## Line Chart: NDCG@10/% vs. Dimensions for Different Algorithms ### Overview The image is a line chart comparing the performance of four different algorithms (PCA, Search-Adaptor, MRL-Adaptor, and SMEC) based on their NDCG@10/% score across varying dimensions. The x-axis represents the number of dimensions, and the y-axis represents the NDCG@10/% score. ### Components/Axes * **Title:** There is no explicit title on the chart. * **X-axis:** * Label: "Dimensions" * Scale: 128, 256, 512, 768, 1024 * **Y-axis:** * Label: "NDCG@10/%" * Scale: 40, 42, 44, 46, 48, 50, 52 * **Legend:** Located in the bottom-right corner. * PCA (Blue line with circle markers) * Search-Adaptor (Orange line with cross markers) * MRL-Adaptor (Green line with triangle markers) * SMEC (Yellow/Orange line with square markers) ### Detailed Analysis * **PCA (Blue):** The line starts at approximately 40 at 128 dimensions, increases to approximately 46 at 256 dimensions, reaches approximately 47.3 at 512 dimensions, then increases to approximately 48.1 at 768 dimensions, and ends at approximately 48.6 at 1024 dimensions. The trend is upward, with the most significant increase between 128 and 256 dimensions. * **Search-Adaptor (Orange):** The line starts at approximately 46.5 at 128 dimensions, increases to approximately 49.8 at 256 dimensions, reaches approximately 51.5 at 512 dimensions, then increases to approximately 52.3 at 768 dimensions, and ends at approximately 52.6 at 1024 dimensions. The trend is upward, with a decreasing rate of increase as dimensions increase. * **MRL-Adaptor (Green):** The line starts at approximately 49 at 128 dimensions, increases to approximately 50.3 at 256 dimensions, reaches approximately 51.8 at 512 dimensions, then increases to approximately 52.4 at 768 dimensions, and ends at approximately 52.6 at 1024 dimensions. The trend is upward, with a decreasing rate of increase as dimensions increase. * **SMEC (Yellow/Orange):** The line starts at approximately 49.8 at 128 dimensions, increases to approximately 51.3 at 256 dimensions, reaches approximately 52 at 512 dimensions, then increases to approximately 52.5 at 768 dimensions, and ends at approximately 52.7 at 1024 dimensions. The trend is upward, with a decreasing rate of increase as dimensions increase. ### Key Observations * SMEC and MRL-Adaptor consistently outperform PCA and Search-Adaptor across all dimensions. * The performance of all algorithms generally improves as the number of dimensions increases, but the rate of improvement decreases at higher dimensions. * PCA has the lowest NDCG@10/% score across all dimensions. * The performance difference between MRL-Adaptor and SMEC is minimal, especially at higher dimensions. ### Interpretation The chart suggests that increasing the number of dimensions generally improves the performance of these algorithms, as measured by NDCG@10/%. However, there are diminishing returns, as the rate of improvement decreases at higher dimensions. The choice of algorithm significantly impacts performance, with SMEC and MRL-Adaptor consistently outperforming PCA and Search-Adaptor. PCA shows the most significant performance gain from 128 to 256 dimensions, indicating that increasing dimensions is particularly beneficial for this algorithm in the lower range. The close performance of MRL-Adaptor and SMEC suggests they may have similar underlying mechanisms or be optimized for similar data characteristics.

## Line Chart: NDCG@10% vs. Dimensions ### Overview This image presents a line chart comparing the performance of four different methods (PCA, Search-Adaptor, MRL-Adaptor, and SMEC) across varying dimensions. The performance metric is NDCG@10%, plotted against dimensions ranging from 128 to 1024. ### Components/Axes * **X-axis:** Dimensions, with markers at 128, 256, 512, 768, and 1024. * **Y-axis:** NDCG@10%, ranging from approximately 40 to 53. * **Legend:** Located in the top-right corner, identifying the four data series: * PCA (Blue circle) * Search-Adaptor (Orange cross) * MRL-Adaptor (Green triangle) * SMEC (Yellow square) * **Gridlines:** Present to aid in reading values. ### Detailed Analysis Let's analyze each line individually: * **PCA (Blue):** This line starts at approximately 40 at 128 dimensions, increases sharply to around 45 at 256 dimensions, continues to rise more gradually to approximately 47 at 512 dimensions, then plateaus around 48-49 for 768 and 1024 dimensions. * **Search-Adaptor (Orange):** This line begins at approximately 49 at 128 dimensions, rises to around 50 at 256 dimensions, then increases steadily to approximately 52 at 512 dimensions, and continues to around 53 at 768 and 1024 dimensions. * **MRL-Adaptor (Green):** This line starts at approximately 49.5 at 128 dimensions, increases to around 51 at 256 dimensions, then rises to approximately 52.5 at 512 dimensions, and plateaus around 53 for 768 and 1024 dimensions. * **SMEC (Yellow):** This line begins at approximately 51 at 128 dimensions, rises to around 52 at 256 dimensions, then increases to approximately 53 at 512 dimensions, and remains stable at around 53 for 768 and 1024 dimensions. Here's a table summarizing the approximate data points: | Dimensions | PCA (NDCG@10%) | Search-Adaptor (NDCG@10%) | MRL-Adaptor (NDCG@10%) | SMEC (NDCG@10%) | |---|---|---|---|---| | 128 | 40 | 49 | 49.5 | 51 | | 256 | 45 | 50 | 51 | 52 | | 512 | 47 | 52 | 52.5 | 53 | | 768 | 48 | 53 | 53 | 53 | | 1024 | 49 | 53 | 53 | 53 | ### Key Observations * SMEC and MRL-Adaptor consistently outperform PCA across all dimensions. * Search-Adaptor performs better than PCA, but generally lags behind SMEC and MRL-Adaptor. * The performance of all methods appears to plateau after 512 dimensions, with diminishing returns from increasing dimensionality further. * PCA shows the most significant initial improvement with increasing dimensions, but its growth slows down considerably. ### Interpretation The chart demonstrates the impact of dimensionality on the performance of different methods for a specific task (likely information retrieval or ranking, given the NDCG metric). The NDCG@10% metric indicates the normalized discounted cumulative gain at rank 10, measuring the ranking quality of the top 10 results. The plateauing effect observed after 512 dimensions suggests that increasing the dimensionality beyond this point does not significantly improve performance, and may even introduce noise or computational overhead. SMEC and MRL-Adaptor's consistently high performance indicates their effectiveness in capturing relevant information even in high-dimensional spaces. PCA, while showing initial gains, appears to be limited in its ability to represent the data effectively at higher dimensions. The differences in performance between the methods likely stem from their underlying approaches to dimensionality reduction and feature representation. SMEC and MRL-Adaptor may employ more sophisticated techniques that better preserve the relevant information during dimensionality reduction, leading to superior ranking performance. The chart suggests that for this particular task, a dimensionality of around 512 strikes a good balance between performance and computational cost.

\n ## Line Chart: Performance Comparison of Dimensionality Reduction Methods ### Overview The image 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 changes as the dimensionality of the representation increases. ### Components/Axes * **X-Axis (Horizontal):** Labeled "Dimensions". It represents the dimensionality of the embedding space. The axis has five discrete, evenly spaced tick marks at values: **128, 256, 512, 768, 1024**. * **Y-Axis (Vertical):** Labeled "NDCG@10/%". It represents the retrieval performance metric. The axis ranges from **40 to 52**, with major grid lines at intervals of 2 (40, 42, 44, 46, 48, 50, 52). * **Legend:** Located in the **bottom-right corner** of the chart area. It contains four entries, each associating a line color and marker style with a method name: * **Blue line with circle markers (●):** PCA * **Orange line with 'x' markers (×):** Search-Adaptor * **Green line with triangle markers (▲):** MRL-Adaptor * **Yellow line with square markers (■):** SMEC ### Detailed Analysis All four data series show a positive, monotonic trend: performance (NDCG@10) increases as the number of dimensions increases. The rate of improvement generally slows down at higher dimensions, suggesting diminishing returns. **Data Series and Approximate Values:** 1. **PCA (Blue, ●):** * **Trend:** Starts as the lowest-performing method and shows the most dramatic relative improvement, especially between 128 and 256 dimensions. The slope is steep initially and then becomes more gradual. * **Data Points (Approximate):** * 128 Dimensions: ~40.1% * 256 Dimensions: ~46.0% * 512 Dimensions: ~47.3% * 768 Dimensions: ~48.1% * 1024 Dimensions: ~48.6% 2. **Search-Adaptor (Orange, ×):** * **Trend:** Starts significantly above PCA. Shows steady improvement, with a consistent upward slope that is less steep than PCA's initial jump. * **Data Points (Approximate):** * 128 Dimensions: ~46.5% * 256 Dimensions: ~49.7% * 512 Dimensions: ~51.5% * 768 Dimensions: ~52.1% * 1024 Dimensions: ~52.5% 3. **MRL-Adaptor (Green, ▲):** * **Trend:** Starts as the second-highest method. Its performance line runs very close to, but consistently slightly below, the SMEC line. The gap between them narrows at higher dimensions. * **Data Points (Approximate):** * 128 Dimensions: ~48.9% * 256 Dimensions: ~50.3% * 512 Dimensions: ~51.9% * 768 Dimensions: ~52.5% * 1024 Dimensions: ~52.9% 4. **SMEC (Yellow, ■):** * **Trend:** The top-performing method across all measured dimensions. It maintains a small but consistent lead over MRL-Adaptor. * **Data Points (Approximate):** * 128 Dimensions: ~49.8% * 256 Dimensions: ~51.2% * 512 Dimensions: ~52.1% * 768 Dimensions: ~52.7% * 1024 Dimensions: ~53.0% ### Key Observations * **Performance Hierarchy:** A clear and consistent hierarchy is maintained across all dimensions: **SMEC > MRL-Adaptor > Search-Adaptor > PCA**. * **Convergence at High Dimensions:** The performance gap between the top two methods (SMEC and MRL-Adaptor) and between the middle two (Search-Adaptor and MRL-Adaptor) becomes very small at 768 and 1024 dimensions. The lines for SMEC and MRL-Adaptor nearly converge at 1024 dimensions. * **PCA's Lag:** PCA consistently underperforms the other three specialized adaptation methods by a significant margin (approximately 3-9 percentage points), though it does benefit from increased dimensionality. * **Diminishing Returns:** All curves show a concave shape, indicating that the gain in NDCG@10 from doubling the dimensions decreases as the dimensions get larger. The most significant gains for all methods occur between 128 and 512 dimensions. ### Interpretation This chart provides strong evidence for two key conclusions in the context of representation learning for retrieval tasks: 1. **Specialized Adaptation Outperforms Generic Reduction:** Methods designed specifically for the search/retrieval task (Search-Adaptor, MRL-Adaptor, SMEC) dramatically outperform a generic dimensionality reduction technique (PCA). This suggests that simply compressing vectors is insufficient; the adaptation must be tailored to preserve or enhance the properties needed for effective ranking. 2. **Higher Dimensionality is Beneficial, but with Limits:** Increasing the dimensionality of the embedding space consistently improves retrieval performance for all methods. However, the flattening curves suggest a practical ceiling. The cost (computational, storage) of moving from 512 to 1024 dimensions yields a smaller performance benefit than moving from 128 to 256. The optimal dimensionality likely involves a trade-off between performance and efficiency, with 512 or 768 appearing as potential sweet spots where performance is high and the rate of improvement begins to plateau. 3. **SMEC and MRL-Adaptor are State-of-the-Art:** The near-identical performance of SMEC and MRL-Adaptor at high dimensions indicates they are both highly effective approaches. The choice between them might depend on other factors not shown here, such as training stability, inference speed, or performance on other metrics. SMEC's slight edge at lower dimensions (128, 256) could be meaningful in resource-constrained scenarios.

## Line Chart: NDCG@10/% vs Dimensions ### Overview The chart illustrates the performance of four different methods (PCA, Search-Adaptor, MRL-Adaptor, SMEC) in terms of NDCG@10/% across varying dimensions (128, 256, 512, 768, 1024). Each method is represented by a distinct line with unique markers and colors, showing how their performance evolves as the number of dimensions increases. ### Components/Axes - **X-axis (Dimensions)**: Labeled "Dimensions" with discrete values: 128, 256, 512, 768, 1024. - **Y-axis (NDCG@10/%**: Labeled "NDCG@10/%" with a range from 40 to 52. - **Legend**: Located in the bottom-right corner, mapping: - **Blue circles**: PCA - **Orange crosses**: Search-Adaptor - **Green triangles**: MRL-Adaptor - **Yellow squares**: SMEC ### Detailed Analysis 1. **PCA (Blue Circles)**: - Starts at **40%** at 128 dimensions. - Increases steadily to **46%** at 256, **47.5%** at 512, **48%** at 768, and **48.5%** at 1024. - **Trend**: Gradual upward slope with minimal acceleration. 2. **Search-Adaptor (Orange Crosses)**: - Begins at **46.5%** at 128 dimensions. - Rises sharply to **49.5%** at 256, **51.5%** at 512, **52%** at 768, and **52.5%** at 1024. - **Trend**: Steep initial increase, then plateaus slightly. 3. **MRL-Adaptor (Green Triangles)**: - Starts at **49%** at 128 dimensions. - Increases to **50.5%** at 256, **51.8%** at 512, **52.2%** at 768, and **52.5%** at 1024. - **Trend**: Consistent upward trajectory with moderate growth. 4. **SMEC (Yellow Squares)**: - Begins at **50%** at 128 dimensions. - Rises to **51%** at 256, **52%** at 512, **52.5%** at 768, and **53%** at 1024. - **Trend**: Steady linear increase with minimal fluctuation. ### Key Observations - **PCA** consistently underperforms compared to other methods, showing the slowest growth. - **Search-Adaptor** and **MRL-Adaptor** exhibit similar performance, with Search-Adaptor slightly outperforming at higher dimensions. - **SMEC** maintains the highest performance across all dimensions, with a slight edge over MRL-Adaptor at 1024. - All methods show improvement as dimensions increase, but the rate of improvement varies. ### Interpretation The data suggests that increasing the number of dimensions generally enhances NDCG@10/% performance for all methods. However, **SMEC** and **MRL-Adaptor** demonstrate superior scalability, achieving higher scores even at lower dimensions. **PCA** lags behind, indicating it may not be as effective for this task. The sharp rise of **Search-Adaptor** at lower dimensions suggests it is particularly sensitive to dimensionality changes, potentially making it a strong candidate for scenarios where dimensionality is constrained. The plateau in Search-Adaptor’s growth at higher dimensions implies diminishing returns beyond a certain point. This chart highlights the trade-offs between computational complexity (dimensions) and performance gains, guiding method selection based on specific use cases.