ColossalAI/colossalai/nn/layer/parallel_2p5d/_operation.py

from typing import Any, Tuple

import torch
import torch.distributed as dist
from colossalai.communication.collective import (all_gather, all_reduce, reduce_scatter)
from colossalai.context.parallel_mode import ParallelMode
from colossalai.core import global_context as gpc
from colossalai.utils import get_current_device
from torch import Tensor
from torch.cuda.amp import custom_bwd, custom_fwd


def get_parallel_group(parallel_mode: ParallelMode):
    return gpc.get_group(parallel_mode)


def get_global_rank():
    return gpc.get_global_rank()


def get_parallel_rank(parallel_mode: ParallelMode):
    return gpc.get_local_rank(parallel_mode)


class _Classifier2p5D(torch.autograd.Function):

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(
        ctx: Any,
        A: Tensor,
        B: Tensor,
        bias,
        tesseract_dim: int,
        out_shape: Tuple[int, ...],
        row_rank: int,
        col_rank: int,
        row_parallel_mode: ParallelMode,
        col_parallel_mode: ParallelMode,
        data_parallel_rank: int,
        pipeline_parallel_rank: int,
        pipeline_parallel_size: int,
        tensor_parallel_size: int,
    ) -> Tensor:
        A = A.clone().detach()
        A_shape = A.shape
        A = A.reshape((-1, A_shape[-1]))
        B_shape = B.shape
        B = B.reshape((-1, B_shape[-1]))
        B_temp = all_gather(B, -1, col_parallel_mode)
        if ctx:
            ctx.save_for_backward(A, B_temp)

        C = torch.matmul(A, B_temp.transpose(0, 1))

        C = all_reduce(C, row_parallel_mode)

        ctx.use_bias = bias is not None
        if bias is not None:
            C = C + bias

        out = C.reshape(out_shape)

        if ctx:
            ctx.tesseract_dim = tesseract_dim
            ctx.row_rank = row_rank
            ctx.col_rank = col_rank
            ctx.row_parallel_mode = row_parallel_mode
            ctx.col_parallel_mode = col_parallel_mode
            ctx.A_shape = A_shape
            ctx.B_shape = B_shape
            ctx.data_parallel_rank = data_parallel_rank
            ctx.pipeline_parallel_rank = pipeline_parallel_rank
            ctx.pipeline_parallel_size = pipeline_parallel_size
            ctx.tensor_parallel_size = tensor_parallel_size

        return out

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        A, B = ctx.saved_tensors

        with torch.no_grad():
            A_grad = torch.matmul(output_grad, B)
            A_grad = A_grad.reshape(ctx.A_shape)
            B_grad = torch.matmul(output_grad.reshape(-1, output_grad.shape[-1]).transpose(0, 1), A)
            B_grad = reduce_scatter(B_grad, -1, ctx.col_parallel_mode)
            B_grad = B_grad.reshape(ctx.B_shape)

            if ctx.use_bias:
                bias_grad = torch.sum(output_grad, dim=tuple(range(output_grad.ndim - 1)))
                bias_grad = all_reduce(bias_grad, ctx.col_parallel_mode)
            else:
                bias_grad = None

        return A_grad, B_grad, bias_grad, None, None, None, None, None, None, None, None, None, None


def classifier_2p5d(A: Tensor, B: Tensor, bias, tesseract_dim: int, out_shape: Tuple[int,
                                                                                     ...], row_rank: int, col_rank: int,
                    row_parallel_mode: ParallelMode, col_parallel_mode: ParallelMode, data_parallel_rank: int,
                    pipeline_parallel_rank: int, pipeline_parallel_size: int, tensor_parallel_size: int) -> Tensor:
    r"""Classifier.

    Args:
        A (:class:`torch.tensor`): matrix :math:`A`.
        B (:class:`torch.tensor`): matrix :math:`B`.
        bias (:class:`torch.tensor`): matrix of bias.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism.
        out_shape (:class:`torch.size`): shape of output tensor.
        row_rank (int): the rank of row.
        col_rank (int): the rank of column.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.
        data_parallel_rank (int): data parallel rank.
        pipeline_parallel_rank (int): pipeline parallel rank
        pipeline_parallel_size (int): pipeline parallel size.
        tensor_parallel_size (int): tensor parallel size.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """
    return _Classifier2p5D.apply(A, B, bias, tesseract_dim, out_shape, row_rank, col_rank, row_parallel_mode,
                                 col_parallel_mode, data_parallel_rank, pipeline_parallel_rank, pipeline_parallel_size,
                                 tensor_parallel_size)


class Matmul_AB_2p5D(torch.autograd.Function):
    r"""Matrix multiplication for :math:`C = AB`.

    Args:
        A (:class:`torch.tensor`): matrix :math:`A`.
        B (:class:`torch.tensor`): matrix :math:`B`.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism.
        out_shape (:class:`torch.size`): shape of output tensor.
        row_rank (int): the rank of row.
        col_rank (int): the rank of column.
        dep_rank (int): the rank of depth.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.
        data_parallel_rank (int): data parallel rank.
        pipeline_parallel_rank (int): pipeline parallel rank
        pipeline_parallel_size (int): pipeline parallel size.
        tensor_parallel_size (int): tensor parallel size.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, A: Tensor, B: Tensor, tesseract_dim: int, out_shape: Tuple[int, ...], row_rank: int,
                col_rank: int, dep_rank: int, row_parallel_mode: ParallelMode, col_parallel_mode: ParallelMode,
                data_parallel_rank: int, pipeline_parallel_rank: int, pipeline_parallel_size: int,
                tensor_parallel_size: int) -> Tensor:
        # A: [b / dq, s, h / q] -> [(b * s) / dq, h / q]
        # B: [h / dq, s / q]
        # C: [b / dq, s, s / q] -> [(b * s) / dq, s / q]

        assert A.shape[-1] == B.shape[-2], \
            'Invalid shapes: A={}, B={} for AB.'.format(A.shape, B.shape)

        if ctx:
            ctx.save_for_backward(A, B)

        A_shape = A.shape
        A = A.reshape((-1, A_shape[-1]))
        B_shape = B.shape
        B = B.reshape((-1, B_shape[-1]))
        C_shape = (A.shape[0], B.shape[-1])
        C = torch.zeros(C_shape, dtype=A.dtype, device=get_current_device())

        # use circular buffer to store the communication tensor
        # 2 is enough for all cases
        A_list = [torch.empty_like(A) for _ in range(2)]
        B_list = [torch.empty_like(B) for _ in range(2)]

        row_group = gpc.get_group(row_parallel_mode)
        col_group = gpc.get_group(col_parallel_mode)

        src_a = \
            tesseract_dim * row_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size
        src_b = \
            col_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size

        opa = [None] * 2
        opb = [None] * 2

        A_list[0].copy_(A)
        B_list[0].copy_(B)
        opa[0] = dist.broadcast(A_list[0], src=src_a, group=row_group, async_op=True)
        opb[0] = dist.broadcast(B_list[0], src=src_b, group=col_group, async_op=True)
        cur = 0

        for i in range(tesseract_dim):
            if i != tesseract_dim - 1:
                A_list[1 - cur].copy_(A)
                opa[1 - cur] = dist.broadcast(A_list[1 - cur], src=src_a + 1, group=row_group, async_op=True)
                B_list[1 - cur].copy_(B)
                opb[1 - cur] = dist.broadcast(B_list[1 - cur],
                                              src=src_b + tesseract_dim,
                                              group=col_group,
                                              async_op=True)

            if opa[cur] is not None:
                opa[cur].wait()
            if opb[cur] is not None:
                opb[cur].wait()

            torch.addmm(C, A_list[cur], B_list[cur], out=C)
            cur = 1 - cur
            src_a += 1
            src_b += tesseract_dim
        out = C.reshape(out_shape)

        if ctx:
            ctx.tesseract_dim = tesseract_dim
            ctx.row_rank = row_rank
            ctx.col_rank = col_rank
            ctx.dep_rank = dep_rank
            ctx.row_parallel_mode = row_parallel_mode
            ctx.col_parallel_mode = col_parallel_mode
            ctx.A_shape = A_shape
            ctx.B_shape = B_shape
            ctx.data_parallel_rank = data_parallel_rank
            ctx.pipeline_parallel_rank = pipeline_parallel_rank
            ctx.pipeline_parallel_size = pipeline_parallel_size
            ctx.tensor_parallel_size = tensor_parallel_size

        return out

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        A, B = ctx.saved_tensors
        with torch.no_grad():
            A_grad = Matmul_ABT_2p5D.apply(output_grad, B, ctx.tesseract_dim, ctx.A_shape, ctx.row_rank, ctx.col_rank,
                                           ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                           ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                           ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
            B_grad = Matmul_ATB_2p5D.apply(A, output_grad, ctx.tesseract_dim, ctx.B_shape, ctx.row_rank, ctx.col_rank,
                                           ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                           ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                           ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
        return A_grad, B_grad, None, None, None, None, None, None, None, None, None, None, None, None, None


class Matmul_ABT_2p5D(torch.autograd.Function):
    r"""Matrix multiplication for :math:`C = AB^T`.

    Args:
        A (:class:`torch.tensor`): matrix :math:`A`.
        B (:class:`torch.tensor`): matrix :math:`B`.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism.
        out_shape (:class:`torch.size`): shape of output tensor.
        row_rank (int): the rank of row.
        col_rank (int): the rank of column.
        dep_rank (int): the rank of depth.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.
        data_parallel_rank (int): data parallel rank.
        pipeline_parallel_rank (int): pipeline parallel rank
        pipeline_parallel_size (int): pipeline parallel size.
        tensor_parallel_size (int): tensor parallel size.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, A: Tensor, B: Tensor, tesseract_dim: int, out_shape: Tuple[int, ...], row_rank: int,
                col_rank: int, dep_rank: int, row_parallel_mode: ParallelMode, col_parallel_mode: ParallelMode,
                data_parallel_rank: int, pipeline_parallel_rank: int, pipeline_parallel_size: int,
                tensor_parallel_size: int) -> Tensor:

        assert A.shape[-1] == B.shape[-1], \
            'Invalid shapes: A={}, B={} for ABT.'.format(A.shape, B.shape)

        if ctx:
            ctx.save_for_backward(A, B)

        A_shape = A.shape
        A = A.reshape((-1, A_shape[-1]))
        B_shape = B.shape
        B = B.reshape((-1, B_shape[-1]))
        C_shape = (A.shape[0], B.shape[0])
        C = torch.empty(C_shape, dtype=A.dtype, device=get_current_device())

        # use circular buffer to store the communication tensor
        # 2 is enough for all cases
        B_list = [torch.empty_like(B) for _ in range(2)]
        C_list = [torch.empty_like(C) for _ in range(2)]

        row_group = gpc.get_group(row_parallel_mode)
        col_group = gpc.get_group(col_parallel_mode)

        src_b = \
            col_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size
        src_c = \
            tesseract_dim * row_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size

        opb = [None] * 2
        opr = [None] * 2

        B_list[0].copy_(B)
        opb[0] = dist.broadcast(B_list[0], src=src_b, group=col_group, async_op=True)
        cur = 0

        for i in range(tesseract_dim):
            if i != tesseract_dim - 1:
                B_list[1 - cur].copy_(B)
                opb[1 - cur] = dist.broadcast(B_list[1 - cur],
                                              src=src_b + tesseract_dim,
                                              group=col_group,
                                              async_op=True)

            if opr[cur] is not None:
                opr[cur].wait()
                if i - 2 == col_rank:
                    C.copy_(C_list[cur])

            if opb[cur] is not None:
                opb[cur].wait()

            torch.matmul(A, B_list[cur].transpose(0, 1), out=C_list[cur])
            opr[cur] = dist.reduce(C_list[cur], dst=src_c, group=row_group, async_op=True)
            cur = 1 - cur
            src_b += tesseract_dim
            src_c += 1

        for op in opr:
            op.wait()

        if tesseract_dim - 2 == col_rank:
            C.copy_(C_list[cur])
        if tesseract_dim - 1 == col_rank:
            C.copy_(C_list[1 - cur])
        out = C.reshape(out_shape)

        if ctx:
            ctx.tesseract_dim = tesseract_dim
            ctx.row_rank = row_rank
            ctx.col_rank = col_rank
            ctx.dep_rank = dep_rank
            ctx.row_parallel_mode = row_parallel_mode
            ctx.col_parallel_mode = col_parallel_mode
            ctx.A_shape = A_shape
            ctx.B_shape = B_shape
            ctx.data_parallel_rank = data_parallel_rank
            ctx.pipeline_parallel_rank = pipeline_parallel_rank
            ctx.pipeline_parallel_size = pipeline_parallel_size
            ctx.tensor_parallel_size = tensor_parallel_size

        return out

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        A, B = ctx.saved_tensors
        with torch.no_grad():
            A_grad = Matmul_AB_2p5D.apply(output_grad, B, ctx.tesseract_dim, ctx.A_shape, ctx.row_rank, ctx.col_rank,
                                          ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                          ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                          ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
            B_grad = Matmul_ATB_2p5D.apply(output_grad, A, ctx.tesseract_dim, ctx.B_shape, ctx.row_rank, ctx.col_rank,
                                           ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                           ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                           ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
        return A_grad, B_grad, None, None, None, None, None, None, None, None, None, None, None, None, None


class Matmul_ATB_2p5D(torch.autograd.Function):
    r"""Matrix multiplication for :math:`C = A^TB`

    Args:
        A (:class:`torch.tensor`): matrix :math:`A`.
        B (:class:`torch.tensor`): matrix :math:`B`.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism.
        out_shape (:class:`torch.size`): shape of output tensor.
        row_rank (int): the rank of row.
        col_rank (int): the rank of column.
        dep_rank (int): the rank of depth.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.
        data_parallel_rank (int): data parallel rank.
        pipeline_parallel_rank (int): pipeline parallel rank
        pipeline_parallel_size (int): pipeline parallel size.
        tensor_parallel_size (int): tensor parallel size.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, A: Tensor, B: Tensor, tesseract_dim: int, out_shape: Tuple[int, ...], row_rank: int,
                col_rank: int, dep_rank: int, row_parallel_mode: ParallelMode, col_parallel_mode: ParallelMode,
                data_parallel_rank: int, pipeline_parallel_rank: int, pipeline_parallel_size: int,
                tensor_parallel_size: int):

        assert A.shape[-2] == B.shape[-2], \
            'Invalid shapes: A={}, B={} for ATB.'.format(A.shape, B.shape)

        if ctx:
            ctx.save_for_backward(A, B)

        A_shape = A.shape
        A = A.reshape((-1, A_shape[-1]))
        B_shape = B.shape
        B = B.reshape((-1, B_shape[-1]))
        C_shape = (A.shape[-1], B.shape[-1])
        C = torch.empty(C_shape, dtype=A.dtype, device=get_current_device())

        # use circular buffer to store the communication tensor
        # 2 is enough for all cases
        A_list = [torch.empty_like(A) for _ in range(2)]
        C_list = [torch.empty_like(C) for _ in range(2)]

        row_group = gpc.get_group(row_parallel_mode)
        col_group = gpc.get_group(col_parallel_mode)

        src_a = \
            tesseract_dim * row_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size
        src_c = \
            col_rank + tesseract_dim ** 2 * dep_rank + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size

        opa = [None] * 2
        opr = [None] * 2

        A_list[0].copy_(A)
        opa[0] = dist.broadcast(A_list[0], src=src_a, group=row_group, async_op=True)
        cur = 0

        for i in range(tesseract_dim):
            if i != tesseract_dim - 1:
                A_list[1 - cur].copy_(A)
                opa[1 - cur] = dist.broadcast(A_list[1 - cur], src=src_a + 1, group=row_group, async_op=True)

            if opr[cur] is not None:
                opr[cur].wait()
                if i - 2 == row_rank:
                    C.copy_(C_list[cur])

            if opa[cur] is not None:
                opa[cur].wait()

            torch.matmul(A_list[cur].transpose(0, 1), B, out=C_list[cur])
            opr[cur] = dist.reduce(C_list[cur], dst=src_c, group=col_group, async_op=True)
            cur = 1 - cur
            src_a += 1
            src_c += tesseract_dim

        for op in opr:
            op.wait()

        if tesseract_dim - 2 == row_rank:
            C.copy_(C_list[cur])
        if tesseract_dim - 1 == row_rank:
            C.copy_(C_list[1 - cur])
        out = C.reshape(out_shape)

        if ctx:
            ctx.tesseract_dim = tesseract_dim
            ctx.row_rank = row_rank
            ctx.col_rank = col_rank
            ctx.dep_rank = dep_rank
            ctx.row_parallel_mode = row_parallel_mode
            ctx.col_parallel_mode = col_parallel_mode
            ctx.A_shape = A_shape
            ctx.B_shape = B_shape
            ctx.data_parallel_rank = data_parallel_rank
            ctx.pipeline_parallel_rank = pipeline_parallel_rank
            ctx.pipeline_parallel_size = pipeline_parallel_size
            ctx.tensor_parallel_size = tensor_parallel_size

        return out

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        A, B = ctx.saved_tensors
        with torch.no_grad():
            A_grad = Matmul_ABT_2p5D.apply(B, output_grad, ctx.tesseract_dim, ctx.A_shape, ctx.row_rank, ctx.col_rank,
                                           ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                           ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                           ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
            B_grad = Matmul_AB_2p5D.apply(A, output_grad, ctx.tesseract_dim, ctx.B_shape, ctx.row_rank, ctx.col_rank,
                                          ctx.dep_rank, ctx.row_parallel_mode, ctx.col_parallel_mode,
                                          ctx.data_parallel_rank, ctx.pipeline_parallel_rank,
                                          ctx.pipeline_parallel_size, ctx.tensor_parallel_size)
        return A_grad, B_grad, None, None, None, None, None, None, None, None, None, None, None, None, None


class _Add_Bias_2p5D(torch.autograd.Function):

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, input: Tensor, bias: Tensor, output_size_per_partition: int, tesseract_dim: int,
                row_rank: int, col_rank: int, dep_rank: int, col_parallel_mode: ParallelMode, skip_bias_add: bool,
                data_parallel_rank: int, pipeline_parallel_rank: int, pipeline_parallel_size: int,
                tensor_parallel_size: int) -> Tensor:
        if row_rank == 0:
            bias_temp = bias.clone()
        else:
            bias_temp = torch.zeros(output_size_per_partition, dtype=bias.dtype, device=get_current_device())
        src_rank = \
            col_rank + dep_rank * tesseract_dim ** 2 + \
            data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
            pipeline_parallel_rank * tensor_parallel_size
        dist.broadcast(bias_temp, src=src_rank, group=get_parallel_group(col_parallel_mode))

        ctx.row_rank = row_rank
        ctx.col_rank = col_rank
        ctx.dep_rank = dep_rank
        ctx.tesseract_dim = tesseract_dim
        ctx.col_parallel_mode = col_parallel_mode
        ctx.bias = skip_bias_add
        ctx.data_parallel_rank = data_parallel_rank
        ctx.pipeline_parallel_rank = pipeline_parallel_rank
        ctx.pipeline_parallel_size = pipeline_parallel_size
        ctx.tensor_parallel_size = tensor_parallel_size

        if skip_bias_add:
            return bias_temp
        else:
            output = input + bias_temp
            return output

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        row_rank = ctx.row_rank
        col_rank = ctx.col_rank
        dep_rank = ctx.dep_rank
        tesseract_dim = ctx.tesseract_dim
        col_parallel_mode = ctx.col_parallel_mode
        data_parallel_rank = ctx.data_parallel_rank
        pipeline_parallel_rank = ctx.pipeline_parallel_rank
        pipeline_parallel_size = ctx.pipeline_parallel_size
        tensor_parallel_size = ctx.tensor_parallel_size

        if ctx.bias:
            dst_rank = \
                col_rank + dep_rank * (tesseract_dim ** 2) + \
                data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
                pipeline_parallel_rank * tensor_parallel_size
            dist.reduce(output_grad, dst=dst_rank, group=get_parallel_group(col_parallel_mode))
            if row_rank == 0:
                return \
                    None, output_grad, None, None, None, None, None, None, \
                    None, None, None, None, None, None, None, None
            else:
                grad_tmp = torch.zeros_like(output_grad)
                return \
                    None, grad_tmp, None, None, None, None, None, None, \
                    None, None, None, None, None, None, None, None
        else:
            reduce_dim = tuple(range(output_grad.ndim - 1))
            reduce = torch.sum(output_grad, dim=reduce_dim)
            dst_rank = \
                col_rank + dep_rank * (tesseract_dim ** 2) + \
                data_parallel_rank * pipeline_parallel_size * tensor_parallel_size + \
                pipeline_parallel_rank * tensor_parallel_size
            dist.reduce(reduce, dst=dst_rank, group=get_parallel_group(col_parallel_mode))
            if row_rank == 0:
                return \
                    output_grad, reduce, None, None, None, None, None, None, None, \
                    None, None, None, None, None, None, None, None
            else:
                reduce_tmp = torch.zeros_like(reduce)
                return \
                    output_grad, reduce_tmp, None, None, None, None, None, None, \
                    None, None, None, None, None, None, None, None, None


def add_bias_2p5d(input: Tensor, bias: Tensor, output_size_per_partition: int, tesseract_dim: int, row_rank: int,
                  col_rank: int, dep_rank: int, col_parallel_mode: ParallelMode, skip_bias_add: bool,
                  data_parallel_rank: int, pipeline_parallel_rank: int, pipeline_parallel_size: int,
                  tensor_parallel_size: int) -> Tensor:
    r"""Matrix add bias: :math:`C = A + b`.

    Args:
        input (:class:`torch.tensor`): matrix :math:`A`.
        bias (:class:`torch.tensor`): matrix :math:`B`.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism.
        output_size_per_partition (int): output size in each partition.
        row_rank (int): the rank of row.
        col_rank (int): the rank of column.
        dep_rank (int): the rank of depth.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.
        skip_bias_add (bool): If set to ``True``, it will skip bias add for linear layer,
            which is preserved for kernel fusion.
        data_parallel_rank (int): data parallel rank.
        pipeline_parallel_rank (int): pipeline parallel rank
        pipeline_parallel_size (int): pipeline parallel size.
        tensor_parallel_size (int): tensor parallel size.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """
    return _Add_Bias_2p5D.apply(input, bias, output_size_per_partition, tesseract_dim, row_rank, col_rank, dep_rank,
                                col_parallel_mode, skip_bias_add, data_parallel_rank, pipeline_parallel_rank,
                                pipeline_parallel_size, tensor_parallel_size)


class _Layernorm2p5D(torch.autograd.Function):
    r"""Layernorm.

    Args:
        input (:class:`torch.tensor`): input matrix.
        E_x (:class:`torch.tensor`): mean.
        Var_x (:class:`torch.tensor`): variance.
        hidden_size (int): hidden size.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """

    @staticmethod
    @custom_fwd(cast_inputs=torch.float32)
    def forward(ctx: Any, input: Tensor, E_x: Tensor, Var_x: Tensor, hidden_size: int,
                row_parallel_mode: ParallelMode) -> Tensor:
        input = input - E_x
        # in here, input = x - E[x], Var_x = 1 / sqrt(Var[x] + eps)
        ctx.hidden_size = hidden_size
        output = input * Var_x
        ctx.save_for_backward(output, Var_x)
        ctx.row_parallel_mode = row_parallel_mode
        return output

    @staticmethod
    @custom_bwd
    def backward(ctx, output_grad):
        row_parallel_mode = ctx.row_parallel_mode
        x, Var_x = ctx.saved_tensors
        # in here, Var_x = 1 / sqrt(Var[x] + eps), x = (x - E[x]) * Var_x
        with torch.no_grad():
            output_grad_sum = torch.sum(output_grad, dim=-1, keepdim=True)
            torch.distributed.all_reduce(output_grad_sum, group=get_parallel_group(row_parallel_mode))
            output_grad_sum /= ctx.hidden_size

            output_grad_mul_x_sum = torch.sum(output_grad * x, dim=-1, keepdim=True)
            torch.distributed.all_reduce(output_grad_mul_x_sum, group=get_parallel_group(row_parallel_mode))
            output_grad_mul_x_sum /= ctx.hidden_size

            input_grad = output_grad.clone()
            input_grad -= x * output_grad_mul_x_sum
            input_grad -= output_grad_sum
            input_grad *= Var_x

        return input_grad, None, None, None, None, None, None


def layernorm_2p5d(input: Tensor, E_x: Tensor, Var_x: Tensor, hidden_size: int,
                   row_parallel_mode: ParallelMode) -> Tensor:
    r"""Layernorm.

    Args:
        input (:class:`torch.tensor`): input matrix.
        E_x (:class:`torch.tensor`): mean.
        Var_x (:class:`torch.tensor`): variance.
        hidden_size (int): hidden size.
        row_parallel_mode (:class:`colossalai.context.ParallelMode`): row parallel mode.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_.
    """
    return _Layernorm2p5D.apply(input, E_x, Var_x, hidden_size, row_parallel_mode)


class _AllGatherTensor2p5D(torch.autograd.Function):

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, inputs: Tensor, dim: int, col_parallel_mode: ParallelMode) -> Tensor:
        ctx.dim = dim
        ctx.col_parallel_mode = col_parallel_mode

        outputs = all_gather(inputs, dim, col_parallel_mode)
        return outputs

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        grad = reduce_scatter(output_grad, ctx.dim, ctx.col_parallel_mode)
        return grad.contiguous(), None, None


def all_gather_tensor_2p5d(inputs: Tensor, dim: int, col_parallel_mode: ParallelMode) -> Tensor:
    r"""all gather the weight of 2.5D parallelism.

    Args:
        inputs (:class:`torch.tensor`): input tensor.
        dim (int): dimension of all-gather.
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_.
    """
    return _AllGatherTensor2p5D.apply(inputs, dim, col_parallel_mode)


class SplitFirst(torch.autograd.Function):
    r"""

    Args:
        inputs (:class:`torch.tensor`): input tensor.
        tesseract_dim (int): dimension of TESSERACT fo 2.5D parallelism
        col_parallel_mode (:class:`colossalai.context.ParallelMode`): column parallel mode.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_.
    """

    @staticmethod
    @custom_fwd(cast_inputs=torch.float16)
    def forward(ctx: Any, inputs: Tensor, tesseract_dim: int, col_parallel_mode: ParallelMode) -> Tensor:
        ctx.tesseract_dim = tesseract_dim
        ctx.batch_size = inputs.size(0)
        ctx.para_mode = col_parallel_mode
        row_rank = gpc.get_local_rank(col_parallel_mode)

        outputs = inputs.chunk(tesseract_dim, dim=0)[row_rank]
        return outputs

    @staticmethod
    @custom_bwd
    def backward(ctx: Any, output_grad: Tensor) -> Tuple[Tensor, ...]:
        grad_shape = (ctx.batch_size,) + output_grad.shape[1:]
        grad = torch.empty(grad_shape, dtype=output_grad.dtype, device=get_current_device())
        dist.all_gather(list(grad.chunk(ctx.tesseract_dim, dim=0)),
                        output_grad.contiguous(),
                        group=gpc.get_group(ctx.para_mode))
        return grad, None, None


def split_batch_2p5d(input_: Tensor, dim: int = 0) -> Tensor:
    """Splits 2P5D tensor in specified dimension across cols.

    Args:
        input_ (:class:`torch.tensor`): Input tensor.
        dim (int): Specified dimension in which to split.

    Returns:
        :class:`torch.tensor`: The tensor has been split.
    """
    dim_size = input_.size(dim)
    world_size = gpc.get_world_size(ParallelMode.PARALLEL_2P5D_COL)

    if world_size <= 1:
        return input_

    assert dim_size % world_size == 0, \
        f'The batch size ({dim_size}) is not a multiple of 2.5D size * depth ({world_size}).'

    return torch.chunk(input_, gpc.get_world_size(ParallelMode.PARALLEL_2P5D_COL),
                       dim=dim)[gpc.get_local_rank(ParallelMode.PARALLEL_2P5D_COL)].contiguous()


class _ReduceTensor2p5D(torch.autograd.Function):

    @staticmethod
    def forward(ctx, input_, parallel_mode):
        return all_reduce(input_, parallel_mode)

    @staticmethod
    def backward(ctx, output_grad):
        return output_grad, None


def reduce_tensor_2p5d(input_: Tensor, parallel_mode: ParallelMode) -> Tensor:
    r"""All-reduce the input.

    Args:
        input_ (:class:`torch.tensor`): Input tensor.
        parallel_mode (:class:`colossalai.context.ParallelMode`): The parallel mode tensor used.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """
    return _ReduceTensor2p5D.apply(input_, parallel_mode)


class _ReduceScatterTensor2p5D(torch.autograd.Function):

    @staticmethod
    def forward(ctx, input_, dim, parallel_mode):
        ctx.dim = dim
        ctx.parallel_mode = parallel_mode
        return reduce_scatter(input_, dim, parallel_mode)

    @staticmethod
    def backward(ctx, output_grad):
        return all_gather(output_grad, ctx.dim, ctx.parallel_mode), None, None


def reduce_scatter_tensor_2p5d(input_: Tensor, dim: int, parallel_mode: ParallelMode) -> Tensor:
    r"""Reduce-scatter the input.

    Args:
        input_ (:class:`torch.tensor`): Input tensor.
        dim (int): Dimension to reduce.
        parallel_mode (:class:`colossalai.context.ParallelMode`): The parallel mode tensor used.

    Note:
        The parallel_mode should be concluded in ``ParallelMode``. More details about ``ParallelMode`` could be found
        in `parallel_mode <https://github.com/hpcaitech/ColossalAI/blob/main/colossalai/context/parallel_mode.py>`_
    """
    dim_size = input_.size(dim)
    world_size = gpc.get_world_size(parallel_mode)
    assert dim_size % world_size == 0, \
        f'The batch size ({dim_size}) is not a multiple of 2.5D size * depth ({world_size}).'

    return _ReduceScatterTensor2p5D.apply(input_, dim, parallel_mode)


class _RreduceByBatch2p5D(torch.autograd.Function):

    @staticmethod
    def symbolic(graph, input_, reduce_mean: bool = False):
        output = all_reduce(input_, ParallelMode.PARALLEL_2P5D_COL)
        if reduce_mean:
            reduce_size = gpc.get_world_size(ParallelMode.PARALLEL_2P5D_COL)
            return output / reduce_size
        return output

    @staticmethod
    @custom_fwd(cast_inputs=torch.float32)
    def forward(ctx, input_, reduce_mean: bool = False):
        output = all_reduce(input_, ParallelMode.PARALLEL_2P5D_COL)
        ctx.reduce_mean = reduce_mean
        if reduce_mean:
            reduce_size = gpc.get_world_size(ParallelMode.PARALLEL_2P5D_COL)
            ctx.reduce_size = reduce_size
            return output.clone() / reduce_size
        return output.clone()

    @staticmethod
    @custom_bwd
    def backward(ctx, output_grad):
        if ctx.reduce_mean:
            return output_grad / ctx.reduce_size, None
        else:
            return output_grad, None


def reduce_by_batch_2p5d(input_, reduce_mean: bool = False) -> Tensor:
    r"""All-reduce the input from the model parallel region.

    Args:
        input_ (:class:`torch.tensor`): input matrix.
        reduce_mean (bool, optional):
            If set to ``True``, it will divide the output by column parallel size, default to False.
    """
    return _RreduceByBatch2p5D.apply(input_, reduce_mean)