.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "getting-started/tutorials/05-layer-norm.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_getting-started_tutorials_05-layer-norm.py: Layer Normalization ==================== .. GENERATED FROM PYTHON SOURCE LINES 5-262 .. image:: /getting-started/tutorials/images/sphx_glr_05-layer-norm_001.png :alt: 05 layer norm :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none layer-norm-backward: N Triton Torch Apex 0 1024.0 307.200008 97.912354 303.407414 1 1536.0 347.773587 134.540150 341.333333 2 2048.0 420.102553 161.684218 323.368435 3 2560.0 458.507457 181.238943 330.322572 4 3072.0 511.999982 192.501302 320.556515 5 3584.0 547.872604 208.271186 312.785456 6 4096.0 568.231237 220.907859 300.623865 7 4608.0 507.302750 232.825259 287.999990 8 5120.0 527.381977 242.845844 285.104413 9 5632.0 540.671974 241.371422 288.204696 10 6144.0 548.163546 250.349744 287.438593 11 6656.0 534.260858 256.000009 286.279570 12 7168.0 512.000004 255.240352 280.182402 13 7680.0 485.052616 263.690977 277.172933 14 8192.0 463.698115 268.223740 281.673345 15 8704.0 418.629245 266.109560 282.291896 16 9216.0 432.845409 272.394084 288.375482 17 9728.0 439.683593 278.606213 287.173424 18 10240.0 446.025405 286.767793 288.112552 19 10752.0 423.724151 244.827326 288.321786 20 11264.0 426.397479 245.983625 287.285864 21 11776.0 421.198220 247.807112 287.219500 22 12288.0 420.701865 254.453844 294.911986 23 12800.0 413.458944 252.009851 287.910035 24 13312.0 411.181478 253.763296 290.972683 25 13824.0 403.620451 258.191439 292.829653 26 14336.0 394.116833 255.240352 289.372589 27 14848.0 385.245405 256.552919 289.952797 28 15360.0 379.649845 262.751252 289.811315 29 15872.0 370.913333 261.806182 289.899545 | .. code-block:: default import torch import triton import triton.language as tl try: # This is https://github.com/NVIDIA/apex, NOT the apex on PyPi, so it # should not be added to extras_require in setup.py. import apex HAS_APEX = True except ModuleNotFoundError: HAS_APEX = False # Forward Pass @triton.jit def _layer_norm_fwd_fused(X, Y, W, B, M, V, stride, N, eps, BLOCK_SIZE: tl.constexpr): # position of elements processed by this program row = tl.program_id(0) cols = tl.arange(0, BLOCK_SIZE) mask = cols < N # offset data pointers to start at the row of interest X += row * stride Y += row * stride # load data and cast to float32 x = tl.load(X + cols, mask=mask, other=0).to(tl.float32) # compute mean mean = tl.sum(x, axis=0) / N # compute std xmean = tl.where(mask, x - mean, 0.) var = tl.sum(xmean * xmean, axis=0) / N rstd = 1 / tl.sqrt(var + eps) xhat = xmean * rstd # write-back mean/rstd tl.store(M + row, mean) tl.store(V + row, rstd) # multiply by weight and add bias w = tl.load(W + cols, mask=mask) b = tl.load(B + cols, mask=mask) y = xhat * w + b # write-back tl.store(Y + cols, y, mask=mask) # Backward pass (DX + partial DW + partial DB) @triton.jit def _layer_norm_bwd_dx_fused(DX, DY, DW, DB, X, W, B, M, V, Lock, stride, N, eps, GROUP_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr): # position of elements processed by this program row = tl.program_id(0) cols = tl.arange(0, BLOCK_SIZE_N) mask = cols < N # offset data pointers to start at the row of interest X += row * stride DY += row * stride DX += row * stride # offset locks and weight/bias gradient pointer # each kernel instance accumulates partial sums for # DW and DB into one of GROUP_SIZE_M independent buffers # these buffers stay in the L2, which allow this kernel # to be fast lock_id = row % GROUP_SIZE_M Lock += lock_id Count = Lock + GROUP_SIZE_M DW = DW + lock_id * N + cols DB = DB + lock_id * N + cols # load data to SRAM x = tl.load(X + cols, mask=mask, other=0).to(tl.float32) dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32) w = tl.load(W + cols, mask=mask).to(tl.float32) mean = tl.load(M + row) rstd = tl.load(V + row) # compute dx xhat = (x - mean) * rstd wdy = w * dy xhat = tl.where(mask, xhat, 0.) wdy = tl.where(mask, wdy, 0.) mean1 = tl.sum(xhat * wdy, axis=0) / N mean2 = tl.sum(wdy, axis=0) / N dx = (wdy - (xhat * mean1 + mean2)) * rstd # write-back dx tl.store(DX + cols, dx, mask=mask) # accumulate partial sums for dw/db partial_dw = (dy * xhat).to(w.dtype) partial_db = (dy).to(w.dtype) while tl.atomic_cas(Lock, 0, 1) == 1: pass count = tl.load(Count) # first store doesn't accumulate if count == 0: tl.atomic_xchg(Count, 1) else: partial_dw += tl.load(DW, mask=mask) partial_db += tl.load(DB, mask=mask) tl.store(DW, partial_dw, mask=mask) tl.store(DB, partial_db, mask=mask) # release lock tl.atomic_xchg(Lock, 0) # Backward pass (total DW + total DB) @triton.jit def _layer_norm_bwd_dwdb(DW, DB, FINAL_DW, FINAL_DB, M, N, BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr): pid = tl.program_id(0) cols = pid * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) dw = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) db = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) for i in range(0, M, BLOCK_SIZE_M): rows = i + tl.arange(0, BLOCK_SIZE_M) mask = (rows[:, None] < M) & (cols[None, :] < N) offs = rows[:, None] * N + cols[None, :] dw += tl.load(DW + offs, mask=mask, other=0.) db += tl.load(DB + offs, mask=mask, other=0.) sum_dw = tl.sum(dw, axis=0) sum_db = tl.sum(db, axis=0) tl.store(FINAL_DW + cols, sum_dw, mask=cols < N) tl.store(FINAL_DB + cols, sum_db, mask=cols < N) class LayerNorm(torch.autograd.Function): @staticmethod def forward(ctx, x, normalized_shape, weight, bias, eps): # allocate output y = torch.empty_like(x) # reshape input data into 2D tensor x_arg = x.reshape(-1, x.shape[-1]) M, N = x_arg.shape mean = torch.empty((M, ), dtype=torch.float32, device='cuda') rstd = torch.empty((M, ), dtype=torch.float32, device='cuda') # Less than 64KB per feature: enqueue fused kernel MAX_FUSED_SIZE = 65536 // x.element_size() BLOCK_SIZE = min(MAX_FUSED_SIZE, triton.next_power_of_2(N)) if N > BLOCK_SIZE: raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.") # heuristics for number of warps num_warps = min(max(BLOCK_SIZE // 256, 1), 8) # enqueue kernel _layer_norm_fwd_fused[(M,)](x_arg, y, weight, bias, mean, rstd, x_arg.stride(0), N, eps, BLOCK_SIZE=BLOCK_SIZE, num_warps=num_warps) ctx.save_for_backward(x, weight, bias, mean, rstd) ctx.BLOCK_SIZE = BLOCK_SIZE ctx.num_warps = num_warps ctx.eps = eps return y @staticmethod def backward(ctx, dy): x, w, b, m, v = ctx.saved_tensors # heuristics for amount of parallel reduction stream for DG/DB N = w.shape[0] GROUP_SIZE_M = 64 if N <= 8192: GROUP_SIZE_M = 96 if N <= 4096: GROUP_SIZE_M = 128 if N <= 1024: GROUP_SIZE_M = 256 # allocate output locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda') _dw = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) _db = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) dx = torch.empty_like(dy) # enqueue kernel using forward pass heuristics # also compute partial sums for DW and DB x_arg = x.reshape(-1, x.shape[-1]) M, N = x_arg.shape _layer_norm_bwd_dx_fused[(M,)](dx, dy, _dw, _db, x, w, b, m, v, locks, x_arg.stride(0), N, ctx.eps, BLOCK_SIZE_N=ctx.BLOCK_SIZE, GROUP_SIZE_M=GROUP_SIZE_M, num_warps=ctx.num_warps) grid = lambda meta: [triton.cdiv(N, meta['BLOCK_SIZE_N'])] # accumulate partial sums in separate kernel _layer_norm_bwd_dwdb[grid](_dw, _db, dw, db, GROUP_SIZE_M, N, BLOCK_SIZE_M=32, BLOCK_SIZE_N=128) return dx, None, dw, db, None layer_norm = LayerNorm.apply def test_layer_norm(M, N, dtype, eps=1e-5, device='cuda'): # create data x_shape = (M, N) w_shape = (x_shape[-1], ) weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') dy = .1 * torch.randn_like(x) x.requires_grad_(True) # forward pass y_tri = layer_norm(x, w_shape, weight, bias, eps) y_ref = torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps).to(dtype) # backward pass (triton) y_tri.backward(dy, retain_graph=True) dx_tri, dw_tri, db_tri = [_.grad.clone() for _ in [x, weight, bias]] x.grad, weight.grad, bias.grad = None, None, None # backward pass (torch) y_ref.backward(dy, retain_graph=True) dx_ref, dw_ref, db_ref = [_.grad.clone() for _ in [x, weight, bias]] # compare triton.testing.assert_almost_equal(y_tri, y_ref) triton.testing.assert_almost_equal(dx_tri, dx_ref) triton.testing.assert_almost_equal(db_tri, db_ref, decimal=1) triton.testing.assert_almost_equal(dw_tri, dw_ref, decimal=1) @triton.testing.perf_report( triton.testing.Benchmark( x_names=['N'], x_vals=[512 * i for i in range(2, 32)], line_arg='provider', line_vals=['triton', 'torch'] + (['apex'] if HAS_APEX else []), line_names=['Triton', 'Torch'] + (['Apex'] if HAS_APEX else []), styles=[('blue', '-'), ('green', '-'), ('orange', '-')], ylabel='GB/s', plot_name='layer-norm-backward', args={'M': 4096, 'dtype': torch.float16, 'mode': 'backward'} ) ) def bench_layer_norm(M, N, dtype, provider, mode='backward', eps=1e-5, device='cuda'): # create data x_shape = (M, N) w_shape = (x_shape[-1], ) weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') dy = .1 * torch.randn_like(x) x.requires_grad_(True) # utility functions if provider == 'triton': y_fwd = lambda: layer_norm(x, w_shape, weight, bias, eps) if provider == 'torch': y_fwd = lambda: torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps) if provider == 'apex': apex_layer_norm = apex.normalization.FusedLayerNorm(w_shape).to(x.device).to(x.dtype) y_fwd = lambda: apex_layer_norm(x) # forward pass if mode == 'forward': gbps = lambda ms: 2 * x.numel() * x.element_size() / ms * 1e-6 ms, min_ms, max_ms = triton.testing.do_bench(y_fwd, rep=500) # backward pass if mode == 'backward': gbps = lambda ms: 3 * x.numel() * x.element_size() / ms * 1e-6 y = y_fwd() ms, min_ms, max_ms = triton.testing.do_bench(lambda: y.backward(dy, retain_graph=True), grad_to_none=[x], rep=500) return gbps(ms), gbps(max_ms), gbps(min_ms) bench_layer_norm.run(save_path='.', print_data=True) .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 2 minutes 12.137 seconds) .. _sphx_glr_download_getting-started_tutorials_05-layer-norm.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 05-layer-norm.py <05-layer-norm.py>` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 05-layer-norm.ipynb <05-layer-norm.ipynb>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_