## Heatmap: Classification Accuracies ### Overview The image is a heatmap titled "Classification accuracies" that displays the performance (accuracy with standard deviation) of four different methods (TTPD, LR, CCS, MM) across 14 distinct classification tasks or datasets. The tasks are listed as rows, and the methods as columns. Each cell contains a numerical accuracy value (as a percentage) followed by its standard deviation (±). A color bar on the right provides a visual scale for the accuracy values, ranging from 0.0 (dark purple) to 1.0 (bright yellow). ### Components/Axes * **Title:** "Classification accuracies" (top center). * **Column Headers (Methods):** TTPD, LR, CCS, MM (top row, left to right). * **Row Labels (Tasks/Datasets):** Listed vertically on the left side. The 14 tasks are: 1. `cities_conj` 2. `cities_disj` 3. `sp_en_trans_conj` 4. `sp_en_trans_disj` 5. `inventors_conj` 6. `inventors_disj` 7. `animal_class_conj` 8. `animal_class_disj` 9. `element_symb_conj` 10. `element_symb_disj` 11. `facts_conj` 12. `facts_disj` 13. `common_claim_true_false` 14. `counterfact_true_false` * **Color Bar/Legend:** Positioned vertically on the far right. It maps color to accuracy value, with a scale marked at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. The gradient runs from dark purple (0.0) through red/orange to bright yellow (1.0). * **Data Grid:** A 14-row by 4-column grid of colored cells, each containing the text "[Accuracy] ± [Standard Deviation]". ### Detailed Analysis The following table reconstructs the data from the heatmap. Values are percentages. | Task | TTPD | LR | CCS | MM | | :--- | :--- | :--- | :--- | :--- | | **cities_conj** | 83 ± 1 | 86 ± 5 | 85 ± 9 | 82 ± 1 | | **cities_disj** | 87 ± 2 | 72 ± 12 | 77 ± 9 | 82 ± 3 | | **sp_en_trans_conj** | 87 ± 2 | 84 ± 3 | 82 ± 6 | 84 ± 1 | | **sp_en_trans_disj** | 65 ± 3 | 67 ± 6 | 64 ± 7 | 68 ± 2 | | **inventors_conj** | 70 ± 1 | 71 ± 3 | 72 ± 7 | 71 ± 0 | | **inventors_disj** | 77 ± 2 | 60 ± 9 | 59 ± 8 | 78 ± 2 | | **animal_class_conj** | 85 ± 1 | 73 ± 5 | 80 ± 8 | 83 ± 1 | | **animal_class_disj** | 58 ± 1 | 51 ± 1 | 59 ± 4 | 55 ± 1 | | **element_symb_conj** | 88 ± 2 | 88 ± 4 | 88 ± 10 | 88 ± 1 | | **element_symb_disj** | 70 ± 1 | 66 ± 5 | 66 ± 8 | 71 ± 0 | | **facts_conj** | 72 ± 2 | 68 ± 3 | 68 ± 5 | 70 ± 1 | | **facts_disj** | 60 ± 1 | 65 ± 4 | 64 ± 6 | 62 ± 2 | | **common_claim_true_false** | 79 ± 0 | 74 ± 1 | 74 ± 8 | 78 ± 1 | | **counterfact_true_false** | 74 ± 0 | 76 ± 2 | 77 ± 10 | 68 ± 2 | **Visual Trend Verification:** * **High Accuracy (Yellow/Orange Cells):** The `element_symb_conj` row is uniformly bright yellow/orange, indicating consistently high accuracy (~88%) across all methods. The `cities_conj` and `sp_en_trans_conj` rows also show strong performance. * **Low Accuracy (Purple/Red Cells):** The `animal_class_disj` row contains the darkest cells, particularly for LR (51 ± 1), indicating the lowest performance in the set. The `sp_en_trans_disj` and `facts_disj` rows also show relatively lower accuracies. * **Method Consistency:** The TTPD and MM columns generally show lower standard deviations (e.g., ±0, ±1, ±2) compared to LR and CCS, which often have higher variance (e.g., ±12, ±10), suggesting more stable performance for TTPD and MM across runs or folds. * **Task Difficulty Pattern:** For most tasks, the "_disj" variant (e.g., `cities_disj`, `inventors_disj`) shows lower accuracy than its "_conj" counterpart, with a few exceptions like `facts_disj` vs `facts_conj` for LR and CCS. ### Key Observations 1. **Best Overall Performance:** The task `element_symb_conj` achieves the highest and most consistent accuracy (88%) across all four methods. 2. **Worst Overall Performance:** The task `animal_class_disj` has the lowest accuracy, with LR performing worst at 51 ± 1%. 3. **Largest Performance Gap:** The `inventors_disj` task shows a significant gap between methods, with TTPD (77%) and MM (78%) far outperforming LR (60%) and CCS (59%). 4. **Highest Variance:** The LR and CCS methods exhibit the highest standard deviations in several cells (e.g., LR on `cities_disj`: ±12, CCS on `element_symb_conj`: ±10), indicating less reliable or more variable results for those method-task combinations. 5. **Task Naming Convention:** The row labels suggest a systematic evaluation across different knowledge domains (cities, translations, inventors, animal classification, element symbols, general facts) and logical constructs ("_conj" likely for conjunctions, "_disj" for disjunctions, and "true_false" for binary verification tasks). ### Interpretation This heatmap provides a comparative benchmark of four classification methods across a diverse set of tasks, likely from a natural language processing or knowledge reasoning domain. The data suggests several insights: * **Task Complexity:** The consistent drop in accuracy from "_conj" to "_disj" tasks implies that disjunctive reasoning (involving "or") is generally more challenging for these models than conjunctive reasoning (involving "and"). This is a common finding in logical reasoning benchmarks. * **Method Specialization:** No single method is universally superior. TTPD and MM appear more robust (lower variance) and perform particularly well on tasks like `inventors_disj` and `animal_class_conj`. LR and CCS, while sometimes competitive (e.g., on `cities_conj`), show greater instability and struggle significantly on specific tasks like `animal_class_disj`. * **Domain-Specific Strengths:** The perfect consistency on `element_symb_conj` (all methods at 88%) suggests this task may be more about factual recall (knowing element symbols) than complex reasoning, making it equally solvable by all approaches. In contrast, tasks involving real-world knowledge (`animal_class`, `inventors`) reveal larger performance disparities between methods. * **Reliability Indicator:** The standard deviation values are crucial. A method with high accuracy but high variance (like CCS on `element_symb_conj`: 88 ± 10) may be less trustworthy in practice than a slightly less accurate but more stable method (like MM on the same task: 88 ± 1). In summary, the heatmap reveals that the choice of optimal method is highly dependent on the specific nature of the classification task, with clear patterns emerging around logical structure and knowledge domain. It serves as a diagnostic tool to identify strengths, weaknesses, and reliability of different algorithmic approaches.