\n ## Bar Chart: Ratio of Content Words to Function Words (R1-Llama | AIME25) ### Overview This is a horizontal bar chart displaying the ratio (in percentage) of content words to function words across different percentile ranges. The chart is titled "R1-Llama | AIME25". The x-axis represents the ratio in percentage, ranging from 0 to 100. The y-axis represents percentile ranges, from "Top 10%" to "90-100%". Two data series are presented: "Content Words" (represented by dark red bars) and "Function Words" (represented by light gray bars). ### Components/Axes * **Title:** R1-Llama | AIME25 (top-center) * **X-axis Label:** Ratio (%) (bottom-center) * **Y-axis:** Percentile Ranges (left side) * Top 10% * 10-20% * 20-30% * 30-40% * 40-50% * 50-60% * 60-70% * 70-80% * 80-90% * 90-100% * **Legend:** (top-right) * Content Words (dark red) * Function Words (light gray) ### Detailed Analysis The chart shows the percentage of content words for each percentile range. The function word percentage is implicitly represented by the remaining portion of each bar. Here's a breakdown of the data points: * **Top 10%:** Content Words: 44.3% * **10-20%:** Content Words: 39.3% * **20-30%:** Content Words: 35.5% * **30-40%:** Content Words: 32.6% * **40-50%:** Content Words: 31.5% * **50-60%:** Content Words: 30.0% * **60-70%:** Content Words: 30.1% * **70-80%:** Content Words: 30.7% * **80-90%:** Content Words: 29.6% * **90-100%:** Content Words: 29.3% The function word percentages can be calculated by subtracting the content word percentage from 100%. For example: * **Top 10%:** Function Words: 100% - 44.3% = 55.7% * **10-20%:** Function Words: 100% - 39.3% = 60.7% * **20-30%:** Function Words: 100% - 35.5% = 64.5% * **30-40%:** Function Words: 100% - 32.6% = 67.4% * **40-50%:** Function Words: 100% - 31.5% = 68.5% * **50-60%:** Function Words: 100% - 30.0% = 70.0% * **60-70%:** Function Words: 100% - 30.1% = 69.9% * **70-80%:** Function Words: 100% - 30.7% = 69.3% * **80-90%:** Function Words: 100% - 29.6% = 70.4% * **90-100%:** Function Words: 100% - 29.3% = 70.7% The content word percentage decreases as the percentile range increases, while the function word percentage increases. ### Key Observations * The highest proportion of content words is found in the "Top 10%" range (44.3%). * The lowest proportion of content words is found in the "90-100%" range (29.3%). * The function word percentage is consistently higher than the content word percentage across all percentile ranges. * The difference between content and function word percentages is smallest in the "Top 10%" range and largest in the "90-100%" range. ### Interpretation The data suggests that the most important or frequently used words (those in the top 10%) are more likely to be content words, while less frequent words (those in the 90-100% range) are more likely to be function words. This is expected, as content words carry the primary meaning of a text, while function words serve grammatical purposes. The increasing proportion of function words as we move down the percentile ranks indicates that the less frequent words are primarily those that provide structure and connection rather than core meaning. This chart provides insight into the lexical distribution within the R1-Llama model, specifically as measured by the AIME25 metric. The trend suggests that the model prioritizes and utilizes content words more heavily in its most frequent vocabulary.