with calculating an software’s efficiency is that the real-world efficiency and theoretical efficiency can differ. With an ecosystem of merchandise that’s rising with excessive efficiency wants akin to Excessive Efficiency Computing (HPC), gaming, or within the present panorama – Massive Language Fashions (LLMs), it’s important to calculate precisely the efficiency of an software.
Merely measuring theoretical GFLOPs (Floating-Level Operations Per Second) isn’t sufficient, as purposes not often attain these maximums in the true world. That is the place the Roofline Mannequin is available in, providing a transparent visible methodology to estimate an software’s efficiency and highlighting the important position of hardware-specific optimizations.
Why easy metrics aren’t sufficient
Once we take into consideration measuring efficiency, there are just a few metrics that come to thoughts:
- Execution time: This tells you how lengthy a activity took however provides no perception into why.
- Cycles per Directions (CPI): This only measures the processor’s compute efficiency.
- Serial vs Parallel execution: Measures compute efficiency overlooking any {hardware} optimizations.
- Floating Level Operations Per Second (FLOP/s): This only represents a theoretical most which is commonly not achievable in a real-world situation.
Whereas these are good metrics, they typically don’t present sufficient data. As an example, utilizing the Floating Level Operations Per Seconds is a theoretical restrict which isn’t usually achieved. So utilizing that because the solely metric isn’t sufficient because it ignores a typical efficiency limiter – information motion.
Roofline Modeling
The Roofline Mannequin is a strong instrument that visually maps an software’s efficiency in opposition to the capabilities of a selected {hardware} structure, akin to a CPU or GPU. The mannequin will get its title from the form of the graph it produces, which contains a “roof” composed of a slanted line and a flat, horizontal line. This form represents the last word efficiency limits imposed by the {hardware}.
From this modeling approach, there are two parameters which outline the achievable limits with {hardware}:
- Knowledge motion: The time it takes to maneuver information, calculated as the whole information measurement divided by the system’s peak reminiscence bandwidth.
- Computation: The time required for calculations, decided by dividing the whole variety of floating-point operations by the system’s peak compute efficiency (generally measured in GFLOP/s).
The full execution time of an software is decided by the larger of those two values: max {data_movement, computation}.
Regardless of the {hardware} having higher compute efficiency, information motion can usually develop into the bottleneck. Roofline Modeling introduces the idea of Arithmetic Depth (AI). AI is the ratio of floating-point operations carried out for each byte of information moved from reminiscence.
- An algorithm with excessive Arithmetic Depth is taken into account compute-hungry. Its efficiency is restricted by how shortly calculations might be carried out.
- An algorithm with low Arithmetic Depth is taken into account data-hungry. Its efficiency is restricted by how shortly information might be moved.
Understanding the graph
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A Roofline graph plots the Attainable FLOP/s (y-axis) in opposition to the Arithmetic Depth (x-axis). The “roof” itself reveals the {hardware}’s limitations. The slanted a part of the roof represents the height information bandwidth (in GB/s), whereas the flat half represents the height computational efficiency (in GFLOPS). Notice that the whole lot within the picture is in a logarithmic scale.
- Factors beneath the roof: Point out suboptimal efficiency indicating scope of enchancment.
- Factors hitting the slanted line: Knowledge hungry software. Its efficiency is restricted by information bandwidth.
- Factors hitting the flat line: Compute hungry software. It’s utilizing the complete computational energy of the processor.
Why is Roofline Modeling vital?
Roofline Modeling offers a visible, intuitive strategy to perceive software efficiency, exhibiting key traits like Operational Depth, GPU capabilities, and attainable FLOP/s. This sort of modeling helps the programmer make focused optimizations to their software for {hardware} with which higher outcomes might be obtained.
- Bottleneck evaluation: Having a visible support makes it straightforward for the developer to determine the place the bottleneck is – reminiscence or efficiency. If the applying is reminiscence intensive, a developer can deal with bettering information locality with strategies like caching or loop tiling. If it’s compute intensive, the main focus can shift to enabling extra parallel computations or leveraging compiler optimizations.
- {Hardware} and software program design: Software program engineers mustn’t worry the underlying {hardware}. As an alternative, the {hardware} design ought to be embraced and optimized. Software program engineers can use insights from Roofline Modeling to embrace and optimize for the precise structure they’re utilizing.
Roofline Modeling in Motion
To carry out Roofline Modeling, we have to profile the applying to know the efficiency. From profiling, we are able to get metrics akin to Floating Level Operations (FLOPs) and reminiscence bandwidth utilization, each of that are required for Roofline Modeling. This text explores two of those instruments – Nvidia’s ncu which is the Nsight Compute CLI for GPU evaluation and PyTorch’s profiler, particularly for purposes utilizing PyTorch.
For detailed CUDA kernel optimization and exact FLOP/byte calculations, ncu offers direct GPU {hardware} counter data. In distinction, torch.profiler.profile provides a higher-level perspective inside PyTorch, serving to within the understanding of operator-level efficiency, tensor reminiscence utilization, and the general software conduct encompassing each CPU and GPU actions.
Profiling with ncu
ncu is the command line interface which is used for profiling CUDA kernels [2]. It could show outcomes immediately within the terminal or save them to a log file for later evaluation. To construct a Roofline mannequin, we have to seize the precise metrics that may enable us to calculate Arithmetic Depth.
We’ll use the PyTorch ImageNet repository [3] as our instance. It’s a good selection as a result of it’s straightforward to know, well-documented by PyTorch, and works with their profiler, so we are able to actually dig into the efficiency.
Step 1: Run the ncu command to gather metrics
Step one is to run the applying by ncu to gather the required hardware-level information. The command appears like this:
ncu --log-file
--metrics
--target-processes all
python3 - log-file: The log file through which we wish to retailer the outcomes.
- metrics: That is an important parameter and depicts the metrics that we wish to seize. For calculating Arithmetic Depth, we contemplate:
dram__sectors_write.sum: sum of DRAM sectors writtendram__sectors_read.sum: sum of DRAM sectors learnsmsp__sass_thread_inst_executed_op_fadd_pred_on.sum: sum of floating-point additionssmsp__sass_thread_inst_executed_op_fmul_pred_on.sum: sum of floating-point multiplicationssmsp__sass_thread_inst_executed_op_ffma_pred_on.sum: sum of floating-point fused multiply add operations
- target-process:
allflag ensures that we profile the complete software.
Our ncu command modifications to:
ncu --log-file logs_example --metrics dram__sectors_write.sum,
dram__sectors_read.sum,
smsp__sass_thread_inst_executed_op_fadd_pred_on.sum,
smsp__sass_thread_inst_executed_op_fmul_pred_on.sum,
smsp__sass_thread_inst_executed_op_ffma_pred_on.sum
--target-processes all python3
principal.py /imagenet --arch resnet50 --epochs 1 --batch-size 10
--print-freq 10 --seed 42Step 2: Calculating FLOPs from the metrics
As soon as the profiler has run, we are able to mixture the collected metrics to calculate the whole floating-point operations. The formulation is:
[FLOPs = 2 * FMA_count + FADD_count + FMUL_count]
- FLOPs: Rely of Floating Level Operations.
- FMA_count: Fused Multiply-Add (FMA) operations usually depend as 2 FLOPs (one multiplication and one addition). That is represented by the
smsp__sass_thread_inst_executed_op_ffma_pred_on.summetric. - FADD_count: That is represented by the
smsp__sass_thread_inst_executed_op_fadd_pred_on.summetric. - FMUL_count: That is represented by the
smsp__sass_thread_inst_executed_op_fmul_pred_on.summetric.
Step 3: Calculate the bytes transferred
Subsequent, we calculate the whole information transferred to and from DRAM. The ncu metrics present the variety of DRAM sectors learn and written. Assuming a typical sector measurement of 32 bytes for contemporary GPUs:
[Total_DRAM_bytes = (dram__sectors_read.sum + dram__sectors_write.sum) * 32]
Step 4: Calculate the Arithmetic Depth
With FLOPs and complete bytes, we are able to now calculate the Arithmetic Depth:
[AI = FLOPs / Total_DRAM_Bytes]
Step 5: Calculate execution time
To seek out the applying’s efficiency in FLOP/s, we additionally want the execution time. For this, we are able to use NVIDIA Nsight Methods (nsys), a system-wide profiler that may precisely measure the runtime of software segments. We run our software once more, this time with nsys, to generate a time-based report. From this report, we are able to extract the whole GPU operating time.
nsys profile -f true -o python3
Our nsys command modifications to:
nsys profile -f true -o time.qdrep python3 principal.py /imagenet
--arch resnet50 --epochs 1 --batch-size 10 --print-freq 10
--seed 42After operating this command, we are able to get the GPU_RUNNING_TIME.
Step 6: Calculate the applying efficiency
Lastly, we calculate the achieved efficiency in FLOP/s by dividing the whole FLOPs by the execution time:
[FLOP/s = FLOPs / GPU_RUNNING_TIME]
This worth provides us the “attainable FLOP/s” that we are able to plot on our Roofline graph.
Profiling with torch
For purposes written in PyTorch, the built-in torch.profiler.profile provides a user-friendly strategy to collect efficiency information. There are 2 choices which are supplied to the builders:
- Use the Profiler Context Supervisor
- Concentrating on Profiling for particular neural community layers
Profiler Context Supervisor
The a part of the code that we wish to profile might be wrapped throughout the with torch.profiler.profile() context supervisor. Within the with assertion, you possibly can outline the actions to hint (CPU, CUDA, or each), set a schedule to profile particular coaching steps, and select whether or not to file tensor shapes, reminiscence utilization, or FLOPs. As soon as contained in the context, you will need to name prof.step() on the finish of every iteration to sign the profiler to advance, particularly when a schedule is used.
with profile(
actions=,
schedule=torch.profiler.schedule(),
record_shapes=,
profile_memory=,
with_flops=
) as prof:
....
prof.step() - actions: Specify whether or not to profile the CPU, CUDA or each.
- schedule: Helpful for profiling a number of steps within the coaching loop. If the schedule parameter is used, the profiler must name prof.step() to maneuver to the subsequent step.
- record_shapes: Whether or not to file the shapes of the tensors.
- profile_memory: To seize reminiscence utilization
- with_flops: That is experimental however is used to FLOPs with operators.
Our profiler command modifications to:
with profile(
actions=[ProfilerActivity.CPU, ProfilerActivity.CUDA],
schedule=torch.profiler.schedule(wait=1, warmup=1, lively=3, repeat=2),
record_shapes=True,
profile_memory=True,
with_flops=True
) as prof:Concentrating on Profiling for particular neural community layers
The profiler may also be utilized in a extra focused method to research particular layers of a neural community. That is helpful to examine whether or not some particular layer is contributing extra to the efficiency than the opposite layers giving the developer the choice of modifying particular layers. Whereas utilizing that is very straightforward to make use of, most often, the primary choice works higher. The PyTorch profiler outcomes may also be exported and visualized on a TensorBoard.
profiler.begin()
self.conv2(x)
profiler.cease()LLMs and Roofline Modeling
Coming to the subject everybody has been ready for – does Roofline Modeling assist with LLM efficiency calculation? The quick reply is sure.
LLMs are advanced neural community architectures with billions of parameters and the huge datasets that they course of. Whereas coaching is a really resource-intensive activity, inference and high-quality tuning the mannequin additionally have to be environment friendly.
- Bottlenecks: LLMs throughout inference can undergo from bottlenecks as a result of sheer quantity of parameters that it’s working with. These parameters are the weights of the fashions they usually trigger reminiscence bandwidth points. Utilizing Roofline Modeling, the precise layers might be profiled for the bottlenecks.
- {Hardware} choice: As most organizations fine-tune current fashions reasonably than coaching them from scratch, choosing the proper infrastructure is essential for managing prices. This underscores the significance of selecting optimum infrastructure for coaching. For instance, selecting the {hardware} in keeping with your LLM structure or optimizing your mannequin to run on a selected structure can reduce coaching and inference prices.
Conclusion
The Roofline Mannequin provides a strong visible evaluation of software efficiency optimization. By visualizing the applying efficiency throughout reminiscence and compute, a transparent steerage is supplied in selecting the easiest way to method optimizations. Whereas this text solely thought-about Naive Roofline Fashions, there are extra superior strategies akin to Hierarchical Roofline Fashions or including ceilings for particular compute optimizations.
References
[1] https://docs.nersc.gov/instruments/efficiency/roofline/
[2] https://docs.nvidia.com/nsight-compute/NsightComputeCli/index.html
[3] https://github.com/pytorch/examples/tree/principal/imagenet
