[pytorch] Layer norm backward speed gain with warp shuffles

[valentinandrei]

Summary:
Improved native layer norm backward performance.

Rewrote GammaBetaBackwardCUDAKernel to use shared memory only for the reduction step, but not for loading mean and rstd. The previous implementation used only threadIdx.x = 0 to load mean and rstd into shared memory, and then all threads would access the values in order to do loop unrolling. This approached increased register usage and decreased occupancy, without much benefit from using shared memory (this is because the values were already cached in L1). The new implementation is simpler and register usage is smaller, thus occupancy is better.

Added another implementation called GammaBetaBackwardCUDAKernel_32x32 which is only for shapes dividing exactly to a (32 x 32) block. This permits using warp shuffles for speeding up loading mean and rstd as well as for the final reduction stage. The effective bandwidth of this implementation is equal to STREAM Triad.

Observed that we can get additional benefit if we lower the threshold for calling GammaBetaBackwardSimpleCUDAKernel (simple col-wise reduction implementation) from 512 to 128.

Test Plan:
Wrote a simple CUDA app that calls the previous implementation of GammaBetaBackwardCUDAKernel and the current one, using FP32 values and compares the results. The epsilon value we used for FP comparison is 0.00001 for the weight and 0.0001 for the bias.
Ran the benchmark for various sizes A100 GPU and got the results below. Almost all sizes show good speedup.

Size (32, 32); Mismatches: dg = 0 db = 0 out of 32. reference = 0.0073 (ms); optimized = 0.0071 (ms); bw_opt = 1.14 GB/s; speedup = 2.68%
Size (64, 32); Mismatches: dg = 0 db = 0 out of 32. reference = 0.0107 (ms); optimized = 0.0107 (ms); bw_opt = 1.50 GB/s; speedup = 0.22%
Size (256, 128); Mismatches: dg = 0 db = 0 out of 128. reference = 0.0323 (ms); optimized = 0.0075 (ms); bw_opt = 32.89 GB/s; speedup = 330.16%
Size (512, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0103 (ms); optimized = 0.0089 (ms); bw_opt = 440.54 GB/s; speedup = 15.82%
Size (1024, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.0197 (ms); optimized = 0.0136 (ms); bw_opt = 1151.44 GB/s; speedup = 44.91%
Size (2048, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.0416 (ms); optimized = 0.0283 (ms); bw_opt = 1105.31 GB/s; speedup = 47.01%
Size (4096, 16384); Mismatches: dg = 0 db = 0 out of 16384. reference = 0.4420 (ms); optimized = 0.3915 (ms); bw_opt = 1277.58 GB/s; speedup = 12.90%
Size (70000, 64); Mismatches: dg = 0 db = 0 out of 64. reference = 0.5908 (ms); optimized = 0.6850 (ms); bw_opt = 49.49 GB/s; speedup = -13.75%
Size (131072, 512); Mismatches: dg = 0 db = 0 out of 512. reference = 1.1961 (ms); optimized = 0.9234 (ms); bw_opt = 542.54 GB/s; speedup = 29.53%
Size (1000, 520); Mismatches: dg = 0 db = 0 out of 520. reference = 0.0132 (ms); optimized = 0.0113 (ms); bw_opt = 343.83 GB/s; speedup = 16.88%
Size (4005, 4005); Mismatches: dg = 0 db = 0 out of 4005. reference = 0.1441 (ms); optimized = 0.1054 (ms); bw_opt = 1134.36 GB/s; speedup = 36.71%
Size (10000, 1000); Mismatches: dg = 0 db = 0 out of 1000. reference = 0.1293 (ms); optimized = 0.1248 (ms); bw_opt = 597.71 GB/s; speedup = 3.63%
Size (1024, 10000); Mismatches: dg = 0 db = 0 out of 10000. reference = 0.0738 (ms); optimized = 0.0735 (ms); bw_opt = 1039.40 GB/s; speedup = 0.45%
Size (8192, 4096); Mismatches: dg = 0 db = 0 out of 4096. reference = 0.2673 (ms); optimized = 0.2223 (ms); bw_opt = 1125.01 GB/s; speedup = 20.25%
Size (10000, 10000); Mismatches: dg = 0 db = 0 out of 10000. reference = 0.7331 (ms); optimized = 0.8940 (ms); bw_opt = 833.54 GB/s; speedup = -18.00%
Size (3072, 10000); Mismatches: dg = 0 db = 0 out of 10000. reference = 0.2087 (ms); optimized = 0.2364 (ms); bw_opt = 968.64 GB/s; speedup = -11.71%
Size (6144, 10000); Mismatches: dg = 0 db = 0 out of 10000. reference = 0.4197 (ms); optimized = 0.5118 (ms); bw_opt = 894.63 GB/s; speedup = -18.00%
Size (1024, 20000); Mismatches: dg = 0 db = 0 out of 20000. reference = 0.1480 (ms); optimized = 0.1297 (ms); bw_opt = 1177.68 GB/s; speedup = 14.12%
Size (1024, 20000); Mismatches: dg = 0 db = 0 out of 20000. reference = 0.1483 (ms); optimized = 0.1278 (ms); bw_opt = 1195.26 GB/s; speedup = 16.04%
Size (512, 1536); Mismatches: dg = 0 db = 0 out of 1536. reference = 0.0104 (ms); optimized = 0.0091 (ms); bw_opt = 646.72 GB/s; speedup = 14.44%
Size (512, 6144); Mismatches: dg = 0 db = 0 out of 6144. reference = 0.0219 (ms); optimized = 0.0156 (ms); bw_opt = 1506.30 GB/s; speedup = 40.52%
Size (512, 10240); Mismatches: dg = 0 db = 0 out of 10240. reference = 0.0424 (ms); optimized = 0.0370 (ms); bw_opt = 1057.84 GB/s; speedup = 14.63%
Size (1000, 1000); Mismatches: dg = 0 db = 0 out of 1000. reference = 0.0139 (ms); optimized = 0.0119 (ms); bw_opt = 627.51 GB/s; speedup = 16.83%
Size (2000, 2000); Mismatches: dg = 0 db = 0 out of 2000. reference = 0.0421 (ms); optimized = 0.0412 (ms); bw_opt = 724.10 GB/s; speedup = 2.20%
Size (10240, 10240); Mismatches: dg = 0 db = 0 out of 10240. reference = 0.7210 (ms); optimized = 0.6098 (ms); bw_opt = 1281.40 GB/s; speedup = 18.24%
Size (384, 128); Mismatches: dg = 0 db = 0 out of 128. reference = 0.0449 (ms); optimized = 0.0089 (ms); bw_opt = 41.50 GB/s; speedup = 403.48%
Size (2048, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0208 (ms); optimized = 0.0169 (ms); bw_opt = 925.70 GB/s; speedup = 23.13%
Size (267, 513); Mismatches: dg = 0 db = 0 out of 513. reference = 0.0342 (ms); optimized = 0.0090 (ms); bw_opt = 114.18 GB/s; speedup = 280.64%
Size (67, 123479); Mismatches: dg = 0 db = 0 out of 123479. reference = 0.0562 (ms); optimized = 0.0552 (ms); bw_opt = 1133.46 GB/s; speedup = 1.81%
Size (1024, 123479); Mismatches: dg = 0 db = 0 out of 123479. reference = 0.8573 (ms); optimized = 0.9245 (ms); bw_opt = 1020.02 GB/s; speedup = -7.27%
Size (2048, 66679); Mismatches: dg = 0 db = 0 out of 66679. reference = 0.8778 (ms); optimized = 0.8590 (ms); bw_opt = 1185.05 GB/s; speedup = 2.19%
Size (200, 256); Mismatches: dg = 0 db = 0 out of 256. reference = 0.0215 (ms); optimized = 0.0066 (ms); bw_opt = 58.49 GB/s; speedup = 226.81%
Size (1000, 256); Mismatches: dg = 0 db = 0 out of 256. reference = 0.0109 (ms); optimized = 0.0092 (ms); bw_opt = 208.27 GB/s; speedup = 18.65%
Size (6000, 256); Mismatches: dg = 0 db = 0 out of 256. reference = 0.0394 (ms); optimized = 0.0301 (ms); bw_opt = 381.90 GB/s; speedup = 30.98%
Size (6272, 256); Mismatches: dg = 0 db = 0 out of 256. reference = 0.0403 (ms); optimized = 0.0300 (ms); bw_opt = 400.48 GB/s; speedup = 34.34%
Size (200, 512); Mismatches: dg = 0 db = 0 out of 512. reference = 0.0218 (ms); optimized = 0.0066 (ms); bw_opt = 116.33 GB/s; speedup = 229.96%
Size (1000, 512); Mismatches: dg = 0 db = 0 out of 512. reference = 0.0110 (ms); optimized = 0.0094 (ms); bw_opt = 407.29 GB/s; speedup = 17.26%
Size (6000, 512); Mismatches: dg = 0 db = 0 out of 512. reference = 0.0535 (ms); optimized = 0.0594 (ms); bw_opt = 386.05 GB/s; speedup = -9.95%
Size (6272, 512); Mismatches: dg = 0 db = 0 out of 512. reference = 0.0573 (ms); optimized = 0.0387 (ms); bw_opt = 619.62 GB/s; speedup = 48.06%
Size (200, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0221 (ms); optimized = 0.0069 (ms); bw_opt = 222.78 GB/s; speedup = 220.76%
Size (1000, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0113 (ms); optimized = 0.0097 (ms); bw_opt = 787.79 GB/s; speedup = 16.46%
Size (6000, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0723 (ms); optimized = 0.0715 (ms); bw_opt = 640.95 GB/s; speedup = 1.10%
Size (6272, 1024); Mismatches: dg = 0 db = 0 out of 1024. reference = 0.0751 (ms); optimized = 0.0572 (ms); bw_opt = 837.57 GB/s; speedup = 31.30%
Size (200, 1536); Mismatches: dg = 0 db = 0 out of 1536. reference = 0.0232 (ms); optimized = 0.0071 (ms); bw_opt = 323.97 GB/s; speedup = 226.51%
Size (1000, 1536); Mismatches: dg = 0 db = 0 out of 1536. reference = 0.0125 (ms); optimized = 0.0114 (ms); bw_opt = 1005.84 GB/s; speedup = 9.62%
Size (6000, 1536); Mismatches: dg = 0 db = 0 out of 1536. reference = 0.0807 (ms); optimized = 0.0830 (ms); bw_opt = 828.02 GB/s; speedup = -2.76%
Size (6272, 1536); Mismatches: dg = 0 db = 0 out of 1536. reference = 0.0836 (ms); optimized = 0.0695 (ms); bw_opt = 1033.62 GB/s; speedup = 20.27%
Size (200, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.0224 (ms); optimized = 0.0075 (ms); bw_opt = 408.58 GB/s; speedup = 198.10%
Size (1000, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.0165 (ms); optimized = 0.0135 (ms); bw_opt = 1132.42 GB/s; speedup = 22.26%
Size (6000, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.0993 (ms); optimized = 0.0989 (ms); bw_opt = 926.35 GB/s; speedup = 0.41%
Size (6272, 2048); Mismatches: dg = 0 db = 0 out of 2048. reference = 0.1033 (ms); optimized = 0.0826 (ms); bw_opt = 1159.55 GB/s; speedup = 25.09%
Size (200, 3072); Mismatches: dg = 0 db = 0 out of 3072. reference = 0.0230 (ms); optimized = 0.0076 (ms); bw_opt = 605.09 GB/s; speedup = 202.51%
Size (1000, 3072); Mismatches: dg = 0 db = 0 out of 3072. reference = 0.0207 (ms); optimized = 0.0213 (ms); bw_opt = 1076.45 GB/s; speedup = -2.69%
Size (6000, 3072); Mismatches: dg = 0 db = 0 out of 3072. reference = 0.1198 (ms); optimized = 0.1274 (ms); bw_opt = 1078.58 GB/s; speedup = -5.95%
Size (6272, 3072); Mismatches: dg = 0 db = 0 out of 3072. reference = 0.1293 (ms); optimized = 0.1189 (ms); bw_opt = 1207.95 GB/s; speedup = 8.76%

Average speedup = 52.88%

For additional numerical validation used the following script:

def run_model_on_device(fs, X, gO, device_string, numeric_type):
    ln = torch.nn.LayerNorm((fs,), device=device_string, dtype=numeric_type)
    ln.reset_parameters()
    X.grad = None
    ln.zero_grad(set_to_none=True)
    out = ln(X)
    out.backward(gO)
    return (ln.weight.grad, ln.bias.grad)

def run_correctness_test(eps_weight, eps_bias):
    dtype = torch.float
    for fs in (512, 1024, 2048, 4096, 8192, 10000, 500, 1000, 2001, 4005, 8117):
        for bs in (512, 1024, 2048, 4096, 525, 1033, 2064, 3000):
            mean_adjustment = torch.randn(fs, device="cpu", dtype=torch.float)
            X = mean_adjustment * torch.randn(
                bs, fs, device="cpu", dtype=torch.float, requires_grad=True
            )

            X = X.detach().requires_grad_()
            gO = torch.rand_like(X)
            X_gpu = X.to("cuda")
            X_gpu = X_gpu.detach().requires_grad_()
            gO_gpu = gO.to("cuda")
            gO_gpu = gO_gpu.detach().requires_grad_()

            grad_cpu_ref = run_model_on_device(fs, X, gO, "cpu", dtype)
            grad_gpu = run_model_on_device(fs, X_gpu, gO_gpu, "cuda", dtype)
            weight_grad_gpu_target = grad_gpu[0].detach().to("cpu")
            bias_grad_gpu_target = grad_gpu[1].detach().to("cpu")

            weight_delta = torch.abs(grad_cpu_ref[0] - weight_grad_gpu_target)
            weight_mismatches = (weight_delta >= eps_weight).nonzero()
            weight_mismatch_pct = len(weight_mismatches) / len(weight_delta) * 100

            bias_delta = torch.abs(grad_cpu_ref[1] - bias_grad_gpu_target)
            bias_mismatches = (bias_delta >= eps_bias).nonzero()
            bias_mismatch_pct = len(bias_mismatches) / len(bias_delta) * 100

            print(
                "Size ({} x {}) mismatch percentage: weight {:3.2f} bias {:3.2f}".format(
                    fs, bs, weight_mismatch_pct, bias_mismatch_pct
                )
            )

NVFuserTest.FusionMagicSchedulerLayerNormBackward_CUDA test also does additional numerical validation and it passes.

Differential Revision: D40730981

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This pull request was exported from Phabricator. Differential Revision: D40730981

[valentinandrei]

@pytorchbot label "topic: performance"

[weiwangmeta]

@pytorchbot merge

[weiwangmeta]

Skipping reviews as this is largely the same as #87445 that has been reviewed and approved.

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[weiwangmeta]

LGTM

[weiwangmeta]

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