## Line Chart: I-Don't-Know Rate vs. Layer for Llama Models ### Overview The image presents two line charts comparing the "I-Don't-Know Rate" across different layers of two Llama models (Llama-3.2-1B and Llama-3.2-3B). Each chart displays the rate for various question-answering datasets, anchored either by question (Q-Anchored) or answer (A-Anchored). The x-axis represents the layer number, and the y-axis represents the I-Don't-Know Rate, ranging from 0 to 100. ### Components/Axes * **Titles:** * Left Chart: "Llama-3.2-1B" * Right Chart: "Llama-3.2-3B" * **Y-Axis:** "I-Don't-Know Rate" (ranging from 0 to 100, with markers at 0, 20, 40, 60, 80, and 100) * **X-Axis:** "Layer" * Left Chart: Layer numbers from 0 to 15, with markers at 0, 5, 10, and 15. * Right Chart: Layer numbers from 0 to 25, with markers at 0, 5, 10, 15, 20, and 25. * **Legend:** Located at the bottom of the image, describing the lines: * Blue: Q-Anchored (PopQA) * Brown dashed: A-Anchored (PopQA) * Green dotted: Q-Anchored (TriviaQA) * Pink dashed: A-Anchored (TriviaQA) * Red dashed: Q-Anchored (NQ) * Gray dotted: A-Anchored (NQ) * Purple dashed: Q-Anchored (HotpotQA) * Orange dashed: A-Anchored (HotpotQA) ### Detailed Analysis **Left Chart: Llama-3.2-1B** * **Q-Anchored (PopQA) (Blue):** Starts at approximately 60, drops sharply to near 0 around layer 3, then fluctuates between 0 and 20 until the end. * **A-Anchored (PopQA) (Brown dashed):** Starts around 60, remains relatively stable between 55 and 65 across all layers. * **Q-Anchored (TriviaQA) (Green dotted):** Starts around 90, drops to approximately 60 by layer 2, fluctuates between 60 and 80. * **A-Anchored (TriviaQA) (Pink dashed):** Starts around 60, drops to approximately 40 by layer 2, fluctuates between 30 and 60. * **Q-Anchored (NQ) (Red dashed):** Starts around 50, fluctuates between 40 and 60. * **A-Anchored (NQ) (Gray dotted):** Starts around 50, fluctuates between 30 and 60. * **Q-Anchored (HotpotQA) (Purple dashed):** Starts around 80, drops to approximately 20 by layer 3, fluctuates between 20 and 60. * **A-Anchored (HotpotQA) (Orange dashed):** Starts around 50, remains relatively stable between 50 and 70 across all layers. **Right Chart: Llama-3.2-3B** * **Q-Anchored (PopQA) (Blue):** Starts at approximately 50, drops sharply to near 10 around layer 4, then fluctuates between 10 and 50 until the end. * **A-Anchored (PopQA) (Brown dashed):** Starts around 50, rises to approximately 70 by layer 10, then remains relatively stable between 60 and 70 across all layers. * **Q-Anchored (TriviaQA) (Green dotted):** Starts around 90, drops to approximately 10 by layer 4, fluctuates between 10 and 40. * **A-Anchored (TriviaQA) (Pink dashed):** Starts around 50, drops to approximately 10 by layer 4, fluctuates between 10 and 40. * **Q-Anchored (NQ) (Red dashed):** Starts around 50, rises to approximately 80 by layer 10, then remains relatively stable between 70 and 80 across all layers. * **A-Anchored (NQ) (Gray dotted):** Starts around 50, fluctuates between 40 and 60. * **Q-Anchored (HotpotQA) (Purple dashed):** Starts around 100, drops to approximately 20 by layer 4, fluctuates between 20 and 50. * **A-Anchored (HotpotQA) (Orange dashed):** Starts around 50, rises to approximately 80 by layer 10, then remains relatively stable between 70 and 80 across all layers. ### Key Observations * For both models, the "I-Don't-Know Rate" varies significantly depending on the dataset and whether the anchoring is done by question or answer. * The Q-Anchored (PopQA) line shows a dramatic drop in the "I-Don't-Know Rate" in the initial layers for both models. * The A-Anchored (PopQA) line remains relatively stable across all layers for both models. * The Q-Anchored (TriviaQA) and A-Anchored (TriviaQA) lines show a dramatic drop in the "I-Don't-Know Rate" in the initial layers for the Llama-3.2-3B model. * The Q-Anchored (HotpotQA) line shows a dramatic drop in the "I-Don't-Know Rate" in the initial layers for both models. * The A-Anchored (HotpotQA) line rises in the initial layers for the Llama-3.2-3B model. ### Interpretation The charts illustrate how the "I-Don't-Know Rate" changes across different layers of the Llama models when processing various question-answering datasets. The differences between Q-Anchored and A-Anchored rates suggest that the model's confidence varies depending on whether the question or the answer is used as the anchor. The initial drop in the "I-Don't-Know Rate" for certain datasets (PopQA, TriviaQA, HotpotQA) in the early layers indicates that the model quickly gains confidence or learns to provide answers for those specific types of questions. The stability of the A-Anchored (PopQA) line suggests a consistent level of uncertainty when the answer is used as the anchor for the PopQA dataset. The Llama-3.2-3B model shows a more pronounced drop in the "I-Don't-Know Rate" for TriviaQA and HotpotQA, indicating that it may be better at processing these types of questions compared to Llama-3.2-1B.

\n ## Line Chart: I-Don't-Know Rate vs. Layer for Llama Models ### Overview The image presents two line charts, side-by-side, displaying the "I-Don't-Know Rate" as a function of "Layer" for two different Llama models: Llama-3.2-1B and Llama-3.2-3B. Each chart shows multiple lines representing different question-answering datasets and anchoring methods. The charts are designed to compare how the rate of the model responding with "I-Don't-Know" changes as the model's layers increase. ### Components/Axes * **X-axis:** "Layer" - Ranges from approximately 0 to 15 for the Llama-3.2-1B chart and from 0 to 25 for the Llama-3.2-3B chart. * **Y-axis:** "I-Don't-Know Rate" - Ranges from 0 to 100. * **Title (Left Chart):** "Llama-3.2-1B" * **Title (Right Chart):** "Llama-3.2-3B" * **Legend:** Located at the bottom of the image, contains the following labels and corresponding line styles/colors: * Q-Anchored (PopQA) - Solid Blue Line * A-Anchored (PopQA) - Solid Orange Line * Q-Anchored (TriviaQA) - Solid Green Line * A-Anchored (TriviaQA) - Solid Purple Line * Q-Anchored (HotpotQA) - Dashed Blue Line * A-Anchored (HotpotQA) - Dashed Orange Line * Q-Anchored (NQ) - Dashed Green Line * A-Anchored (NQ) - Dashed Purple Line ### Detailed Analysis or Content Details **Llama-3.2-1B Chart:** * **Q-Anchored (PopQA):** Starts at approximately 15, drops to a minimum of around 10 at layer 3, then gradually increases to approximately 55 by layer 15. * **A-Anchored (PopQA):** Starts at approximately 60, decreases to a minimum of around 40 at layer 3, then fluctuates between 50 and 65 until layer 15. * **Q-Anchored (TriviaQA):** Starts at approximately 85, drops sharply to around 20 at layer 3, then increases to approximately 50 by layer 15. * **A-Anchored (TriviaQA):** Starts at approximately 70, decreases to around 30 at layer 3, then increases to approximately 60 by layer 15. * **Q-Anchored (HotpotQA):** Starts at approximately 60, decreases to around 25 at layer 3, then fluctuates between 40 and 60 until layer 15. * **A-Anchored (HotpotQA):** Starts at approximately 65, decreases to around 35 at layer 3, then fluctuates between 45 and 65 until layer 15. * **Q-Anchored (NQ):** Starts at approximately 75, drops to around 25 at layer 3, then increases to approximately 55 by layer 15. * **A-Anchored (NQ):** Starts at approximately 70, decreases to around 30 at layer 3, then increases to approximately 60 by layer 15. **Llama-3.2-3B Chart:** * **Q-Anchored (PopQA):** Starts at approximately 15, drops to a minimum of around 10 at layer 3, then fluctuates between 30 and 60 until layer 25. * **A-Anchored (PopQA):** Starts at approximately 60, decreases to a minimum of around 40 at layer 3, then fluctuates between 50 and 70 until layer 25. * **Q-Anchored (TriviaQA):** Starts at approximately 85, drops sharply to around 20 at layer 3, then increases to approximately 50 by layer 25. * **A-Anchored (TriviaQA):** Starts at approximately 70, decreases to around 30 at layer 3, then increases to approximately 60 by layer 25. * **Q-Anchored (HotpotQA):** Starts at approximately 60, decreases to around 25 at layer 3, then fluctuates between 40 and 60 until layer 25. * **A-Anchored (HotpotQA):** Starts at approximately 65, decreases to around 35 at layer 3, then fluctuates between 45 and 65 until layer 25. * **Q-Anchored (NQ):** Starts at approximately 75, drops to around 25 at layer 3, then increases to approximately 55 by layer 25. * **A-Anchored (NQ):** Starts at approximately 70, decreases to around 30 at layer 3, then increases to approximately 60 by layer 25. ### Key Observations * All lines in both charts exhibit a significant drop in "I-Don't-Know Rate" within the first few layers (up to layer 3). * After the initial drop, the lines generally stabilize or exhibit more gradual increases. * The "Q-Anchored" lines tend to have lower "I-Don't-Know Rates" than the corresponding "A-Anchored" lines across all datasets. * The "TriviaQA" dataset consistently shows a higher initial "I-Don't-Know Rate" compared to other datasets. * The Llama-3.2-3B model generally exhibits a more stable "I-Don't-Know Rate" across layers compared to the Llama-3.2-1B model. ### Interpretation The data suggests that increasing the number of layers in the Llama models initially improves their ability to answer questions, as evidenced by the decrease in the "I-Don't-Know Rate." However, beyond a certain point (around layer 3), the improvement plateaus, and the rate may even slightly increase. The difference between "Q-Anchored" and "A-Anchored" methods indicates that anchoring questions may be more effective than anchoring answers in reducing uncertainty. The higher initial "I-Don't-Know Rate" for the "TriviaQA" dataset suggests that this dataset presents more challenging questions for the models. The greater stability observed in the Llama-3.2-3B model suggests that a larger model size can lead to more consistent performance across layers. The charts provide valuable insights into the behavior of these language models and can inform strategies for improving their performance and reducing uncertainty in their responses.

\n ## Comparative Analysis: "I-Don't-Know Rate" Across Model Layers ### Overview The image displays two side-by-side line charts comparing the "I-Don't-Know Rate" across the internal layers of two different Large Language Models: **Llama-3.2-1B** (left chart) and **Llama-3.2-3B** (right chart). Each chart plots the performance of eight different experimental conditions, which are combinations of two methods (Q-Anchored and A-Anchored) applied to four different question-answering datasets (PopQA, TriviaQA, HotpotQA, NQ). The charts visualize how the model's tendency to output an "I don't know" response changes as information propagates through its layers. ### Components/Axes * **Chart Titles:** * Left Chart: `Llama-3.2-1B` * Right Chart: `Llama-3.2-3B` * **Y-Axis (Both Charts):** * **Label:** `I-Don't-Know Rate` * **Scale:** 0 to 100 (percentage). * **Ticks:** 0, 20, 40, 60, 80, 100. * **X-Axis (Both Charts):** * **Label:** `Layer` * **Scale (Left Chart - 1B Model):** 0 to 16. Ticks at 0, 5, 10, 15. * **Scale (Right Chart - 3B Model):** 0 to 28. Ticks at 0, 5, 10, 15, 20, 25. * **Legend (Positioned at the bottom, spanning both charts):** * The legend defines eight series, differentiated by color and line style (solid vs. dashed). Each entry follows the format: `[Method] ([Dataset])`. * **Solid Lines (Q-Anchored):** 1. `Q-Anchored (PopQA)` - **Blue, solid line** 2. `Q-Anchored (TriviaQA)` - **Green, solid line** 3. `Q-Anchored (HotpotQA)` - **Purple, solid line** 4. `Q-Anchored (NQ)` - **Pink, solid line** * **Dashed Lines (A-Anchored):** 5. `A-Anchored (PopQA)` - **Orange, dashed line** 6. `A-Anchored (TriviaQA)` - **Red, dashed line** 7. `A-Anchored (HotpotQA)` - **Brown, dashed line** 8. `A-Anchored (NQ)` - **Gray, dashed line** * **Visual Elements:** Each data series is represented by a line with a surrounding shaded area of the same color, likely indicating variance or confidence intervals. ### Detailed Analysis #### **Chart 1: Llama-3.2-1B (Left)** * **Trend Verification & Data Points (Approximate):** * **Q-Anchored (PopQA) [Blue, Solid]:** Starts very high (~90% at Layer 0), plummets dramatically to near 0% by Layer 3, then exhibits high volatility, fluctuating between ~10% and ~60% for the remaining layers, ending near ~40% at Layer 16. * **A-Anchored (PopQA) [Orange, Dashed]:** Shows remarkable stability. Hovers consistently in a narrow band between approximately 50% and 60% across all layers. * **Q-Anchored (TriviaQA) [Green, Solid]:** Starts moderately high (~70%), dips, then peaks sharply around Layer 4 (~80%). After this peak, it generally trends downward with fluctuations, ending near ~30%. * **A-Anchored (TriviaQA) [Red, Dashed]:** Relatively stable, similar to its PopQA counterpart. Fluctuates gently between ~50% and ~65%. * **Q-Anchored (HotpotQA) [Purple, Solid]:** Highly volatile. Starts around ~60%, drops, spikes to ~70% near Layer 5, then sees a deep trough (~10%) around Layer 10 before rising again. Ends near ~50%. * **A-Anchored (HotpotQA) [Brown, Dashed]:** More stable than its Q-Anchored version. Generally stays between ~45% and ~60%. * **Q-Anchored (NQ) [Pink, Solid]:** Starts high (~80%), drops, then shows a broad peak between Layers 5-10 (~60-70%). Trends downward thereafter, ending near ~20%. * **A-Anchored (NQ) [Gray, Dashed]:** Stable, fluctuating between ~40% and ~55%. #### **Chart 2: Llama-3.2-3B (Right)** * **Trend Verification & Data Points (Approximate):** * **Q-Anchored (PopQA) [Blue, Solid]:** Starts high (~80%), drops sharply to a low of ~10-20% by Layer 5. Then enters a volatile phase with multiple peaks (e.g., ~60% near Layer 12, ~50% near Layer 22) and troughs, ending near ~10%. * **A-Anchored (PopQA) [Orange, Dashed]:** Stable, but with a slight downward trend. Starts near ~55%, ends near ~45%. * **Q-Anchored (TriviaQA) [Green, Solid]:** Starts very high (~100%), crashes to near 0% by Layer 5. Remains very low (<20%) for the rest of the layers, with minor fluctuations. * **A-Anchored (TriviaQA) [Red, Dashed]:** Very stable, hovering around 60-70% for the entire depth. * **Q-Anchored (HotpotQA) [Purple, Solid]:** Extremely volatile. Shows large swings, from lows near 0% (Layer 15) to peaks near 60% (Layer 8, Layer 25). No clear directional trend. * **A-Anchored (HotpotQA) [Brown, Dashed]:** Moderately stable, fluctuating between ~40% and ~55%. * **Q-Anchored (NQ) [Pink, Solid]:** Starts high (~90%), drops to a low (~10%) by Layer 7. Recovers to a peak of ~40% near Layer 18, then declines again. * **A-Anchored (NQ) [Gray, Dashed]:** Stable, centered around ~50%. ### Key Observations 1. **Method Dichotomy:** The most striking pattern is the fundamental difference between **Q-Anchored (solid lines)** and **A-Anchored (dashed lines)** methods. A-Anchored lines are consistently stable across layers for all datasets, while Q-Anchored lines are highly volatile, often showing dramatic drops and recoveries. 2. **Model Size Effect:** The volatility of the Q-Anchored methods appears more pronounced in the larger **3B model**. The drops are steeper (e.g., TriviaQA green line crashes from 100% to 0%), and the subsequent fluctuations are more extreme compared to the 1B model. 3. **Dataset Influence:** The dataset used significantly impacts the absolute level and pattern of the "I-Don't-Know Rate," especially for Q-Anchored methods. For example, in the 3B model, Q-Anchored on TriviaQA (green) stays near zero after the initial drop, while on HotpotQA (purple) it continues to swing wildly. 4. **Layer Sensitivity:** For Q-Anchored methods, the early layers (0-5) often show the most dramatic changes, suggesting this is where the anchoring mechanism has the strongest initial effect on the model's uncertainty expression. ### Interpretation This data suggests a fundamental difference in how the "Q-Anchored" and "A-Anchored" techniques influence the model's internal processing of uncertainty. * **A-Anchored methods** appear to induce a **consistent, layer-invariant bias** towards expressing uncertainty (or not). The stable "I-Don't-Know Rate" implies this method sets a fixed propensity for hedging that is maintained throughout the network's depth. * **Q-Anchored methods** seem to interact dynamically with the model's representations as they are processed layer-by-layer. The initial high rate suggests the question anchor initially triggers uncertainty, which is then rapidly resolved (the sharp drop) in early layers. The subsequent volatility indicates that later layers continually re-evaluate this uncertainty based on the evolving internal context, leading to fluctuations. The greater volatility in the 3B model may reflect its larger capacity for nuanced, layer-specific processing. The stark contrast implies that **A-Anchoring acts more like a global setting, while Q-Anchoring engages with the model's step-by-step reasoning process.** The choice of dataset further modulates this interaction, likely due to differences in question complexity, answer ambiguity, or the model's pre-trained knowledge about those domains. The charts effectively visualize not just a performance metric, but the *dynamics* of uncertainty expression within the neural network.

## Line Graphs: I-Don't-Know Rate Across Layers in LLaMA-3.2 Models ### Overview The image contains two line graphs comparing the "I-Don't-Know Rate" (y-axis) across model layers (x-axis) for two versions of the LLaMA-3.2 architecture: **LLaMA-3.2-1B** (left) and **LLaMA-3.2-3B** (right). Each graph includes six data series representing different question-answering (QA) anchoring methods and datasets. The graphs use shaded regions to indicate variability (confidence intervals) around the mean values. --- ### Components/Axes - **X-Axis (Layer)**: - Left graph: Layers 0–15 (LLaMA-3.2-1B). - Right graph: Layers 0–25 (LLaMA-3.2-3B). - Labels: "Layer" with tick marks at intervals of 5. - **Y-Axis (I-Don't-Know Rate)**: - Range: 0–100%. - Labels: "I-Don't-Know Rate" with increments of 20. - **Legend**: - Located at the bottom of both graphs. - Six data series, differentiated by line style and color: 1. **Q-Anchored (PopQA)**: Solid blue. 2. **A-Anchored (PopQA)**: Dashed orange. 3. **Q-Anchored (TriviaQA)**: Solid green. 4. **A-Anchored (TriviaQA)**: Dashed brown. 5. **Q-Anchored (HotpotQA)**: Solid purple. 6. **Q-Anchored (NQ)**: Dashed pink. 7. **A-Anchored (HotpotQA)**: Dashed gray. 8. **A-Anchored (NQ)**: Dotted gray. --- ### Detailed Analysis #### Left Graph (LLaMA-3.2-1B) - **Q-Anchored (PopQA)**: - Starts at ~90% in layer 0, drops sharply to ~10% by layer 5, then fluctuates between 10–30%. - **A-Anchored (PopQA)**: - Starts at ~60%, remains relatively stable (~50–70%) with minor peaks. - **Q-Anchored (TriviaQA)**: - Begins at ~80%, dips to ~20% by layer 5, then rises to ~60% by layer 15. - **A-Anchored (TriviaQA)**: - Starts at ~50%, fluctuates between 40–60%. - **Q-Anchored (HotpotQA)**: - Starts at ~70%, drops to ~30% by layer 5, then rises to ~50% by layer 15. - **Q-Anchored (NQ)**: - Starts at ~60%, dips to ~20% by layer 5, then rises to ~40% by layer 15. - **A-Anchored (HotpotQA)**: - Starts at ~50%, fluctuates between 40–60%. - **A-Anchored (NQ)**: - Starts at ~40%, fluctuates between 30–50%. #### Right Graph (LLaMA-3.2-3B) - **Q-Anchored (PopQA)**: - Starts at ~80%, drops to ~20% by layer 5, then fluctuates between 10–40%. - **A-Anchored (PopQA)**: - Starts at ~60%, remains stable (~50–70%) with minor peaks. - **Q-Anchored (TriviaQA)**: - Begins at ~80%, dips to ~10% by layer 5, then rises to ~70% by layer 25. - **A-Anchored (TriviaQA)**: - Starts at ~50%, fluctuates between 40–60%. - **Q-Anchored (HotpotQA)**: - Starts at ~70%, drops to ~20% by layer 5, then rises to ~60% by layer 25. - **Q-Anchored (NQ)**: - Starts at ~60%, dips to ~10% by layer 5, then rises to ~50% by layer 25. - **A-Anchored (HotpotQA)**: - Starts at ~50%, fluctuates between 40–60%. - **A-Anchored (NQ)**: - Starts at ~40%, fluctuates between 30–50%. --- ### Key Observations 1. **Layer-Specific Variability**: - Both models show significant fluctuations in I-Don't-Know rates, particularly in layers 5–15 (1B) and 10–20 (3B). - The 3B model exhibits more pronounced volatility, especially in layers 20–25. 2. **Dataset-Specific Trends**: - **PopQA** (solid blue/orange lines) generally shows lower rates in early layers but stabilizes later. - **TriviaQA** (solid green/brown lines) has sharp drops in early layers, followed by recovery. - **HotpotQA** (solid purple/dashed gray lines) exhibits the most dramatic early-layer drops. - **NQ** (dashed pink/dotted gray lines) consistently shows lower rates but with occasional spikes. 3. **Model Size Impact**: - The 3B model’s lines are more erratic, suggesting increased sensitivity to layer-specific factors. --- ### Interpretation The data suggests that anchoring methods and datasets significantly influence the model’s uncertainty across layers. Early layers (0–5) show high I-Don't-Know rates for most methods, likely due to insufficient contextual understanding. Later layers demonstrate recovery, but the 3B model’s larger size introduces greater variability, possibly reflecting architectural complexity. Methods like **Q-Anchored (HotpotQA)** and **A-Anchored (NQ)** appear more stable, indicating robustness in handling uncertainty. The spikes in the 3B model (e.g., layer 20 for Q-Anchored HotpotQA) may highlight critical layers where the model struggles with specific datasets. This analysis underscores the importance of dataset choice and anchoring strategy in mitigating uncertainty in large language models.