\n ## Line Charts: Llama-3.2 Model Layer-wise ΔP Analysis ### Overview The image displays two side-by-side line charts comparing the layer-wise change in probability (ΔP) for two different-sized language models (Llama-3.2-1B and Llama-3.2-3B) across four question-answering datasets. The analysis contrasts two anchoring methods: "Q-Anchored" (solid lines) and "A-Anchored" (dashed lines). ### Components/Axes * **Chart Titles:** * Left Chart: `Llama-3.2-1B` * Right Chart: `Llama-3.2-3B` * **X-Axis (Both Charts):** Label: `Layer`. Represents the layer number within the neural network model. * Left Chart Scale: 0 to 15, with major ticks at 0, 5, 10, 15. * Right Chart Scale: 0 to 25, with major ticks at 0, 5, 10, 15, 20, 25. * **Y-Axis (Both Charts):** Label: `ΔP`. Represents the change in probability. The scale is negative, indicating a decrease. * Left Chart Scale: 0 to -80, with major ticks at 0, -20, -40, -60. * Right Chart Scale: 0 to -80, with major ticks at 0, -20, -40, -60, -80. * **Legend (Bottom Center, spanning both charts):** Contains 8 entries, differentiating by line style (solid/dashed) and color. * **Q-Anchored (Solid Lines):** * Blue: `Q-Anchored (PopQA)` * Green: `Q-Anchored (TriviaQA)` * Purple: `Q-Anchored (HotpotQA)` * Pink: `Q-Anchored (NQ)` * **A-Anchored (Dashed Lines):** * Orange: `A-Anchored (PopQA)` * Red: `A-Anchored (TriviaQA)` * Gray: `A-Anchored (HotpotQA)` * Brown: `A-Anchored (NQ)` ### Detailed Analysis **Left Chart (Llama-3.2-1B):** * **A-Anchored Series (Dashed Lines):** All four dashed lines (Orange, Red, Gray, Brown) remain clustered tightly near the top of the chart, fluctuating between approximately ΔP = 0 and ΔP = -10 across all layers (0-15). They show minimal downward trend. * **Q-Anchored Series (Solid Lines):** All four solid lines show a pronounced downward trend. * **General Trend:** They start near ΔP = 0 at Layer 0, drop steeply until approximately Layer 7-8, then continue a more gradual decline with some fluctuations, ending between ΔP = -60 and -70 at Layer 15. * **Specific Series (Approximate End Values at Layer 15):** * Blue (PopQA): ~ -65 * Green (TriviaQA): ~ -60 * Purple (HotpotQA): ~ -68 * Pink (NQ): ~ -62 **Right Chart (Llama-3.2-3B):** * **A-Anchored Series (Dashed Lines):** Similar to the 1B model, the dashed lines remain near the top, fluctuating between ΔP = 0 and ΔP = -10 across layers 0-25. * **Q-Anchored Series (Solid Lines):** The downward trend is even more pronounced and extends over more layers. * **General Trend:** A steep decline from Layer 0 to approximately Layer 10, followed by a plateau or slower decline with notable fluctuations between Layers 10-20, and a final drop towards Layer 25. * **Specific Series (Approximate End Values at Layer 25):** * Blue (PopQA): ~ -75 * Green (TriviaQA): ~ -70 * Purple (HotpotQA): ~ -78 * Pink (NQ): ~ -72 ### Key Observations 1. **Fundamental Dichotomy:** There is a stark and consistent separation between the behavior of Q-Anchored (solid) and A-Anchored (dashed) methods across both models and all datasets. A-Anchoring results in near-zero ΔP, while Q-Anchoring leads to significant negative ΔP. 2. **Model Size Effect:** The Llama-3.2-3B model (right chart) shows a more extended and slightly deeper decline for Q-Anchored series compared to the 1B model, correlating with its greater number of layers. 3. **Dataset Consistency:** The relative ordering and shape of the Q-Anchored lines are remarkably consistent across datasets within each model. For example, the Purple line (HotpotQA) is consistently among the lowest, while the Pink line (NQ) is often among the highest of the solid lines. 4. **Mid-Layer Fluctuations:** Both models exhibit non-monotonic behavior in the Q-Anchored series, with noticeable "bumps" or temporary recoveries in ΔP around Layers 10-14 (1B) and Layers 12-18 (3B). ### Interpretation This visualization demonstrates a core finding about the internal mechanics of these language models during a specific task (likely related to question answering or knowledge recall). The **ΔP** metric likely measures how much the model's probability assignment to a target answer changes as information is processed through its layers. * **Anchoring Effect:** The "A-Anchored" condition (dashed lines) appears to provide a stable reference point that prevents significant probability drift, keeping ΔP near zero. In contrast, the "Q-Anchored" condition (solid lines) leads to a progressive and substantial decrease in probability as the signal propagates through the network. This suggests the model's internal representation or confidence in the answer is being systematically altered when anchored to the question versus the answer itself. * **Layer-wise Processing:** The steep initial drop in Q-Anchored ΔP indicates that the most significant transformations occur in the early-to-mid layers. The fluctuations in deeper layers suggest complex, non-linear processing where the model may be integrating information or resolving conflicts, leading to temporary reversals in the probability trend. * **Scalability:** The pattern holds across model sizes (1B vs. 3B parameters), indicating this is a fundamental characteristic of the model architecture or training, not an artifact of scale. The deeper model simply extends the process over more layers. * **Robustness Across Domains:** The consistency across four distinct QA datasets (PopQA, TriviaQA, HotpotQA, NQ) implies this anchoring phenomenon is a general property of the model's operation, not specific to a single type of knowledge or question format. In essence, the charts provide empirical evidence that the choice of anchoring point (question vs. answer) fundamentally dictates the trajectory of probability change through a transformer's layers, with Q-Anchoring inducing a strong, consistent decay in ΔP.