## Heatmap Comparison: COPA vs. E-CARE Benchmark Correlations ### Overview The image displays two side-by-side heatmaps comparing the correlation of various Large Language Model (LLM) performance metrics across two different evaluation benchmarks: **COPA** (left) and **E-CARE** (right). The heatmaps visualize the strength and direction of correlation (positive or negative) between specific LLM characteristics (Consistency, Depth, Coherence, Uncertainty, Drift) and model performance on these benchmarks. The color intensity represents the correlation value, with a shared legend indicating the scale. ### Components/Axes * **Chart Type:** Two separate correlation heatmaps. * **Y-Axis (Both Charts):** Labeled "LLM". Lists three models: * LLaMA 2 7B * LLaMA 2 13B * GPT 3.5 * **X-Axis (Both Charts):** Lists five performance metrics: * Consistency * Depth * Coherence * Uncertainty * Drift * **Legend:** Positioned centrally between the two heatmaps. Titled "Corr." (Correlation). It is a vertical color bar with the following scale: * **Top (Green):** 2.5 * **Middle (Light Yellow/White):** 0.0 * **Bottom (Red):** -2.5 * This indicates that green shades represent positive correlations, red shades represent negative correlations, and the intensity corresponds to the magnitude. * **Data Labels:** Each cell in the heatmaps contains a numerical correlation value. Many values are followed by asterisks indicating statistical significance (e.g., `*`, `**`, `***`). ### Detailed Analysis #### **COPA Heatmap (Left)** * **LLaMA 2 7B:** * Consistency: 1.37 (light green, positive) * Depth: -2.95 ** (medium red, strong negative) * Coherence: 1.22 (light green, positive) * Uncertainty: -3.10 ** (medium red, strong negative) * Drift: -0.27 (very light pink, weak negative) * **LLaMA 2 13B:** * Consistency: 1.36 (light green, positive) * Depth: -1.28 (light red, negative) * Coherence: 3.87 *** (dark green, very strong positive) * Uncertainty: -2.17 * (medium red, negative) * Drift: -3.33 *** (dark red, very strong negative) * **GPT 3.5:** * Consistency: 4.67 *** (dark green, very strong positive) * Depth: -4.893 *** (dark red, very strong negative) * Coherence: 3.60 *** (dark green, very strong positive) * Uncertainty: -4.34 *** (dark red, very strong negative) * Drift: -3.22 ** (dark red, strong negative) #### **E-CARE Heatmap (Right)** * **LLaMA 2 7B:** * Consistency: 0.20 (very light green, very weak positive) * Depth: -0.53 (very light pink, weak negative) * Coherence: 2.18 * (light green, positive) * Uncertainty: -2.11 ** (medium red, negative) * Drift: -0.78 * (light pink, weak negative) * **LLaMA 2 13B:** * Consistency: 1.167 (light green, positive) * Depth: -1.18 (light red, negative) * Coherence: 1.67 * (light green, positive) * Uncertainty: -1.52 * (light red, negative) * Drift: -1.91 * (medium red, negative) * **GPT 3.5:** * Consistency: 3.10 ** (green, strong positive) * Depth: -2.91 ** (red, strong negative) * Coherence: 0.98 (very light green, weak positive) * Uncertainty: -2.61 ** (red, strong negative) * Drift: -5.14 *** (dark red, very strong negative) ### Key Observations 1. **Consistent Negative Correlation with Depth and Uncertainty:** Across both benchmarks and all three models, the "Depth" and "Uncertainty" metrics show a consistent pattern of negative correlation (red cells). This suggests that higher scores on these metrics are associated with lower performance on the COPA and E-CARE tasks. 2. **Consistency and Coherence Show Positive Correlation:** The "Consistency" and "Coherence" metrics generally show positive correlation (green cells), particularly for the larger GPT 3.5 model. This indicates these traits are beneficial for these benchmarks. 3. **Model Scaling Effect:** GPT 3.5 exhibits the most extreme correlation values (both positive and negative) in the COPA benchmark, suggesting its performance is more strongly tied to these measured characteristics compared to the LLaMA 2 models. 4. **Benchmark Differences:** The correlation patterns are broadly similar but not identical between COPA and E-CARE. For instance, the "Coherence" correlation for GPT 3.5 is very strong in COPA (3.60***) but weak in E-CARE (0.98). The "Drift" metric shows a particularly strong negative correlation for GPT 3.5 in E-CARE (-5.14***). 5. **Statistical Significance:** Most of the stronger correlations (magnitude > ~1.5) are marked with asterisks, indicating they are statistically significant. The weakest correlations (e.g., LLaMA 2 7B on COPA Drift: -0.27) lack significance markers. ### Interpretation This visualization provides a diagnostic look at what internal model characteristics (as measured by Consistency, Depth, Coherence, Uncertainty, Drift) align with success on specific reasoning benchmarks (COPA and E-CARE). * **What the data suggests:** The strong negative correlations for "Depth" and "Uncertainty" are the most striking finding. This could imply that for these particular tasks, models that exhibit more "depth" (perhaps in terms of reasoning steps or complexity) or higher calibrated "uncertainty" perform worse. Conversely, models that are more "consistent" and "coherent" in their outputs tend to perform better. This might indicate that COPA and E-CARE reward reliable, straightforward reasoning over more complex or hesitant deliberation. * **Relationship between elements:** The heatmaps directly link abstract model properties (columns) to concrete benchmark performance (implied by the correlation value). The side-by-side comparison allows us to see if these relationships are benchmark-specific or general. The shared color scale enables direct visual comparison of correlation strength across both charts. * **Notable anomalies:** The drastic difference in the "Coherence" correlation for GPT 3.5 between the two benchmarks is a key anomaly. It suggests that while coherent output is highly predictive of success on COPA, it is much less so for E-CARE. This could point to a fundamental difference in what the two benchmarks measure. Furthermore, the extremely strong negative correlation for "Drift" in GPT 3.5 on E-CARE (-5.14***) is an outlier in magnitude, highlighting "Drift" as a particularly detrimental factor for that model on that specific task. **In summary, the image presents evidence that for the COPA and E-CARE benchmarks, model performance is positively associated with consistency and coherence, and negatively associated with depth, uncertainty, and drift. The strength of these associations varies by model and benchmark, with GPT 3.5 showing the most pronounced relationships.**