## Diagram: Comparative Evaluation of Mastermind Game Solving Approaches ### Overview The image is a three-panel diagram comparing two methods for solving a Mastermind-style code-breaking game. The left panel shows a visual game board, the middle panel shows an "Agentic Evaluation" dialogue, and the right panel shows a "Deductive Reasoning Evaluation" dialogue. The diagram illustrates how a Large Language Model (LLM) interacts with an evaluator to solve the puzzle using different reasoning strategies. ### Components/Axes The image is divided into three vertical panels of roughly equal width. **1. Left Panel: Mastermind Game Board** * **Title:** "Mastermind" (top center). * **Sub-section 1: "Possible Colors"** (top). Displays six colored circles in a row: light blue, light green, yellow, orange, red, and purple. * **Sub-section 2: Guess Grid.** A grid with 4 columns (for code positions) and 6 rows (for guesses). The first four rows contain guesses. The last two rows are empty (white circles). * **Row 1 (Guess 1):** Yellow, Green, Blue, Orange. Feedback (right side): Two white circles (indicating correct color, wrong position). * **Row 2 (Guess 2):** Red, Red, Yellow, Green. Feedback: Two white circles, one black circle (indicating correct color and position). * **Row 3 (Guess 3):** Purple, Yellow, Green, Red. Feedback: Two black circles, two white circles. * **Row 4 (Guess 4):** Green, Yellow, Purple, Red. Feedback: Four black circles (indicating the code is solved). * **Sub-section 3: "Secret Code"** (bottom). Displays the solution: Green, Yellow, Purple, Red. * **Legend (Bottom Center):** A light green rectangle labeled "Evaluator Class" and a light yellow rectangle labeled "LLM". **2. Middle Panel: Agentic Evaluation** * **Title:** "Agentic Evaluation" (top center). * **Content:** A simulated chat dialogue between the "Evaluator Class" (green speech bubbles) and the "LLM" (yellow speech bubbles). * **Evaluator (Green):** "Your task is to find the secret code! [...] I'll provide you with feedback how close your guesses are to the secret code." * **LLM (Yellow):** "My first guess is: yellow, green, blue, orange." * **Evaluator (Green):** "Two guessed colors are in the code but not in their right positions." * **[Ellipsis "..." indicating omitted steps]** * **LLM (Yellow):** "My next guess is: purple, yellow, green, red." * **Evaluator (Green):** "Two guessed colors are in their correct positons and two colors are correct but in their wrong positions." (Note: "positons" is a typo in the image). * **LLM (Yellow):** "Based on my previous guesses, I need to swap green and prupule. It is the only option that is valid based on the proivded feedback. My next guess is: green, yellow, purple, red." (Note: "prupule" and "proivded" are typos in the image). * **Evaluator (Green):** "You solved it! 🏆" **3. Right Panel: Deductive Reasoning Evaluation** * **Title:** "Deductive Reasoning Evaluation" (top center). * **Content:** A simulated chat dialogue with a more constrained, logic-puzzle format. * **Evaluator (Green):** "Your task is to find the **two-color secret code!** The following colors are allowed: **yellow, red, green, and blue.** I'll provide you with hints that allow you to unambiguously deduce the final secret code." * **Evaluator (Green):** "**Guess 1: Red, Green. Feedback:** One guessed color is in the secret code but is **not** in the correct position." * **Evaluator (Green):** "**Guess 2: Red, Blue. Feedback:** One guessed color is in the secret code and is **in** the correct position." * **Evaluator (Green):** "**What is the secret color code?**" * **LLM (Yellow):** "Given the guess history, I can deduce that **red cannot be in the final code** because it would create a contradiction between the two feedbacks. This, in turn, means that the other colors in both guesses **must** be in the code, and **blue is already in the correct position.** So, the secret code must be: **green, blue.**" ### Detailed Analysis * **Game Logic (Left Panel):** The Mastermind board uses a standard feedback system: a black circle means a correct color in the correct position, a white circle means a correct color in the wrong position. The secret code is four colors long. The LLM successfully solves it in four guesses. * **Agentic Evaluation Process (Middle Panel):** This shows an interactive, trial-and-error approach. The LLM makes guesses, receives descriptive feedback about color presence and position, and iteratively refines its next guess based on that feedback. The process includes a logical deduction step ("swap green and purple") before the final correct guess. * **Deductive Reasoning Process (Right Panel):** This presents a more formal logic puzzle. The constraints are tighter (two-color code, four allowed colors). The feedback is phrased to enable pure deduction. The LLM's response demonstrates deductive reasoning: it identifies a contradiction if Red were in the code, thereby eliminating it and logically concluding the code must be Green and Blue, with Blue in the correct (second) position. ### Key Observations 1. **Two Distinct Evaluation Paradigms:** The diagram contrasts an open-ended, agentic interaction (middle) with a closed, deductive logic puzzle (right). 2. **Feedback Complexity:** The Agentic Evaluation provides richer, more natural language feedback ("in the code but not in their right positions"). The Deductive Reasoning Evaluation provides minimal, binary-style feedback ("in the correct position" / "not in the correct position") designed for unambiguous logic. 3. **LLM Reasoning Styles:** The LLM adapts its reasoning to the task. In the agentic task, it uses iterative refinement. In the deductive task, it uses contradiction and elimination. 4. **Visual vs. Textual Representation:** The left panel provides a complete visual record of the game state, while the middle and right panels provide a textual transcript of the reasoning process. The visual board in the left panel corresponds to the Agentic Evaluation dialogue. ### Interpretation This diagram serves as a technical illustration for evaluating AI reasoning capabilities. It demonstrates how the same underlying concept (solving a color code game) can be framed as two different types of cognitive tasks: 1. **Agentic Problem-Solving:** This tests an AI's ability to engage in a multi-turn dialogue, interpret nuanced feedback, maintain context over a long interaction, and perform iterative hypothesis testing. It mimics a more human-like, exploratory problem-solving approach. 2. **Deductive Reasoning:** This tests an AI's ability to perform formal logic, handle constraints, and derive a unique solution from a limited set of premises. It evaluates pure logical deduction without the noise of iterative guessing. The inclusion of the visual Mastermind board grounds the abstract dialogues in a concrete, familiar game. The typos in the Agentic Evaluation panel ("positons," "prupule," "proivded") may be intentional to show the model working with imperfect input or could be artifacts of the diagram's creation. Overall, the image argues that comprehensive AI evaluation requires testing across a spectrum of reasoning styles, from flexible agentic interaction to rigid deductive logic.