cross_entropy.py

# Copyright (c) 2022-2025, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# See LICENSE for license information.

"""Efficient Cross Entropy kernels written with OpenAI Triton."""

import triton
import triton.language as tl


@triton.jit
def online_softmax_kernel(
    X_ptr,
    X_stride,
    Y_ptr,
    Y_stride,
    m_d_X_y_ptr,
    m_d_X_y_stride,
    rank,
    n_cols,
    ignore_idx,
    n_non_ignore,
    BLOCK_SIZE: tl.constexpr,
):
    """
    This kernel computes the m/d components on this TP rank for the online softmax.

    Parameters:
    X_ptr: Pointer to input tensor.
    X_stride (int): The stride of the input tensor.
    Y_ptr: Pointer to target tensor.
    Y_stride (int): The stride of the target tensor.
    m_d_X_y_ptr: Pointer to m/d/X_y tensor.
    m_d_X_y_stride (int): The stride of the m/d/X_y tensor.
    rank (int): The rank of this device in the TP group.
    n_cols (int): The number of columns in the input tensor.
    ignore_idx (int): The index to ignore for loss calculation.
    n_non_ignore: The number of non-ignored elements in the batch.
    BLOCK_SIZE (int): The block size for Triton operations.
    """

    program_id = tl.program_id(0).to(tl.int64)

    # locate the start index
    X_ptr += program_id * X_stride

    # Load Y_ptr
    Y_ptr += program_id * Y_stride
    y = tl.load(Y_ptr)

    if y != ignore_idx:
        tl.atomic_add(n_non_ignore, 1)

    vocab_start_idx = rank * n_cols
    vocab_end_idx = (rank + 1) * n_cols
    if y >= vocab_start_idx:
        if y < vocab_end_idx:
            X_y = tl.load(X_ptr + y - vocab_start_idx).to(tl.float32)
        else:
            X_y = float("-inf")
    else:
        X_y = float("-inf")

    m_d_X_y_ptr += program_id * m_d_X_y_stride * 3

    # 3. [Online softmax] first pass: find max + sum
    m = float("-inf")  # m is the max value. use the notation from the paper
    d = 0.0  # d is the sum. use the notation from the paper

    for i in range(0, n_cols, BLOCK_SIZE):
        X_offsets = i + tl.arange(0, BLOCK_SIZE)
        X_block = tl.load(X_ptr + X_offsets, mask=X_offsets < n_cols, other=float("-inf")).to(
            tl.float32
        )
        block_max = tl.max(X_block)
        m_new = tl.maximum(m, block_max)
        d = d * tl.exp(m - m_new) + tl.sum(tl.exp(X_block - m_new))
        m = m_new

    tl.store(m_d_X_y_ptr, m)
    tl.store(m_d_X_y_ptr + m_d_X_y_stride, d)
    tl.store(m_d_X_y_ptr + (2 * m_d_X_y_stride), X_y)


@triton.jit
def cross_entropy_kernel(
    X_ptr,
    X_stride,
    Y_ptr,
    Y_stride,
    loss_ptr,
    loss_stride,
    m_d_X_y_ptr,
    m_d_X_y_stride,
    rank,
    world_size,
    ignore_idx,
    n_cols,
    n_rows,
    n_non_ignore,
    reduce_loss: tl.constexpr,
    label_smoothing: tl.constexpr,
    BLOCK_SIZE: tl.constexpr,
):
    """
    This kernel computes both cross entropy loss and the gradient of the input.

    Parameters:
    X_ptr: Pointer to input tensor.
    X_stride (int): The stride of the input tensor.
    Y_ptr: Pointer to target tensor.
    Y_stride (int): The stride of the target tensor.
    loss_ptr: Pointer to tensor to store the loss.
    loss_stride (int): The stride of the loss tensor.
    m_d_X_y_ptr: Pointer to m/d/X_y tensor.
    m_d_X_y_stride: The stride of m/d/X_y tensor.
    rank (int): The rank of this device in the TP group.
    world_size (int): The size of world involved in this distributed loss calculation.
    ignore_idx (int): Tokens to be ignored for loss and gradient calculation.
    n_cols (int): The number of columns in the input tensor.
    n_rows (int): The number of rows in the batch (B * SQ), used for buffer indexing.
    n_non_ignore: The number of non-ignored elements in the batch.
    label_smoothing (float): The amount of smoothing when computing the loss, where 0.0 means no smoothing.
    BLOCK_SIZE (int): The block size for Triton operations.
    """

    program_id = tl.program_id(0).to(tl.int64)
    n_non_ignore = tl.load(n_non_ignore)

    # locate the start index
    X_ptr += program_id * X_stride

    # Load Y_ptr
    Y_ptr += program_id * Y_stride
    y = tl.load(Y_ptr)

    if y == ignore_idx:
        # set all X_ptr as 0
        for i in range(0, n_cols, BLOCK_SIZE):
            X_offsets = i + tl.arange(0, BLOCK_SIZE)
            tl.store(X_ptr + X_offsets, 0.0, mask=X_offsets < n_cols)
        return

    loss_ptr += program_id * loss_stride
    m_d_X_y_ptr += program_id * 3 * m_d_X_y_stride

    # Need to reduce the m/d/X_y values from other TP ranks
    m = tl.load(m_d_X_y_ptr)
    d = tl.load(m_d_X_y_ptr + m_d_X_y_stride)
    ori_X_y = tl.load(m_d_X_y_ptr + (2 * m_d_X_y_stride))

    for i in range(1, world_size):
        offset = i * 3 * n_rows * m_d_X_y_stride
        access_ptr = m_d_X_y_ptr + offset
        m_new = tl.load(access_ptr)
        d_new = tl.load(access_ptr + m_d_X_y_stride)
        X_y_new = tl.load(access_ptr + (2 * m_d_X_y_stride))

        d = d * tl.exp(m - tl.maximum(m, m_new)) + d_new * tl.exp(m_new - tl.maximum(m, m_new))
        m = tl.maximum(m, m_new)
        ori_X_y = tl.maximum(ori_X_y, X_y_new)

    # Label smoothing is a general case of normal cross entropy
    scaled_x_sum = 0.0
    eps = label_smoothing / (n_cols * world_size)

    # 4. [Online softmax] second pass: calculate the gradients
    # dx_y = (softmax(x_y) - 1) / N
    # dx_i = softmax(x_i) / N, i != y
    # N is the number of non ignored elements in the batch
    # For label smoothing:
    # dx_i = (softmax(x_y) - label_smoothing / V) / N, V = n_cols, i != y
    # dx_y = (softmax(x_y) - label_smoothing / V - (1 - label_smoothing)) / N
    #      = dx_i - (1 - label_smoothing) / N
    for i in range(0, n_cols, BLOCK_SIZE):
        X_offsets = i + tl.arange(0, BLOCK_SIZE)
        X_block = tl.load(X_ptr + X_offsets, mask=X_offsets < n_cols, other=float("-inf"))
        grad_dtype = X_block.dtype
        X_block = X_block.to(tl.float32)
        if label_smoothing > 0:
            # scale X beforehand to avoid overflow
            scaled_x_sum += tl.sum(tl.where(X_offsets < n_cols, -eps * X_block, 0.0))
        # Scale gradients based on reduction mode
        # For reduce_loss=True: PyTorch will scale by 1/n_rows, so we need to scale by n_rows/n_non_ignore
        # For reduce_loss=False: No additional scaling from PyTorch, so we don't scale here
        if reduce_loss:
            X_block = (tl.exp(X_block - m) / d - eps) / (n_non_ignore)
        else:
            X_block = tl.exp(X_block - m) / d - eps
        tl.store(X_ptr + X_offsets, X_block.to(grad_dtype), mask=X_offsets < n_cols)

    # We need tl.debug_barrier() to ensure the new result of X_ptr is written
    tl.debug_barrier()

    # 5. Calculate the loss

    # loss = log (softmax(X_y)) = log ((e ^ (X_y - max(X)) / sum(e ^ (X - max(X))))
    #      = (X_y - max(X)) - log(sum(e ^ (X - max(X))))
    loss = -(ori_X_y - m - tl.log(d))

    # Orginal loss = H(q, p),  with label smoothing regularization = H(q', p) and (label_smoothing / V) = eps
    # H(q', p) = (1 - label_smoothing) * H(q, p) + label_smoothing * H(u, p)
    #          = (1 - label_smoothing) * H(q, p) + eps * sum(logsoftmax(x_i))
    # By using m (global max of xi) and d (sum of e^(xi-m)), we can simplify as:
    #          = (1 - label_smoothing) * H(q, p) + (-sum(x_i * eps) + label_smoothing * (m + logd))
    # Refer to H(q', p) in section 7 of the paper: https://arxiv.org/pdf/1512.00567
    if label_smoothing > 0:
        smooth_loss = scaled_x_sum + label_smoothing * (m + tl.log(d))
        loss = loss * (1 - label_smoothing) + smooth_loss

    # 6. Specially handle the i==y case where `dx_y = (softmax(x_y) - (1 - label_smoothing) / N`
    vocab_start_idx = rank * n_cols
    vocab_end_idx = (rank + 1) * n_cols
    if y >= vocab_start_idx:
        if y < vocab_end_idx:
            X_y = tl.load(X_ptr + y - vocab_start_idx)
            # Apply the same conditional scaling logic for the target token
            if reduce_loss:
                X_y += -(1 - label_smoothing) / (n_non_ignore)
            else:
                X_y += -(1 - label_smoothing)
            tl.store(X_ptr + y - vocab_start_idx, X_y)

    tl.store(loss_ptr, loss)


@triton.jit
def element_mul_kernel(
    X_ptr,
    X_stride,
    grad_output_ptr,
    grad_output_stride,
    n_cols,
    BLOCK_SIZE: tl.constexpr,
):
    """
    This function multiplies each element of the tensor pointed by X_ptr with the value pointed by grad_output_ptr.
    The multiplication is performed in-place on the tensor pointed by X_ptr.

    Parameters:
    X_ptr: Pointer to the input tensor.
    X_stride (int): The stride of the input tensor.
    grad_output_ptr: Pointer to the gradient output value.
    n_cols (int): The number of columns in the input tensor.
    BLOCK_SIZE (int): The block size for Triton operations.
    """

    # Get the program ID and convert it to int64 to avoid overflow
    program_id = tl.program_id(0).to(tl.int64)

    # Locate the start index
    X_ptr += program_id * X_stride

    # Load the gradient output value
    grad_output_ptr += program_id * grad_output_stride
    grad_output = tl.load(grad_output_ptr)

    # Perform the element-wise multiplication
    for i in range(0, n_cols, BLOCK_SIZE):
        X_offsets = i + tl.arange(0, BLOCK_SIZE)
        X_block = tl.load(X_ptr + X_offsets, mask=X_offsets < n_cols)
        tl.store(X_ptr + X_offsets, X_block * grad_output, mask=X_offsets < n_cols)