## Bar Chart: Normalized Runtime Comparison ### Overview The image is a bar chart comparing the normalized runtime performance of three different architectures (TPU-like, DPU-like, and REASON) across four different task types: Neuro-Only, Symbolic-Only (logical/probabilistic), and End-to-End Neuro+Symbolic. The x-axis represents different configurations (AlphaG, Guard, GeLaTo, Ctrl-G, NPC, LINC) for each task type. The y-axis represents the normalized runtime on a logarithmic scale. ### Components/Axes * **Title:** None explicitly given, but the chart compares normalized runtime. * **Y-Axis:** "Norm. Runtime (X)" with a logarithmic scale. The values 10⁰, 10¹, and 10² are marked. * **X-Axis:** Categorical, divided into four main sections: "Neuro-Only", "Symbolic-Only (logical/probabilistic)", and "End-to-End Neuro+Symbolic". Each section contains the same sub-categories: "AlphaG", "Guard", "GeLaTo", "Ctrl-G", "NPC", and "LINC". * **Legend:** Located at the top-left of the chart. * Green with diagonal lines: "TPU-like (systolic-based array)" * Pink with vertical lines: "DPU-like (tree-based array)" * Blue with a checkered pattern: "REASON" ### Detailed Analysis **Neuro-Only** * **AlphaG:** * TPU-like: 0.69 * DPU-like: 4.31 * REASON: 1.00 * **Guard:** * TPU-like: 0.71 * DPU-like: 4.40 * REASON: 1.00 * **GeLaTo:** * TPU-like: 0.68 * DPU-like: 4.29 * REASON: 1.00 * **Ctrl-G:** * TPU-like: 0.66 * DPU-like: 4.49 * REASON: 1.00 * **NPC:** * TPU-like: 0.73 * DPU-like: 4.32 * REASON: 1.00 * **LINC:** * TPU-like: 0.68 * DPU-like: 4.30 * REASON: 1.00 **Symbolic-Only (logical/probabilistic)** * **AlphaG:** * TPU-like: 81.35 * DPU-like: 25.13 * REASON: 1.00 * **Guard:** * TPU-like: 76.10 * DPU-like: 4.84 * REASON: 1.00 * **GeLaTo:** * TPU-like: 109.24 * DPU-like: 5.03 * REASON: 1.00 * **Ctrl-G:** * TPU-like: 78.48 * DPU-like: 6.07 * REASON: 1.00 * **NPC:** * TPU-like: 74.71 * DPU-like: 4.97 * REASON: 1.00 * **LINC:** * TPU-like: 90.89 * DPU-like: 23.97 * REASON: 1.00 **End-to-End Neuro+Symbolic** * **AlphaG:** * TPU-like: 21.31 * DPU-like: 7.86 * REASON: 1.00 * **Guard:** * TPU-like: 17.77 * DPU-like: 2.31 * REASON: 1.00 * **GeLaTo:** * TPU-like: 10.54 * DPU-like: 2.15 * REASON: 1.00 * **Ctrl-G:** * TPU-like: 18.02 * DPU-like: 2.90 * REASON: 1.00 * **NPC:** * TPU-like: 9.76 * DPU-like: 2.33 * REASON: 1.00 * **LINC:** * TPU-like: 8.59 * DPU-like: 6.10 * REASON: 1.00 ### Key Observations * For "Neuro-Only" tasks, TPU-like consistently has the lowest normalized runtime, followed by REASON, and then DPU-like. * For "Symbolic-Only" tasks, TPU-like has significantly higher normalized runtime compared to DPU-like and REASON. REASON consistently has a normalized runtime of 1.00. * For "End-to-End Neuro+Symbolic" tasks, TPU-like has a higher normalized runtime than DPU-like and REASON. REASON consistently has a normalized runtime of 1.00. * REASON consistently has a normalized runtime of 1.00 across all configurations and task types. ### Interpretation The chart demonstrates the relative performance of three different architectures (TPU-like, DPU-like, and REASON) across different types of tasks. The "Neuro-Only" tasks show that TPU-like architectures are the most efficient. However, for "Symbolic-Only" tasks, TPU-like architectures become significantly less efficient, with much higher normalized runtimes. The "End-to-End Neuro+Symbolic" tasks show a similar trend, although the differences are less extreme than in the "Symbolic-Only" case. The REASON architecture consistently maintains a normalized runtime of 1.00, suggesting it serves as a baseline or reference point for comparison. This could indicate that the normalized runtime is calculated relative to the performance of the REASON architecture. The data suggests that the choice of architecture should be tailored to the specific task. TPU-like architectures are well-suited for "Neuro-Only" tasks, but less efficient for "Symbolic-Only" tasks. DPU-like architectures show a more balanced performance across different task types, although they are not as efficient as TPU-like architectures for "Neuro-Only" tasks.

\n ## Bar Chart: Normalized Runtime Comparison of Different Architectures ### Overview This bar chart compares the normalized runtime (denoted as "Norm. Runtime (x)") of several neural network architectures (AlphaG, Guard, GelatoToCtrl-G, NPC, LINC) across three different categories: Neuro-Only, Symbolic-Only (logical/probabilistic), and End-to-End Neuro+Symbolic. Each architecture is represented by two bars: one for a TPU-like (systolic-based array) and one for a DPU-like (tree-based array). The y-axis is on a logarithmic scale. ### Components/Axes * **X-axis:** Represents the different architectures and categories. The categories are: * Neuro-Only: AlphaG, Guard, GelatoToCtrl-G, NPC, LINC * Symbolic-Only (logical/probabilistic): AlphaG, Guard, GelatoToCtrl-G, NPC, LINC * End-to-End Neuro+Symbolic: AlphaG, Guard, GelatoToCtrl-G, NPC, LINC * **Y-axis:** "Norm. Runtime (x)" on a logarithmic scale (base 10). The scale ranges from approximately 0.5 to 110. * **Legend:** Located at the top-left corner, distinguishing between: * TPU-like (systolic-based array) - Green bars with diagonal hatching. * DPU-like (tree-based array) - Pink bars with diagonal hatching. * **Title:** "REASON" is present in a yellow box above the chart. ### Detailed Analysis The chart consists of 30 bars (5 architectures x 2 array types x 3 categories). Here's a breakdown of the approximate normalized runtime values for each combination, referencing the legend colors for verification: **Neuro-Only:** * AlphaG (TPU): ~0.69 * AlphaG (DPU): ~4.31 * Guard (TPU): ~0.71 * Guard (DPU): ~4.40 * GelatoToCtrl-G (TPU): ~0.68 * GelatoToCtrl-G (DPU): ~4.29 * NPC (TPU): ~0.66 * NPC (DPU): ~4.49 * LINC (TPU): ~0.73 * LINC (DPU): ~4.32 **Symbolic-Only (logical/probabilistic):** * AlphaG (TPU): ~81.35 * AlphaG (DPU): ~25.13 * Guard (TPU): ~109.24 * Guard (DPU): ~76.10 * GelatoToCtrl-G (TPU): ~5.03 * GelatoToCtrl-G (DPU): ~78.48 * NPC (TPU): ~1.00 * NPC (DPU): ~74.71 * LINC (TPU): ~0.67 * LINC (DPU): ~23.97 **End-to-End Neuro+Symbolic:** * AlphaG (TPU): ~7.86 * AlphaG (DPU): ~21.31 * Guard (TPU): ~11.77 * Guard (DPU): ~10.54 * GelatoToCtrl-G (TPU): ~2.31 * GelatoToCtrl-G (DPU): ~18.02 * NPC (TPU): ~1.00 * NPC (DPU): ~9.76 * LINC (TPU): ~2.90 * LINC (DPU): ~8.59 **Trends:** * **TPU vs. DPU:** Generally, the DPU-like arrays have significantly higher normalized runtimes than the TPU-like arrays, especially in the Symbolic-Only and End-to-End categories. * **Category Impact:** The normalized runtime increases dramatically when moving from Neuro-Only to Symbolic-Only. The End-to-End category shows intermediate values. * **Architecture Variation:** Within each category, the normalized runtime varies considerably between the different architectures. ### Key Observations * The largest runtime values are observed for Guard with the TPU-like array in the Symbolic-Only category (~109.24). * NPC consistently shows a runtime of 1.00 for the TPU-like array in both the Symbolic-Only and End-to-End categories. * The Neuro-Only category has the lowest normalized runtimes, generally below 5. * The DPU-like arrays consistently show higher runtimes than the TPU-like arrays. ### Interpretation This chart demonstrates the performance trade-offs between different neural network architectures and hardware platforms (TPU vs. DPU) when performing different types of reasoning tasks (Neuro-Only, Symbolic-Only, End-to-End). The substantial increase in runtime for the Symbolic-Only category suggests that symbolic reasoning is significantly more computationally expensive than purely neural processing, at least for these architectures and hardware. The End-to-End approach attempts to bridge the gap, but still exhibits higher runtimes than the Neuro-Only approach. The consistent performance of NPC with a runtime of 1.00 on the TPU-like array in the Symbolic-Only and End-to-End categories suggests it may be a particularly efficient architecture for these tasks on this hardware. The difference in performance between TPU and DPU suggests that the systolic array architecture of the TPU is better suited for these workloads than the tree-based architecture of the DPU. The "REASON" title suggests the chart is evaluating architectures for reasoning tasks. The logarithmic scale emphasizes the large differences in runtime, particularly for the Symbolic-Only category.

## Grouped Bar Chart: Normalized Runtime Comparison Across Neuro-Symbolic AI Approaches ### Overview The image displays a grouped bar chart comparing the normalized runtime (in multiples, X) of three different computational architectures—TPU-like (systolic-based array), DPU-like (tree-based array), and REASON—across six different AI systems (AlphaG, Guard, GeLaTo, Ctrl-G, NPC, LINC). The comparison is segmented into three distinct task categories: Neuro-Only, Symbolic-Only (logical/probabilistic), and End-to-End Neuro+Symbolic. The y-axis uses a logarithmic scale. ### Components/Axes * **Chart Title:** Not fully visible in the provided crop. * **Y-Axis:** * **Label:** `Norm. Runtime (X)` * **Scale:** Logarithmic, ranging from `10^0` (1) to `10^2` (100). * **Major Ticks:** `10^0`, `10^1`, `10^2`. * **X-Axis:** Grouped by task category, with six AI systems listed under each. * **Primary Groups (Bottom Labels):** 1. `Neuro-Only` 2. `Symbolic-Only (logical/probabilistic)` 3. `End-to-End Neuro+Symbolic` * **Sub-categories (AI Systems):** `AlphaG`, `Guard`, `GeLaTo`, `Ctrl-G`, `NPC`, `LINC` (repeated under each primary group). * **Legend (Top-Left):** * **Green (diagonal hatch):** `TPU-like (systolic-based array)` * **Pink (vertical hatch):** `DPU-like (tree-based array)` * **Blue (cross-hatch):** `REASON` * **Data Labels:** Each bar has its exact numerical value printed directly above it. ### Detailed Analysis **1. Neuro-Only Tasks:** * **Trend:** REASON bars are uniformly flat at the baseline (1.00). TPU-like and DPU-like bars show modest, similar runtimes slightly above 1. * **Data Points (TPU-like / DPU-like / REASON):** * AlphaG: 0.69 / 4.31 / 1.00 * Guard: 0.71 / 4.40 / 1.00 * GeLaTo: 0.68 / 4.29 / 1.00 * Ctrl-G: 0.66 / 4.49 / 1.00 * NPC: 0.73 / 4.32 / 1.00 * LINC: 0.68 / 4.30 / 1.00 **2. Symbolic-Only (logical/probabilistic) Tasks:** * **Trend:** A dramatic increase in runtime for TPU-like architectures, with bars reaching near or above the `10^2` (100) mark. DPU-like runtimes also increase significantly but remain an order of magnitude lower than TPU-like. REASON remains constant at 1.00. * **Data Points (TPU-like / DPU-like / REASON):** * AlphaG: 81.35 / 25.13 / 1.00 * Guard: 76.10 / 4.84 / 1.00 * GeLaTo: 109.24 / 5.03 / 1.00 * Ctrl-G: 78.48 / 6.07 / 1.00 * NPC: 74.71 / 4.97 / 1.00 * LINC: 90.89 / 23.97 / 1.00 **3. End-to-End Neuro+Symbolic Tasks:** * **Trend:** Runtimes for TPU-like and DPU-like architectures decrease compared to the Symbolic-Only category but remain higher than in the Neuro-Only category. REASON continues to hold at 1.00. * **Data Points (TPU-like / DPU-like / REASON):** * AlphaG: 21.31 / 7.86 / 1.00 * Guard: 17.77 / 2.31 / 1.00 * GeLaTo: 10.54 / 2.15 / 1.00 * Ctrl-G: 18.02 / 2.90 / 1.00 * NPC: 9.76 / 2.33 / 1.00 * LINC: 8.59 / 6.10 / 1.00 ### Key Observations 1. **REASON's Consistency:** The REASON architecture (blue bars) maintains a normalized runtime of exactly 1.00 across all six AI systems and all three task categories. This serves as the baseline for comparison. 2. **Symbolic Task Performance Gap:** The most striking feature is the massive performance gap in the **Symbolic-Only** category. TPU-like architectures are 75-109x slower than the REASON baseline, while DPU-like architectures are 5-25x slower. 3. **Task Category Impact:** For both TPU-like and DPU-like architectures, the runtime order from fastest to slowest is consistently: Neuro-Only < End-to-End Neuro+Symbolic < Symbolic-Only. 4. **System-Specific Variance:** Within the Symbolic-Only category, the `GeLaTo` system shows the highest runtime for TPU-like (109.24), while `LINC` shows the highest for DPU-like (23.97). In the Neuro-Only category, runtimes are very uniform across systems for a given architecture. ### Interpretation This chart demonstrates a clear architectural advantage for the REASON system in terms of computational efficiency, particularly for symbolic reasoning tasks. The data suggests that traditional systolic (TPU-like) and tree-based (DPU-like) arrays incur a severe performance penalty when handling purely logical or probabilistic workloads, with runtimes exploding by one to two orders of magnitude. The "End-to-End" results indicate that combining neuro and symbolic components mitigates this penalty somewhat, but does not eliminate it. The consistent 1.00 runtime for REASON implies it is either the reference system against which others are normalized, or it possesses a fundamentally different and more efficient computational model for these mixed workloads. The chart effectively argues that for AI systems requiring significant symbolic reasoning, the REASON architecture offers substantial and consistent runtime benefits over the compared TPU-like and DPU-like alternatives.

## Bar Chart: Normalized Runtime Comparison Across Array Architectures ### Overview The chart compares normalized runtime (logarithmic scale) of three array architectures (TPU-like, DPU-like, REASON) across three computational paradigms: Neuro-Only, Symbolic-Only (logical/probabilistic), and End-to-End Neuro+Symbolic. Data is presented for six computational frameworks: AlphaG, Guard, GeLaTo, Ctrl-G, NPC, and LINC. ### Components/Axes - **X-axis**: Computational paradigms (Neuro-Only, Symbolic-Only, End-to-End Neuro+Symbolic) with subcategories (AlphaG, Guard, GeLaTo, Ctrl-G, NPC, LINC) - **Y-axis**: Normalized Runtime (X) on logarithmic scale (10⁰ to 10²) - **Legend**: - Green (TPU-like, stochastic-based array) - Pink (DPU-like, tree-based array) - Blue (REASON) - **Placement**: Legend in top-left corner; bars grouped by paradigm with subcategories as clustered bars ### Detailed Analysis #### Neuro-Only - **AlphaG**: TPU-like (0.69), DPU-like (4.31), REASON (1.00) - **Guard**: TPU-like (0.71), DPU-like (4.40), REASON (1.00) - **GeLaTo**: TPU-like (0.68), DPU-like (4.29), REASON (1.00) - **Ctrl-G**: TPU-like (0.66), DPU-like (4.49), REASON (1.00) - **NPC**: TPU-like (0.73), DPU-like (4.32), REASON (1.00) - **LINC**: TPU-like (0.68), DPU-like (4.30), REASON (1.00) #### Symbolic-Only (logical/probabilistic) - **AlphaG**: TPU-like (81.35), DPU-like (25.13), REASON (1.00) - **Guard**: TPU-like (76.10), DPU-like (4.84), REASON (1.00) - **GeLaTo**: TPU-like (78.48), DPU-like (6.07), REASON (1.00) - **Ctrl-G**: TPU-like (74.71), DPU-like (4.97), REASON (1.00) - **NPC**: TPU-like (109.24), DPU-like (5.03), REASON (1.00) - **LINC**: TPU-like (90.89), DPU-like (23.97), REASON (1.00) #### End-to-End Neuro+Symbolic - **AlphaG**: TPU-like (21.31), DPU-like (7.86), REASON (1.00) - **Guard**: TPU-like (17.77), DPU-like (2.31), REASON (1.00) - **GeLaTo**: TPU-like (18.02), DPU-like (2.90), REASON (1.00) - **Ctrl-G**: TPU-like (10.54), DPU-like (2.15), REASON (1.00) - **NPC**: TPU-like (9.76), DPU-like (2.33), REASON (1.00) - **LINC**: TPU-like (8.59), DPU-like (6.10), REASON (1.00) ### Key Observations 1. **TPU-like Dominance**: TPU-like arrays consistently show the highest runtime across all paradigms, with Symbolic-Only reaching extreme values (e.g., 109.24 for NPC). 2. **REASON Efficiency**: REASON arrays maintain the lowest runtime (1.00) in all cases, suggesting optimal performance. 3. **End-to-End Reduction**: End-to-End Neuro+Symbolic paradigms show ~50-70% runtime reduction compared to Symbolic-Only (e.g., NPC drops from 109.24 to 9.76). 4. **DPU-like Variability**: DPU-like arrays show mixed performance, with some subcategories (e.g., LINC in Symbolic-Only) having notably higher values (23.97). ### Interpretation The data demonstrates that: - **TPU-like architectures** are resource-intensive, particularly in symbolic processing, likely due to complex stochastic operations. - **REASON arrays** achieve near-optimal efficiency, possibly through streamlined logical/probabilistic computation. - **End-to-End integration** significantly reduces runtime, indicating that combining neuro and symbolic processing mitigates individual architecture bottlenecks. - **DPU-like performance** varies widely, suggesting tree-based arrays may struggle with certain symbolic tasks but perform better in hybrid scenarios. The logarithmic scale emphasizes exponential differences in runtime, particularly in Symbolic-Only paradigms, where TPU-like arrays show orders-of-magnitude higher resource demands compared to REASON.