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Add MFU formula as reference material (#395)
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* add MFU formula as reference material

* Update previous_chapters.py
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@rasbt
rasbt authored Oct 11, 2024
1 parent 1a8d292 commit 6d0f59a
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362 changes: 354 additions & 8 deletions ch04/02_performance-analysis/flops-analysis.ipynb
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Expand Up @@ -53,19 +53,27 @@
"output_type": "stream",
"text": [
"thop version: 0.1.1-2209072238\n",
"torch version: 2.2.2\n",
"tiktoken version: 0.5.1\n"
"torch version: 2.2.1+cu121\n"
]
}
],
"source": [
"from importlib.metadata import version\n",
"\n",
"import matplotlib\n",
"import torch\n",
"\n",
"print(\"thop version:\", version(\"thop\"))\n",
"print(\"torch version:\", version(\"torch\"))"
"pkgs = [\n",
" \"thop\",\n",
" \"torch\",\n",
"]\n",
"for p in pkgs:\n",
" print(f\"{p} version: {version(p)}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"# Simple benchmark with fixed batch size"
]
},
{
Expand Down Expand Up @@ -112,7 +120,8 @@
"}\n",
"\n",
"device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
"input_tensor = torch.randint(0, 50257, (2, 1024)).to(device)\n",
"batch_size = 2\n",
"input_tensor = torch.randint(0, 50257, (batch_size, 1024)).to(device)\n",
"\n",
"for size in model_configs:\n",
" BASE_CONFIG.update(model_configs[size])\n",
Expand All @@ -129,6 +138,343 @@
" del model\n",
" torch.cuda.empty_cache()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"# Simple benchmark with automatic batch size finding"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Processing gpt-small (124M)\n",
" Batch size 128: 3.2e+13 FLOPS\n",
" Batch size 160: 4.0e+13 FLOPS\n",
" Batch size 176: 4.5e+13 FLOPS\n",
" Batch size 184: 4.7e+13 FLOPS\n",
" Batch size 186: 4.7e+13 FLOPS\n",
"\n",
"Processing gpt-medium (355M)\n",
" Batch size 128: 9.3e+13 FLOPS\n",
" Batch size 136: 9.8e+13 FLOPS\n",
" Batch size 140: 1.0e+14 FLOPS\n",
" Batch size 142: 1.0e+14 FLOPS\n",
" Batch size 143: 1.0e+14 FLOPS\n",
"\n",
"Processing gpt-large (774M)\n",
" Batch size 128: 2.0e+14 FLOPS\n",
"\n",
"Processing gpt-xl (1558M)\n",
" Batch size 64: 2.0e+14 FLOPS\n",
" Batch size 96: 3.1e+14 FLOPS\n"
]
}
],
"source": [
"for size in model_configs:\n",
" print(f\"\\nProcessing {size}\")\n",
" config = BASE_CONFIG.copy()\n",
" config.update(model_configs[size])\n",
"\n",
" min_batch_size = 1\n",
" max_batch_size = None\n",
" max_possible_batch_size = 4096\n",
"\n",
" while min_batch_size <= max_possible_batch_size:\n",
" batch_size = (min_batch_size + max_possible_batch_size) // 2\n",
" try:\n",
" input_tensor = torch.randint(\n",
" 0, config[\"vocab_size\"],\n",
" (batch_size, config[\"context_length\"]),\n",
" device=device\n",
" )\n",
"\n",
" model = GPTModel(config).bfloat16().to(device)\n",
"\n",
" # MACS = multiply-accumulate operations\n",
" # MACS are typically counted as two FLOPS (one multiply and one accumulate)\n",
" macs, params = profile(model, inputs=(input_tensor,), verbose=False)\n",
" flops = 2 * macs\n",
" print(f\" Batch size {batch_size}: {flops:.1e} FLOPS\")\n",
"\n",
" # If successful, try a larger batch size\n",
" min_batch_size = batch_size + 1\n",
" max_batch_size = batch_size\n",
"\n",
" # Clean up\n",
" del model, input_tensor\n",
" torch.cuda.empty_cache()\n",
"\n",
" except RuntimeError as e:\n",
" if \"out of memory\" in str(e):\n",
" # Try smaller batch size\n",
" max_possible_batch_size = batch_size - 1\n",
"\n",
" # Clean up\n",
" try:\n",
" del model, input_tensor\n",
" torch.cuda.empty_cache()\n",
" except NameError:\n",
" pass\n",
" else:\n",
" raise e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"&nbsp;\n",
"# Benchmark with automatic batch size finding and Model FLOP Utilization (MFU)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Model FLOPs Utilization (MFU) explanation from the [PaLM paper](https://arxiv.org/abs/2204.02311)\n",
"\n",
"> We propose a new metric for efficiency that is implementation-independent and permits a cleaner comparison of system efficiency, called model FLOPs utilization (MFU). This is the ratio of the observed throughput (tokens-per-second) relative to the theoretical maximum throughput of a system operating at peak FLOPs. Crucially, the “theoretical maximum” throughput only accounts for the required operations to compute the forward+backward passes, and not rematerialization.\n",
"\n",
"\n",
"$$\\text{MFU} = \\frac{\\text{Observed Tokens per Second}}{\\text{Theoretical Max Tokens per Second}}$$\n",
"\n",
"where \n",
"\n",
"$$\\text{Theoretical Max Tokens per Second} = \\frac{\\text{Max FLOPs per Second}}{\\text{Total FLOPs per Token}}$$\n",
"\n",
"and\n",
"\n",
"$$\\text{Tokens per Second} = \\frac{\\text{Batch Size} \\times \\text{Sequence Length}}{\\text{Total Time}}$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Max flops per second provided by the GPU manufacturer\n",
"\n",
"flops_per_second = {\n",
" \"H100\": {\n",
" torch.float32: 60e12, # 60 TFLOPs for FP32 on NVIDIA H100\n",
" torch.float16: 1.979e15, # 1979 TFLOPs for FP16 on NVIDIA H100\n",
" torch.bfloat16: 1.979e15\n",
" },\n",
" \"L4\": {\n",
" torch.float32: 15e12, # 15 TFLOPs for FP32 on NVIDIA L4\n",
" torch.float16: 30e12, # 30 TFLOPs for FP16 on NVIDIA L4\n",
" torch.bfloat16: 30e12 \n",
" },\n",
" \"T4\": {\n",
" torch.float32: 8.1e12, # 8.1 TFLOPs for FP32 on NVIDIA T4\n",
" torch.float16: 130e12, # 130 TFLOPs for FP16 on NVIDIA T4\n",
" torch.bfloat16: 130e12\n",
" },\n",
" \"A10G\": {\n",
" torch.float32: 15.6e12, # 15.6 TFLOPs for FP32 on NVIDIA A10G\n",
" torch.float16: 78e12, # 78 TFLOPs for FP16 on NVIDIA A10G\n",
" torch.bfloat16: 78e12\n",
" },\n",
" \"A100\": {\n",
" torch.float32: 19.5e12, # 19.5 TFLOPs for FP32 on NVIDIA A100\n",
" torch.float16: 1.248e15, # 1248 TFLOPs for FP16 on NVIDIA A100\n",
" torch.bfloat16: 1.248e15\n",
" },\n",
" \"H200\": {\n",
" torch.float32: 70e12, # 70 TFLOPs for FP32 on NVIDIA H200\n",
" torch.float16: 1.2e15, # Assuming 1200 TFLOPs for FP16 on NVIDIA H200\n",
" torch.bfloat16: 1.2e15\n",
" },\n",
" \"RTX_3080\": {\n",
" torch.float32: 29.8e12, # 29.8 TFLOPs for FP32 on NVIDIA RTX 3080\n",
" torch.float16: 59.6e12, # 59.6 TFLOPs for FP16 on NVIDIA RTX 3080\n",
" torch.bfloat16: 59.6e12\n",
" },\n",
" \"RTX_3090\": {\n",
" torch.float32: 35.6e12, # 35.6 TFLOPs for FP32 on NVIDIA RTX 3090\n",
" torch.float16: 71.2e12, # 71.2 TFLOPs for FP16 on NVIDIA RTX 3090\n",
" torch.bfloat16: 71.2e12\n",
" },\n",
" \"GTX_1080\": {\n",
" torch.float32: 8.9e12, # 8.9 TFLOPs for FP32 on NVIDIA GTX 1080\n",
" torch.float16: 8.9e12, # No dedicated FP16 performance; using FP32 value\n",
" torch.bfloat16: 8.9e12\n",
" },\n",
" \"GTX_1080Ti\": {\n",
" torch.float32: 11.3e12, # 11.3 TFLOPs for FP32 on NVIDIA GTX 1080Ti\n",
" torch.float16: 11.3e12, # No dedicated FP16 performance; using FP32 value\n",
" torch.bfloat16: 11.3e12\n",
" },\n",
" \"GTX_1660\": {\n",
" torch.float32: 5e12, # 5 TFLOPs for FP32 on NVIDIA GTX 1660\n",
" torch.float16: 5e12, # No dedicated FP16 performance; using FP32 value\n",
" torch.bfloat16: 5e12\n",
" },\n",
" \"GTX_1660Ti\": {\n",
" torch.float32: 5.5e12, # 5.5 TFLOPs for FP32 on NVIDIA GTX 1660Ti\n",
" torch.float16: 5.5e12, # No dedicated FP16 performance; using FP32 value\n",
" torch.bfloat16: 5.5e12\n",
" }\n",
"}\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"GPU Model: L4\n",
"\n",
"Processing gpt-small (124M)\n",
" Batch size 8: Tokens/sec: 14488.21, MFU: 0.3580\n",
" Batch size 12: Tokens/sec: 15378.16, MFU: 0.3799\n",
"\n",
"Processing gpt-medium (355M)\n",
" Batch size 2: Tokens/sec: 6493.81, MFU: 0.4591\n",
" Batch size 3: Tokens/sec: 6328.82, MFU: 0.4474\n",
"\n",
"Processing gpt-large (774M)\n",
" Batch size 4: Tokens/sec: 3130.38, MFU: 0.4834\n",
"\n",
"Processing gpt-xl (1558M)\n",
" Batch size 2: Tokens/sec: 1896.17, MFU: 0.5897\n"
]
}
],
"source": [
"import time\n",
"\n",
"def get_gpu_model(flops_per_second_dict):\n",
" device_name = torch.cuda.get_device_name(0)\n",
" for model in flops_per_second_dict.keys():\n",
" if model in device_name:\n",
" return model\n",
" return \"Unknown\" # Default if no matching model is found\n",
"\n",
"\n",
"gpu_model = get_gpu_model(flops_per_second)\n",
"print(\"GPU Model:\", gpu_model)\n",
"\n",
"if gpu_model != \"Unknown\":\n",
"\n",
" for size in model_configs:\n",
" print(f\"\\nProcessing {size}\")\n",
" config = BASE_CONFIG.copy()\n",
" config.update(model_configs[size])\n",
"\n",
" min_batch_size = 1\n",
" max_batch_size = None\n",
" max_possible_batch_size = 4096\n",
"\n",
" while min_batch_size <= max_possible_batch_size:\n",
" batch_size = (min_batch_size + max_possible_batch_size) // 2\n",
" try:\n",
" input_tensor = torch.randint(\n",
" 0, config[\"vocab_size\"],\n",
" (batch_size, config[\"context_length\"]),\n",
" device=device\n",
" )\n",
"\n",
" model = GPTModel(config).bfloat16().to(device)\n",
" model.train()\n",
"\n",
" # Start timing\n",
" torch.cuda.synchronize()\n",
" start_time = time.time()\n",
"\n",
" # Forward & backward pass\n",
" output = model(input_tensor)\n",
" loss = output.sum() # Compute a dummy loss \n",
" loss.backward()\n",
"\n",
" # End timing\n",
" torch.cuda.synchronize()\n",
" end_time = time.time()\n",
"\n",
" total_time_seconds = end_time - start_time\n",
"\n",
" # Calculate FLOPs for forward pass\n",
" macs, params = profile(model, inputs=(input_tensor,), verbose=False)\n",
" flops_forward = 2 * macs # Assuming one MAC equals two FLOPs\n",
"\n",
" # Estimate FLOPs for backward pass (typically 2x forward FLOPs)\n",
" flops_backward = 2 * flops_forward\n",
"\n",
" # Total FLOPs for forward + backward passes\n",
" total_flops = flops_forward + flops_backward # Or total_flops = flops_forward * 3\n",
"\n",
" data_type = next(model.parameters()).dtype\n",
" max_flops_per_second = flops_per_second[gpu_model].get(data_type, 0)\n",
"\n",
" # Compute tokens per second\n",
" tokens_processed = batch_size * config[\"context_length\"]\n",
" tokens_per_second = tokens_processed / total_time_seconds\n",
"\n",
" # Compute FLOPs per token\n",
" flops_per_token = total_flops / tokens_processed\n",
"\n",
" # Compute theoretical max tokens per second\n",
" if flops_per_token > 0:\n",
" theoretical_max_tokens_per_second = max_flops_per_second / flops_per_token\n",
" else:\n",
" theoretical_max_tokens_per_second = 0 # Avoid division by zero\n",
"\n",
" # Compute MFU\n",
" if theoretical_max_tokens_per_second > 0:\n",
" mfu = tokens_per_second / theoretical_max_tokens_per_second\n",
" else:\n",
" mfu = 0 # Avoid division by zero\n",
"\n",
" print(f\" Batch size {batch_size}: Tokens/sec: {tokens_per_second:.2f}, MFU: {mfu:.4f}\")\n",
"\n",
" # If successful, try a larger batch size\n",
" min_batch_size = batch_size + 1\n",
" max_batch_size = batch_size\n",
"\n",
" # Clean up\n",
" del model, input_tensor, output, loss\n",
" torch.cuda.empty_cache()\n",
"\n",
" except RuntimeError as e:\n",
" if \"out of memory\" in str(e).lower():\n",
" # Try smaller batch size\n",
" max_possible_batch_size = batch_size - 1\n",
"\n",
" # Clean up\n",
" try:\n",
" del model, input_tensor\n",
" torch.cuda.empty_cache()\n",
" except NameError:\n",
" pass\n",
" else:\n",
" raise e\n",
"\n",
"else:\n",
" print(\"Unknown GPU model. Please update the flops_per_second dictionary with your GPU information.\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Note that the batch sizes are smaller than previously because we also carry out the backward pass here, which is more memory-intensive"
]
}
],
"metadata": {
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