## 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.**