## Heatmap: Layer Activation Patterns ### Overview The image displays a series of heatmaps representing activation patterns in different layers of a neural network. The heatmaps are arranged in three groups, labeled TE-L, TE-R, and TE-C, each showing the activation patterns for the 1st, 2nd, and 3rd layers. The heatmaps are square, with axes ranging from 0 to 180. Arrows indicate the progression from one layer to the next within each group. ### Components/Axes * **X-axis:** Ranges from 0 to 180. * **Y-axis:** Ranges from 0 to 180. * **Heatmap Color Scale:** Dark purple indicates low activation, transitioning to light blue/green for higher activation. * **Titles:** * 1st layer TE-L * 2nd layer TE-L * 3rd layer TE-L * 1st layer TE-R * 2nd layer TE-R * 3rd layer TE-R * 1st layer TE-C * 2nd layer TE-C * 3rd layer TE-C * **Arrows:** Indicate the progression from the 1st layer to the 2nd, and from the 2nd layer to the 3rd, for each of the TE-L, TE-R, and TE-C groups. ### Detailed Analysis **TE-L Group:** * **1st layer TE-L:** Shows a diagonal line of higher activation from the bottom-left to the top-right corner. There are also scattered points and short vertical lines of activation. * **2nd layer TE-L:** The diagonal line is less prominent. Vertical lines of activation are more pronounced and frequent. * **3rd layer TE-L:** Vertical lines of activation are even more dominant and distinct. **TE-R Group:** * **1st layer TE-R:** Similar to the 1st layer TE-L, with a diagonal line of activation and scattered points. * **2nd layer TE-R:** Vertical lines of activation become more prominent. * **3rd layer TE-R:** Vertical lines of activation are the most dominant feature. **TE-C Group:** * **1st layer TE-C:** Shows a diagonal line of higher activation from the bottom-left to the top-right corner. There are also scattered points and short vertical lines of activation. * **2nd layer TE-C:** The diagonal line is less prominent. Vertical lines of activation are more pronounced and frequent. * **3rd layer TE-C:** Vertical lines of activation are even more dominant and distinct. ### Key Observations * All three groups (TE-L, TE-R, TE-C) show a similar trend: a shift from a diagonal activation pattern in the first layer to a predominantly vertical line activation pattern in the later layers. * The intensity of the vertical lines seems to increase from the 1st to the 3rd layer in all groups. * The diagonal line is most visible in the first layer of each group and diminishes in subsequent layers. ### Interpretation The heatmaps illustrate how activation patterns evolve through the layers of a neural network under different conditions or configurations (TE-L, TE-R, TE-C). The shift from diagonal to vertical activation patterns suggests that the network is learning to emphasize specific features or relationships as information propagates through the layers. The increasing intensity of the vertical lines indicates that certain neurons or feature detectors are becoming more strongly activated in the deeper layers. The similarity in trends across TE-L, TE-R, and TE-C suggests a common underlying learning process, although the specific details of the activation patterns may differ.

## Heatmaps: Tensor Embedding Layers ### Overview The image presents six heatmaps, arranged in a 2x3 grid. Each heatmap represents a tensor embedding (TE) layer – specifically, the 1st, 2nd, and 3rd layers – for both Left (L) and Right (R) sides, as well as a Center (C) view. The heatmaps visualize the relationships between values on a 0-180 scale for both the x and y axes. Each heatmap has a black arrow pointing to the upper-right corner. ### Components/Axes Each heatmap shares the following components: * **X-axis:** Labeled "0" to "180" with approximately 10 tick marks. * **Y-axis:** Labeled "0" to "180" with approximately 10 tick marks. * **Title:** Indicates the layer number (1st, 2nd, or 3rd) and the view (TE-L, TE-R, or TE-C). * **Color Scale:** The heatmaps use a color gradient ranging from dark purple (low values) to bright magenta (high values). There is no explicit legend, but the color intensity represents the magnitude of the values. ### Detailed Analysis or Content Details **1st layer TE-L:** The heatmap shows a diagonal pattern with higher intensity (magenta) along the main diagonal. There are also several horizontal and vertical lines of varying intensity. The pattern appears somewhat chaotic, but with a clear concentration of higher values along the diagonal. **2nd layer TE-L:** Similar to the 1st layer, this heatmap also exhibits a diagonal pattern with higher intensity along the main diagonal. However, the pattern appears more structured and less chaotic than the 1st layer. There are more distinct horizontal and vertical lines. **3rd layer TE-L:** This heatmap shows a very strong diagonal pattern with a very high intensity (bright magenta) along the main diagonal. The horizontal and vertical lines are also more pronounced and structured. **1st layer TE-R:** This heatmap displays a similar pattern to the 1st layer TE-L, with a diagonal concentration of higher values. The pattern is also somewhat chaotic, but with a clear diagonal emphasis. **2nd layer TE-R:** Similar to the 2nd layer TE-L, this heatmap shows a more structured diagonal pattern with higher intensity along the main diagonal. The horizontal and vertical lines are more distinct. **3rd layer TE-R:** This heatmap exhibits a very strong diagonal pattern with a very high intensity along the main diagonal, similar to the 3rd layer TE-L. The horizontal and vertical lines are also more pronounced. **1st layer TE-C:** This heatmap shows a pattern of vertical lines with varying intensity. The diagonal pattern is less prominent compared to the TE-L and TE-R views. **2nd layer TE-C:** This heatmap displays a pattern of vertical lines with varying intensity. The lines appear more distinct and structured than in the 1st layer TE-C. **3rd layer TE-C:** This heatmap shows a pattern of vertical lines with varying intensity. The lines are very distinct and structured, with a clear separation between them. ### Key Observations * **Diagonal Dominance (TE-L & TE-R):** The TE-L and TE-R views consistently show a strong diagonal pattern, indicating a correlation between values along the main diagonal. * **Layer Progression:** As the layer number increases (1st to 3rd), the diagonal pattern becomes more pronounced and structured in the TE-L and TE-R views. * **Vertical Lines (TE-C):** The TE-C view consistently displays a pattern of vertical lines, suggesting a different type of relationship between values. * **Arrow Placement:** The black arrows in each heatmap consistently point to the upper-right corner, potentially indicating a direction of increasing values or a specific feature of the embedding. ### Interpretation The heatmaps likely represent the output of a tensor embedding process, possibly within a neural network or machine learning model. The different views (L, R, C) could correspond to different aspects or perspectives of the embedded data. The strong diagonal patterns in the TE-L and TE-R views suggest that the embedding process is capturing correlations between features or elements along the main diagonal. The increasing structure and intensity of the diagonal pattern as the layer number increases indicate that the embedding is becoming more refined and focused on these correlations. The vertical line patterns in the TE-C view suggest a different type of relationship, possibly representing distinct categories or features. The increasing structure of the vertical lines as the layer number increases indicates that the embedding is becoming more capable of distinguishing between these categories. The arrows pointing to the upper-right corner could indicate that higher values represent a specific feature or characteristic of the embedded data. Overall, the heatmaps demonstrate a complex and structured embedding process that is capturing different types of relationships between values. The different views and layer numbers provide insights into the evolution and refinement of the embedding.

## Heatmaps: Layer-wise Transformations Across Three Processing Stages ### Overview The image displays six heatmaps arranged in a 3x2 grid, representing transformations across three processing layers (1st, 2nd, 3rd) for three modalities: **TE-L** (left), **TE-R** (right), and **TE-C** (central). Each heatmap uses a color gradient from purple (low intensity) to blue (high intensity) to encode values. Arrows between heatmaps indicate sequential progression. ### Components/Axes - **Axes**: - X-axis: Labeled `0` to `180` (no explicit title). - Y-axis: Labeled `0` to `180` (no explicit title). - **Labels**: - Top row: `1st layer TE-L`, `2nd layer TE-L`, `3rd layer TE-L`. - Middle row: `1st layer TE-R`, `2nd layer TE-R`, `3rd layer TE-R`. - Bottom row: `1st layer TE-C`, `2nd layer TE-C`, `3rd layer TE-C`. - **Legends**: None visible. - **Arrows**: Thin gray arrows connect heatmaps horizontally, suggesting sequential processing. ### Detailed Analysis 1. **TE-L Heatmaps (Top Row)**: - **1st layer**: Diagonal blue streaks dominate the lower-left quadrant, fading into purple elsewhere. - **2nd layer**: Vertical blue stripes emerge, concentrated in the right half (X=90–180). - **3rd layer**: Vertical stripes persist but with reduced intensity, showing slight horizontal dispersion. 2. **TE-R Heatmaps (Middle Row)**: - **1st layer**: Diagonal blue streaks mirror TE-L’s 1st layer but shifted to the upper-right quadrant. - **2nd layer**: Vertical stripes appear, overlapping with TE-L’s 2nd layer pattern. - **3rd layer**: Vertical stripes dominate, with faint diagonal remnants in the lower-left. 3. **TE-C Heatmaps (Bottom Row)**: - **1st layer**: Diagonal blue streaks span the entire diagonal (X=Y). - **2nd layer**: Vertical stripes dominate, with faint diagonal traces near X=Y. - **3rd layer**: Uniform vertical stripes, with minimal diagonal interference. ### Key Observations - **Vertical Stripes**: Appear consistently in TE-L and TE-R heatmaps after the 2nd layer, suggesting stabilization of features. - **Diagonal Elements**: Dominant in early layers (1st) for TE-L and TE-R, fading in later layers. - **Color Intensity**: Blue regions (high values) concentrate in specific quadrants early on, becoming more uniform in later layers. - **Asymmetry**: TE-L and TE-R heatmaps show mirrored patterns in early layers but diverge in later stages. ### Interpretation The heatmaps likely represent feature maps or attention weights in a neural network or signal processing pipeline. The progression from diagonal to vertical stripes across layers suggests: 1. **Early Layers (1st)**: Capture coarse, spatially varying patterns (diagonals). 2. **Middle Layers (2nd)**: Begin organizing features into structured vertical bands, possibly aligning with hierarchical feature extraction. 3. **Late Layers (3rd)**: Stabilize into uniform vertical distributions, indicating convergence or refinement of features. The TE-C modality shows the most consistent diagonal-to-vertical transition, implying it may represent a central or aggregated processing pathway. The absence of a legend limits quantitative interpretation of color intensity, but the spatial progression of patterns aligns with typical deep learning layer dynamics. ### Uncertainties - No explicit axis titles or legends prevent precise quantification of values. - The meaning of "0–180" axes (e.g., time, spatial coordinates) is unspecified. - The role of TE-L/TE-R/TE-C modalities (e.g., left/right visual streams, sensor channels) is not clarified.