# 3D 张量并行

## 引言​

3D 张量并行 是一种将神经网络模型的计算并行化，以期望获得最佳通信成本优化的方法。

$\left[\begin{matrix} X_{000} & X_{001} \\ X_{010} & X_{011} \\ X_{100} & X_{101} \\ X_{110} & X_{111} \end{matrix} \right] \text{~and~} \left[\begin{matrix} A_{000} & A_{001} & A_{010} & A_{011} \\ A_{100} & A_{101} & A_{110} & A_{111} \end{matrix} \right] \text{~respectively,}$

$Y= \left[\begin{matrix} Y_{000} & Y_{001} \\ Y_{010} & Y_{011} \\ Y_{100} & Y_{101} \\ Y_{110} & Y_{111} \end{matrix} \right].$

## 效率​

$O(1/q^3)$$O(1/q^3)$$O(1/q^3)$$O(6(q-1)/q^3)$$O(6(q-1))$

## 使用​

CONFIG = dict(parallel=dict(    data=1,    pipeline=1,    tensor=dict(size=8, mode='3d'),))

import colossalaiimport colossalai.nn as col_nnimport torchfrom colossalai.utils import print_rank_0class MLP(torch.nn.Module):    def __init__(self, dim: int = 256):        super().__init__()        intermediate_dim = dim * 4        self.dense_1 = col_nn.Linear(dim, intermediate_dim)        print_rank_0(f'Weight of the first linear layer: {self.dense_1.weight.shape}')        self.activation = torch.nn.GELU()        self.dense_2 = col_nn.Linear(intermediate_dim, dim)        print_rank_0(f'Weight of the second linear layer: {self.dense_2.weight.shape}')        self.dropout = col_nn.Dropout(0.1)    def forward(self, x):        x = self.dense_1(x)        print_rank_0(f'Output of the first linear layer: {x.shape}')        x = self.activation(x)        x = self.dense_2(x)        print_rank_0(f'Output of the second linear layer: {x.shape}')        x = self.dropout(x)        return x

parser = colossalai.get_default_parser()colossalai.launch(config=CONFIG,                  rank=args.rank,                  world_size=args.world_size,                  local_rank=args.local_rank,                  host=args.host,                  port=args.port)m = MLP()

Weight of the first linear layer: torch.Size([128, 256])Weight of the second linear layer: torch.Size([512, 64])

from colossalai.context import ParallelModefrom colossalai.core import global_context as gpcfrom colossalai.utils import get_current_devicex = torch.randn((16, 256), device=get_current_device())# partition inputtorch.distributed.broadcast(x, src=0)x = torch.chunk(x, 2, dim=0)[gpc.get_local_rank(ParallelMode.PARALLEL_3D_WEIGHT)]x = torch.chunk(x, 2, dim=0)[gpc.get_local_rank(ParallelMode.PARALLEL_3D_INPUT)]x = torch.chunk(x, 2, dim=-1)[gpc.get_local_rank(ParallelMode.PARALLEL_3D_OUTPUT)]print_rank_0(f'Input: {x.shape}')x = m(x)

Input: torch.Size([4, 128])Output of the first linear layer: torch.Size([4, 512])Output of the second linear layer: torch.Size([4, 128])

3D并行中的 activation 张量都是同时在$q^2$行和$q$列分割的。例如，第一个线性层的输出是 [4, 512], 而第二层的输出为 [4, 128]。 注意，虽然这里3D并行的结果与2.5D并行的结果形状相同，但每个划分的内容是不同的。