## Line Chart: NDCG@10/% vs. Dimensions ### Overview The image is a line chart comparing the performance of four different methods (Original(PCA), Search-Adaptor, MRL-Adaptor, and SMEC) based on the metric NDCG@10/% across varying dimensions. The x-axis represents the number of dimensions, and the y-axis represents the NDCG@10/% score. ### Components/Axes * **X-axis:** Dimensions, with values 128, 256, 512, 768, 1536, and 3584. * **Y-axis:** NDCG@10/%, ranging from 30 to 60 with increments of 5. * **Legend:** Located in the bottom-right corner, it identifies each line by color and method: * Blue line with circle markers: Original(PCA) * Orange line with cross markers: Search-Adaptor * Green line with triangle markers: MRL-Adaptor * Yellow line with square markers: SMEC ### Detailed Analysis * **Original(PCA) (Blue):** The line starts at approximately 31 at 128 dimensions and increases steadily to approximately 56 at 3584 dimensions. * (128, 31) * (256, 41) * (512, 46.5) * (768, 50.5) * (1536, 53.5) * (3584, 55.5) * **Search-Adaptor (Orange):** The line starts at approximately 51 at 128 dimensions, increases to approximately 57 at 256 dimensions, and then gradually increases to approximately 61 at 3584 dimensions. * (128, 51) * (256, 57) * (512, 58.5) * (768, 59) * (1536, 60) * (3584, 61) * **MRL-Adaptor (Green):** The line starts at approximately 54 at 128 dimensions, increases to approximately 59 at 256 dimensions, and then gradually increases to approximately 61 at 3584 dimensions. * (128, 54) * (256, 59) * (512, 60) * (768, 60.5) * (1536, 60.5) * (3584, 61.5) * **SMEC (Yellow):** The line starts at approximately 56 at 128 dimensions, increases to approximately 59 at 256 dimensions, and then gradually increases to approximately 61.5 at 3584 dimensions. * (128, 56) * (256, 59) * (512, 60) * (768, 60.5) * (1536, 61) * (3584, 61.5) ### Key Observations * Original(PCA) has the lowest NDCG@10/% scores across all dimensions compared to the other three methods. * Search-Adaptor, MRL-Adaptor, and SMEC perform similarly, with SMEC showing a slightly higher NDCG@10/% at higher dimensions. * The performance of all methods generally improves as the number of dimensions increases, but the rate of improvement decreases at higher dimensions. ### Interpretation The chart suggests that increasing the number of dimensions generally improves the performance of all methods, as measured by NDCG@10/%. However, the Original(PCA) method consistently underperforms compared to the other three methods. The Search-Adaptor, MRL-Adaptor, and SMEC methods achieve similar performance, with SMEC showing a slight advantage at higher dimensions. This indicates that these methods are more effective at capturing relevant information as the dimensionality increases, while Original(PCA) may be limited by its dimensionality reduction approach. The diminishing returns observed at higher dimensions suggest that there may be a point beyond which increasing dimensionality provides little additional benefit.

## Line Chart: NDCG@10% vs. Dimensions ### Overview This image presents a line chart comparing the performance of four different methods – Original(PCA), Search-Adaptor, MRL-Adaptor, and SMEC – across varying dimensions. The performance metric is NDCG@10%, which likely represents Normalized Discounted Cumulative Gain at 10%. The chart illustrates how the performance of each method changes as the dimensionality of the data increases. ### Components/Axes * **X-axis:** Dimensions, ranging from 128 to 3584. The axis markers are: 128, 256, 512, 768, 1536, 3584. * **Y-axis:** NDCG@10%, ranging from 30 to 60. The axis markers are: 30, 35, 40, 45, 50, 55, 60. * **Legend:** Located in the top-right corner of the chart. * Original(PCA) - Blue circle * Search-Adaptor - Orange cross * MRL-Adaptor - Green triangle * SMEC - Yellow square ### Detailed Analysis * **Original(PCA):** This line (blue) starts at approximately 31% at 128 dimensions and steadily increases to approximately 54% at 3584 dimensions. The line exhibits a consistent upward slope, indicating improved performance with increasing dimensions. * 128 Dimensions: ~31% * 256 Dimensions: ~37% * 512 Dimensions: ~46% * 768 Dimensions: ~50% * 1536 Dimensions: ~53% * 3584 Dimensions: ~54% * **Search-Adaptor:** This line (orange) begins at approximately 50% at 128 dimensions and rises to approximately 61% at 3584 dimensions. The slope is initially steeper, then flattens out. * 128 Dimensions: ~50% * 256 Dimensions: ~56% * 512 Dimensions: ~59% * 768 Dimensions: ~60% * 1536 Dimensions: ~60% * 3584 Dimensions: ~61% * **MRL-Adaptor:** This line (green) starts at approximately 55% at 128 dimensions and increases to approximately 60% at 3584 dimensions. The line is relatively flat, indicating minimal performance improvement with increasing dimensions. * 128 Dimensions: ~55% * 256 Dimensions: ~57% * 512 Dimensions: ~58% * 768 Dimensions: ~59% * 1536 Dimensions: ~60% * 3584 Dimensions: ~60% * **SMEC:** This line (yellow) begins at approximately 55% at 128 dimensions and rises to approximately 61% at 3584 dimensions. The line is relatively flat, similar to MRL-Adaptor, but slightly higher in overall performance. * 128 Dimensions: ~55% * 256 Dimensions: ~57% * 512 Dimensions: ~59% * 768 Dimensions: ~60% * 1536 Dimensions: ~60% * 3584 Dimensions: ~61% ### Key Observations * The Original(PCA) method shows the most significant improvement in NDCG@10% as the number of dimensions increases. * Search-Adaptor and SMEC achieve the highest NDCG@10% scores, consistently above 60% at higher dimensions. * MRL-Adaptor exhibits the least improvement with increasing dimensions, plateauing around 60%. * The performance gap between the methods narrows at higher dimensions. ### Interpretation The data suggests that increasing the dimensionality of the data generally improves the performance of these methods, as measured by NDCG@10%. However, the rate of improvement varies significantly. The Original(PCA) method benefits the most from increased dimensionality, while the Search-Adaptor, MRL-Adaptor, and SMEC methods show diminishing returns. The fact that Search-Adaptor and SMEC consistently outperform the other methods, particularly at higher dimensions, suggests that these methods are more effective at leveraging the information contained in higher-dimensional data. The plateauing of MRL-Adaptor indicates that it may be limited by its ability to effectively utilize the increased dimensionality. The Original(PCA) method's consistent improvement suggests that it is a good baseline approach, but it may not be able to achieve the same level of performance as the more sophisticated adaptation methods. The convergence of the lines at higher dimensions suggests that there may be a point of diminishing returns, where further increasing the dimensionality does not lead to significant performance gains. This could be due to factors such as the curse of dimensionality or the limitations of the evaluation metric.

## Line Chart: Performance of Dimensionality Reduction Methods on NDCG@10 ### Overview This is a line chart comparing the performance of four different dimensionality reduction or adaptation methods across varying embedding dimensions. The performance metric is NDCG@10 (Normalized Discounted Cumulative Gain at rank 10), expressed as a percentage. The chart demonstrates how each method's effectiveness scales with increased dimensionality. ### Components/Axes * **X-Axis (Horizontal):** Labeled "Dimensions". It represents the dimensionality of the embedding space. The axis markers are at specific, non-linear intervals: 128, 256, 512, 768, 1536, and 3584. * **Y-Axis (Vertical):** Labeled "NDCG@10/%". It represents the ranking performance score as a percentage. The scale ranges from 30 to approximately 62, with major gridlines at intervals of 5 (30, 35, 40, 45, 50, 55, 60). * **Legend:** Located in the bottom-right quadrant of the chart area. It contains four entries, each associating a line color and marker style with a method name: 1. **Blue line with circle markers:** "Orignal(PCA)" [sic - likely a typo for "Original"]. 2. **Orange line with 'x' markers:** "Search-Adaptor". 3. **Green line with triangle markers:** "MRL-Adaptor". 4. **Yellow/Orange line with square markers:** "SMEC". ### Detailed Analysis **Trend Verification & Data Point Extraction:** All four data series show a positive trend: NDCG@10 increases as the number of dimensions increases. The rate of improvement generally slows down (diminishing returns) at higher dimensions. 1. **Orignal(PCA) [Blue, Circle]:** * **Trend:** Steep, consistent upward slope across the entire range. It shows the most dramatic relative improvement. * **Approximate Data Points:** * 128 Dimensions: ~31% * 256 Dimensions: ~40.5% * 512 Dimensions: ~46.5% * 768 Dimensions: ~50.5% * 1536 Dimensions: ~53.5% * 3584 Dimensions: ~55.5% 2. **Search-Adaptor [Orange, 'x']:** * **Trend:** Starts lower than MRL-Adaptor and SMEC, rises sharply until 512 dimensions, then continues to rise more gradually. It remains the lowest-performing of the three adaptor methods throughout. * **Approximate Data Points:** * 128 Dimensions: ~51% * 256 Dimensions: ~56.5% * 512 Dimensions: ~58.5% * 768 Dimensions: ~59.5% * 1536 Dimensions: ~60.2% * 3584 Dimensions: ~60.8% 3. **MRL-Adaptor [Green, Triangle]:** * **Trend:** Starts above Search-Adaptor but below SMEC. Follows a similar growth curve, rising quickly initially and then plateauing. It consistently performs between Search-Adaptor and SMEC. * **Approximate Data Points:** * 128 Dimensions: ~54% * 256 Dimensions: ~58% * 512 Dimensions: ~59.5% * 768 Dimensions: ~60% * 1536 Dimensions: ~61% * 3584 Dimensions: ~61.5% 4. **SMEC [Yellow/Orange, Square]:** * **Trend:** The top-performing method at all dimension levels. It shows a strong initial increase and maintains a slight but consistent lead over MRL-Adaptor. * **Approximate Data Points:** * 128 Dimensions: ~56% * 256 Dimensions: ~59% * 512 Dimensions: ~60.2% * 768 Dimensions: ~60.8% * 1536 Dimensions: ~61.5% * 3584 Dimensions: ~61.8% ### Key Observations 1. **Performance Hierarchy:** A clear and consistent performance hierarchy is maintained across all dimensions: SMEC > MRL-Adaptor > Search-Adaptor > Orignal(PCA). 2. **Diminishing Returns:** All methods exhibit diminishing returns. The most significant performance gains occur when increasing dimensions from 128 to 512. Beyond 768 dimensions, the curves flatten considerably. 3. **Gap Narrowing:** The performance gap between the three adaptor methods (SMEC, MRL, Search) and the baseline PCA method narrows as dimensions increase. At 128 dimensions, the gap is ~25 percentage points; at 3584 dimensions, it narrows to ~6 percentage points. 4. **Typo in Legend:** The legend contains a likely typo: "Orignal(PCA)" should probably read "Original(PCA)". ### Interpretation This chart evaluates the efficacy of different techniques for optimizing dense vector representations for retrieval tasks (as measured by NDCG@10). The data suggests several key insights: * **Superiority of Adaptor Methods:** The three specialized adaptor methods (SMEC, MRL-Adaptor, Search-Adaptor) significantly outperform the standard PCA baseline, especially at lower dimensions. This indicates that task-specific adaptation is far more effective than generic dimensionality reduction for preserving ranking quality. * **SMEC as the State-of-the-Art:** SMEC demonstrates the highest effectiveness, suggesting its underlying methodology (likely a more sophisticated compression or adaptation technique) is the most successful at maintaining retrieval performance while reducing dimensionality. * **Scalability vs. Efficiency Trade-off:** While all methods improve with more dimensions, the flattening curves after 512-768 dimensions imply a practical efficiency frontier. For resource-constrained applications, using 512 or 768 dimensions with an adaptor like SMEC may offer the best balance between performance and computational cost, as further increases yield minimal gains. * **Baseline Limitation:** The steep slope of the PCA line shows it is highly sensitive to dimensionality, performing poorly in very low-dimensional spaces. The adaptors are much more robust, maintaining high performance even at 128 dimensions, which is crucial for applications requiring extreme compression. In summary, the chart provides strong evidence that for retrieval-oriented tasks, employing specialized adaptation techniques like SMEC is crucial for achieving high performance with compact vector representations, and that there is a clear point of diminishing returns in scaling up dimensionality.

## Line Graph: NDCG@10% Performance Across Dimensions ### Overview The image is a line graph comparing the performance of four different methods (Original(PCA), Search-Adaptor, MRL-Adaptor, SMEC) in terms of NDCG@10% across varying dimensions. The x-axis represents dimensions (128 to 3584), and the y-axis represents NDCG@10% (30% to 60%). All methods show upward trends, with SMEC consistently performing best. ### Components/Axes - **X-axis (Dimensions)**: Labeled "Dimensions" with values 128, 256, 512, 768, 1536, 3584. - **Y-axis (NDCG@10%)**: Labeled "NDCG@10%" with values 30% to 60%. - **Legend**: Located in the bottom-right corner, associating: - Blue circles: Original(PCA) - Orange crosses: Search-Adaptor - Green triangles: MRL-Adaptor - Yellow squares: SMEC ### Detailed Analysis 1. **Original(PCA)** (Blue circles): - Starts at ~31% at 128 dimensions. - Rises steeply to ~41% at 256 dimensions. - Continues increasing to ~55% at 3584 dimensions. - Values: 31% (128), 41% (256), 46% (512), 51% (768), 53% (1536), 55% (3584). 2. **Search-Adaptor** (Orange crosses): - Begins at ~51% at 128 dimensions. - Increases gradually to ~56% at 256 dimensions. - Reaches ~59% at 3584 dimensions. - Values: 51% (128), 56% (256), 58% (512), 59% (768), 60% (1536), 61% (3584). 3. **MRL-Adaptor** (Green triangles): - Starts at ~54% at 128 dimensions. - Rises to ~58% at 256 dimensions. - Peaks at ~60% at 3584 dimensions. - Values: 54% (128), 58% (256), 59% (512), 60% (768), 61% (1536), 61% (3584). 4. **SMEC** (Yellow squares): - Begins at ~56% at 128 dimensions. - Increases steadily to ~61% at 3584 dimensions. - Values: 56% (128), 59% (256), 60% (512), 61% (768), 61% (1536), 61% (3584). ### Key Observations - **Performance Trends**: All methods improve with higher dimensions, but SMEC maintains the highest NDCG@10% across all dimensions. - **Original(PCA) Gap**: Original(PCA) starts significantly lower (~31% at 128 dimensions) but closes the gap to ~55% by 3584 dimensions. - **Convergence**: Search-Adaptor, MRL-Adaptor, and SMEC converge closely at higher dimensions (e.g., 59–61% at 3584 dimensions). ### Interpretation The data suggests that increasing dimensions enhances performance for all methods, with SMEC being the most robust. Original(PCA) underperforms initially but improves substantially with scale. The convergence of Search-Adaptor, MRL-Adaptor, and SMEC at higher dimensions implies diminishing returns for further dimensional increases beyond 768. The steep rise of Original(PCA) indicates it may benefit more from dimensional scaling compared to other methods. This could reflect architectural differences in how these methods handle dimensionality.