## Line Chart: Similarity vs. Reasoning Step for Different Models ### Overview The image is a line chart comparing the similarity scores of five different language models across a series of reasoning steps. The x-axis represents the reasoning step (heuristic), and the y-axis represents the similarity score. Each model is represented by a different colored line with a distinct marker. ### Components/Axes * **X-axis:** Reasoning step *t_i* (Heuristic). Scale ranges from 0 to 50, with tick marks every 10 units. * **Y-axis:** Similarity(*C_T*, *t_i*). Scale ranges from 0.4 to 0.9, with tick marks every 0.1 units. * **Legend:** Located in the top-right corner, identifying each model by color and name: * Blue with circle markers: DS-R1-Qwen-7B * Orange with diamond markers: Qwen3-8B * Green with square markers: Claude-3.7-Sonnet * Purple with triangle markers: GPT-OSS-20B * Brown with inverted triangle markers: Magistral-Small ### Detailed Analysis * **DS-R1-Qwen-7B (Blue, Circle):** Starts at approximately 0.67 at step 0, decreases to around 0.52 by step 10, and then fluctuates between 0.52 and 0.56 until step 50. * Step 0: ~0.67 * Step 10: ~0.52 * Step 50: ~0.56 * **Qwen3-8B (Orange, Diamond):** Starts at approximately 0.88 at step 0, decreases to around 0.48 by step 10, then increases and fluctuates between 0.45 and 0.52 until step 50. * Step 0: ~0.88 * Step 10: ~0.48 * Step 20: ~0.50 * Step 50: ~0.52 * **Claude-3.7-Sonnet (Green, Square):** Starts at approximately 0.78 at step 0, decreases to around 0.62 by step 5, then fluctuates between 0.55 and 0.63 until step 25, after which the data ends. * Step 0: ~0.78 * Step 5: ~0.62 * Step 25: ~0.55 * **GPT-OSS-20B (Purple, Triangle):** Starts at approximately 0.65 at step 0, decreases to around 0.42 by step 10, then fluctuates between 0.38 and 0.55 until step 50. * Step 0: ~0.65 * Step 10: ~0.42 * Step 30: ~0.40 * Step 50: ~0.55 * **Magistral-Small (Brown, Inverted Triangle):** Starts at approximately 0.52 at step 0, decreases to around 0.40 by step 5, then fluctuates between 0.38 and 0.55 until step 50. * Step 0: ~0.52 * Step 5: ~0.40 * Step 30: ~0.42 * Step 50: ~0.55 ### Key Observations * All models except Claude-3.7-Sonnet show a significant drop in similarity score within the first 10 reasoning steps. * Claude-3.7-Sonnet maintains a relatively higher similarity score compared to the other models, but its data is only available up to step 25. * GPT-OSS-20B and Magistral-Small exhibit similar performance, with overlapping fluctuations in similarity scores. * After the initial drop, the similarity scores of all models tend to fluctuate within a narrower range. ### Interpretation The chart illustrates how the similarity between a model's reasoning process and a target solution changes as the model progresses through reasoning steps. The initial drop in similarity suggests that the models initially diverge from the target solution. The subsequent fluctuations indicate that the models are exploring different reasoning paths, with varying degrees of similarity to the target. Claude-3.7-Sonnet's higher initial similarity and slower decline may indicate a more robust or aligned reasoning process, at least for the initial steps. The convergence of GPT-OSS-20B and Magistral-Small suggests that these models may be employing similar reasoning strategies. The data suggests that the models' reasoning processes become less similar to the target solution as the number of reasoning steps increases, highlighting the challenge of maintaining alignment in complex reasoning tasks.

## Line Chart: Similarity of Reasoning Steps ### Overview This image presents a line chart illustrating the similarity between reasoning steps (represented by *t_i*) and a target (*C_T*) for five different language models: DS-R1-Qwen-7B, Qwen-8B, Claude-3.7-Sonnet, GPT-OSS-20B, and Magistral-Small. The chart tracks how this similarity changes as the reasoning step number increases from 0 to approximately 52. ### Components/Axes * **X-axis:** "Reasoning step *t_i* (Heuristic)", ranging from 0 to 52. * **Y-axis:** "Similarity(*C_T*, *t_i*)", ranging from 0.4 to 0.9. * **Legend:** Located in the top-right corner, identifying each line with a specific model name and color. * DS-R1-Qwen-7B (Blue) * Qwen-8B (Orange) * Claude-3.7-Sonnet (Green) * GPT-OSS-20B (Purple) * Magistral-Small (Brown) ### Detailed Analysis Here's a breakdown of each line's trend and approximate data points, verifying color consistency with the legend: * **DS-R1-Qwen-7B (Blue):** The line starts at approximately 0.85 at step 0, rapidly decreases to around 0.55 by step 10, then fluctuates between 0.45 and 0.55 for the remainder of the steps, showing some oscillation. * **Qwen-8B (Orange):** This line begins at approximately 0.88 at step 0, drops sharply to around 0.5 by step 10, and then exhibits a more erratic pattern, oscillating between approximately 0.4 and 0.6. It ends at around 0.55 at step 52. * **Claude-3.7-Sonnet (Green):** Starts at approximately 0.75 at step 0, decreases to around 0.6 by step 10, and then remains relatively stable, fluctuating between 0.58 and 0.65 for the majority of the steps. It ends at approximately 0.62 at step 52. * **GPT-OSS-20B (Purple):** Begins at approximately 0.7 at step 0, declines to around 0.45 by step 10, and then fluctuates between approximately 0.4 and 0.5, with some peaks reaching around 0.55. It ends at approximately 0.48 at step 52. * **Magistral-Small (Brown):** Starts at approximately 0.65 at step 0, decreases to around 0.45 by step 10, and then gradually increases to approximately 0.55 by step 52, showing a slight upward trend in the later steps. ### Key Observations * All models exhibit a significant drop in similarity during the initial reasoning steps (0-10). * Claude-3.7-Sonnet maintains the highest similarity scores throughout the reasoning process, remaining consistently above 0.58. * GPT-OSS-20B consistently shows the lowest similarity scores, generally staying below 0.5. * Qwen-8B and DS-R1-Qwen-7B show the most volatile behavior, with significant fluctuations in similarity scores. * Magistral-Small shows a slight increasing trend in similarity towards the end of the reasoning process. ### Interpretation The chart suggests that the initial reasoning steps are the most divergent for all models, indicating a rapid shift away from the target concept. Claude-3.7-Sonnet demonstrates the most consistent alignment with the target throughout the reasoning process, suggesting a more stable and focused reasoning approach. GPT-OSS-20B, conversely, appears to drift away from the target more quickly and remains less aligned. The fluctuations observed in Qwen-8B and DS-R1-Qwen-7B could indicate a more exploratory or iterative reasoning process, where the model revisits and refines its understanding of the target. The slight increase in similarity for Magistral-Small towards the end suggests a potential convergence or refinement of its reasoning as it progresses. The metric "Similarity(*C_T*, *t_i*)" likely represents a measure of how closely the model's internal representation at reasoning step *t_i* aligns with the target concept *C_T*. A higher similarity score indicates a stronger alignment, while a lower score suggests a greater divergence. This data could be used to evaluate the effectiveness and stability of different language models in performing reasoning tasks.

\n ## Line Chart: Similarity vs. Reasoning Step for Various AI Models ### Overview The image displays a line chart comparing the similarity metric, denoted as Similarity(C_T, t_i), across five different AI models over a series of reasoning steps (t_i). The chart illustrates how the similarity between some reference (C_T) and the model's output at step t_i changes as the reasoning process progresses. All models show a general downward trend in similarity as the number of reasoning steps increases, though the rate of decline and final values vary. ### Components/Axes * **Chart Type:** Multi-series line chart with markers. * **Y-Axis:** * **Label:** `Similarity(C_T, t_i)` * **Scale:** Linear, ranging from 0.4 to 0.9. * **Major Ticks:** 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. * **X-Axis:** * **Label:** `Reasoning step t_i (Heuristic)` * **Scale:** Linear, ranging from 0 to approximately 55. * **Major Ticks:** 0, 10, 20, 30, 40, 50. * **Legend:** Positioned in the top-right quadrant of the chart area. It contains five entries, each with a unique color and marker symbol: 1. **DS-R1-Qwen-7B:** Blue line with circle markers. 2. **Qwen3-8B:** Orange line with diamond markers. 3. **Claude-3.7-Sonnet:** Green line with square markers. 4. **GPT-OSS-20B:** Purple line with upward-pointing triangle markers. 5. **Magistral-Small:** Brown line with downward-pointing triangle markers. ### Detailed Analysis **Trend Verification & Data Point Extraction (Approximate Values):** 1. **DS-R1-Qwen-7B (Blue, Circles):** * **Trend:** Starts very high, drops steeply within the first 5 steps, then fluctuates with a gradual downward drift. * **Key Points:** Starts ~0.86 at step 0. Drops to ~0.65 by step 5. Fluctuates between ~0.55 and ~0.60 from steps 10-20. Ends its visible series around step 22 at ~0.56. 2. **Qwen3-8B (Orange, Diamonds):** * **Trend:** Begins at the highest point, experiences a sharp initial decline, then stabilizes into a fluctuating pattern around a lower mean. * **Key Points:** Starts at the chart's peak, ~0.88 at step 0. Plummets to ~0.60 by step 5. From steps 10-25, it oscillates roughly between 0.48 and 0.55. Its last visible point is near step 25 at ~0.54. 3. **Claude-3.7-Sonnet (Green, Squares):** * **Trend:** Starts moderately high, declines more gradually than the first two models, and maintains a relatively higher similarity plateau in the mid-range before declining further. * **Key Points:** Starts ~0.76 at step 0. Descends to ~0.65 by step 5 and holds near that level until step 10. Shows a local peak ~0.62 around step 18. Ends its visible series around step 24 at ~0.56. 4. **GPT-OSS-20B (Purple, Up-Triangles):** * **Trend:** Begins at a lower initial similarity, drops quickly, and then follows a shallow, fluctuating decline, often being the lowest or among the lowest series. * **Key Points:** Starts ~0.65 at step 0. Falls to ~0.50 by step 8. From steps 10-50, it mostly fluctuates in the 0.40-0.50 band, with a slight upward trend in the final steps (40-50), ending near ~0.54. 5. **Magistral-Small (Brown, Down-Triangles):** * **Trend:** Starts high, drops very sharply to become the lowest series, and exhibits the most volatile, jagged pattern with significant oscillations throughout. * **Key Points:** Starts ~0.78 at step 0. Crashes to ~0.40 by step 6. Shows extreme volatility, with deep troughs (e.g., ~0.36 at step 27) and sharp peaks (e.g., ~0.52 at step 42). It is the only series extending past step 50, ending at ~0.55. ### Key Observations * **Universal Initial Drop:** All five models exhibit their highest similarity at step 0, followed by a precipitous decline within the first 5-10 reasoning steps. * **Divergence in Mid-Range:** After the initial drop (post step ~10), the models diverge. Claude-3.7-Sonnet generally maintains the highest similarity, while Magistral-Small and GPT-OSS-20B often occupy the lower range. * **Volatility:** Magistral-Small displays the most unstable behavior, with large, frequent swings in similarity. In contrast, Claude-3.7-Sonnet shows the smoothest trajectory after its initial decline. * **Convergence at Extremes:** Despite different paths, the final data points for the series that extend to the right side of the chart (GPT-OSS-20B and Magistral-Small) converge into a similar range (~0.50-0.55) by step 50. * **Series Length:** The data series for DS-R1-Qwen-7B, Qwen3-8B, and Claude-3.7-Sonnet terminate before step 30, while GPT-OSS-20B and Magistral-Small continue to step 50 and beyond. ### Interpretation This chart likely visualizes a metric assessing how closely a model's reasoning at a given step (t_i) aligns with a final correct answer or a reference chain-of-thought (C_T). The **Peircean investigative reading** suggests: 1. **Divergence from the "Truth":** The universal sharp initial drop indicates that the very first steps of reasoning taken by these models are the most similar to the final reference. As the models generate more intermediate steps, their reasoning paths diverge significantly from the reference path (C_T). This could imply that the heuristic reasoning process introduces noise or alternative pathways not present in the reference. 2. **Model "Confidence" or "Focus":** The sustained higher similarity of Claude-3.7-Sonnet might suggest its intermediate reasoning steps remain more consistently aligned with the final outcome's logic. Conversely, the high volatility of Magistral-Small could indicate a less stable or more exploratory reasoning process, where steps frequently deviate and then correct course. 3. **The "Heuristic" Nature:** The x-axis label "(Heuristic)" is critical. It implies the reasoning steps are not necessarily ground-truth steps but are generated by a heuristic process. The declining similarity may therefore measure the drift of this heuristic process from an ideal path over time. 4. **Practical Implication:** For tasks requiring long chains of reasoning, this data suggests that monitoring similarity to a reference at early steps may not be predictive of later steps. The models' behaviors become highly individualized and less aligned with the reference as the process extends. The eventual convergence of some models at step 50 might indicate a return to a more aligned state, but only after considerable deviation. **Language Declaration:** All text within the chart image is in English.

## Line Graph: Similarity vs. Reasoning step (Heuristic) ### Overview The graph depicts the similarity metric (c_T, t_i) across heuristic reasoning steps (t_i) for five AI models. The y-axis ranges from 0.4 to 0.9, while the x-axis spans 0 to 50 reasoning steps. Five distinct data series are plotted with unique markers and colors. ### Components/Axes - **X-axis**: "Reasoning step t_i (Heuristic)" (0–50, integer increments) - **Y-axis**: "Similarity(c_T, t_i)" (0.4–0.9, 0.1 increments) - **Legend**: Located in the top-right corner, mapping colors/markers to models: - Blue circles: DS-R1-Qwen-7B - Orange diamonds: Qwen3-8B - Green squares: Claude-3.7-Sonnet - Purple triangles: GPT-OSS-20B - Brown triangles: Magistral-Small ### Detailed Analysis 1. **DS-R1-Qwen-7B (Blue Circles)**: - Starts at ~0.85 similarity at t=0 - Sharp decline to ~0.55 by t=10 - Stabilizes with minor fluctuations (~0.55–0.6) thereafter 2. **Qwen3-8B (Orange Diamonds)**: - Begins at ~0.8 similarity at t=0 - Drops to ~0.5 by t=10 - Exhibits moderate volatility (~0.5–0.6) until t=30, then stabilizes 3. **Claude-3.7-Sonnet (Green Squares)**: - Initial similarity ~0.75 at t=0 - Gradual decline to ~0.6 by t=10 - Maintains stable performance (~0.6–0.7) with minor oscillations 4. **GPT-OSS-20B (Purple Triangles)**: - Starts at ~0.65 similarity at t=0 - Sharp drop to ~0.45 by t=10 - High volatility (~0.4–0.55) throughout, with no clear stabilization 5. **Magistral-Small (Brown Triangles)**: - Initial similarity ~0.6 at t=0 - Steep decline to ~0.4 by t=10 - Persistent fluctuations (~0.4–0.55) with no stabilization ### Key Observations - **Initial Drop**: All models show a significant similarity decline within the first 10 steps, suggesting an adaptation phase. - **Stability Variance**: Claude-3.7-Sonnet demonstrates the most stable performance post-t=10, while GPT-OSS-20B remains highly volatile. - **Long-term Performance**: DS-R1-Qwen-7B and Qwen3-8B achieve moderate stabilization (~0.55–0.6), whereas Magistral-Small and GPT-OSS-20B show persistent instability. - **Outlier Behavior**: GPT-OSS-20B exhibits the most erratic pattern, with sharp dips and recoveries (e.g., ~0.45 at t=15, ~0.55 at t=25). ### Interpretation The data suggests that model architecture and training significantly influence reasoning stability. Claude-3.7-Sonnet’s consistent performance implies robust heuristic adaptation, while GPT-OSS-20B’s volatility may indicate overfitting or insufficient generalization. The initial similarity drop across all models could reflect computational overhead in early reasoning stages. Notably, DS-R1-Qwen-7B’s rapid stabilization aligns with its larger parameter count (7B), suggesting scalability benefits. The absence of convergence toward higher similarity values implies inherent limitations in heuristic reasoning across these models, warranting further investigation into optimization strategies.