## Chart: Accuracy vs. Noise Intensity Coefficient for Different Models ### Overview The image presents three line charts comparing the accuracy of two methods, "DiffCoT" and "Full-Step DPO," across different noise intensity coefficients for three models: Llama3-8B, Qwen3-8B, and Qwen3-4B. Each chart plots accuracy (Acc(%)) on the y-axis against the noise intensity coefficient (ω) on the x-axis. ### Components/Axes * **Titles (Top of each chart):** * Left: Llama3-8B * Middle: Qwen3-8B * Right: Qwen3-4B * **X-Axis (Horizontal):** * Label: Noise Intensity Coefficient ω * Scale: 0, 0.1, 0.2, 0.3, 0.4 * **Y-Axis (Vertical):** * Label: Acc(%) * Scale: * Llama3-8B: 15, 20, 25, 30, 35, 40 * Qwen3-8B: 40, 45, 50, 55, 60, 65, 70 * Qwen3-4B: 35, 40, 45, 50, 55, 60, 65 * **Legend (Bottom of each chart):** * Blue Line: DiffCoT * Orange Line: Full-Step DPO ### Detailed Analysis **Chart 1: Llama3-8B** * **DiffCoT (Blue):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 38 * ω = 0.1: Acc(%) ≈ 34 * ω = 0.2: Acc(%) ≈ 30 * ω = 0.3: Acc(%) ≈ 25 * ω = 0.4: Acc(%) ≈ 19 * **Full-Step DPO (Orange):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 38 * ω = 0.1: Acc(%) ≈ 33 * ω = 0.2: Acc(%) ≈ 26 * ω = 0.3: Acc(%) ≈ 21 * ω = 0.4: Acc(%) ≈ 15 **Chart 2: Qwen3-8B** * **DiffCoT (Blue):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 66 * ω = 0.1: Acc(%) ≈ 62 * ω = 0.2: Acc(%) ≈ 57 * ω = 0.3: Acc(%) ≈ 52 * ω = 0.4: Acc(%) ≈ 47 * **Full-Step DPO (Orange):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 67 * ω = 0.1: Acc(%) ≈ 62 * ω = 0.2: Acc(%) ≈ 54 * ω = 0.3: Acc(%) ≈ 48 * ω = 0.4: Acc(%) ≈ 42 **Chart 3: Qwen3-4B** * **DiffCoT (Blue):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 65 * ω = 0.1: Acc(%) ≈ 60 * ω = 0.2: Acc(%) ≈ 54 * ω = 0.3: Acc(%) ≈ 47 * ω = 0.4: Acc(%) ≈ 41 * **Full-Step DPO (Orange):** The accuracy decreases as the noise intensity coefficient increases. * ω = 0: Acc(%) ≈ 64 * ω = 0.1: Acc(%) ≈ 59 * ω = 0.2: Acc(%) ≈ 51 * ω = 0.3: Acc(%) ≈ 44 * ω = 0.4: Acc(%) ≈ 38 ### Key Observations * For all three models, both DiffCoT and Full-Step DPO show a decrease in accuracy as the noise intensity coefficient increases. * The Qwen3-8B and Qwen3-4B models generally exhibit higher accuracy than the Llama3-8B model across all noise intensity coefficients. * The DiffCoT method generally performs slightly better than the Full-Step DPO method, especially at lower noise intensity coefficients. ### Interpretation The charts demonstrate the impact of noise intensity on the accuracy of different language models and training methods. The consistent downward trend in accuracy as noise increases suggests that both DiffCoT and Full-Step DPO are susceptible to noise. The Qwen3 models appear to be more robust to noise than the Llama3-8B model, potentially indicating differences in their architecture or training data. The slight advantage of DiffCoT over Full-Step DPO suggests that DiffCoT may be a more effective training method for mitigating the effects of noise.

\n ## Line Charts: Accuracy vs. Noise Intensity Coefficient for Different Models ### Overview The image presents three separate line charts, each depicting the relationship between Accuracy (Acc(%) on the y-axis) and Noise Intensity Coefficient (ω) on the x-axis. Each chart represents a different model: Llama3-8B, Qwen3-8B, and Qwen3-4B. Within each chart, two lines represent different training methods: "DiffCoT" (blue line) and "Full-Step DPO" (orange line). The charts aim to compare the robustness of these models and training methods to increasing levels of noise. ### Components/Axes * **X-axis Label (all charts):** "Noise Intensity Coefficient ω" with markers at 0.0, 0.1, 0.2, 0.3, and 0.4. * **Y-axis Label (all charts):** "Acc(%)" with a scale ranging from approximately 15% to 70%. * **Chart Titles:** * Left: "Llama3-8B" * Center: "Qwen3-8B" * Right: "Qwen3-4B" * **Legend (bottom-left of each chart):** * Blue Line: "DiffCoT" * Orange Line: "Full-Step DPO" ### Detailed Analysis or Content Details **Llama3-8B (Left Chart):** * The "DiffCoT" line (blue) starts at approximately 38% accuracy at ω = 0.0 and decreases linearly to approximately 19% accuracy at ω = 0.4. * The "Full-Step DPO" line (orange) starts at approximately 36% accuracy at ω = 0.0 and decreases more steeply to approximately 17% accuracy at ω = 0.4. **Qwen3-8B (Center Chart):** * The "DiffCoT" line (blue) starts at approximately 67% accuracy at ω = 0.0 and decreases linearly to approximately 44% accuracy at ω = 0.4. * The "Full-Step DPO" line (orange) starts at approximately 65% accuracy at ω = 0.0 and decreases more steeply to approximately 40% accuracy at ω = 0.4. **Qwen3-4B (Right Chart):** * The "DiffCoT" line (blue) starts at approximately 63% accuracy at ω = 0.0 and decreases linearly to approximately 48% accuracy at ω = 0.4. * The "Full-Step DPO" line (orange) starts at approximately 62% accuracy at ω = 0.0 and decreases more steeply to approximately 38% accuracy at ω = 0.4. ### Key Observations * In all three charts, both training methods show a decrease in accuracy as the noise intensity coefficient increases. * "Full-Step DPO" consistently exhibits a steeper decline in accuracy compared to "DiffCoT" across all models and noise levels. * Qwen3-8B and Qwen3-4B generally achieve higher initial accuracy levels (at ω = 0.0) than Llama3-8B. * The rate of accuracy decline appears relatively consistent for "DiffCoT" across all models. ### Interpretation The data suggests that increasing noise negatively impacts the accuracy of all three models, regardless of the training method used. "Full-Step DPO" appears to be more sensitive to noise than "DiffCoT," as evidenced by the steeper decline in accuracy. This could indicate that "DiffCoT" provides a more robust training approach in the presence of noisy data. The higher initial accuracy of the Qwen models suggests they may have a stronger baseline performance compared to Llama3-8B. The linear relationship between noise intensity and accuracy decline suggests a predictable degradation in performance as noise levels increase. The consistent trends across all three models indicate that the observed behavior is likely not model-specific but rather a general characteristic of these types of language models when exposed to noise. The charts provide a comparative analysis of model robustness and training method effectiveness under varying noise conditions.

## Line Charts: Model Accuracy vs. Noise Intensity ### Overview The image displays three horizontally arranged line charts comparing the performance of two methods, **DiffCoT** and **Full-Step DPO**, across three different language models (Llama3-8B, Qwen3-8B, Qwen3-4B). Each chart plots model accuracy (Acc%) against an increasing "Noise Intensity Coefficient ω". The consistent visual pattern shows that accuracy for both methods decreases as noise increases, but DiffCoT consistently maintains higher accuracy than Full-Step DPO. ### Components/Axes * **Titles (Top of each chart):** "Llama3-8B" (left), "Qwen3-8B" (center), "Qwen3-4B" (right). * **X-Axis (All charts):** Label: "Noise Intensity Coefficient ω". Ticks/Markers: 0, 0.1, 0.2, 0.3, 0.4. * **Y-Axis (All charts):** Label: "Acc(%)". Scale varies per chart. * **Legend (Bottom of each chart):** Located centrally below the x-axis label. Contains two entries: * Blue line with square markers: "DiffCoT" * Orange line with diamond markers: "Full-Step DPO" ### Detailed Analysis **Chart 1: Llama3-8B (Left)** * **Y-Axis Scale:** 15 to 40, in increments of 5. * **Data Series & Trends:** * **DiffCoT (Blue, Squares):** Starts at ~38% (ω=0). Slopes downward steadily. Points (approximate): (0.1, ~34%), (0.2, ~30%), (0.3, ~25%), (0.4, ~19%). * **Full-Step DPO (Orange, Diamonds):** Starts at the same point as DiffCoT, ~38% (ω=0). Slopes downward more steeply than DiffCoT. Points (approximate): (0.1, ~33%), (0.2, ~26%), (0.3, ~21%), (0.4, ~15%). * **Relationship:** The gap between the two lines widens as ω increases, with DiffCoT maintaining a clear advantage. **Chart 2: Qwen3-8B (Center)** * **Y-Axis Scale:** 40 to 70, in increments of 5. * **Data Series & Trends:** * **DiffCoT (Blue, Squares):** Starts at ~67% (ω=0). Slopes downward. Points (approximate): (0.1, ~62%), (0.2, ~57%), (0.3, ~49%), (0.4, ~42%). * **Full-Step DPO (Orange, Diamonds):** Starts at the same point, ~67% (ω=0). Slopes downward more steeply. Points (approximate): (0.1, ~62%), (0.2, ~54%), (0.3, ~45%), (0.4, ~40%). * **Relationship:** Similar to the first chart, DiffCoT degrades more gracefully. The lines are nearly identical at ω=0.1 but diverge significantly thereafter. **Chart 3: Qwen3-4B (Right)** * **Y-Axis Scale:** 35 to 65, in increments of 5. * **Data Series & Trends:** * **DiffCoT (Blue, Squares):** Starts at ~65% (ω=0). Slopes downward. Points (approximate): (0.1, ~60%), (0.2, ~54%), (0.3, ~47%), (0.4, ~41%). * **Full-Step DPO (Orange, Diamonds):** Starts at the same point, ~65% (ω=0). Slopes downward more steeply. Points (approximate): (0.1, ~59%), (0.2, ~51%), (0.3, ~44%), (0.4, ~38%). * **Relationship:** The pattern holds. DiffCoT's line is consistently above Full-Step DPO's line for all ω > 0. ### Key Observations 1. **Universal Negative Correlation:** For all three models and both methods, accuracy (Acc%) has a strong, negative, near-linear correlation with the Noise Intensity Coefficient (ω). 2. **Consistent Performance Hierarchy:** DiffCoT (blue line) demonstrates superior robustness to noise compared to Full-Step DPO (orange line) across all tested models and noise levels. This is visually evident as the blue line is always above the orange line for ω > 0. 3. **Convergent Starting Points:** At zero noise (ω=0), the performance of both methods is virtually identical for each respective model, suggesting they have similar baseline capabilities. 4. **Divergent Degradation:** The performance gap between the two methods generally widens as noise intensity increases, indicating DiffCoT's advantage becomes more pronounced under more challenging (noisier) conditions. 5. **Model-Specific Baselines:** The baseline accuracy (at ω=0) varies by model: Llama3-8B (~38%) is significantly lower than both Qwen models (~65-67%). ### Interpretation This set of charts provides a clear comparative analysis of two techniques (DiffCoT and Full-Step DPO) for improving or maintaining the reasoning accuracy of Large Language Models (LLMs) when subjected to input noise. * **What the data suggests:** The primary finding is that **DiffCoT confers greater noise robustness than Full-Step DPO**. While both methods suffer from performance degradation as input noise increases, DiffCoT mitigates this loss more effectively. This is a critical property for real-world applications where input data may be imperfect, ambiguous, or corrupted. * **How elements relate:** The charts are designed for direct comparison. Placing the three models side-by-side with identical x-axes and legend allows the viewer to quickly assess if the observed trend (DiffCoT > Full-Step DPO under noise) is consistent across different model architectures and sizes. The consistency of the pattern across Llama3 and Qwen3 models strengthens the conclusion that the advantage is method-specific, not model-specific. * **Notable implications:** The identical starting points at ω=0 are crucial. They indicate that the observed advantage of DiffCoT is not due to a higher inherent capability but specifically due to its **resilience to perturbation**. This makes DiffCoT a potentially more reliable method for deployment in uncontrolled environments. The charts effectively argue that for tasks where input quality cannot be guaranteed, employing DiffCoT would lead to more stable and predictable model performance.

## Line Graphs: Accuracy vs. Noise Intensity Coefficient (α) for Different Models ### Overview The image contains three line graphs comparing the performance of two methods—**DiffCoT** (blue) and **Full-Step DPO** (orange)—across three language models: **Llama3-8B**, **Qwen3-8B**, and **Qwen3-4B**. Each graph plots accuracy (y-axis, %) against the noise intensity coefficient (α, x-axis, ranging from 0 to 0.4). Both methods show declining accuracy as α increases, but **DiffCoT** consistently outperforms **Full-Step DPO** across all models. --- ### Components/Axes - **X-axis**: Noise Intensity Coefficient (α) with markers at 0, 0.1, 0.2, 0.3, 0.4. - **Y-axis**: Accuracy (Acc, %) with increments of 5%. - **Legends**: - Blue line: **DiffCoT** - Orange line: **Full-Step DPO** - **Graph Titles**: - Llama3-8B (left) - Qwen3-8B (center) - Qwen3-4B (right) --- ### Detailed Analysis #### Llama3-8B - **DiffCoT**: Starts at ~38% (α=0), declines to ~19% (α=0.4). - **Full-Step DPO**: Starts at ~38% (α=0), declines to ~15% (α=0.4). - **Trend**: Both methods show a steep downward slope, with **DiffCoT** maintaining a ~3–5% advantage. #### Qwen3-8B - **DiffCoT**: Starts at ~66% (α=0), declines to ~42% (α=0.4). - **Full-Step DPO**: Starts at ~66% (α=0), declines to ~40% (α=0.4). - **Trend**: Similar to Llama3-8B, but with higher absolute accuracy values. The gap between methods narrows slightly at α=0.4. #### Qwen3-4B - **DiffCoT**: Starts at ~64% (α=0), declines to ~41% (α=0.4). - **Full-Step DPO**: Starts at ~64% (α=0), declines to ~38% (α=0.4). - **Trend**: Steeper decline compared to other models. **DiffCoT** retains a ~3% edge at α=0.4. --- ### Key Observations 1. **Consistent Performance Gap**: **DiffCoT** outperforms **Full-Step DPO** across all models and α values. 2. **Model Sensitivity**: - **Qwen3-4B** shows the steepest decline in accuracy for both methods, suggesting higher sensitivity to noise. - **Llama3-8B** exhibits the least sensitivity, with a smaller drop in accuracy. 3. **Noise Impact**: Accuracy decreases non-linearly as α increases, with sharper drops at higher α values. --- ### Interpretation The data demonstrates that **DiffCoT** is more robust to noise than **Full-Step DPO** across all tested models. This could indicate that **DiffCoT**’s methodology (e.g., incremental noise injection during training) better prepares models for noisy environments. The steeper decline in **Qwen3-4B** suggests architectural or training differences that make it more vulnerable to noise. Practically, **DiffCoT** may be preferable for applications requiring noise resilience, while **Full-Step DPO** might suffice in cleaner environments. Further investigation into the noise-handling mechanisms of these methods could clarify their relative strengths.