triton/v1.1.2/_sources/getting-started/tutorials/05-layer-norm.rst.txt

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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_getting-started_tutorials_05-layer-norm.py>`
        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 5-252



.. 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   99.497980  307.200008
    1    1536.0  351.085717  133.565214  341.333333
    2    2048.0  423.724127  159.067963  319.168844
    3    2560.0  461.954908  183.402991  325.079368
    4    3072.0  511.999982  192.501302  319.168834
    5    3584.0  551.384634  207.768111  309.410081
    6    4096.0  568.231237  220.412561  299.707322
    7    4608.0  498.162157  232.825259  286.507772
    8    5120.0  525.128191  240.941184  283.787523
    9    5632.0  538.517949  243.985547  290.060087
    10   6144.0  542.117638  249.502530  286.322318
    11   6656.0  527.207907  256.410903  285.767438
    12   7168.0  512.000004  258.306304  282.947381
    13   7680.0  485.052616  263.314295  282.266452
    14   8192.0  463.698115  264.613724  281.270376
    15   8704.0  415.300208  267.472468  286.158893
    16   9216.0  427.822068  273.066667  289.129410
    17   9728.0  437.213490  279.942444  289.308559
    18  10240.0  446.025405  287.102804  291.876482
    19  10752.0  430.797982  246.699797  290.267711
    20  11264.0  427.746848  246.656943  288.512281
    21  11776.0  422.457417  249.667843  288.686414
    22  12288.0  420.102570  254.234486  294.617366
    23  12800.0  414.016170  253.884294  289.811310
    24  13312.0  411.711355  252.360194  290.179836
    25  13824.0  403.620451  256.991469  292.056329
    26  14336.0  395.021816  254.862216  287.919661
    27  14848.0  383.999990  257.108233  289.481735
    28  15360.0  373.495460  258.332158  288.000007
    29  15872.0  365.573890  262.708969  290.562936






|

.. code-block:: default


    import torch
    import triton.language as tl
    import triton

    # Forward Pass
    @triton.jit
    def _layer_norm_fwd_fused(X, Y, W, B, M, V, stride, N, eps, **META):
        BLOCK_SIZE = META['BLOCK_SIZE']
        # 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, 
                           **META):
        GROUP_SIZE_M = META['GROUP_SIZE_M']
        BLOCK_SIZE_N = META['BLOCK_SIZE_N']
        # 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, **meta):
        pid = tl.program_id(0)
        BLOCK_SIZE_M = meta['BLOCK_SIZE_M']
        BLOCK_SIZE_N = meta['BLOCK_SIZE_N']
        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, meta['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'],
            line_names=['Triton', 'Torch', 'Apex'],
            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':
            import 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)


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   **Total running time of the script:** ( 2 minutes  13.195 seconds)


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     :download:`Download Python source code: 05-layer-norm.py <05-layer-norm.py>`



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