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  "model_id": "qwen3.6_4bit_dwq",
  "model": "/Volumes/fast/ai/weights/qwen3.6-35b-a3b-4bit-dwq",
  "task_id": "rs_04",
  "category": "reasoning",
  "slug": "bandwidth_tps_calc",
  "timestamp": "2026-04-19T17:56:09",
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            "role": "assistant",
            "content": "\n\nHere's the step-by-step calculation:\n\n### (1) Theoretical Maximum Tokens Per Second\n- **Active parameters per token**: 3B = 3 × 10⁹ parameters\n- **Bytes per parameter**: 2 bytes (standard BF16/FP16 precision for LLM inference)\n- **Weight data loaded per token**: `3B × 2 bytes = 6 GB`\n- **Available bandwidth**: 900 GB/s\n\n\\[\n\\text{Theoretical TPS} = \\frac{\\text{Bandwidth}}{\\text{Data per token}} = \\frac{900\\ \\text{GB/s}}{6\\ \\text{GB/token}} = \\mathbf{150\\ \\text{tokens/second}}\n\\]\n\n### (2) Realistic Range (30–50% of Peak)\nvLLM and similar inference engines typically achieve 30–50% of theoretical memory bandwidth peak due to kernel launch overhead, memory management, KV-cache handling, and system-level bottlenecks.\n\n- Lower bound: `150 × 0.30 = 45 tokens/second`\n- Upper bound: `150 × 0.50 = 75 tokens/second`\n\n\\[\n\\text{Realistic range} = \\mathbf{45\\text{–}75\\ \\text{tokens/second}}\n\\]\n\n**Note:** This calculation assumes the workload is strictly memory-bandwidth bound (typical for autoregressive decoding), single-stream or small-batch generation, and that the 900 GB/s C2C link is fully utilized for weight streaming. Real-world throughput may vary with batch size, sequence length, quantization, and system configuration.",
            "reasoning": "Here's a thinking process:\n\n1.  **Understand User Input:**\n   - Hardware: GB10 chip (likely refers to NVIDIA Grace Blackwell or similar, but the key spec given is NVLink-C2C bandwidth = 900 GB/s)\n   - Model: 35B MoE (Mixture of Experts) with 3B active parameters\n   - Data loading per token: active_params × 2 bytes (assuming FP16/BF16 precision, which is standard for LLM inference)\n   - Questions:\n     (1) Theoretical maximum tokens per second (TPS)\n     (2) Realistic range given vLLM achieves 30-50% of theoretical peak\n\n2.  **Identify Key Variables & Formulas:**\n   - Bandwidth (B) = 900 GB/s = 900 × 10^9 bytes/s\n   - Active parameters per token (P) = 3B = 3 × 10^9 parameters\n   - Bytes per parameter (D) = 2 bytes\n   - Data per token (Data) = P × D = 3 × 10^9 × 2 = 6 × 10^9 bytes = 6 GB\n   - Theoretical TPS = Bandwidth / Data per token\n   - Realistic TPS = Theoretical TPS × (0.30 to 0.50)\n\n3.  **Calculate Theoretical Maximum TPS:**\n   - Data per token = 6 GB\n   - Bandwidth = 900 GB/s\n   - TPS = 900 GB/s ÷ 6 GB/token = 150 tokens/second\n\n4.  **Calculate Realistic Range:**\n   - Lower bound: 150 × 0.30 = 45 TPS\n   - Upper bound: 150 × 0.50 = 75 TPS\n   - Realistic range: 45–75 tokens/second\n\n5.  **Verify Assumptions & Context:**\n   - \"GB10 chip\" likely refers to NVIDIA's Grace Blackwell architecture (GB200/GB100 etc.), but the exact model name isn't critical since the bandwidth is explicitly given.\n   - NVLink-C2C (Chip-to-Chip) bandwidth of 900 GB/s is plausible for modern interconnects.\n   - MoE model: 35B total, 3B active. Only active parameters need to be loaded per token. Correct.\n   - 2 bytes per parameter: Standard for BF16/FP16 inference. Correct.\n   - vLLM efficiency: 30-50% of theoretical peak is a reasonable assumption for memory-bound LLM inference workloads due to overhead, kernel launch, memory management, etc.\n   - Calculation: 900 / (3 × 2) = 150. Correct.\n   - Range: 45-75. Correct.\n\n6.  **Structure the Answer:**\n   - State assumptions clearly\n   - Show step-by-step calculation for (1)\n   - Show step-by-step calculation for (2)\n   - Provide final answers concisely\n   - Add brief context/notes if necessary (e.g., memory bandwidth vs compute, real-world factors)\n\n   Draft:\n   (1) Theoretical maximum TPS:\n   - Data per token = 3B active params × 2 bytes = 6 GB\n   - Bandwidth = 900 GB/s\n   - TPS = 900 / 6 = 150 tokens/second\n\n   (2) Realistic range (30–50% efficiency):\n   - 150 × 0.30 = 45 TPS\n   - 150 × 0.50 = 75 TPS\n   - Range: 45–75 tokens/second\n\n   Add notes: This assumes memory bandwidth is the sole bottleneck, which is typical for LLM inference. Real-world performance may vary based on batch size, sequence length, KV cache management, and system overhead.\n\n7.  **Self-Correction/Refinement:**\n   - Check units: GB/s vs GB/token → tokens/s. Correct.\n   - Check parameter count: 3B = 3,000,000,000. 3B × 2 = 6B bytes = 6 GB. Correct.\n   - 900 / 6 = 150. Correct.\n   - 30-50% of 150 = 45-75. Correct.\n   - The question is straightforward. No hidden tricks.\n   - I'll present it clearly with formulas and final numbers.\n   - I should mention that this is a memory-bound calculation, which is standard for autoregressive LLM decoding.\n   - All good.\n\n   Final output matches the draft.✅\n"
          }
        }
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  "final_text": "\n\nHere's the step-by-step calculation:\n\n### (1) Theoretical Maximum Tokens Per Second\n- **Active parameters per token**: 3B = 3 × 10⁹ parameters\n- **Bytes per parameter**: 2 bytes (standard BF16/FP16 precision for LLM inference)\n- **Weight data loaded per token**: `3B × 2 bytes = 6 GB`\n- **Available bandwidth**: 900 GB/s\n\n\\[\n\\text{Theoretical TPS} = \\frac{\\text{Bandwidth}}{\\text{Data per token}} = \\frac{900\\ \\text{GB/s}}{6\\ \\text{GB/token}} = \\mathbf{150\\ \\text{tokens/second}}\n\\]\n\n### (2) Realistic Range (30–50% of Peak)\nvLLM and similar inference engines typically achieve 30–50% of theoretical memory bandwidth peak due to kernel launch overhead, memory management, KV-cache handling, and system-level bottlenecks.\n\n- Lower bound: `150 × 0.30 = 45 tokens/second`\n- Upper bound: `150 × 0.50 = 75 tokens/second`\n\n\\[\n\\text{Realistic range} = \\mathbf{45\\text{–}75\\ \\text{tokens/second}}\n\\]\n\n**Note:** This calculation assumes the workload is strictly memory-bandwidth bound (typical for autoregressive decoding), single-stream or small-batch generation, and that the 900 GB/s C2C link is fully utilized for weight streaming. Real-world throughput may vary with batch size, sequence length, quantization, and system configuration.",
  "final_reasoning": "Here's a thinking process:\n\n1.  **Understand User Input:**\n   - Hardware: GB10 chip (likely refers to NVIDIA Grace Blackwell or similar, but the key spec given is NVLink-C2C bandwidth = 900 GB/s)\n   - Model: 35B MoE (Mixture of Experts) with 3B active parameters\n   - Data loading per token: active_params × 2 bytes (assuming FP16/BF16 precision, which is standard for LLM inference)\n   - Questions:\n     (1) Theoretical maximum tokens per second (TPS)\n     (2) Realistic range given vLLM achieves 30-50% of theoretical peak\n\n2.  **Identify Key Variables & Formulas:**\n   - Bandwidth (B) = 900 GB/s = 900 × 10^9 bytes/s\n   - Active parameters per token (P) = 3B = 3 × 10^9 parameters\n   - Bytes per parameter (D) = 2 bytes\n   - Data per token (Data) = P × D = 3 × 10^9 × 2 = 6 × 10^9 bytes = 6 GB\n   - Theoretical TPS = Bandwidth / Data per token\n   - Realistic TPS = Theoretical TPS × (0.30 to 0.50)\n\n3.  **Calculate Theoretical Maximum TPS:**\n   - Data per token = 6 GB\n   - Bandwidth = 900 GB/s\n   - TPS = 900 GB/s ÷ 6 GB/token = 150 tokens/second\n\n4.  **Calculate Realistic Range:**\n   - Lower bound: 150 × 0.30 = 45 TPS\n   - Upper bound: 150 × 0.50 = 75 TPS\n   - Realistic range: 45–75 tokens/second\n\n5.  **Verify Assumptions & Context:**\n   - \"GB10 chip\" likely refers to NVIDIA's Grace Blackwell architecture (GB200/GB100 etc.), but the exact model name isn't critical since the bandwidth is explicitly given.\n   - NVLink-C2C (Chip-to-Chip) bandwidth of 900 GB/s is plausible for modern interconnects.\n   - MoE model: 35B total, 3B active. Only active parameters need to be loaded per token. Correct.\n   - 2 bytes per parameter: Standard for BF16/FP16 inference. Correct.\n   - vLLM efficiency: 30-50% of theoretical peak is a reasonable assumption for memory-bound LLM inference workloads due to overhead, kernel launch, memory management, etc.\n   - Calculation: 900 / (3 × 2) = 150. Correct.\n   - Range: 45-75. Correct.\n\n6.  **Structure the Answer:**\n   - State assumptions clearly\n   - Show step-by-step calculation for (1)\n   - Show step-by-step calculation for (2)\n   - Provide final answers concisely\n   - Add brief context/notes if necessary (e.g., memory bandwidth vs compute, real-world factors)\n\n   Draft:\n   (1) Theoretical maximum TPS:\n   - Data per token = 3B active params × 2 bytes = 6 GB\n   - Bandwidth = 900 GB/s\n   - TPS = 900 / 6 = 150 tokens/second\n\n   (2) Realistic range (30–50% efficiency):\n   - 150 × 0.30 = 45 TPS\n   - 150 × 0.50 = 75 TPS\n   - Range: 45–75 tokens/second\n\n   Add notes: This assumes memory bandwidth is the sole bottleneck, which is typical for LLM inference. Real-world performance may vary based on batch size, sequence length, KV cache management, and system overhead.\n\n7.  **Self-Correction/Refinement:**\n   - Check units: GB/s vs GB/token → tokens/s. Correct.\n   - Check parameter count: 3B = 3,000,000,000. 3B × 2 = 6B bytes = 6 GB. Correct.\n   - 900 / 6 = 150. Correct.\n   - 30-50% of 150 = 45-75. Correct.\n   - The question is straightforward. No hidden tricks.\n   - I'll present it clearly with formulas and final numbers.\n   - I should mention that this is a memory-bound calculation, which is standard for autoregressive LLM decoding.\n   - All good.\n\n   Final output matches the draft.✅\n",
  "final_tool_calls": [],
  "auto_pass": true,
  "auto_notes": "",
  "auto_reasoning_hit": "11/11"
}