## Bar Chart: GSM8K Solve Rate by Prompting Method ### Overview The image is a bar chart comparing the GSM8K solve rate (in percentage) for two language models, LaMDA and PaLM, using different prompting methods. The prompting methods are: Standard prompting, Equation only, Variable compute only, Reasoning after answer, and Chain-of-thought prompting. ### Components/Axes * **Y-axis:** GSM8K solve rate (%), ranging from 0 to 60. * **X-axis:** Language models: LaMDA and PaLM. * **Legend (top-left):** * Yellow: Standard prompting * Diagonal Lines: Equation only * Horizontal Lines: Variable compute only * Dotted: Reasoning after answer * Brown: Chain-of-thought prompting ### Detailed Analysis * **LaMDA:** * Standard prompting (Yellow): Approximately 6% * Equation only (Diagonal Lines): Approximately 6% * Variable compute only (Horizontal Lines): Approximately 6% * Reasoning after answer (Dotted): Approximately 6% * Chain-of-thought prompting (Brown): Approximately 14% * **PaLM:** * Standard prompting (Yellow): Approximately 18% * Equation only (Diagonal Lines): Approximately 22% * Variable compute only (Horizontal Lines): Approximately 18% * Reasoning after answer (Dotted): Approximately 18% * Chain-of-thought prompting (Brown): Approximately 58% ### Key Observations * For LaMDA, all prompting methods except Chain-of-thought prompting yield similar solve rates, around 6%. Chain-of-thought prompting significantly improves the solve rate to approximately 14%. * For PaLM, Chain-of-thought prompting dramatically outperforms all other prompting methods, achieving a solve rate of approximately 58%. The other methods yield solve rates between 18% and 22%. * PaLM consistently outperforms LaMDA across all prompting methods. * Chain-of-thought prompting is the most effective method for both models, but its impact is much more pronounced for PaLM. ### Interpretation The data suggests that Chain-of-thought prompting is a highly effective technique for improving the performance of language models on the GSM8K math problem-solving benchmark. The significant difference in performance between Chain-of-thought prompting and other methods, especially for PaLM, indicates that this prompting strategy enables the model to better reason through the problem and arrive at the correct solution. The fact that PaLM consistently outperforms LaMDA suggests that PaLM has a superior architecture or training data that allows it to better leverage the benefits of Chain-of-thought prompting. The similar performance of the other prompting methods for LaMDA suggests that these methods are not as effective at eliciting the model's reasoning capabilities.

\n ## Bar Chart: GSM8K Solve Rate by Prompting Method and Model ### Overview This bar chart compares the GSM8K solve rate (in percentage) for two language models, LaMDA and PaLM, across five different prompting methods. The solve rate is represented by the height of the bars. ### Components/Axes * **X-axis:** Model - LaMDA and PaLM. * **Y-axis:** GSM8K solve rate (%). Scale ranges from 0 to 60, with increments of 10. * **Legend:** Located in the top-left corner, it defines the color-coding for each prompting method: * Yellow: Standard prompting * Light Gray (diagonal lines): Equation only * Dark Gray (diagonal lines): Variable compute only * Dotted: Reasoning after answer * Orange: Chain-of-thought prompting ### Detailed Analysis The chart consists of 10 bars, grouped by model (LaMDA and PaLM) and prompting method. **LaMDA:** * **Standard prompting (Yellow):** Approximately 8% solve rate. * **Equation only (Light Gray):** Approximately 4% solve rate. * **Variable compute only (Dark Gray):** Approximately 6% solve rate. * **Reasoning after answer (Dotted):** Approximately 5% solve rate. * **Chain-of-thought prompting (Orange):** Approximately 18% solve rate. **PaLM:** * **Standard prompting (Yellow):** Approximately 22% solve rate. * **Equation only (Light Gray):** Approximately 21% solve rate. * **Variable compute only (Dark Gray):** Approximately 20% solve rate. * **Reasoning after answer (Dotted):** Approximately 18% solve rate. * **Chain-of-thought prompting (Orange):** Approximately 58% solve rate. The bars for PaLM are generally higher than those for LaMDA, indicating a better solve rate across all prompting methods. Chain-of-thought prompting consistently yields the highest solve rate for both models, but the effect is much more pronounced for PaLM. ### Key Observations * Chain-of-thought prompting significantly improves the GSM8K solve rate for both LaMDA and PaLM. * PaLM consistently outperforms LaMDA across all prompting methods. * The difference in performance between prompting methods is more substantial for PaLM than for LaMDA. * The solve rates for Equation only, Variable compute only, and Reasoning after answer are relatively similar for both models. ### Interpretation The data suggests that the Chain-of-thought prompting method is highly effective in improving the performance of large language models on mathematical reasoning tasks, as measured by the GSM8K benchmark. The substantial increase in solve rate for PaLM when using this method indicates that PaLM is particularly well-suited to benefit from this type of prompting. The relatively low solve rates for the other prompting methods suggest that simply providing equations, computing variables, or reasoning after generating an answer is not as effective as guiding the model through a step-by-step reasoning process. The consistent outperformance of PaLM over LaMDA suggests differences in model architecture or training data that make PaLM more capable of leveraging these prompting techniques. The large gap between PaLM with Chain-of-thought prompting and all other methods is a notable outlier, highlighting the power of this technique.

## Bar Chart: GSM8K Solve Rate Comparison Across Prompting Methods for LaMDA and PaLM ### Overview The chart compares the performance of five prompting methods on two language models (LaMDA and PaLM) in solving GSM8K math problems. The y-axis represents solve rate percentage, while the x-axis categorizes results by model. Chain-of-thought prompting shows dramatically higher performance for PaLM compared to other methods. ### Components/Axes - **X-axis**: Model names ("LaMDA", "PaLM") - **Y-axis**: "GSM8K solve rate (%)" (0-60% scale) - **Legend**: - Yellow: Standard prompting - Striped: Equation only - Dotted: Variable compute only - Crosshatched: Reasoning after answer - Orange: Chain-of-thought prompting ### Detailed Analysis **LaMDA Results**: - All methods show near-identical performance (~5% solve rate) - Chain-of-thought prompting (orange) slightly outperforms others at ~15% **PaLM Results**: - Standard prompting (yellow): ~18% - Equation only (striped): ~20% - Variable compute only (dotted): ~18% - Reasoning after answer (crosshatched): ~18% - Chain-of-thought prompting (orange): ~58% (3x higher than other methods) ### Key Observations 1. **PaLM's Superiority with Chain-of-Thought**: The orange bar for PaLM is 3-4x taller than all other bars, indicating chain-of-thought prompting enables near-human-level performance on these problems. 2. **LaMDA's Uniform Performance**: All prompting methods yield similar low results for LaMDA, suggesting limited reasoning capability regardless of approach. 3. **PaLM's Method-Specific Gains**: While PaLM performs better overall, chain-of-thought prompting creates a stark performance gap compared to other methods. ### Interpretation The data reveals fundamental architectural differences between LaMDA and PaLM in handling reasoning tasks. PaLM's transformer-based architecture appears better suited for chain-of-thought prompting, which mimics human step-by-step reasoning. This suggests: - PaLM's design enables better decomposition of complex problems - LaMDA may lack internal mechanisms to benefit from explicit reasoning scaffolding - Chain-of-thought prompting acts as a "reasoning amplifier" for PaLM but not LaMDA The 58% solve rate for PaLM with chain-of-thought prompting approaches human performance levels on these problems, demonstrating the effectiveness of this prompting strategy for advanced language models.