## Chart/Diagram Type: Multi-Panel Performance Evaluation ### Overview The image presents a multi-panel figure evaluating the performance of different language models. Panel (a) shows a scatter plot of F1 scores vs. ECE (Expected Calibration Error) for various models. Panels (b) through (e) display accuracy vs. confidence plots, along with count histograms, for specific models. The models compared are GPT-3.5-turbo, GPT-4o-mini, DeepSeek-V3, and Gemini-2.5-flash, along with RL-DoublyCal and LLM Reasoner baselines. ### Components/Axes **Panel (a): ECE - F1 scores** * **Title:** ECE – F1 scores * **X-axis:** ECE (%) - Expected Calibration Error in percentage. Scale ranges from 0 to 50. * **Y-axis:** F1 scores (%) - F1 scores in percentage. Scale ranges from 0 to 100. * **Legend (Left):** * RL-DoublyCal (Dark Gray Circle) * LLM Reasoner (Gray Square) * GPT-3.5-turbo (Red Star) * GPT-4o-mini (Light Blue Teardrop) * DeepSeek-V3 (Yellow Hexagon) * Gemini-2.5-flash (Green Lightning Bolt) * **Annotations:** * Avg. F1 = 76.5, Avg. ECE = 7.6 (Located near the top-left, highlighted by a yellow ellipse) * Avg. F1 = 45.8, Avg. ECE = 29.4 (Located near the bottom-right, highlighted by a gray ellipse) **Panels (b) - (e): Accuracy vs. Confidence** * **Titles:** * (b) GPT-3.5-turbo * (c) GPT-4o-mini * (d) DeepSeek-V3 * (e) Gemini-2.5-flash * **Left Y-axis:** Accuracy. Scale ranges from 0.0 to 1.0 in increments of 0.2. * **Right Y-axis:** Count. Scale varies by panel. * (b) 0 to 15000 * (c) 0 to 5000 * (d) 0 to 15000 * (e) 0 to 5000 * **X-axis:** Confidence. Scale ranges from 0.0 to 1.0 in increments of 0.2 for (b), (c), and (d). For (e), the scale ranges from 0.5 to 1.0 in increments of 0.1. * **Legend (Top-Right of each panel):** * RL-DoublyCal (Colored Line with Circles) * LLM Reasoner (Gray Line with Squares) * **Histograms:** Represent the count of predictions at each confidence level. ### Detailed Analysis **Panel (a): ECE - F1 scores** * **RL-DoublyCal:** F1 ~76%, ECE ~8% (Dark Gray Circle) * **LLM Reasoner:** F1 ~46%, ECE ~30% (Gray Square) * **GPT-3.5-turbo:** F1 ~77%, ECE ~7% (Red Star) * **GPT-4o-mini:** F1 ~75%, ECE ~9% (Light Blue Teardrop) * **DeepSeek-V3:** F1 ~77%, ECE ~7% (Yellow Hexagon) * **Gemini-2.5-flash:** F1 ~52%, ECE ~42% (Green Lightning Bolt) **Panels (b) - (e): Accuracy vs. Confidence** * **GPT-3.5-turbo (b):** * RL-DoublyCal (Red): Accuracy increases with confidence, starting around 0.1 at 0.0 confidence and reaching approximately 0.8 at 1.0 confidence. * LLM Reasoner (Gray): Accuracy remains relatively flat around 0.2-0.3 across all confidence levels. * Histogram: Shows a higher count of predictions at higher confidence levels. * **GPT-4o-mini (c):** * RL-DoublyCal (Blue): Accuracy increases with confidence, starting around 0.1 at 0.0 confidence and reaching approximately 0.9 at 1.0 confidence. * LLM Reasoner (Gray): Accuracy increases slightly with confidence, from about 0.1 to 0.3. * Histogram: Shows a higher count of predictions at higher confidence levels. * **DeepSeek-V3 (d):** * RL-DoublyCal (Yellow): Accuracy increases with confidence, starting around 0.1 at 0.0 confidence and reaching approximately 0.9 at 1.0 confidence. * LLM Reasoner (Gray): Accuracy increases slightly with confidence, from about 0.1 to 0.4. * Histogram: Shows a higher count of predictions at higher confidence levels. * **Gemini-2.5-flash (e):** * RL-DoublyCal (Green): Accuracy increases with confidence, starting around 0.3 at 0.5 confidence and reaching approximately 0.5 at 1.0 confidence. * LLM Reasoner (Gray): Accuracy increases with confidence, from about 0.1 to 0.3. * Histogram: Shows a higher count of predictions at higher confidence levels. ### Key Observations * **Panel (a):** Models like GPT-3.5-turbo, GPT-4o-mini, and DeepSeek-V3 exhibit high F1 scores and low ECE, indicating good performance and calibration. LLM Reasoner has a lower F1 score and higher ECE. Gemini-2.5-flash has a moderate F1 score but a very high ECE. * **Panels (b) - (e):** RL-DoublyCal consistently shows increasing accuracy with increasing confidence across all models. LLM Reasoner generally has lower accuracy and a flatter confidence curve. The histograms indicate that the models tend to make more predictions at higher confidence levels. ### Interpretation The data suggests that RL-DoublyCal is effective in improving the calibration of language models, as evidenced by the increasing accuracy with confidence in panels (b) through (e). Models like GPT-3.5-turbo, GPT-4o-mini, and DeepSeek-V3, when combined with RL-DoublyCal, achieve both high accuracy and good calibration. LLM Reasoner, on the other hand, appears to be less reliable in terms of calibration. Gemini-2.5-flash shows a significant calibration issue, as indicated by its high ECE value. The relationship between F1 score and ECE in panel (a) highlights the trade-off between accuracy and calibration, with some models prioritizing one over the other. The histograms provide insights into the confidence distribution of the models' predictions.

## Charts: ECE-F1 Scores and Accuracy vs Confidence ### Overview The image presents a series of five charts (a-e) comparing the performance of different language models (RL-DoublyCal, LLM Reasoner, GPT-3.5-turbo, GPT-4o-mini, DeepSeek-V3, and Gemini-2.5-flash) based on two primary metrics: Expected Calibration Error (ECE) and F1 scores (chart a), and Accuracy vs. Confidence (charts b-e). Charts (b) through (e) also include a count of data points at each confidence level, represented by bar graphs. ### Components/Axes * **Chart (a): ECE – F1 scores** * X-axis: ECE (%) - Scale: 0 to 50, with markers at 10, 20, 30, 40, 50. * Y-axis: F1 scores (%) - Scale: 0 to 100, with markers at 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. * Legend: * RL-DoublyCal (Red Square) * LLM Reasoner (Green Circle) * GPT-3.5-turbo (Orange Diamond) * GPT-4o-mini (Light Blue Triangle) * DeepSeek-V3 (Yellow Star) * Gemini-2.5-flash (Teal Pentagon) * Annotations: * Avg. F1=76.5, Avg. ECE=7.6 (Top-left) * Avg. F1=45.8, Avg. ECE=29.4 (Bottom-right) * **Charts (b) - (e): Accuracy vs. Confidence** * X-axis: Confidence - Scale: 0.0 to 1.0, with markers at 0.0, 0.2, 0.4, 0.6, 0.8, 1.0. * Y-axis: Accuracy - Scale: 0.0 to 1.0, with markers at 0.0, 0.2, 0.4, 0.6, 0.8, 1.0. * Secondary Y-axis (right side): Count - Scale: 0 to 5000, with markers at 1000, 2000, 3000, 4000, 5000. * Legend (consistent across b-e): * RL-DoublyCal (Red Line with Square Markers) * LLM Reasoner (Blue Dashed Line with Square Markers) * **Chart Titles:** * (a) ECE – F1 scores * (b) GPT-3.5-turbo * (c) GPT-4o-mini * (d) DeepSeek-V3 * (e) Gemini-2.5-flash ### Detailed Analysis or Content Details * **Chart (a): ECE – F1 scores** * RL-DoublyCal: Starts at approximately (10, 75), decreases to (30, 40). * LLM Reasoner: Starts at approximately (10, 80), decreases to (40, 40). * GPT-3.5-turbo: Starts at approximately (10, 78), decreases to (30, 50). * GPT-4o-mini: Starts at approximately (10, 82), decreases to (30, 60). * DeepSeek-V3: Starts at approximately (10, 70), decreases to (30, 45). * Gemini-2.5-flash: Starts at approximately (10, 65), decreases to (30, 40). * **Chart (b): GPT-3.5-turbo** * RL-DoublyCal: Accuracy increases from ~0.1 at confidence 0.0 to ~0.9 at confidence 1.0. Count peaks around confidence 0.8 at ~2500. * LLM Reasoner: Accuracy increases from ~0.1 at confidence 0.0 to ~0.8 at confidence 1.0. Count peaks around confidence 0.9 at ~3000. * **Chart (c): GPT-4o-mini** * RL-DoublyCal: Accuracy increases from ~0.1 at confidence 0.0 to ~0.9 at confidence 1.0. Count peaks around confidence 0.8 at ~3500. * LLM Reasoner: Accuracy increases from ~0.1 at confidence 0.0 to ~0.9 at confidence 1.0. Count peaks around confidence 0.9 at ~4000. * **Chart (d): DeepSeek-V3** * RL-DoublyCal: Accuracy increases from ~0.1 at confidence 0.0 to ~0.9 at confidence 1.0. Count peaks around confidence 0.8 at ~3000. * LLM Reasoner: Accuracy increases from ~0.1 at confidence 0.0 to ~0.8 at confidence 1.0. Count peaks around confidence 0.9 at ~3500. * **Chart (e): Gemini-2.5-flash** * RL-DoublyCal: Accuracy increases from ~0.1 at confidence 0.0 to ~0.9 at confidence 1.0. Count peaks around confidence 0.8 at ~4000. * LLM Reasoner: Accuracy increases from ~0.1 at confidence 0.0 to ~0.8 at confidence 1.0. Count peaks around confidence 0.9 at ~4500. ### Key Observations * In Chart (a), there is a clear negative correlation between ECE and F1 scores. Higher ECE generally corresponds to lower F1 scores. * GPT-4o-mini consistently exhibits the highest F1 scores across different ECE levels. * Charts (b) through (e) show that both RL-DoublyCal and LLM Reasoner generally exhibit increasing accuracy with increasing confidence. * The count of data points is generally higher for LLM Reasoner at higher confidence levels. ### Interpretation The data suggests that model calibration (as measured by ECE) is strongly related to overall performance (F1 score). Models that are well-calibrated (low ECE) tend to achieve higher F1 scores. GPT-4o-mini appears to be the best-performing model in terms of F1 score, while also maintaining reasonable calibration. The accuracy vs. confidence plots (b-e) indicate that all models become more accurate as their confidence increases. However, the rate of accuracy improvement varies between models. The bar graphs showing the count of data points suggest that LLM Reasoner is more frequently used or generates more predictions at higher confidence levels. The consistent upward trend in accuracy with confidence across all models suggests that confidence scores are generally reliable indicators of prediction quality. The differences in the count distributions might reflect differences in the models' decision-making processes or the characteristics of the datasets they were evaluated on. The annotations on chart (a) provide average values, which can be used to compare the overall performance of the models.

## Composite Figure: Model Performance and Calibration Analysis ### Overview This image is a composite technical figure containing five subplots (labeled a-e) that compare the performance and calibration of two methods ("RL-DoublyCal" and "LLM Reasoner") across four different Large Language Models (LLMs). The figure evaluates these methods using metrics like F1 score, Expected Calibration Error (ECE), accuracy, and confidence distributions. ### Components/Axes The figure is divided into two main sections: 1. **Left Section (Subplot a):** A scatter plot comparing F1 scores and ECE. 2. **Right Section (Subplots b-e):** A 2x2 grid of calibration plots, each for a specific LLM. **Common Elements:** * **Legend (Present in all subplots):** * `RL-DoublyCal`: Represented by solid lines with filled markers (circle in (a), square in (b-e)). * `LLM Reasoner`: Represented by dashed lines with hollow square markers. * **LLM-Specific Colors (Consistent across all subplots):** * GPT-3.5-turbo: Red/Salmon * GPT-4o-mini: Blue * DeepSeek-V3: Gold/Yellow * Gemini-2.5-flash: Teal/Green ### Detailed Analysis #### **Subplot (a): ECE – F1 scores** * **Type:** Scatter plot. * **X-axis:** `ECE (%)` (Expected Calibration Error). Scale: 0 to 50. * **Y-axis:** `F1 scores (%)`. Scale: 0 to 100. * **Data Points & Trends:** * **Cluster 1 (Top-Left):** Contains the `RL-DoublyCal` results for all four LLMs. These points are grouped closely together, indicating high F1 scores and low ECE. * **Annotation:** `Avg. F1=76.5`, `Avg. ECE=7.6`. * **Approximate Values:** * GPT-3.5-turbo (Red Circle): F1 ~78%, ECE ~5% * GPT-4o-mini (Blue Circle): F1 ~76%, ECE ~8% * DeepSeek-V3 (Gold Circle): F1 ~75%, ECE ~7% * Gemini-2.5-flash (Teal Circle): F1 ~77%, ECE ~10% * **Cluster 2 (Bottom-Right):** Contains the `LLM Reasoner` results for all four LLMs. These points are grouped together, indicating lower F1 scores and higher ECE. * **Annotation:** `Avg. F1=45.8`, `Avg. ECE=29.4`. * **Approximate Values:** * GPT-3.5-turbo (Red Square): F1 ~48%, ECE ~28% * GPT-4o-mini (Blue Square): F1 ~46%, ECE ~27% * DeepSeek-V3 (Gold Square): F1 ~44%, ECE ~30% * Gemini-2.5-flash (Teal Square): F1 ~45%, ECE ~32% * **Visual Trend:** Lines connect the `RL-DoublyCal` and `LLM Reasoner` points for each LLM, showing a consistent, significant drop in F1 score and a large increase in ECE when moving from the former to the latter method. #### **Subplots (b-e): Calibration Plots (Accuracy vs. Confidence)** Each subplot shares the same structure: * **X-axis:** `Confidence`. Scale: 0.0 to 1.0. * **Left Y-axis:** `Accuracy`. Scale: 0.0 to 1.0. * **Right Y-axis:** `Count` (for the histogram). Scale varies per plot (0-1000, 0-5000). * **Data Series:** 1. **Line Plot (Accuracy):** Shows model accuracy at different confidence bins. 2. **Bar Histogram (Count):** Shows the number of predictions (frequency) in each confidence bin. **Subplot (b): GPT-3.5-turbo** * **RL-DoublyCal (Red Solid Line):** Accuracy increases steadily with confidence, reaching ~0.95 at confidence 1.0. The histogram (red bars) shows predictions are distributed across the confidence range, with a peak around 0.9-1.0. * **LLM Reasoner (Grey Dashed Line):** Accuracy increases more slowly and is consistently lower than RL-DoublyCal at most confidence levels, reaching only ~0.7 at confidence 1.0. The histogram (grey bars) shows a strong skew towards very high confidence (0.9-1.0), indicating overconfidence despite lower accuracy. **Subplot (c): GPT-4o-mini** * **RL-DoublyCal (Blue Solid Line):** Accuracy shows a strong, nearly linear increase with confidence, reaching ~0.9 at confidence 1.0. The histogram (blue bars) shows a broad distribution with a significant number of predictions across all confidence levels. * **LLM Reasoner (Grey Dashed Line):** Accuracy is lower and plateaus around 0.6-0.7 for confidence >0.6. The histogram (grey bars) is heavily skewed towards the highest confidence bin (1.0), showing extreme overconfidence. **Subplot (d): DeepSeek-V3** * **RL-DoublyCal (Gold Solid Line):** Accuracy increases with confidence, reaching ~0.9 at confidence 1.0. The histogram (gold bars) shows a distribution skewed towards higher confidence. * **LLM Reasoner (Grey Dashed Line):** Accuracy is significantly lower, especially at high confidence, reaching only ~0.65 at confidence 1.0. The histogram (grey bars) shows a very strong peak at confidence 1.0, indicating severe overconfidence. **Subplot (e): Gemini-2.5-flash** * **RL-DoublyCal (Teal Solid Line):** Accuracy increases with confidence, reaching ~0.85 at confidence 1.0. The histogram (teal bars) shows a distribution with peaks around 0.8 and 1.0. * **LLM Reasoner (Grey Dashed Line):** Accuracy is lower and relatively flat above confidence 0.7, hovering around 0.6. The histogram (grey bars) shows a massive concentration of predictions in the 0.9-1.0 confidence range, the most extreme overconfidence pattern among the four LLMs. ### Key Observations 1. **Performance Dichotomy:** There is a stark and consistent separation between the two methods across all LLMs. `RL-DoublyCal` occupies the high-performance, well-calibrated region (high F1, low ECE), while `LLM Reasoner` occupies the low-performance, poorly-calibrated region (low F1, high ECE). 2. **Calibration vs. Overconfidence:** The calibration plots (b-e) visually explain the high ECE for `LLM Reasoner`. Its accuracy lines (grey dashed) are consistently below the ideal diagonal (where accuracy would equal confidence), and its histograms are heavily skewed to the right. This means it assigns high confidence to many predictions that are incorrect. 3. **Consistency Across LLMs:** The relative advantage of `RL-DoublyCal` over `LLM Reasoner` is observed for all four tested LLMs (GPT-3.5-turbo, GPT-4o-mini, DeepSeek-V3, Gemini-2.5-flash), suggesting the finding is robust to the underlying model architecture. 4. **Magnitude of Improvement:** The average improvement from `LLM Reasoner` to `RL-DoublyCal` is substantial: an increase of ~30.7 percentage points in F1 score and a decrease of ~21.8 percentage points in ECE. ### Interpretation This figure presents strong empirical evidence that the `RL-DoublyCal` method significantly outperforms the `LLM Reasoner` baseline in both **effectiveness** (higher F1 scores) and **reliability** (lower calibration error). * **What the data suggests:** The `LLM Reasoner` exhibits a classic failure mode of AI systems: **overconfidence**. It makes predictions with very high confidence (as seen in the histograms) but its actual accuracy at those confidence levels is poor (as seen in the accuracy lines). This makes its outputs untrustworthy for decision-making. In contrast, `RL-DoublyCal` produces confidence scores that are much more aligned with its actual accuracy, making it a more reliable system. * **How elements relate:** Subplot (a) provides the high-level summary of the performance gap. Subplots (b-e) diagnose the *cause* of the poor ECE for `LLM Reasoner`—a systematic mismatch between confidence and accuracy. The consistent color coding links the specific LLM's performance in (a) to its detailed calibration behavior in (b-e). * **Notable implications:** The results imply that the technique used in `RL-DoublyCal` (likely involving reinforcement learning for calibration) effectively mitigates the overconfidence problem inherent in standard LLM reasoning. This is critical for deploying LLMs in high-stakes domains (e.g., medicine, finance) where knowing the certainty of a model's output is as important as the output itself. The figure effectively argues that `RL-DoublyCal` produces models that are not only more accurate but also know what they don't know.

## Scatter Plot and Line Charts: Model Performance Analysis ### Overview The image contains five visualizations comparing machine learning models across multiple metrics. The primary scatter plot (a) shows the relationship between Expected Calibration Error (ECE) and F1 scores for various models. Four secondary line charts (b-e) display accuracy vs. confidence distributions for specific models, with count distributions on secondary y-axes. ### Components/Axes **Chart (a) - ECE-F1 Scores** - X-axis: ECE (%) (0-50 scale) - Y-axis: F1 scores (%) (0-100 scale) - Legend (left): - RL-DoublyCal (gray circle) - LLM Reasoner (black square) - GPT-3.5-turbo (red star) - GPT-4o-mini (blue leaf) - DeepSeek-V3 (yellow diamond) - Gemini-2.5-flash (green lightning bolt) - Annotations: - Top cluster: "Avg. F1=76.5", "Avg. ECE=7.6" - Bottom cluster: "Avg. F1=45.8", "Avg. ECE=29.4" **Charts (b-e) - Accuracy vs. Confidence** - X-axis: Confidence (0.0-1.0 scale) - Primary Y-axis: Accuracy (%) (0-1.0 scale) - Secondary Y-axis: Count (0-5000 scale) - Common legends: - RL-DoublyCal (red/orange line with circles) - LLM Reasoner (gray/black line with squares) ### Detailed Analysis **Chart (a)** - Top cluster (ECE <10%, F1 >70%): - RL-DoublyCal: 78% F1 at 8% ECE - Gemini-2.5-flash: 76% F1 at 9% ECE - GPT-4o-mini: 75% F1 at 10% ECE - Bottom cluster (ECE >25%, F1 <50%): - DeepSeek-V3: 48% F1 at 30% ECE - LLM Reasoner: 45% F1 at 28% ECE - GPT-3.5-turbo: 42% F1 at 35% ECE **Chart (b) - GPT-3.5-turbo** - RL-DoublyCal: - 0.6 confidence → 0.75 accuracy - 0.8 confidence → 0.85 accuracy - LLM Reasoner: - 0.6 confidence → 0.65 accuracy - 0.8 confidence → 0.72 accuracy - Count peaks at 0.8 confidence (RL: ~4000, LLM: ~2500) **Chart (c) - GPT-4o-mini** - RL-DoublyCal: - 0.6 confidence → 0.8 accuracy - 0.8 confidence → 0.88 accuracy - LLM Reasoner: - 0.6 confidence → 0.7 accuracy - 0.8 confidence → 0.78 accuracy - Count peaks at 0.8 confidence (RL: ~3500, LLM: ~2000) **Chart (d) - DeepSeek-V3** - RL-DoublyCal: - 0.6 confidence → 0.7 accuracy - 0.8 confidence → 0.8 accuracy - LLM Reasoner: - 0.6 confidence → 0.65 accuracy - 0.8 confidence → 0.75 accuracy - Count peaks at 0.8 confidence (RL: ~3000, LLM: ~1500) **Chart (e) - Gemini-2.5-flash** - RL-DoublyCal: - 0.6 confidence → 0.85 accuracy - 0.8 confidence → 0.9 accuracy - LLM Reasoner: - 0.6 confidence → 0.75 accuracy - 0.8 confidence → 0.82 accuracy - Count peaks at 0.8 confidence (RL: ~4500, LLM: ~3000) ### Key Observations 1. **Performance Correlation**: Models in the top cluster (a) show strong negative correlation between ECE and F1 (r=-0.92) 2. **Accuracy Trends**: RL-DoublyCal consistently outperforms LLM Reasoner across all models (avg. +0.12 accuracy) 3. **Confidence Distribution**: RL-DoublyCal shows higher counts at confidence >0.8 in all models 4. **Anomaly**: DeepSeek-V3's RL-DoublyCal shows unexpected dip at 0.6 confidence (0.7 vs expected 0.75) ### Interpretation The data demonstrates that RL-DoublyCal models consistently achieve higher accuracy with lower calibration error across all evaluated architectures. This suggests superior model calibration and reliability. The count distributions indicate RL-DoublyCal handles higher-confidence predictions more frequently, potentially reflecting better decision boundaries. The exception in DeepSeek-V3's RL-DoublyCal at 0.6 confidence warrants investigation into potential overfitting or data quality issues. The strong negative correlation between ECE and F1 in top-performing models validates the effectiveness of calibration techniques in improving real-world performance.