objects" remain challenging even with CoT prompting, indicating a need for more sophisticated approaches.

\n ## Heatmap: Accuracy of Large Language Models on Various Tasks ### Overview This image presents a heatmap visualizing the accuracy (%) of a large language model across 22 different tasks, evaluated under three different prompt types: AO (presumably "Automatic Operation"), CoT ("Chain of Thought"), and CoT (Invalid). The accuracy is represented by color, with a gradient from blue (low accuracy) to red (high accuracy). The tasks are listed vertically on the y-axis, and the prompt types are listed horizontally on the x-axis. ### Components/Axes * **Y-axis (Tasks):** Lists the following tasks: * boolean expressions * causal judgement * date understanding * disambiguation_qa * dyck languages * formal fallacies * geometric_shapes * hyperberon * logical deduction_five_objects * logical deduction_seven_objects * logical_deduction_three_objects * movie recommendation * multistep_arithmetic_two * navigate * object counting * penguins_in_a_table * reasoning_about_colored_objects * ruin names * salient_translation_error_detection * snarks * sports understanding * temporal sequences * tracking_shuffled_objects_five_objects * tracking_shuffled_objects_seven_objects * tracking_shuffled_objects_three_objects * web_of_lies * word_sorting * **X-axis (Prompt Type):** Categorized into three prompt types: * AO (Purple) * CoT (Orange) * CoT (Invalid) (Green) * **Color Scale:** Represents accuracy percentage, ranging from approximately 0% (dark blue) to 100% (dark red). The scale is marked at 0, 20, 40, 60, 80, and 100. * **Title:** "Accuracy (%)" positioned at the top-center of the heatmap. ### Detailed Analysis The heatmap displays accuracy values for each task and prompt type combination. Here's a breakdown of some key values (approximate, based on color mapping): * **boolean expressions:** AO: 88.0%, CoT: 93.6%, CoT (Invalid): 88.0% * **causal judgement:** AO: 57.2%, CoT: 65.8%, CoT (Invalid): 52.9% * **date understanding:** AO: 87.6%, CoT: 84.8%, CoT (Invalid): 60.4% * **disambiguation_qa:** AO: 67.2%, CoT: 76.0%, CoT (Invalid): 33.6% * **dyck languages:** AO: 45.2%, CoT: 34.0%, CoT (Invalid): 44.0% * **formal fallacies:** AO: 55.2%, CoT: 21.6%, CoT (Invalid): 45.3% * **geometric_shapes:** AO: 64.0%, CoT: 59.6%, CoT (Invalid): 58.4% * **hyperberon:** AO: 64.0%, CoT: 59.6%, CoT (Invalid): 58.4% * **logical deduction_five_objects:** AO: 31.2%, CoT: 52.4%, CoT (Invalid): 51.2% * **logical deduction_seven_objects:** AO: 29.2%, CoT: 12.4%, CoT (Invalid): 34.4% * **logical_deduction_three_objects:** AO: 54.8%, CoT: 86.4%, CoT (Invalid): 70.0% * **movie recommendation:** AO: 85.6%, CoT: 90.8%, CoT (Invalid): 90.0% * **multistep_arithmetic_two:** AO: 0.4%, CoT: 46.4%, CoT (Invalid): 22.0% * **navigate:** AO: 42.8%, CoT: 96.0%, CoT (Invalid): 96.8% * **object counting:** AO: 64.4%, CoT: 78.8%, CoT (Invalid): 65.8% * **reasoning_about_colored_objects:** AO: 66.4%, CoT: 91.2%, CoT (Invalid): 82.8% * **ruin names:** AO: 75.2%, CoT: 96.0%, CoT (Invalid): 96.4% * **salient_translation_error_detection:** AO: 59.6%, CoT: 60.1%, CoT (Invalid): 59.0% * **snarks:** AO: 61.0%, CoT: 60.1%, CoT (Invalid): 61.0% * **sports understanding:** AO: 71.0%, CoT: 98.4%, CoT (Invalid): 52.4% * **temporal sequences:** AO: 70.8%, CoT: 94.4%, CoT (Invalid): 92.8% * **tracking_shuffled_objects_five_objects:** AO: 0.0%, CoT: 74.0%, CoT (Invalid): 76.0% * **tracking_shuffled_objects_seven_objects:** AO: 15.6%, CoT: 40.0%, CoT (Invalid): 84.4% * **tracking_shuffled_objects_three_objects:** AO: 36.0%, CoT: 90.8%, CoT (Invalid): 60.8% * **web_of_lies:** AO: 61.0%, CoT: 66.0%, CoT (Invalid): 66.0% * **word_sorting:** AO: 46.8%, CoT: 84.0%, CoT (Invalid): 70.0% **Trends:** * Generally, CoT prompts yield higher accuracy than AO prompts. * CoT (Invalid) prompts show variable accuracy, sometimes performing better than AO, sometimes worse than CoT. * Some tasks (e.g., navigate, ruin names, sports understanding) consistently achieve high accuracy with CoT prompts. * Tasks like multistep\_arithmetic\_two and tracking\_shuffled\_objects\_five\_objects have very low accuracy with AO prompts. ### Key Observations * The "navigate" task shows nearly perfect accuracy with both CoT and CoT (Invalid) prompts. * "multistep\_arithmetic\_two" is a particularly challenging task for the model, with extremely low accuracy under the AO prompt. * The performance difference between prompt types is most pronounced for tasks like "logical deduction\_seven\_objects" and "multistep\_arithmetic\_two". * The CoT (Invalid) prompt type sometimes outperforms AO, suggesting that even flawed CoT prompts can be beneficial. ### Interpretation This heatmap demonstrates the significant impact of prompt engineering (specifically, the use of Chain of Thought prompting) on the performance of large language models across a diverse set of reasoning tasks. The consistent improvement observed with CoT prompts suggests that guiding the model to articulate its reasoning process enhances its ability to solve complex problems. The variability in performance with the "CoT (Invalid)" prompt type highlights the sensitivity of these models to prompt quality and structure. The tasks where AO performs poorly but CoT performs well indicate areas where the model benefits most from explicit reasoning guidance. The heatmap provides valuable insights for optimizing prompt design and understanding the strengths and weaknesses of these models in different reasoning scenarios. The data suggests that while LLMs have made strides in reasoning, they still struggle with tasks requiring complex arithmetic or tracking multiple objects, even with CoT prompting.

## Heatmap: Accuracy of Various Natural Language Processing Tasks ### Overview The heatmap displays the accuracy percentages of various natural language processing (NLP) tasks. The tasks are categorized by their complexity and the type of language processing they involve. The accuracy is represented by a color gradient, with darker shades indicating lower accuracy and lighter shades indicating higher accuracy. ### Components/Axes - **Tasks**: Boolean expressions, date causal judgment, disambiguation QA, dyck languages, formal fallacies, geometric shapes, hyperbotion, logical deduction five objects, logical deduction seven objects, logical deduction three objects, movie recommendation, multipath arithmetic two, object counting, reasoning about colored objects, reasoning about colored objects in a table, ruin names, salient translation error detection, snarks, sports understanding, temporal sequences, tracking shuffled objects five objects, tracking shuffled objects seven objects, tracking shuffled objects three objects, web of lies, word sorting. - **Accuracy (%)**: The accuracy percentage for each task is displayed on the right side of the heatmap. - **Prompt Type**: The type of prompt used for each task is displayed at the bottom of the heatmap. - **AO**: The accuracy of the AI model. - **CoT**: The accuracy of the human model. - **CoT (Invalid)**: The accuracy of the model when the prompt type is invalid. ### Detailed Analysis or ### Content Details The heatmap shows that the accuracy of the AI model (AO) is generally lower than the human model (CoT) across all tasks. The highest accuracy for the AI model is 93.6% for the task of "boolean expressions," while the lowest accuracy is 0.0% for the task of "word sorting." The human model (CoT) has the highest accuracy for the task of "reasoning about colored objects in a table," with an accuracy of 92.8%. The lowest accuracy for the human model is 0.0% for the task of "word sorting." ### Key Observations - The AI model (AO) performs better than the human model (CoT) in tasks that involve logical deduction and reasoning about colored objects. - The AI model (AO) performs worse than the human model (CoT) in tasks that involve disambiguation and word sorting. - The AI model (AO) performs better than the human model (CoT) in tasks that involve temporal sequences and sports understanding. ### Interpretation The heatmap suggests that the AI model (AO) is currently outperforming the human model (CoT) in terms of accuracy across various NLP tasks. However, there are still areas where the human model (CoT) performs better, particularly in tasks that involve logical deduction and reasoning about colored objects. The AI model (AO) may need further training and development to improve its performance in these areas.

## Heatmap: Task Accuracy by Prompt Type ### Overview This heatmap compares the accuracy (%) of various AI tasks across three prompt types: AO (Answer Only), CoT (Chain of Thought), and CoT Invalid. Tasks range from logical reasoning to language understanding, with color intensity indicating performance (blue = low, red = high). ### Components/Axes - **Y-Axis (Tasks)**: 25 tasks including: - boolean_expressions, causal_judgement, date_understanding, disambiguation_qa, dyck_languages, formal_fallacies, geometric_shapes, hyperbaton, logical_deduction_five_objects, logical_deduction_seven_objects, logical_deduction_three_objects, movie_recommendation, multistep_arithmetic_two, navigate, object_counting, penguins_in_a_table, reasoning_about_colored_objects, ruin_names, salient_translation_error_detection, sharks, sports_understanding, temporal_sequences, tracking_shuffled_objects_five_objects, tracking_shuffled_objects_seven_objects, tracking_shuffled_objects_three_objects, web_of_lies, word_sorting. - **X-Axis (Prompt Types)**: AO, CoT, CoT Invalid. - **Legend**: Color gradient from blue (0%) to red (100%), with labeled thresholds (e.g., 20%, 40%, 60%, 80%, 100%). ### Detailed Analysis - **AO Column**: - Highest accuracy: sports_understanding (71.0%), tracking_shuffled_objects_three_objects (36.0%). - Lowest accuracy: geometric_shapes (31.2%), word_sorting (0.0%). - **CoT Column**: - Highest accuracy: sports_understanding (98.4%), tracking_shuffled_objects_three_objects (76.8%). - Lowest accuracy: geometric_shapes (55.6%), word_sorting (0.0%). - **CoT Invalid Column**: - Highest accuracy: sports_understanding (52.4%), tracking_shuffled_objects_three_objects (66.4%). - Lowest accuracy: geometric_shapes (53.6%), word_sorting (20.8%). ### Key Observations 1. **CoT Dominance**: CoT generally outperforms AO and CoT Invalid across most tasks (e.g., boolean_expressions: 93.6% vs. 88.0% AO). 2. **CoT Invalid Anomalies**: - Some tasks degrade under CoT Invalid (e.g., geometric_shapes: 53.6% vs. 55.6% CoT). - Others improve (e.g., tracking_shuffled_objects_three_objects: 66.4% vs. 76.8% CoT). 3. **Zero Performance**: word_sorting fails entirely under AO and CoT (0.0%). 4. **Color Consistency**: Red hues dominate CoT, while blue hues cluster in CoT Invalid for tasks like geometric_shapes. ### Interpretation The data suggests **CoT prompting enhances performance** for complex reasoning tasks (e.g., logical_deduction, sports_understanding), likely due to its structured reasoning process. However, **CoT Invalid introduces variability**: - **Degradation**: Tasks requiring precise logic (geometric_shapes, word_sorting) suffer under CoT Invalid, possibly due to invalid intermediate steps. - **Improvement**: Tasks with spatial/temporal reasoning (tracking_shuffled_objects) benefit from CoT Invalid, hinting at robustness to partial reasoning. Notable outliers include **sports_understanding** (consistently high) and **word_sorting** (consistently low), indicating task-specific model biases. The heatmap underscores the importance of prompt design for task alignment.