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  311.088617   97.912354  303.407414
    1    1536.0  351.085717  134.050910  341.333333
    2    2048.0  423.724127  161.154101  334.367350
    3    2560.0  465.454542  180.705883  330.322572
    4    3072.0  515.580429  191.999993  323.368415
    5    3584.0  551.384634  208.271186  311.652167
    6    4096.0  568.231237  220.412561  298.796351
    7    4608.0  500.416301  232.336141  287.251954
    8    5120.0  525.128191  242.366855  284.444444
    9    5632.0  540.671974  243.107920  289.438969
    10   6144.0  544.118087  248.661056  286.322318
    11   6656.0  528.953642  256.000009  285.767438
    12   7168.0  507.469040  259.867079  285.293536
    13   7680.0  485.052616  263.314295  280.547947
    14   8192.0  460.440290  266.406514  284.115618
    15   8704.0  416.127506  267.815384  284.987724
    16   9216.0  428.651187  271.391419  287.999990
    17   9728.0  437.213490  280.278512  289.667485
    18  10240.0  448.467168  286.433562  290.496460
    19  10752.0  431.518385  246.699797  290.267711
    20  11264.0  430.471331  245.313973  286.980888
    21  11776.0  423.089806  249.667843  288.981596
    22  12288.0  419.504980  254.673582  294.617366
    23  12800.0  414.016170  253.884294  289.811310
    24  13312.0  411.181478  252.759501  290.443638
    25  13824.0  405.594132  257.190689  292.056329
    26  14336.0  394.568805  254.862216  287.198654
    27  14848.0  385.245405  257.665934  289.952797
    28  15360.0  376.547496  257.970599  287.326580
    29  15872.0  368.046389  261.446802  290.341468






|

.. 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  12.490 seconds)


.. _sphx_glr_download_getting-started_tutorials_05-layer-norm.py:


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



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