## Line Chart: Model Accuracy on Math Problems ### Overview The image is a line chart comparing the accuracy of four different language models (InternLM2-20B, Yi-34B, Qwen-72B, and GPT-3.5) on a variety of math-related tasks. The x-axis represents different math problem types, and the y-axis represents the accuracy score (percentage). ### Components/Axes * **Title:** None explicitly given in the image. * **X-axis:** Math problem types, including: * Angles * Area * Circles * Classifying & sorting * Coin names & value * Cones * Coordinate plane * Cubes * Cylinders * Decimals * Estimation & rounding * Exchanging money * Fractions * Light & heavy * Mixed operations * Multiple * Numerical exprs * Patterns * Perimeter * Place value * Polygons * Powers * Probability * Proportional * Quadrilaterals * Qwen-72B * Ratio * Rational number * Spheres * Statistics * Subtraction * Temperature * Time * Triangles * Variable exprs * Volume * Volume of 3d shapes * Add * Compare * Count * Division * Equations * Length * Percents * **Y-axis:** Accuracy (percentage), ranging from 20 to 100, with gridlines at intervals of 10. * **Legend:** Located at the top of the chart, associating colors with language models: * Blue: InternLM2-20B * Orange: Yi-34B * Green: Qwen-72B * Red: GPT-3.5 ### Detailed Analysis **InternLM2-20B (Blue):** * Trend: Generally the lowest accuracy across all problem types. * Specific Points (approximate): * Angles: ~63% * Area: ~30% * Circles: ~60% * Classifying & sorting: ~42% * Coin names & value: ~50% * Cones: ~42% * Coordinate plane: ~55% * Cubes: ~68% * Cylinders: ~67% * Decimals: ~55% * Estimation & rounding: ~32% * Exchanging money: ~40% * Fractions: ~50% * Light & heavy: ~78% * Mixed operations: ~50% * Multiple: ~55% * Numerical exprs: ~50% * Patterns: ~40% * Perimeter: ~55% * Place value: ~63% * Polygons: ~50% * Powers: ~40% * Probability: ~63% * Proportional: ~40% * Quadrilaterals: ~50% * Qwen-72B: ~55% * Ratio: ~28% * Rational number: ~58% * Spheres: ~55% * Statistics: ~55% * Subtraction: ~55% * Temperature: ~55% * Time: ~55% * Triangles: ~55% * Variable exprs: ~55% * Volume: ~55% * Volume of 3d shapes: ~55% * Add: ~55% * Compare: ~55% * Count: ~55% * Division: ~55% * Equations: ~55% * Length: ~55% * Percents: ~55% **Yi-34B (Orange):** * Trend: Generally performs better than InternLM2-20B, but lower than Qwen-72B and GPT-3.5. * Specific Points (approximate): * Angles: ~70% * Area: ~80% * Circles: ~58% * Classifying & sorting: ~70% * Coin names & value: ~60% * Cones: ~58% * Coordinate plane: ~70% * Cubes: ~70% * Cylinders: ~70% * Decimals: ~70% * Estimation & rounding: ~70% * Exchanging money: ~70% * Fractions: ~70% * Light & heavy: ~70% * Mixed operations: ~70% * Multiple: ~70% * Numerical exprs: ~70% * Patterns: ~70% * Perimeter: ~70% * Place value: ~70% * Polygons: ~70% * Powers: ~70% * Probability: ~70% * Proportional: ~70% * Quadrilaterals: ~70% * Qwen-72B: ~70% * Ratio: ~70% * Rational number: ~70% * Spheres: ~70% * Statistics: ~70% * Subtraction: ~70% * Temperature: ~70% * Time: ~70% * Triangles: ~70% * Variable exprs: ~70% * Volume: ~70% * Volume of 3d shapes: ~70% * Add: ~70% * Compare: ~70% * Count: ~70% * Division: ~70% * Equations: ~70% * Length: ~70% * Percents: ~70% **Qwen-72B (Green):** * Trend: Generally performs well, often close to GPT-3.5. * Specific Points (approximate): * Angles: ~70% * Area: ~82% * Circles: ~70% * Classifying & sorting: ~50% * Coin names & value: ~80% * Cones: ~50% * Coordinate plane: ~70% * Cubes: ~50% * Cylinders: ~50% * Decimals: ~50% * Estimation & rounding: ~50% * Exchanging money: ~50% * Fractions: ~50% * Light & heavy: ~50% * Mixed operations: ~50% * Multiple: ~50% * Numerical exprs: ~50% * Patterns: ~50% * Perimeter: ~50% * Place value: ~50% * Polygons: ~50% * Powers: ~50% * Probability: ~50% * Proportional: ~50% * Quadrilaterals: ~50% * Qwen-72B: ~50% * Ratio: ~50% * Rational number: ~50% * Spheres: ~50% * Statistics: ~50% * Subtraction: ~50% * Temperature: ~50% * Time: ~50% * Triangles: ~50% * Variable exprs: ~50% * Volume: ~50% * Volume of 3d shapes: ~50% * Add: ~50% * Compare: ~50% * Count: ~50% * Division: ~50% * Equations: ~50% * Length: ~50% * Percents: ~50% **GPT-3.5 (Red):** * Trend: Generally the highest accuracy across most problem types. * Specific Points (approximate): * Angles: ~93% * Area: ~78% * Circles: ~95% * Classifying & sorting: ~70% * Coin names & value: ~85% * Cones: ~70% * Coordinate plane: ~95% * Cubes: ~70% * Cylinders: ~70% * Decimals: ~70% * Estimation & rounding: ~70% * Exchanging money: ~70% * Fractions: ~70% * Light & heavy: ~70% * Mixed operations: ~70% * Multiple: ~70% * Numerical exprs: ~70% * Patterns: ~70% * Perimeter: ~70% * Place value: ~70% * Polygons: ~70% * Powers: ~70% * Probability: ~70% * Proportional: ~70% * Quadrilaterals: ~70% * Qwen-72B: ~70% * Ratio: ~70% * Rational number: ~70% * Spheres: ~70% * Statistics: ~70% * Subtraction: ~70% * Temperature: ~70% * Time: ~70% * Triangles: ~70% * Variable exprs: ~70% * Volume: ~70% * Volume of 3d shapes: ~70% * Add: ~70% * Compare: ~70% * Count: ~70% * Division: ~70% * Equations: ~70% * Length: ~70% * Percents: ~70% ### Key Observations * GPT-3.5 generally outperforms the other models across most math problem types. * InternLM2-20B generally has the lowest accuracy. * The performance of all models varies significantly depending on the specific math problem type. * There are some problem types where the performance of all models is relatively similar (e.g., "Light & heavy"). ### Interpretation The chart provides a comparative analysis of the accuracy of four language models on a diverse set of math-related tasks. The data suggests that GPT-3.5 is the most proficient model overall, while InternLM2-20B struggles in comparison. The varying performance across different problem types highlights the strengths and weaknesses of each model in specific areas of mathematical reasoning. This information can be valuable for selecting the most appropriate model for a given task or for identifying areas where further model development is needed. The chart also reveals that certain math problem types are inherently more challenging for these models than others, regardless of the specific architecture.