## Scatter Plot: Attention Output with and without Meaningless Tokens ### Overview The image is a scatter plot visualizing the attention output of a model, comparing scenarios with and without meaningless tokens. The plot shows the distribution of data points, their displacement, and the boundaries of sets. ### Components/Axes * **Data Points:** * Light Blue "x": `Attn_output w/o meaningless tokens` * Light Red "x": `Attn_output w/ meaningless tokens` * **Displacement Arrows:** Blue arrows indicating the displacement from a light blue "x" to a light red "x". * **Set Boundaries:** * Dotted Light Blue Line: `Attn_output set w/o meaningless tokens` (forms a circle) * Solid Light Red Line: `Attn_output set w/ meaningless tokens` (forms an oval) * **Grid:** The background has a faint grid for visual reference. ### Detailed Analysis * **Attn_output w/o meaningless tokens (Light Blue "x"):** These points are concentrated more towards the lower-left quadrant of the plot, with a higher density inside the dotted light blue circle. * **Attn_output w/ meaningless tokens (Light Red "x"):** These points are more dispersed across the plot, with a higher concentration outside the dotted light blue circle and along the solid light red oval. * **Displacement Arrows (Blue):** The arrows generally point from the lower-left towards the upper-right, indicating a shift in attention output when meaningless tokens are included. * **Attn_output set w/o meaningless tokens (Dotted Light Blue Circle):** This circle encompasses a significant portion of the light blue "x" data points, suggesting that the attention output without meaningless tokens is more constrained within this region. The approximate center of the circle is near the center-left of the plot. * **Attn_output set w/ meaningless tokens (Solid Light Red Oval):** This oval encloses a larger area than the circle and appears to capture the spread of the light red "x" data points. The oval extends from the lower-left to the upper-right of the plot. ### Key Observations * The inclusion of meaningless tokens leads to a wider distribution of attention outputs. * The displacement arrows indicate a systematic shift in attention when meaningless tokens are present. * The sets defined by the circle and oval visually separate the two conditions (with and without meaningless tokens). ### Interpretation The plot suggests that meaningless tokens significantly alter the attention output of the model. The shift in data point distribution, as visualized by the displacement arrows and the different set boundaries, indicates that the model's attention mechanism is affected by the presence of these tokens. The concentration of light blue "x" points within the dotted light blue circle suggests that removing meaningless tokens leads to a more focused and constrained attention output. The light red oval shows the boundary of the attention output when meaningless tokens are included, which is more dispersed.

## Scatter Plot: Attention Output Displacement ### Overview This image presents a scatter plot comparing the attention output with and without meaningless tokens. The plot visualizes the displacement between these two outputs, indicated by arrows connecting corresponding points. Two curved lines approximate the general trend of each data set. ### Components/Axes * **X-axis:** The x-axis is not explicitly labeled, but represents a numerical value ranging approximately from 0 to 10. The scale is linear with markers at integer values. * **Y-axis:** The y-axis is also not explicitly labeled, but represents a numerical value ranging approximately from 0 to 6. The scale is linear with markers at integer values. * **Legend:** Located in the top-left corner, the legend defines the following: * Blue 'x' markers: "Attn\_output w/o meaningless tokens" * Red 'x' markers: "Attn\_output w/ meaningless tokens" * Blue dashed arrows: "Displacement from x to x" * Blue dotted line: "Attn\_output set w/o meaningless tokens" * Red solid line: "Attn\_output set w/ meaningless tokens" ### Detailed Analysis The plot contains two sets of scattered data points, one in blue and one in red. Each point represents an attention output value. Arrows connect corresponding points in the two sets, illustrating the displacement caused by the inclusion of meaningless tokens. Two curved lines approximate the trend of each data set. **Blue Data (w/o meaningless tokens):** The blue data points (Attn\_output w/o meaningless tokens) generally follow an upward trend, starting from approximately (0.5, 0.5) and reaching approximately (9.5, 5.5). The blue dotted line (Attn\_output set w/o meaningless tokens) provides a smoothed representation of this trend. * Approximate data points (x, y): (0.5, 0.5), (1.5, 1.0), (2.5, 1.5), (3.5, 2.0), (4.5, 2.5), (5.5, 3.0), (6.5, 3.5), (7.5, 4.0), (8.5, 4.5), (9.5, 5.5). **Red Data (w/ meaningless tokens):** The red data points (Attn\_output w/ meaningless tokens) also exhibit an upward trend, but are generally shifted to the right and slightly above the blue data. The red solid line (Attn\_output set w/ meaningless tokens) represents this trend. * Approximate data points (x, y): (1.0, 1.0), (2.0, 1.5), (3.0, 2.5), (4.0, 3.0), (5.0, 3.5), (6.0, 4.0), (7.0, 4.5), (8.0, 5.0), (9.0, 5.5), (10.0, 6.0). **Displacement Arrows:** The blue dashed arrows indicate the direction and magnitude of the displacement between corresponding blue and red points. The arrows generally point upwards and to the right, indicating that the inclusion of meaningless tokens increases both the x and y values of the attention output. Two large, roughly elliptical shapes are drawn around the data. One encompasses the blue data, and the other the red data. ### Key Observations * The inclusion of meaningless tokens consistently shifts the attention output to higher values. * The displacement is not uniform; the magnitude of the shift varies across the range of x-values. * The trend lines suggest a roughly linear relationship between the attention output and the presence/absence of meaningless tokens. * The elliptical shapes highlight the overall distribution and spread of the data for each condition. ### Interpretation The plot demonstrates the impact of meaningless tokens on attention output. The consistent upward and rightward displacement suggests that these tokens introduce a bias, inflating the attention scores. This could be problematic in applications where accurate attention weights are crucial, as it might lead to the model focusing on irrelevant information. The trend lines provide a visual summary of this effect, while the individual data points and displacement arrows reveal the variability in the impact of meaningless tokens. The elliptical shapes suggest that the data is somewhat clustered, but also exhibits some degree of spread, indicating that the effect of meaningless tokens is not entirely consistent. The visualization strongly suggests that removing meaningless tokens is beneficial for obtaining more accurate and reliable attention outputs.

## Scatter Plot: Effect of Meaningless Tokens on Attention Output Distribution ### Overview The image is a scatter plot visualizing the distribution of attention output vectors in a two-dimensional space. It compares two conditions: attention outputs without meaningless tokens (blue 'x' markers) and attention outputs with meaningless tokens (red 'x' markers). The plot includes displacement vectors showing the shift for specific points and ellipses representing the overall set distributions for each condition. ### Components/Axes * **Legend (Top-Left Corner):** * `Attn_output w/o meaningless tokens`: Blue 'x' marker. * `Attn_output w/ meaningless tokens`: Red 'x' marker. * `Displacement from ✕ to ✕`: Blue arrow (from a blue 'x' to a red 'x'). * `Attn_output set w/o meaningless tokens`: Blue dotted ellipse. * `Attn_output set w/ meaningless tokens`: Red solid ellipse. * **Axes:** The plot has a grid background but **no labeled X or Y axes**. The axes represent an abstract, two-dimensional projection of the attention output vectors. No numerical scales or units are provided. * **Data Series:** 1. **Blue 'x' Series:** Approximately 30-40 data points representing attention outputs without meaningless tokens. They are clustered primarily in the lower-left to central region of the plot. 2. **Red 'x' Series:** Approximately 30-40 data points representing attention outputs with meaningless tokens. They are more dispersed and shifted towards the upper-right relative to the blue cluster. * **Annotations:** * **Displacement Arrows:** Five distinct blue arrows originate from specific blue 'x' points and point towards corresponding red 'x' points. They indicate the direction and magnitude of shift for individual data points when meaningless tokens are introduced. * **Distribution Ellipses:** * A **blue dotted ellipse** encircles the main cluster of blue 'x' points. It is oriented diagonally from lower-left to upper-right. * A **red solid ellipse** encircles the main cluster of red 'x' points. It is larger, more circular, and positioned further to the upper-right compared to the blue ellipse. ### Detailed Analysis * **Data Point Distribution:** * The **blue 'x' points (w/o meaningless tokens)** form a relatively tight, elongated cluster. The densest region is near the center-left of the plot. * The **red 'x' points (w/ meaningless tokens)** are more scattered. While some overlap with the blue cluster, a significant number are displaced towards the top and right edges of the plot. * **Displacement Vectors:** The five visible arrows all point from the blue cluster towards the red cluster, generally in a **north-east (upper-right) direction**. The lengths of the arrows vary, suggesting different magnitudes of shift for different data points. The longest arrow originates from the lower-left portion of the blue cluster and extends to the upper-right region. * **Set Ellipses (Spatial Grounding):** * The **blue dotted ellipse** is centered roughly in the lower-middle-left area. It encompasses the majority of the blue 'x' markers. * The **red solid ellipse** is centered further to the upper-right. Its larger area visually confirms the greater variance/spread of the red data points. The two ellipses overlap in the central region of the plot. ### Key Observations 1. **Systematic Shift:** There is a clear, systematic displacement of data points from the lower-left/central region (blue) towards the upper-right region (red) when meaningless tokens are added. 2. **Increased Dispersion:** The set of outputs with meaningless tokens (red) exhibits significantly higher variance or dispersion than the set without them (blue), as shown by the larger red ellipse and the more scattered red 'x' markers. 3. **Directional Consistency:** The displacement arrows are all oriented in a similar north-east direction, indicating a consistent directional bias in the effect of adding meaningless tokens. 4. **Overlap Region:** A subset of points, particularly in the central area of the plot, shows less displacement, resulting in an overlap between the two distributions. ### Interpretation This chart demonstrates the **destabilizing and distorting effect of meaningless tokens on a model's attention mechanism**. * **What the data suggests:** The introduction of meaningless tokens does not simply add random noise. Instead, it causes a **systematic drift** in the representation space of attention outputs (the shift to the upper-right). This could imply that the model's internal processing is being consistently biased or "pulled" in a specific direction by these tokens. * **How elements relate:** The displacement arrows provide a microscopic view of this effect on individual data points, while the ellipses offer a macroscopic view of the overall distribution change. The increased size of the red ellipse indicates that meaningless tokens make the model's outputs less consistent and more unpredictable. * **Notable implications:** In a technical context, this visualization argues that meaningless tokens are not benign. They can corrupt the semantic representation space, potentially leading to less reliable or focused model outputs. The systematic nature of the shift (rather than pure random scattering) might be particularly concerning, as it suggests a predictable form of interference. The lack of axis labels means the exact semantic meaning of the shift (e.g., towards more generic or off-topic representations) cannot be determined from the plot alone, but the directional consistency is a strong signal of a non-random effect.

## Scatter Plot: Attention Output Analysis with/without Meaningless Tokens ### Overview The image is a scatter plot comparing attention output distributions with and without meaningless tokens. Two data series (blue crosses and red crosses) are plotted on unlabeled X and Y axes. Concentric circles and trend lines contextualize the data, while displacement arrows indicate directional relationships between data points. ### Components/Axes - **Legend**: Located in the top-left corner, with four entries: - Blue crosses: "Attn_output w/o meaningless tokens" - Red crosses: "Attn_output w/ meaningless tokens" - Dotted blue line: "Attn_output set w/o meaningless tokens" - Solid red line: "Attn_output set w/ meaningless tokens" - **Axes**: - X-axis (horizontal, unlabeled) - Y-axis (vertical, unlabeled) - **Geometric Elements**: - Dotted blue circle (enclosing blue crosses) - Solid red circle (enclosing red crosses) - **Arrows**: Blue displacement vectors labeled "Displacement from x to X" ### Detailed Analysis 1. **Data Series**: - **Blue crosses** (w/o meaningless tokens): Clustered within the dotted blue circle, with a slight upward trend. - **Red crosses** (w/ meaningless tokens): Scattered outside the solid red circle, with a steeper upward trend. 2. **Trend Lines**: - Dotted blue line: Follows the central tendency of blue crosses, curving upward. - Solid red line: Traces the red crosses, showing a sharper upward trajectory. 3. **Circles**: - Dotted blue circle: Encloses ~70% of blue crosses, suggesting a boundary for "normal" outputs. - Solid red circle: Contains ~30% of red crosses, indicating a tighter cluster for outputs with meaningless tokens. 4. **Arrows**: - Blue vectors point from blue crosses to red crosses, illustrating directional displacement. ### Key Observations - **Data Separation**: Blue and red crosses occupy distinct regions, with minimal overlap. - **Trend Divergence**: Red crosses exhibit a steeper upward trend than blue crosses. - **Circular Boundaries**: The circles act as visual thresholds, with red crosses predominantly outside the red circle. - **Displacement Pattern**: Arrows suggest a systematic shift from blue to red regions. ### Interpretation The plot demonstrates that including meaningless tokens (red crosses) alters attention output distributions: 1. **Threshold Effects**: The concentric circles may represent performance or validity boundaries, with meaningless tokens pushing outputs beyond these limits. 2. **Directional Shift**: Displacement arrows imply that meaningless tokens transform outputs from a "baseline" (blue) to a "perturbed" state (red). 3. **Trend Implications**: The steeper red trend suggests meaningless tokens amplify certain features in attention outputs, potentially degrading model performance or introducing noise. The absence of axis labels limits quantitative analysis, but the visual separation and directional cues strongly indicate that meaningless tokens significantly impact attention mechanisms, warranting further investigation into their role in model behavior.