## Chart: I/O Quantization and IR Drop vs. Scaling ### Overview The image presents two scatter plots comparing Root Mean Square Error (RMSE) against Log(Time[s]) for different I/O configurations and scaling factors. Plot 'a' focuses on 64x64 resolution with varying I/O quantization and IR drop settings, while plot 'b' compares 64x64 and 512x512 resolutions with a specific I/O configuration. Both plots include horizontal dashed lines labeled "Prog." and a vertical dashed line labeled "10y". ### Components/Axes **Plot a: 64x64: I/O quantization and IR drop** * **X-axis:** Log(Time[s]), with tick marks at 0, 10, and 20. * **Y-axis:** RMSE, with a logarithmic scale ranging from 10^-2 to 10^0. * **Legend (top-left):** * Green 'x': 64x64: IRdrop, 6/8bit I/O (Manuscript) * Blue square: 64x64: IRdrop, 32/32bit I/O * Orange circle: 64x64: NO\_IRdrop, 32/32bit I/O * **Horizontal Dashed Lines:** * Green: "Prog." located near y = 0.03 * Blue: "Prog." located near y = 0.01 * Orange: "Prog." located near y = 0.006 * **Vertical Dashed Line:** Located at x = 20, labeled "10y". **Plot b: Scaling up to 512x512** * **X-axis:** Log(Time[s]), with tick marks at 0, 10, and 20. * **Y-axis:** RMSE, with a logarithmic scale ranging from 10^-2 to 10^0. * **Legend (top-right):** * Gray diamond: 512x512: IRdrop, 6/8bit I/O * Green 'x': 64x64: IRdrop, 6/8bit I/O (Manuscript) * **Horizontal Dashed Lines:** * Green: "Prog." located near y = 0.03 * Gray: "Prog." located near y = 0.6 * **Vertical Dashed Line:** Located at x = 20, labeled "10y". ### Detailed Analysis **Plot a: 64x64: I/O quantization and IR drop** * **64x64: IRdrop, 6/8bit I/O (Manuscript) (Green 'x'):** * At x=0, RMSE ≈ 0.03 * At x=20, RMSE ≈ 0.03 * Trend: Relatively constant. * **64x64: IRdrop, 32/32bit I/O (Blue square):** * At x=0, RMSE ≈ 0.02 * At x=10, RMSE ≈ 0.09 * At x=20, RMSE ≈ 0.13 * Trend: Increasing. * **64x64: NO\_IRdrop, 32/32bit I/O (Orange circle):** * At x=0, RMSE ≈ 0.015 * At x=10, RMSE ≈ 0.09 * At x=20, RMSE ≈ 0.18 * Trend: Increasing. **Plot b: Scaling up to 512x512** * **512x512: IRdrop, 6/8bit I/O (Gray diamond):** * At x=0, RMSE ≈ 0.6 * At x=10, RMSE ≈ 0.6 * At x=20, RMSE ≈ 0.7 * Trend: Relatively constant. * **64x64: IRdrop, 6/8bit I/O (Manuscript) (Green 'x'):** * At x=0, RMSE ≈ 0.03 * At x=10, RMSE ≈ 0.09 * At x=20, RMSE ≈ 0.1 * Trend: Increasing. ### Key Observations * In plot 'a', increasing the bit depth from 6/8 to 32/32 for the 64x64 resolution, while keeping IRdrop, results in a higher RMSE as Log(Time[s]) increases. Removing IRdrop also results in a higher RMSE. * In plot 'b', scaling up to 512x512 with 6/8bit I/O and IRdrop leads to a significantly higher RMSE compared to the 64x64 configuration with the same settings. * The "Prog." lines seem to represent some kind of performance target or threshold. * The "10y" line at Log(Time[s]) = 20 likely indicates a specific time point of interest (10 years). ### Interpretation The plots suggest that I/O quantization and IR drop significantly impact the RMSE, especially as the simulation time increases. For the 64x64 resolution, using lower bit depths (6/8) and including IR drop results in lower RMSE values compared to higher bit depths (32/32) or removing IR drop. Scaling up to 512x512 dramatically increases the RMSE, indicating a potential trade-off between resolution and accuracy for the given I/O configuration. The "Prog." lines likely represent acceptable error thresholds, and the data indicates whether each configuration meets those thresholds. The "10y" marker suggests a long-term performance evaluation point.

\n ## Charts: I/O Quantization and Scaling Performance ### Overview The image presents two charts (a and b) comparing the Root Mean Squared Error (RMSE) against the logarithm of time for different I/O configurations. Chart 'a' focuses on a 64x64 configuration with varying I/O quantization levels and IR drop considerations. Chart 'b' demonstrates scaling performance up to a 512x512 configuration. Both charts use a logarithmic scale for both the x and y axes. ### Components/Axes **Common Elements:** * **X-axis:** Log(Time[s]) - Logarithmic scale representing time in seconds. Ranges from approximately 0 to 20. * **Y-axis:** RMSE - Root Mean Squared Error, representing the error magnitude. Logarithmic scale ranging from 10^-2 to 10⁰. * **Annotation:** "10y" - Appears in the top-right corner of both charts, likely indicating a time scale or a reference point. * **Annotation:** "Prog." - Appears in both charts, likely indicating a progress marker or a point of interest. **Chart a (64x64: I/O quantization and IR drop):** * **Title:** "64x64: I/O quantization and IR drop" * **Legend:** Located in the top-left corner. * Black Circle: "64x64: IRdrop, 6/8bit I/O (Manuscript)" * Gray Square: "64x64: IRdrop, 32/32bit I/O" * Orange Circle: "64x64: NO_IRdrop, 32/32bit I/O" **Chart b (Scaling up to 512x512):** * **Title:** "Scaling up to 512x512" * **Legend:** Located in the top-left corner. * Green Diamond: "512x512: IRdrop, 6/8bit I/O" * Green Cross: "64x64: IRdrop, 6/8bit I/O (Manuscript)" ### Detailed Analysis or Content Details **Chart a (64x64):** * **Black Circle (IRdrop, 6/8bit I/O):** The line starts at approximately RMSE = 0.02 (2x10^-2) at Log(Time) = 0, remains relatively stable until Log(Time) ≈ 10, then increases to approximately RMSE = 0.1 (1x10^-1) at Log(Time) = 20. * **Gray Square (IRdrop, 32/32bit I/O):** The line starts at approximately RMSE = 0.03 (3x10^-2) at Log(Time) = 0, increases steadily to approximately RMSE = 0.12 (1.2x10^-1) at Log(Time) = 10, and continues to increase to approximately RMSE = 0.2 (2x10^-1) at Log(Time) = 20. * **Orange Circle (NO_IRdrop, 32/32bit I/O):** The line starts at approximately RMSE = 0.01 (1x10^-2) at Log(Time) = 0, increases to approximately RMSE = 0.03 (3x10^-2) at Log(Time) = 10, and reaches approximately RMSE = 0.08 (8x10^-2) at Log(Time) = 20. **Chart b (Scaling up to 512x512):** * **Green Diamond (512x512: IRdrop, 6/8bit I/O):** The line starts at approximately RMSE = 0.03 (3x10^-2) at Log(Time) = 0, increases to approximately RMSE = 0.08 (8x10^-2) at Log(Time) = 10, and reaches approximately RMSE = 0.15 (1.5x10^-1) at Log(Time) = 20. * **Green Cross (64x64: IRdrop, 6/8bit I/O):** The line starts at approximately RMSE = 0.02 (2x10^-2) at Log(Time) = 0, increases to approximately RMSE = 0.05 (5x10^-2) at Log(Time) = 10, and reaches approximately RMSE = 0.1 (1x10^-1) at Log(Time) = 20. ### Key Observations * In Chart a, the 32/32bit I/O configurations (both with and without IR drop) exhibit higher RMSE values compared to the 6/8bit I/O configuration. The configuration *without* IR drop performs best. * In Chart b, the 512x512 configuration shows a higher RMSE than the 64x64 configuration across all time scales, indicating a performance degradation with scaling. * Both charts show an increasing RMSE with increasing Log(Time), suggesting that the error accumulates over time. * The "Prog." annotations appear at similar RMSE values in both charts, potentially indicating a performance threshold or a point of interest in the error behavior. ### Interpretation The data suggests that I/O quantization and IR drop significantly impact the accuracy (as measured by RMSE) of the system. Lower bit-width I/O (6/8bit) generally results in lower RMSE values, especially when IR drop is considered. The absence of IR drop further improves performance. Scaling the system from 64x64 to 512x512 introduces increased RMSE, indicating that the performance benefits of scaling are offset by increased error. This could be due to increased complexity, signal interference, or other factors associated with larger system sizes. The consistent upward trend of RMSE with time suggests that the error is not static but accumulates over time, potentially due to drift or other time-dependent effects. The "Prog." annotations might represent a point where the error reaches an unacceptable level, triggering a corrective action or indicating a system limitation. The charts provide valuable insights into the trade-offs between I/O configuration, system size, and accuracy. Optimizing I/O quantization and mitigating IR drop are crucial for maintaining low error rates, while scaling requires careful consideration of potential performance degradation.

## Scatter Plot Comparison: I/O Quantization, IR Drop, and Scaling ### Overview The image contains two side-by-side scatter plots (labeled **a** and **b**) on a light gray background. Both plots share the same axes: a logarithmic x-axis labeled `Log(Time[s])` and a logarithmic y-axis labeled `RMSE`. The plots compare the Root Mean Square Error (RMSE) performance over time for different computational configurations, focusing on the effects of IR drop and I/O bit width for 64x64 and 512x512 systems. ### Components/Axes **Common Elements (Both Plots):** * **X-axis:** `Log(Time[s])`. Linear scale from 0 to 20. Major ticks at 0, 10, 20. * **Y-axis:** `RMSE`. Logarithmic scale from `10^-2` to `10^0` (0.01 to 1.0). Major ticks at `10^-2`, `10^-1`, `10^0`. * **Vertical Dashed Line:** A black dashed line at `Log(Time[s]) = 20`, annotated with a boxed label `10y` (likely representing 10 years). * **Horizontal Dashed Lines ("Prog."):** Three colored, dashed horizontal lines labeled `Prog.` (likely "Progress" or "Programmed target"). * **Green Dashed Line:** Positioned at approximately `RMSE = 0.03`. * **Blue Dashed Line:** Positioned at approximately `RMSE = 0.01`. * **Orange Dashed Line:** Positioned at approximately `RMSE = 0.005`. **Plot-Specific Elements:** **Plot a (Left): "64x64: I/O quantization and IR drop"** * **Legend (Top-Left):** 1. **Green 'X' marker:** `64x64: IRdrop, 6/8bit I/O (Manuscript)` 2. **Blue Square marker:** `64x64: IRdrop, 32/32bit I/O` 3. **Orange Circle marker:** `64x64: NO_IRdrop, 32/32bit I/O` * **Annotations:** Two curved arrows (one blue, one orange) point from the initial data points at `Log(Time)=0` towards the right, suggesting a progression or comparison. **Plot b (Right): "Scaling up to 512x512"** * **Legend (Top-Left):** 1. **Gray Diamond marker:** `512x512: IRdrop, 6/8bit I/O` 2. **Green 'X' marker:** `64x64: IRdrop, 6/8bit I/O (Manuscript)` (This is the same series from Plot a, included for direct comparison). ### Detailed Analysis **Plot a: 64x64 System Analysis** * **Data Series & Trends:** * **Green 'X' (6/8bit I/O with IR drop):** Shows a clear upward trend. Starts at `Log(Time)=0` with `RMSE ≈ 0.04`. Increases to `RMSE ≈ 0.1` at `Log(Time) ≈ 10`, and reaches `RMSE ≈ 0.2` at `Log(Time) = 20`. * **Blue Square (32/32bit I/O with IR drop):** Shows a very slight upward trend, nearly flat. Starts at `Log(Time)=0` with `RMSE ≈ 0.02`. Increases minimally to `RMSE ≈ 0.025` at `Log(Time) ≈ 10`, and ends at `RMSE ≈ 0.03` at `Log(Time) = 20`. * **Orange Circle (32/32bit I/O, NO IR drop):** Shows a strong upward trend. Starts at `Log(Time)=0` with the lowest `RMSE ≈ 0.015`. Increases to `RMSE ≈ 0.09` at `Log(Time) ≈ 10`, and ends at `RMSE ≈ 0.2` at `Log(Time) = 20`, converging with the green 'X' series. * **Relationship to "Prog." Lines:** The initial points for the blue and orange series are near or below their respective colored "Prog." lines (blue and orange). Over time, both the orange and green series significantly exceed their target lines, while the blue series remains close to its target. **Plot b: Scaling to 512x512 System** * **Data Series & Trends:** * **Gray Diamond (512x512, 6/8bit I/O with IR drop):** Shows a slight upward trend at a high error level. Starts at `Log(Time)=0` with `RMSE ≈ 0.5`. Increases to `RMSE ≈ 0.6` at `Log(Time) ≈ 10`, and ends at `RMSE ≈ 0.7` at `Log(Time) = 20`. * **Green 'X' (64x64, 6/8bit I/O with IR drop):** Included for scale comparison. Its values are identical to those in Plot a, appearing much lower on the RMSE scale than the 512x512 series. * **Relationship to "Prog." Lines:** The 512x512 data points are all far above the green "Prog." line (`RMSE ≈ 0.03`), indicating the larger system operates at a much higher error magnitude for the same I/O configuration. ### Key Observations 1. **Impact of IR Drop:** For the 64x64 system with 32/32bit I/O, the presence of IR drop (blue squares) dramatically stabilizes the RMSE over time compared to the no-IR-drop case (orange circles), which degrades rapidly. 2. **Impact of I/O Bit Width:** In the 64x64 system with IR drop, using lower bit-width I/O (6/8bit, green 'X') results in higher initial and final RMSE compared to using full 32/32bit I/O (blue squares). 3. **Scaling Effect:** Scaling the system from 64x64 to 512x512 (while keeping the same 6/8bit I/O with IR drop) results in an order-of-magnitude increase in RMSE (from ~0.04-0.2 to ~0.5-0.7). 4. **Convergence:** In Plot a, the `NO_IRdrop` (orange) and `IRdrop, 6/8bit` (green) series converge to similar high RMSE values at `Log(Time)=20`, despite starting from different points. 5. **Target Lines:** The "Prog." lines appear to be design targets. The 32/32bit I/O with IR drop (blue) is the only configuration that stays close to its target over the simulated time. ### Interpretation This data demonstrates critical trade-offs in hardware system design for computational tasks, likely related to analog or in-memory computing where IR drop (voltage drop) and I/O quantization are key concerns. * **The central finding is that IR drop, often seen as a non-ideality, can act as a beneficial stabilizing mechanism.** In the 64x64 system, it prevents the rapid error growth seen in the idealized "NO_IRdrop" case (orange circles). This suggests the physical constraints of IR drop may introduce a form of regularization or limit error propagation. * **There is a clear precision-performance trade-off.** Using lower-precision I/O (6/8bit) saves resources but incurs a permanent, higher RMSE penalty compared to full 32-bit I/O, both with IR drop present. * **The scaling plot (b) highlights a significant challenge.** Simply enlarging the system (to 512x512) while keeping the same low-precision I/O and experiencing IR drop leads to unacceptably high error levels (RMSE > 0.5), far exceeding the target. This indicates that scaling such systems requires more than just increasing size; it necessitates improvements in error mitigation, precision, or architecture to maintain performance. * The "10y" marker implies these are long-term reliability or degradation simulations. The upward trends in RMSE for most configurations suggest performance worsens over extended operational time, with the 32/32bit I/O with IR drop being the most robust configuration against this temporal degradation. **In summary, the charts argue that for stable, long-term operation in scaled systems, managing the interplay between physical effects (like IR drop) and architectural choices (like I/O bit width) is more crucial than simply avoiding non-idealities or increasing scale.**

## Scatter Plots: I/O Quantization and IR Drop Analysis ### Overview Two scatter plots compare root mean square error (RMSE) against logarithmic time (Log(Time[s])) for different I/O quantization schemes and IR drop configurations. Chart **a** focuses on 64x64 configurations, while chart **b** examines scaling to 512x512. Both plots use logarithmic axes and include progression reference lines. --- ### Components/Axes #### Chart a: 64x64 Configurations - **X-axis**: Log(Time[s]) (0 to 20) - **Y-axis**: RMSE (10⁻³ to 10⁰) - **Legend**: - Green crosses: 64x64 IRdrop, 6/8bit I/O (Manuscript) - Blue squares: 64x64 IRdrop, 32/32bit I/O - Orange circles: 64x64 NO_IRdrop, 32/32bit I/O - **Dashed Lines**: - Green: "Prog." (RMSE ≈ 10⁻¹) - Blue: "Prog." (RMSE ≈ 10⁻²) - Orange: "Prog." (RMSE ≈ 10⁻³) #### Chart b: 512x512 Scaling - **X-axis**: Log(Time[s]) (0 to 20) - **Y-axis**: RMSE (10⁻² to 10⁰) - **Legend**: - Gray diamonds: 512x512 IRdrop, 6/8bit I/O - Green crosses: 64x64 IRdrop, 6/8bit I/O (Manuscript) - **Dashed Line**: - Gray: "Prog." (RMSE ≈ 10⁻¹) --- ### Detailed Analysis #### Chart a - **Green crosses (6/8bit I/O)**: - RMSE values: ~10⁻¹ to 10⁻² - Time range: 10⁻¹ to 10¹ seconds - **Blue squares (32/32bit I/O)**: - RMSE values: ~10⁻¹ - Time range: 10⁰ to 10¹ seconds - **Orange circles (NO_IRdrop)**: - RMSE values: ~10⁻¹ to 10⁰ - Time range: 10⁰ to 10¹ seconds - **Trends**: - Green crosses show the lowest RMSE, improving with time. - Blue squares and orange circles plateau at higher RMSE values. - Dashed lines indicate progression thresholds. #### Chart b - **Green crosses (64x64 6/8bit I/O)**: - RMSE values: ~10⁻¹ to 10⁻² - Time range: 10⁰ to 10¹ seconds - **Gray diamonds (512x512 6/8bit I/O)**: - RMSE values: ~10⁻¹ to 10⁰ - Time range: 10⁰ to 10¹ seconds - **Trends**: - Green crosses maintain lower RMSE than gray diamonds. - Progression line (10⁻¹) separates high and low performance. --- ### Key Observations 1. **IRdrop Impact**: Configurations with IRdrop (green crosses) consistently outperform NO_IRdrop (orange circles) in RMSE. 2. **Bit Depth Tradeoff**: 6/8bit I/O (green) achieves lower RMSE than 32/32bit I/O (blue/orange) at similar time scales. 3. **Scaling Effects**: 512x512 IRdrop (gray diamonds) shows higher RMSE than 64x64 IRdrop (green crosses), suggesting diminishing returns at larger scales. 4. **Progression Lines**: Dashed lines act as benchmarks, with performance clustering around or below these thresholds. --- ### Interpretation The data demonstrates that **IRdrop with lower bit I/O (6/8bit)** optimizes RMSE across both 64x64 and 512x512 scales, outperforming higher bit I/O (32/32bit) and configurations without IRdrop. The progression lines suggest that as time increases, systems with IRdrop approach or maintain performance near these benchmarks. Scaling to 512x512 introduces higher RMSE compared to 64x64, indicating potential architectural limitations at larger scales. The absence of IRdrop (orange circles) results in significantly worse performance, highlighting its critical role in error minimization. These findings align with the "Prog." thresholds, suggesting that IRdrop-enabled systems are designed to meet or exceed these targets.