## Line Chart: Separation between true and false statements across layers ### Overview The image is a line chart that displays the separation between true and false statements across different layers. The y-axis represents the ratio of "Between class variance / within-class variance", and the x-axis represents the "Layer" number. Four different data series are plotted, each representing a different category: "cities", "neg_cities", "sp_en_trans", and "neg_sp_en_trans". The chart shows how the separation between true and false statements changes as the layer number increases for each category. ### Components/Axes * **Title:** "Separation between true and false statements across layers" * **X-axis:** * Label: "Layer" * Scale: 0 to 25 in increments of 5. * **Y-axis:** * Label: "Between class variance / within-class variance" * Scale: 0.0 to 0.8 in increments of 0.2. * **Legend:** Located in the top-left corner of the chart. * "cities" - Teal line * "neg\_cities" - Orange line * "sp\_en\_trans" - Green line * "neg\_sp\_en\_trans" - Brown line ### Detailed Analysis * **Cities (Teal):** The "cities" line starts at approximately 0 at layer 0, increases to approximately 0.2 at layer 8, peaks at approximately 0.8 at layer 15, and then decreases to approximately 0.35 at layer 25. * **neg\_cities (Orange):** The "neg\_cities" line starts at approximately 0 at layer 0, increases to approximately 0.75 at layer 13, peaks at approximately 0.75 at layer 15, and then decreases to approximately 0.35 at layer 25. * **sp\_en\_trans (Green):** The "sp\_en\_trans" line starts at approximately 0 at layer 0, increases to approximately 0.38 at layer 13, and then decreases to approximately 0.13 at layer 25. * **neg\_sp\_en\_trans (Brown):** The "neg\_sp\_en\_trans" line starts at approximately 0 at layer 0, increases to approximately 0.55 at layer 14, and then decreases to approximately 0.3 at layer 25. ### Key Observations * The "cities" and "neg\_cities" categories show a similar trend, with a peak around layer 15 and a subsequent decrease. * The "sp\_en\_trans" category has the lowest separation between true and false statements across all layers. * All categories start with a separation of approximately 0 at layer 0. * The "neg\_sp\_en\_trans" category peaks earlier than "cities" and "neg_cities". ### Interpretation The chart suggests that the separation between true and false statements varies across different layers and categories. The "cities" and "neg\_cities" categories exhibit a higher degree of separation compared to "sp\_en\_trans" and "neg\_sp\_en\_trans". The peak separation around layer 15 for "cities" and "neg\_cities" might indicate that this layer is particularly effective at distinguishing between true and false statements for these categories. The lower separation for "sp\_en\_trans" suggests that this category might be more challenging to differentiate between true and false statements. The initial separation of 0 at layer 0 for all categories indicates that the model initially struggles to distinguish between true and false statements, and the separation improves as the layer number increases, up to a certain point.

\n ## Line Chart: Separation between true and false statements across layers ### Overview This line chart visualizes the separation between true and false statements across different layers, likely within a neural network or similar layered system. The y-axis represents the ratio of between-class variance to within-class variance, indicating how well the layers separate true and false statements. The x-axis represents the layer number. Four different data series are plotted, each representing a different condition or dataset. ### Components/Axes * **Title:** "Separation between true and false statements across layers" (centered at the top) * **X-axis Label:** "Layer" (bottom-center) * Scale: 0 to 28, with tick marks at integer values. * **Y-axis Label:** "Between class variance / within-class variance" (left-center) * Scale: 0 to 0.85, with tick marks at 0.2 intervals. * **Legend:** Located in the top-right corner. * "cities" - Blue line * "neg\_cities" - Orange line * "sp\_en\_trans" - Green line * "neg\_sp\_en\_trans" - Red line ### Detailed Analysis The chart displays four lines representing the separation ratio across layers. * **cities (Blue Line):** This line starts at approximately 0 at layer 0, increases steadily to a peak of approximately 0.35 at layer 11, then declines gradually to approximately 0.25 at layer 27. * **neg\_cities (Orange Line):** This line also starts at approximately 0 at layer 0. It rises more sharply than the "cities" line, reaching a peak of approximately 0.75 at layer 12, then drops rapidly to approximately 0.3 at layer 27. * **sp\_en\_trans (Green Line):** This line begins at approximately 0 at layer 0, increases slowly to a peak of approximately 0.25 at layer 10, and then decreases to approximately 0.1 at layer 27. * **neg\_sp\_en\_trans (Red Line):** This line starts at approximately 0 at layer 0, increases rapidly to a peak of approximately 0.55 at layer 14, remains relatively stable until layer 18, and then declines to approximately 0.3 at layer 27. ### Key Observations * The "neg\_cities" (orange) line consistently exhibits the highest separation ratio across most layers, indicating the strongest separation between true and false statements for this condition. * All lines show an initial increase in separation ratio, suggesting that the early layers contribute to distinguishing between true and false statements. * The "cities" (blue) and "sp\_en\_trans" (green) lines have lower separation ratios compared to the "neg\_cities" and "neg\_sp\_en\_trans" lines. * The peak separation ratio occurs at different layers for each condition, suggesting that the optimal layer for separation varies depending on the dataset. * All lines show a decline in separation ratio in the later layers (beyond layer 18), indicating that the separation between true and false statements may diminish as the data progresses through deeper layers. ### Interpretation The chart suggests that the negative examples ("neg\_cities" and "neg\_sp\_en\_trans") are more easily separated from the true statements than the positive examples ("cities" and "sp\_en\_trans"). This could indicate that the model is better at identifying falsehoods than truths, or that the negative examples are inherently more distinguishable. The initial increase in separation ratio across all lines suggests that the early layers of the model are effective at learning basic features that differentiate between true and false statements. The subsequent decline in separation ratio in the later layers could be due to overfitting, loss of signal, or the emergence of more complex relationships that are harder to disentangle. The different peak separation layers for each condition suggest that the model learns different representations for each dataset, and that the optimal layer for separation depends on the specific characteristics of the data. Further investigation would be needed to understand the underlying reasons for these observations and to optimize the model for better separation performance.

## Line Chart: Separation between true and false statements across layers ### Overview This is a line chart illustrating how the ratio of between-class variance to within-class variance changes across different layers of a model (likely a neural network) for four distinct categories. The chart aims to show how well the model's internal representations separate true from false statements at each layer, with a higher ratio indicating better separation. ### Components/Axes * **Chart Title:** "Separation between true and false statements across layers" * **X-Axis:** * **Label:** "Layer" * **Scale:** Linear, ranging from 0 to 25. * **Major Tick Marks:** 0, 5, 10, 15, 20, 25. * **Y-Axis:** * **Label:** "Between class variance / within-class variance" * **Scale:** Linear, ranging from 0.0 to 0.8. * **Major Tick Marks:** 0.0, 0.2, 0.4, 0.6, 0.8. * **Legend:** Located in the top-left quadrant of the plot area. It contains four entries, each with a colored line sample and a text label: * **Blue Line:** `cities` * **Orange Line:** `neg_cities` * **Green Line:** `sp_en_trans` * **Red Line:** `neg_sp_en_trans` ### Detailed Analysis The chart plots four data series, each representing a different category or condition. The general trend for all series is an initial increase, reaching a peak, followed by a decline as the layer number increases. **1. `cities` (Blue Line)** * **Trend:** Starts near zero, rises sharply to a peak, then declines steadily. * **Data Points (Approximate):** * Layer 0-3: ~0.0 * Layer 5: ~0.05 * Layer 10: ~0.35 * **Peak:** Layer 13, value ~0.85 (the highest point on the entire chart). * Layer 15: ~0.80 * Layer 20: ~0.50 * Layer 25: ~0.35 **2. `neg_cities` (Orange Line)** * **Trend:** Follows a very similar trajectory to `cities`, rising to a slightly lower peak and declining. * **Data Points (Approximate):** * Layer 0-3: ~0.0 * Layer 5: ~0.05 * Layer 10: ~0.30 * **Peak:** Layer 14, value ~0.75. * Layer 15: ~0.74 * Layer 20: ~0.50 * Layer 25: ~0.34 **3. `sp_en_trans` (Green Line)** * **Trend:** Rises to a much lower peak than the first two series and declines to a lower final value. * **Data Points (Approximate):** * Layer 0-3: ~0.0 * Layer 5: ~0.02 * Layer 10: ~0.20 * **Peak:** Layer 13, value ~0.38. * Layer 15: ~0.25 * Layer 20: ~0.15 * Layer 25: ~0.14 **4. `neg_sp_en_trans` (Red Line)** * **Trend:** Rises to a peak between the `cities` group and `sp_en_trans`, then declines. * **Data Points (Approximate):** * Layer 0-3: ~0.0 * Layer 5: ~0.03 * Layer 10: ~0.28 * **Peak:** Layer 13, value ~0.55. * Layer 15: ~0.52 * Layer 20: ~0.35 * Layer 25: ~0.28 ### Key Observations 1. **Peak Separation Layer:** All four categories achieve their maximum separation ratio between layers 13 and 14. This suggests a critical processing stage in the model's hierarchy. 2. **Magnitude of Separation:** There is a clear hierarchy in separation strength: * `cities` and `neg_cities` show the strongest separation (peak > 0.75). * `neg_sp_en_trans` shows moderate separation (peak ~0.55). * `sp_en_trans` shows the weakest separation (peak < 0.40). 3. **Convergence at Extremes:** At the earliest layers (0-3) and the final layers (25), the separation ratios for all categories are relatively low and closer together, indicating less differentiation in the raw input and final output representations. 4. **Parallel Trends:** The `cities` and `neg_cities` lines are nearly parallel, as are the `sp_en_trans` and `neg_sp_en_trans` lines, suggesting the "neg" (negation) condition affects similar tasks in a consistent way. ### Interpretation This chart visualizes the internal "reasoning" process of a model as it processes statements about cities and Spanish-English translations (`sp_en_trans`), both in their affirmative and negated forms. * **What the data suggests:** The model develops its strongest internal distinctions between true and false statements in its middle layers (around layer 13). This is where the representations are most specialized for the verification task. The distinction is not present in the raw input (early layers) and becomes less pronounced as the information is transformed into a final output format (later layers). * **How elements relate:** The close pairing of `cities`/`neg_cities` and `sp_en_trans`/`neg_sp_en_trans` indicates that the model handles negation within a given domain (cities or translation) in a structurally similar way. The large gap between the `cities` group and the `sp_en_trans` group suggests the model finds it fundamentally easier to separate true/false for factual knowledge about cities than for translation-based statements. This could be due to the nature of the training data or the complexity of the tasks. * **Notable anomalies:** The most striking feature is the significant performance gap between the two task types (`cities` vs. `sp_en_trans`). This implies the model's capability for logical separation is highly domain-dependent. The fact that negation (`neg_`) does not drastically alter the shape of the curve, only its magnitude, suggests negation is processed as a modification of the core factual representation rather than a completely different logical operation.

## Line Chart: Separation between true and false statements across layers ### Overview The chart visualizes the relationship between between-class variance and within-class variance across 25 layers for four distinct data categories. Four colored lines represent different classifications, showing how their separation metrics evolve through the layers. ### Components/Axes - **Title**: "Separation between true and false statements across layers" - **Y-axis**: "Between class variance / within-class variance" (range: 0.0 to 0.8) - **X-axis**: "Layer" (integer values from 0 to 25) - **Legend**: Located in top-left corner with four entries: - Blue: cities - Orange: neg_cities - Green: sp_en_trans - Red: neg_sp_en_trans ### Detailed Analysis 1. **Cities (Blue Line)**: - Starts near 0.0 at layer 0 - Rises sharply to peak at ~0.8 between layers 10-12 - Declines gradually to ~0.35 by layer 25 2. **Neg_cities (Orange Line)**: - Begins at 0.0, rises steeply - Peaks at ~0.75 around layer 10 - Declines to ~0.3 by layer 25 3. **Sp_en_trans (Green Line)**: - Starts at 0.0, rises gradually - Peaks at ~0.35 around layer 12 - Declines to ~0.15 by layer 25 4. **Neg_sp_en_trans (Red Line)**: - Begins at 0.0, rises steadily - Peaks at ~0.5 around layer 10 - Declines to ~0.3 by layer 25 ### Key Observations - All lines show a similar pattern: initial growth, peak between layers 10-12, then gradual decline - Cities (blue) and neg_cities (orange) exhibit the highest variance separation - sp_en_trans (green) shows the lowest peak variance - neg_sp_en_trans (red) demonstrates intermediate behavior - All metrics drop below 0.4 after layer 15 ### Interpretation The data suggests that layers 10-12 represent optimal separation between true/false statements across all categories, with cities and neg_cities showing the strongest distinction. The subsequent decline indicates diminishing effectiveness of layer-based separation. The green line's lower peak suggests sp_en_trans has inherently weaker class separation compared to other categories. The parallel trends across all lines imply a shared architectural limitation in maintaining separation beyond layer 12, potentially indicating overfitting or diminishing returns in model complexity.