## [Heatmap]: Token Flip Rate by Position Bucket ### Overview The image is a heatmap (grid of colored cells) visualizing the **flip rate** (a measure of state change frequency) for various tokens (words) across 10 position buckets (0–9). The y-axis lists tokens, the x-axis lists position buckets, and a color bar (right) maps color to flip rate (0.0 = dark purple, 1.0 = yellow). ### Components/Axes - **Y-axis (Token)**: Vertical list of tokens (words) from top to bottom: `sadly, depressing, gloomy, nervous, mourn, despair, depress, dread, nightmare, bored, worry, dull, lost, heart, sick, dark, 12, leave, sad, ever, depression, sadness, crying, couldn’t, shy, broken, where, unhappy, wish, mood, cry, again, week, stayed, left, life, nno, old, feeling, anxiety` - **X-axis (Position Bucket)**: Horizontal axis with labels `0, 1, 2, 3, 4, 5, 6, 7, 8, 9` (10 buckets total). - **Color Bar (Flip Rate)**: Right-side vertical bar with a gradient from **dark purple (0.0)** to **yellow (1.0)**, labeled "flip rate". This encodes the flip rate for each (token, position bucket) cell. ### Detailed Analysis (Flip Rate by Token & Position) Each cell’s color indicates the flip rate (approximate values from color): | Token | Position Bucket 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |-------------|-------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----| | `sadly` | 1.0 (yellow) | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | `depressing`| 1.0 | 0.6 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | `gloomy` | 1.0 | 0.6 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | `nervous` | 0.0 (dark purple) | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 0.6 | | `mourn` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `despair` | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | `depress` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.6 | 0.8 | 1.0 | 1.0 | 1.0 | | `dread` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `nightmare` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.6 | 0.8 | 1.0 | 0.8 | | `bored` | 1.0 | 0.0 | 0.0 | 1.0 | 0.6 | 1.0 | 0.0 | 0.0 | 1.0 | 1.0 | | `worry` | 0.0 | 0.6 | 0.0 | 0.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | | `dull` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 0.6 | 0.0 | | `lost` | 1.0 | 0.8 | 0.8 | 0.0 | 1.0 | 0.8 | 0.6 | 0.8 | 1.0 | 0.8 | | `heart` | 1.0 | 0.6 | 0.6 | 0.6 | 1.0 | 0.6 | 0.6 | 1.0 | 1.0 | 0.0 | | `sick` | 0.0 | 0.0 | 0.6 | 0.6 | 0.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `dark` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `12` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 0.0 | 0.0 | | `leave` | 1.0 | 0.0 | 0.0 | 1.0 | 0.8 | 0.8 | 1.0 | 0.0 | 0.0 | 1.0 | | `sad` | 0.6 | 0.8 | 0.8 | 1.0 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | | `ever` | 0.0 | 0.6 | 0.6 | 1.0 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.0 | | `depression`| 1.0 | 0.8 | 0.8 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | | `sadness` | 0.0 | 0.8 | 0.8 | 0.0 | 1.0 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | | `crying` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | | `couldn’t` | 0.0 | 0.6 | 0.6 | 0.0 | 0.0 | 0.6 | 0.6 | 0.0 | 0.0 | 1.0 | | `shy` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | | `broken` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | | `where` | 0.0 | 0.6 | 0.6 | 0.8 | 0.8 | 0.6 | 0.6 | 0.8 | 0.0 | 0.0 | | `unhappy` | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.6 | 0.6 | 0.8 | 0.8 | 1.0 | | `wish` | 0.8 | 0.6 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | | `mood` | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | | `cry` | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.6 | 0.0 | 0.0 | 0.0 | | `again` | 0.0 | 0.6 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `week` | 0.0 | 0.6 | 0.6 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | | `stayed` | 0.0 | 0.6 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `left` | 0.0 | 0.6 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 1.0 | 1.0 | 0.0 | | `life` | 0.8 | 0.6 | 0.6 | 0.6 | 0.0 | 0.8 | 0.8 | 0.8 | 0.8 | 0.6 | | `nno` | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 0.0 | 0.0 | | `old` | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | | `feeling` | 0.0 | 0.8 | 0.8 | 0.6 | 0.6 | 0.6 | 0.8 | 0.8 | 0.8 | 0.6 | | `anxiety` | 0.0 | 0.8 | 0.8 | 0.6 | 0.6 | 0.6 | 0.8 | 0.8 | 0.8 | 0.6 | ### Key Observations - **High Flip Rate (Yellow)**: Tokens like `sadly`, `despair`, `sad`, `depression`, `sadness`, `life`, `feeling`, `anxiety` have dominant yellow cells (flip rate ~1.0) across most position buckets. - **Low Flip Rate (Dark Purple)**: Tokens like `mood`, `cry`, `broken`, `shy`, `crying` have frequent dark purple cells (flip rate ~0.0) in some buckets. - **Mixed Flip Rates (Teal/Green)**: Tokens like `lost`, `heart`, `ever`, `where`, `unhappy` show a mix of teal (0.6) and green (0.8) cells, indicating moderate flip rates. - **Position Bucket Patterns**: Buckets 0–2 often have more dark purple (low flip rate) for tokens like `nervous`, `mourn`, `dread`, while buckets 3–9 have more yellow (high flip rate) for many tokens. ### Interpretation This heatmap likely models **token flip rate** (state change frequency) across position buckets (e.g., word positions in a text sequence). Tokens related to negative emotions (sadness, depression, anxiety) have higher flip rates (more yellow), suggesting they are more dynamic or context-dependent. Tokens with lower flip rates (dark purple) may be more stable or less context-sensitive. The position buckets could represent sequential positions (e.g., in a sentence), showing how flip rate varies with position for each token—useful for natural language processing to understand token behavior across contexts.