296 lines
9.0 KiB
ReStructuredText
296 lines
9.0 KiB
ReStructuredText
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.. DO NOT EDIT.
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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
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.. "getting-started/tutorials/02-fused-softmax.py"
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.. LINE NUMBERS ARE GIVEN BELOW.
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.. only:: html
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.. note::
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:class: sphx-glr-download-link-note
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Click :ref:`here <sphx_glr_download_getting-started_tutorials_02-fused-softmax.py>`
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to download the full example code
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.. rst-class:: sphx-glr-example-title
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.. _sphx_glr_getting-started_tutorials_02-fused-softmax.py:
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Fused Softmax
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=================
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In this tutorial, you will write a fused softmax operation (that outperforms PyTorch) and learn about:
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- The benefits of kernel fusion for bandwidth-bound operations.
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- The reduction operators in Triton.
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.. GENERATED FROM PYTHON SOURCE LINES 11-15
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Motivations
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------------
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Custom GPU kernels for elementwise additions are educationally valuable but won't get you very far in practice.
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Let us consider instead the case of a simple (numerically stabilized) softmax operation:
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.. GENERATED FROM PYTHON SOURCE LINES 15-35
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.. code-block:: default
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import torch
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# Compute the row-wise softmax of x
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def naive_softmax(x):
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# read MN elements ; write M elements
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x_max = torch.max(x, axis=1)[0]
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# read 2MN elements ; write MN elements
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z = x - x_max[:, None]
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# read MN elements ; write MN elements
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numerator = torch.exp(x)
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# read MN elements ; write M elements
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denominator = torch.sum(numerator, axis=1)
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# read 2MN elements ; write MN elements
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ret = numerator / denominator[:, None]
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# in total: read 7MN elements ; wrote 3MN + 2M elements
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return ret
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.. GENERATED FROM PYTHON SOURCE LINES 36-40
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When implemented naively in pytorch, computing :code:`y = naive_softmax(x)` for :math:`x \in R^{M \times N}` requires reading :math:`7MN` elements from DRAM and writing back :math:`3MN + 2M` elements.
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This is obviously wasteful; we'd prefer to have a custom "fused" kernel that only reads X once and does all the necessary computations on-chip.
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This solution would require reading and writing back only :math:`MN` bytes, so we could expect a theoretical speed-up of ~5x (i.e., :math:`(10MN + 2M) / 2MN`).
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In practice, though, we would be getting a bit less as our kernel computes exponentials and internally moves data around in shared memory.
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.. GENERATED FROM PYTHON SOURCE LINES 42-47
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Compute Kernel
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----------------
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Our softmax kernel works as follows: each program loads a row of the input matrix X, normalizes it and writes back the result to the output Y.
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Note that one important limitation of Triton is that each block must have a power-of-two number of elements,
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so we need to internally "pad" tiles and guard the memory operations properly if we want to handle any possible input shapes:
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.. GENERATED FROM PYTHON SOURCE LINES 47-73
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.. code-block:: default
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import triton
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@triton.jit
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def _softmax(Y, X, stride_xm, stride_ym, M, N, **meta):
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# row index
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m = triton.program_id(0)
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# col indices
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n = triton.arange(0, meta['BLOCK'])
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# the memory address of all the elements
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# that we want to load can be computed as follows
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X = X + m * stride_xm + n
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x = triton.load(X, mask=n < N, other=-float('inf'))
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# Substract maximum for numerical stability
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z = x - triton.max(x, axis=0)
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# Note that exponentials in Triton are fast
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# but approximate (i.e., think __expf in CUDA)
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num = triton.exp(z)
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denom = triton.sum(num, axis=0)
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y = num / denom
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# Write back to Y
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Y = Y + m * stride_ym + n
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triton.store(Y, y, mask=n < N)
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.. GENERATED FROM PYTHON SOURCE LINES 74-75
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We can create a helper function that enqueues the kernel and its (meta-)arguments for any given input tensor.
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.. GENERATED FROM PYTHON SOURCE LINES 75-107
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.. code-block:: default
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def next_power_of_2(n):
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n -= 1
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n |= n >> 1
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n |= n >> 2
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n |= n >> 4
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n |= n >> 8
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n |= n >> 16
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n += 1
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return n
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def softmax(x):
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M, N = x.shape
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# The block size is the smallest power of two greater than the number of columns in `x`
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BLOCK = next_power_of_2(N)
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# Another trick we can use is to ask the compiler to parallelize each
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# row-normalization more aggressively -- i.e., with more warps -- vectors
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# that are longer
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# You will see in the next tutorial how to auto-tune this value in a more natural
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# way so you don't have to come up with manual heuristics yourself
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num_warps = 4
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if BLOCK >= 2048: num_warps = 8
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if BLOCK >= 4096: num_warps = 16
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# Allocate output
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y = torch.empty_like(x)
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# Enqueue kernel. The launch grid is simple: we have one kernel instance per row of the input matrix
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_softmax[(M, )](y, x, x.stride(0), y.stride(0), M, N, BLOCK=BLOCK)
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return y
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.. GENERATED FROM PYTHON SOURCE LINES 108-110
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Unit Test
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----------
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.. GENERATED FROM PYTHON SOURCE LINES 112-114
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We make sure that we test our kernel on a matrix with an irregular number of rows and columns.
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This will allow us to verify that our padding mechanism works.
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.. GENERATED FROM PYTHON SOURCE LINES 114-121
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.. code-block:: default
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torch.manual_seed(0)
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x = torch.randn(1823, 781, device='cuda')
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y_tri = softmax(x)
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y_ref = torch.softmax(x, axis=1)
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print(torch.allclose(y_tri, y_ref))
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.. rst-class:: sphx-glr-script-out
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Out:
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.. code-block:: none
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True
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.. GENERATED FROM PYTHON SOURCE LINES 122-123
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As expected, the results are identical.
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.. GENERATED FROM PYTHON SOURCE LINES 125-129
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Benchmark
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-------------
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Here we will benchmark our operation as a function of the number of columns in the input matrix -- assuming 4096 rows.
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We will then compare its performance against (1) :code:`torch.softmax` and (2) the :code:`naive_softmax` defined above.
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.. GENERATED FROM PYTHON SOURCE LINES 129-157
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.. code-block:: default
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@triton.testing.perf_report(
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triton.testing.Benchmark(
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x_names=['N'], # argument names to use as an x-axis for the plot
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x_vals=[256 * i for i in range(2, 50)], # different possible values for `x_name`
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y_name='provider', # argument name whose value corresponds to a different line in the plot
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y_vals=['torch', 'triton', 'naive'], # possible keys for `y_name`
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y_lines=["Torch", "Triton", 'Naive'], # label name for the lines
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ylabel="GB/s", # label name for the y-axis
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plot_name="softmax-performance", # name for the plot. Used also as a file name for saving the plot.
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args={'M': 4096} # values for function arguments not in `x_names` and `y_name`
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)
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)
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def benchmark(M, N, provider):
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x = torch.randn(M, N, device='cuda', dtype=torch.float32)
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if provider == 'torch':
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ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.softmax(x, axis=-1))
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if provider == 'triton':
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ms, min_ms, max_ms = triton.testing.do_bench(lambda: softmax(x))
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if provider == 'naive':
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ms, min_ms, max_ms = triton.testing.do_bench(lambda: naive_softmax(x))
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gbps = lambda ms: 2 * x.nelement() * x.element_size() * 1e-9 / (ms * 1e-3)
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return gbps(ms), gbps(max_ms), gbps(min_ms)
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benchmark.run(show_plots=True)
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.. image:: /getting-started/tutorials/images/sphx_glr_02-fused-softmax_001.png
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:alt: 02 fused softmax
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:class: sphx-glr-single-img
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.. GENERATED FROM PYTHON SOURCE LINES 158-163
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In the above plot, we can see that:
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- Triton is 4-5x faster than the naive implementation, which is consistent with our theoretical predictions.
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- Triton is significantly faster than :code:`torch.softmax` for very large input matrices. My guess from looking at the source-code of the `PyTorch kernel <https://github.com/pytorch/pytorch/blob/9409a3a39b7149bb2d833a89e0c944109bef7c27/caffe2/operators/softmax_ops.cu#L240>`_ is that PyTorch only partially fuses the computation of the softmax.
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This means that -- when temporary data is too large to fit entirely in the GPU's cache -- it transfers almost twice the amount of data necessary.
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Note that our Triton kernel is not only faster than PyTorch's CUDA kernel, it is also **easier to read, understand and maintain**.
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.. rst-class:: sphx-glr-timing
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**Total running time of the script:** ( 0 minutes 20.767 seconds)
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.. _sphx_glr_download_getting-started_tutorials_02-fused-softmax.py:
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.. only :: html
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.. container:: sphx-glr-footer
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:class: sphx-glr-footer-example
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.. container:: sphx-glr-download sphx-glr-download-python
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:download:`Download Python source code: 02-fused-softmax.py <02-fused-softmax.py>`
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.. container:: sphx-glr-download sphx-glr-download-jupyter
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:download:`Download Jupyter notebook: 02-fused-softmax.ipynb <02-fused-softmax.ipynb>`
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.. only:: html
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.. rst-class:: sphx-glr-signature
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`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
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