## Line Chart: Math Problem Accuracy by Model ### Overview This line chart compares the accuracy of four different language models – InternLM2-Math-7B, InternLM2-7B, MAmmoTH-13B, and WizardMath-13B – across a range of math problem categories. The x-axis represents the math problem category, and the y-axis represents the accuracy score (ranging from 0 to 100). ### Components/Axes * **X-axis Title:** Math Problem Category * **Y-axis Title:** Accuracy * **Legend:** Located at the top-left corner of the chart. * InternLM2-Math-7B (Blue Line) * InternLM2-7B (Green Line) * MAmmoTH-13B (Orange Line) * WizardMath-13B (Red Line) * **Math Problem Categories (X-axis labels):** Arithmetic, Addition & subtraction, Complex continued fraction, Complete the equation, Combining paths, Domain & range of functions, Distance between two points, Distance & segment lengths, Exponents & scientific notation, Fractions & mixed numbers, Geometry, Linear equations, Linear inequalities, Logarithms, Make fractions, More fractions, One-variable absolute value, One-variable equations, One-variable inequalities, Permutation & combinations, Probability of compound events, Probability of simple events, Proportional relationships, Quadratic equations, Rational & irrational numbers, Square roots & cube roots, Systems & inequalities, Two-variable absolute value, Two-variable equations, Two-variable inequalities, Center & dependent variables, Mean, median, opposite, Pie charts, Ratio & proportions, Transformations, Variable expressions. ### Detailed Analysis The chart displays accuracy scores for each model across each math problem category. The following details are extracted, noting approximate values due to the chart's resolution: * **InternLM2-Math-7B (Blue):** * Starts around 60% accuracy for "Arithmetic". * Fluctuates between approximately 50% and 85% across the categories. * Peaks around 85% for "One-variable equations". * Dips to around 50% for "Systems & inequalities". * Ends around 70% for "Variable expressions". * **InternLM2-7B (Green):** * Starts around 20% accuracy for "Arithmetic". * Generally remains below 40% accuracy throughout most categories. * Shows a slight increase to around 40% for "One-variable equations". * Remains consistently low, ending around 30% for "Variable expressions". * **MAmmoTH-13B (Orange):** * Starts around 60% accuracy for "Arithmetic". * Shows a relatively stable performance between 50% and 70% for most categories. * Peaks around 75% for "One-variable equations". * Dips to around 50% for "Systems & inequalities". * Ends around 65% for "Variable expressions". * **WizardMath-13B (Red):** * Starts around 70% accuracy for "Arithmetic". * Demonstrates the highest overall accuracy, frequently exceeding 80%. * Peaks around 90% for "One-variable equations". * Experiences a dip to around 60% for "Systems & inequalities". * Ends around 80% for "Variable expressions". ### Key Observations * WizardMath-13B consistently outperforms the other models across all categories. * InternLM2-7B exhibits the lowest accuracy scores, significantly underperforming the other models. * InternLM2-Math-7B and MAmmoTH-13B show comparable performance, with moderate accuracy scores. * All models show a dip in accuracy for "Systems & inequalities". * "One-variable equations" appears to be the category where all models achieve their highest accuracy. ### Interpretation The data suggests that model size and specialized training (as seen in WizardMath-13B and InternLM2-Math-7B) significantly impact performance on math problems. WizardMath-13B's consistently high accuracy indicates a strong capability in mathematical reasoning. The lower performance of InternLM2-7B suggests that a larger model size alone is not sufficient for achieving high accuracy; specialized training on mathematical datasets is crucial. The dip in accuracy for "Systems & inequalities" across all models may indicate that this category presents a particularly challenging type of problem, requiring more advanced reasoning skills. The peak accuracy for "One-variable equations" suggests that this type of problem is relatively easier for these models to solve. The chart provides a comparative analysis of the models' strengths and weaknesses, highlighting the importance of both model size and specialized training in achieving high accuracy on math problems.