0.前言

本文从代码角度来谈下Mixtral 8x7B混合专家Pytorch的实现

1.论文概述

Mixtral-8x7B引爆了MoE的技术方向，更多针对MoE优化的Trick出现，回归模型本身来解析：

Mixtral 8x7B采用了
sMoE模型结构，模型的细节如何？路由负载均衡如何计算？代码如何实现？
Mixtral 8x7B的训练流程和推理流程是怎么样的，如何提高训练和推理效率？
Mixtral 8x7B的模型参数是如何计算的？
Mixtral 8x7B性能硬刚
LLaMA2-70B和
GPT-3.5，性能一线水准，在
MBPP代码能力超越
3.5

2. Mixtral 8x7B 模型架构和计算流程

Mixtral is based on atransformer architecture [31]and uses the samemodificationsas described in [18], with the notable exceptions that Mixtral supports a fully dense context length of 32k tokens, and thefeed forwardblocks are replaced by Mixture-of-Expert layers(Section 2.1). The model architecture parameters are summarized in Table 1.

base的模型结构为
Transformers的改版
Mistral-7B
MoE作用在
Feed Forward Blocks上

2.1 Mixtral 模型架构

In a Transformer model, the MoE layer is applied independently per token and replaces the feed-forward (FFN) sub-block of the transformer block. For Mixtral we use the same SwiGLU architecture as the expert function Ei(x) and set K = 2. This means each token is routed to two SwiGLU sub-blocks with different sets of weights. Taking this all together, the output y for an input token x is computed as:

以
LLaMA2或
Mistral-7B来说其
MLP都是
SwiGLU形式
在
Mixtral-8x7B中
每层的
Decoder层的
MLP都以
sMoE来替换掉

Transformers Mixtral-of-Expert

代码实现:

在Huggingface的Transformers框架中,Mixtral主要有两部分组成

MixtralDecoderLayer
MixtralSparseMoeBlock：替换掉原有的MLP层

MixtralForCausalLM(
  (model): MixtralModel(
    (embed_tokens): Embedding(32000, 128)
    (layers): ModuleList(
      (1): MixtralDecoder服务器托管网Layer(
        (self_attn): MixtralAttention(
          (q_proj): Linear(in_features=128, out_features=128, bias=False)
          (k_proj): Linear(in_features=128, out_features=128, bias=False)
          (v_proj): Linear(in_features=128, out_features=128, bias=False)
          (o_proj): Linear(in_features=128, out_features=128, bias=False)
          (rotary_emb): MixtralRotaryEmbedding()
        )
        (block_sparse_moe): MixtralSparseMoeBlock(
          (gate): Linear(in_features=128, out_features=8, bias=False)
          (experts): ModuleList(
            (0-7): 8 x MixtralBLockSparseTop2MLP(
              (w1): Linear(in_features=128, out_features=256, bias=False)
              (w2): Linear(in_features=256, out_features=128, bias=False)
              (w3): Linear(in_features=128, out_features=256, bias=False)
              (act_fn): SiLU()
            )
          )
        )
        (input_layernorm): MixtralRMSNorm()
        (post_attention_layernorm): MixtralRMSNorm()
      )
    )
    (norm): MixtralRMSNorm()
  )

2.2 SMoE 层实现

2.2.1 单个 Expert 实现

import torch
from torch import nn
from transformers import MixtralConfig

class MixtralBLockSparseTop2MLP(nn.Module):
    def __init__(self, config: MixtralConfig):
        super().__init__()
        self.ffn_dim = config.intermediate_size
        self.hidden_dim = config.hidden_size

        self.w1 = nn.Linear(self.hidden_dim, self.ffn_dim, bias=False)
        self.w2 = nn.Linear(self.ffn_dim, self.hidden_dim, bias=False)
        self.w3 = nn.Linear(self.hidden_dim, self.ffn_dim, bias=False)

        self.act_fn = nn.SiLU()

    # Forward 是 SwiGLU
    def forward(self, hidden_states):
        y = self.act_fn(self.w1(hidden_states)) * self.w3(hidden_states)
        y = self.w2(y)
        return y

x = torch.randn(1, 64, 128)
expert = MixtralBLockSparseTop2MLP(config)
print('单个专家为原LLaMA的MLP层')
print(expert)
g = expert(x)
print('单个专家输入:', x.shape)
print('单个专家输出结果：', g.shape)

结果

单个专家为原LLaMA的MLP层
MixtralBLockSparseTop2MLP(
  (w1): Linear(in_features=128, out_features=256, bias=False)
  (w2): Linear(in_features=256, out_features=128, bias=False)
  (w3): Linear(in_features=128, out_features=256, bias=False)
  (act_fn): SiLU()
)
单个专家输入:
torch.Size([1, 64, 128])
单个专家输出结果：
torch.Size([1, 64, 128])

2.2.2混合Expert实现

class MixtralSparseMoeBlock(nn.Module):
    def __init__(self, config):
        super().__init__(服务器托管网)
        self.hidden_dim = config.hidden_size
        self.ffn_dim = config.intermediate_size
        self.num_experts = config.num_local_experts
        self.top_k = config.num_experts_per_tok

        # gating
        self.gate = nn.Linear(self.hidden_dim, self.num_experts, bias=False)

        # 多个 SwiGLU MLP 层组成混合专家
        self.experts = nn.ModuleList([MixtralBLockSparseTop2MLP(config) 
                                      for _ in range(self.num_experts)])

x = torch.randn(1, 64, 128)
experts = MixtralSparseMoeBlock(config)
print('多个专家混合专家')
print(experts)

在以上我们实现了模型的关键结构，但是这里的sMoE的Forward并没有实现

2.3 SMoE 计算流程

2.3.1 Gating流程

以下表示为多个token的gating计算流程

# 阶段一
# 计算稀疏 gating 值
tokens = 6
x = torch.randn(1, tokens, 128) # 6个token
hidden_states = x
batch_size, sequence_length, hidden_dim = hidden_states.shape
hidden_states = hidden_states.view(-1, hidden_dim)

 # 每层都会产生router_logits, 将用于最后作 load balance loss
router_logits = experts.gate(hidden_states)
print(f'experts.gate output router logits : n {router_logits}')

# 计算 TopK 的 专家 logits 和 Top2 专家的位置
routing_weights = F.softmax(router_logits, dim=1, dtype=torch.float)
print(f'softmax weight  : n {routing_weights}')

routing_weights, selected_experts = torch.topk(routing_weights, 
                                               experts.top_k, dim=-1)
print(f'expert select : n {selected_experts}')
print(f'topk : n {routing_weights}')

routing_weights /= routing_weights.sum(dim=-1, keepdim=True)
print(f'topk归一化 : n {routing_weights}')

routing_weights = routing_weights.to(hidden_states.dtype)

## One Hot 编码
expert_mask = torch.nn.functional.one_hot(selected_experts, 
                                          num_classes=experts.num_experts).permute(2, 1, 0)
for i in range(tokens):
    print(f'【token_{i}】n', expert_mask[:,:,i])

追踪x3的结果

2.3.2 Expert 流程

sMoE中是基于专家来选择
token来计算的
token先序：左图为
token3选择
expert 2,
expert 3号来计算
sMoE结果
expert先序：右图为依次计算
expert2和
expert3才得出
token3的
sMoE结果

代码实现结果为：

## 最终结果
final_hidden_states = torch.zeros(
    (batch_size * sequence_length, hidden_dim), 
        dtype=hidden_states.dtype, device=hidden_states.device
)
print(f'final moe result shape for each token: {final_hidden_states.shape}')

# 每个专家收集需要计算token
for expert_idx in range(experts.num_experts):

    print(f'--------expert {expert_idx} ---------')

    expert_layer = experts.experts[expert_idx]
    print(expert_mask[expert_idx])
    idx, top_x = torch.where(expert_mask[expert_idx])
    print(f'专家 {expert_idx} 计算的样本编号:',top_x.tolist()) # select x_idx for expert top1
    print(f'专家 {expert_idx} top1:0, top2:1 ',idx.tolist()) # 0 is top1 ,1 is top2
    print(f'有 {len(top_x)} / {x.shape[1]} token 选到专家 {expert_idx}')
    
    top_x_list = top_x.tolist()
    idx_list = idx.tolist()

    current_state = hidden_states[None, top_x_list].reshape(-1, hidden_dim)

    # expert_0(x) * routing_weights
    current_hidden_states = expert_layer(current_state)  
                            * routing_weights[top_x_list, idx_list, None]

    # 将计算的单个专家结果填入到结果表里
    final_hidden_states.index_add_(0, top_x, current_hidden_states.to(hidden_states.dtype))

    print(current_state.shape) 
    print(routing_weights[top_x_list, idx_list, None].shape)
    print(current_hidden_states.shape)
    print(final_hidden_states.shape)

输出结果为:

2.4 Router Load Balence 计算

路由负载均衡的实现来自Switch Transformers

Computes auxiliary load balancing loss as in Switch Transformer – implemented in Pytorch. See Switch Transformer for more details. This function implements the loss function presented in equations (4) – (6) of the paper. It aims at penalizing cases where the routing between experts is too unbalanced.

2.4.1 Switch Transformers Load Balance Loss

该算法为sMoE简化版load balance, 去除了原版balance loss估计

fi:在一个batch中第i专家分配到token的数量概率

Pi:在一个batch中T个tokens，各个专家选到tokens的概率和

2.4.2手撕Mixtral Load Balance Loss 计算流程

可以想象下layer norm只是在当前层里对所有tokens做，而负载均衡处理范围更广，对所有层的tokens，在每个expert的纵向计算出单专家负载值，求和便得到整个网络的负载均衡 loss

2.4.3 手撕Mixtral Load Balance

import torch

num_experts = 8
batch = 10
seq_length = 6
top_k = 2

print(f'sMoE num_experts:{num_experts} top_k:{top_k} batch:{batch} seq_length:{seq_length}')

router_logits_1 = torch.randn(batch, seq_length, num_experts).view(-1,num_experts) # layer 1
router_logits_2 = torch.randn(batch, seq_length, num_experts).view(-1,num_experts) # layer 2
router_logits = [router_logits_1, router_logits_2] 

concatenated_gate_logits = torch.cat(router_logits, dim = 0)
print('单层gating的路由logits:', router_logits_1.shape) 
print('两层gating的路由logits:', concatenated_gate_logits.shape)

print('根据logits top-k 计算热独编码')
routing_weights = torch.nn.functional.softmax(concatenated_gate_logits, dim=-1)
_, selected_experts = torch.topk(routing_weights, top_k, dim=-1)
expert_mask = torch.nn.functional.one_hot(selected_experts, num_experts)
print(expert_mask.shape)

tokens_sum_expert = torch.sum(expert_mask.float(), dim=0)
tokens_per_expert = torch.mean(expert_mask.float(), dim=0)
print(f'top1 每个专家平均处理的token   :', tokens_sum_expert[0])
print(f'top2 每个专家平均处理的token fi:', tokens_per_expert[1])
print(f'top1与top2水平合计', tokens_per_expert.sum(dim=1))

# Compute the average probability of routing to these experts
router_prob_per_expert = torch.mean(routing_weights, dim=0)
print('router_prob_per_expert Pi: ' , router_prob_per_expert)

print( '每个专家的负载：',  tokens_per_expert * router_prob_per_expert.unsqueeze(0))
overall_loss = torch.sum(tokens_per_expert * router_prob_per_expert.unsqueeze(0))
print('final loss:', overall_loss)

计算结果

sMoE num_experts:8 top_k:2 batch:10 seq_length:6
单层gating的路由logits:
torch.Size([60, 8])
两层gating的路由logits:
torch.Size([120, 8])
根据logits top-k 计算热独编码
torch.Size([120, 2, 8])
top1 每个专家平均处理的token   : tensor([10., 14., 19., 17., 14.,  9., 17., 20.])
top2 每个专家平均处理的token fi: tensor([0.1667, 0.1333, 0.1833, 0.0833, 0.1167, 0.1500, 0.0667, 0.1000])
top1与top2水平合计 tensor([1., 1.])
router_prob_per_expert Pi:  tensor([0.1236, 0.1184, 0.1351, 0.1168, 0.1311, 0.1147, 0.1156, 0.1447])
每个专家的负载：tensor([[0.0103, 0.0138, 0.0214, 0.0165, 0.0153, 0.0086, 0.0164, 0.0241],
        [0.0206, 0.0158, 0.0248, 0.0097, 0.0153, 0.0172, 0.0077, 0.0145]])
final loss: tensor(0.2520)

这里的gating logits是跨batch跨层的，作用在每个token上

3. Mixtral 8x7B 参数量计算

3.1 原论文描述

这里的13B是指单个token涉及的模型参数量，实际推理时每个token都有不同的expert，那么实际运行还是跑47B参数的, 使用了sMoE 并不会减少显存占用。

3.2 模型参数量计算

忽略GQA计算

dim = 4096
n_layers = 32
head_dim = 128
hidden_dim = 14336
n_heads = 32
n_kv_heads = 8# ignore GQA
vocab_size = 32000
num_experts = 8
top_k_experts = 2

# attention mlp layernorm
llama_num = n_layers * (dim * dim * 4 + hidden_dim * dim * 3 + 2 * dim ) 
        + 2 * vocab_size * dim 
print('llama:', llama_num)

# attention 【mlp*8】 layernorm
moe_num = n_layers * (dim * dim * 4 + hidden_dim * dim * 3 * 8 + 2 * dim ) 
        + 2 * vocab_size * dim 
print('moe:', moe_num)

# attention 【mlp*2】 layernorm
# ToP2-inference
moe_num = n_layers * (dim * dim * 4 + hidden_dim * dim * 3 * 2 + 2 * dim ) 
        + 2 * vocab_size * dim 
print('moe top-2:', moe_num)

结果

llama: 8047034368
moe: 47507046400
moe top-2: 13684178944

4. MoE 扩展

4.1 MegaBlocks

MoE layers can be run efficiently on single GPUs with high performance specialized kernels. For example,Megablocks

MegaBlocks实现稀疏的MoE计算

题外话：XFormers也实现了类似思想的算子，batch里的attention通过Mask实现多序列稀疏计算。

4.2 GShard

Mixtral论文里在load balance里提了一下GShard, 是首篇将MoE引入到Transformers的工作

This formulation is similar to the GShard architecture [21], with the exceptions that we replace all FFN sub-blocks by MoE layers while GShard replaces every other block, and that GShard uses a more elaborate gating strategy for the second expert assigned to each token.

GShard在不同GPU上分配不同的专家，其他参数都共享，数据派发到专家，专家结果汇总都由All-to-All算子实现

DeepSpeed-MoE源码对All-to-All的实现如下

class _AllToAll(torch.autograd.Function):

    @staticmethod
    def forward(
            ctx: Any,
            # TODO: replace with DS process group
            group: torch.distributed.ProcessGroup,
            input: Tensor) -> Tensor:# type: ignore
        ctx.group = group
        input = input.contiguous()
        output = torch.empty_like(input)
        dist.all_to_all_single(output, input, group=group)
        return output

    @staticmethod
    def backward(ctx: Any, *grad_output: Tensor) -> Tuple[None, Tensor]:
        return (None, _AllToAll.apply(ctx.group, *grad_output))
        
class MOELayer(Base):
     # ...
     def forward(self, *input: Tensor, **kwargs: Any) -> Tensor:
        # ...
        dispatched_input = _AllToAll.apply(self.ep_group, dispatched_input)

        # Re-shape after all-to-all: ecm -> gecm
        dispatched_input = dispatched_input.reshape(self.ep_size, self.num_local_experts, -1, d_model)

        expert_output = self.experts(dispatched_input)


        expert_output = _AllToAll.apply(self.ep_group, expert_output)

    #...

4.3 DeepSpeed-MoE

更加工程化的实现可以看
DeepSpeed-MoE的开源方案
MoE层使用
Expert-Paralallelism做并行
AlltoAll实现如上
非
MoE层使用
TP+DP

4.4 LLaMA-MoE

Mixtral 8x7B训不动？试试将LLaMA原MLP改造成LLaMA-MoE

LLaMA-MoE 上关键代码是用LinearGLUExperts代替原本LLaMA里的SwiGLU层

 class LinearGLUExperts(nn.Module):
    # ...
    def __init__(...):
        # ... 
        # 每个专家都创建SwiGLU MLP层
        for i in range(num_experts):
            # this matrix will be transposed when performing linear forwarding
            this_expert_weight_gate = nn.Parameter(
                torch.empty((size_experts[i], in_features), **factory_kwargs)
            )
            # this matrix will be transposed when performing linear forwarding
            this_expert_weight_up = nn.Parameter(
                torch.empty((size_experts[i], in_features), **factory_kwargs)
            )
            # this matrix will be transposed when performing linear forwarding
            this_expert_weight_down = nn.Parameter(
                torch.empty((out_features, size_experts[i]), **factory_kwargs)
            )
            self.weight_gate.append(this_expert_weight_gate)
            self.weight_up.append(this_expert_weight_up)
            self.weight_down.append(this_expert_weight_down)
        # ...

5. Mixtral 8x7B 总结 & 进一步阅读

Mixtral 8x7B实现并不复杂，其中
load-balance loss是
expert-wise维度计算的
当前发布的模型还是围绕模型结构展开的，期待
mistral.AI上线创新的对齐方案
涉及到多机多卡的
sMoE分布式训练非常需要工程技巧, 不同的模型架构和集群可以有多种
DPTPEP..组合方案，
在Mixtral中对于实验反直觉论点专家的知识是作用在
token
级别，而不是domain级别，对MoE感兴趣的话可以进一步开盒分析

Reference

Mixture of Experts Explained
方佳瑞：MoE训练论文解读之Megablocks：打破动态路由限制
方佳瑞：MoE训练系统之JANUS：参数服务器助力MoE训练
方佳瑞：MoE训练论文解读之Tutel: 动态切换并行策略实现动态路由
西门宇少：对MoE大模型的训练和推理做分布式加速——DeepSpeed-MoE论文速读
吃果冻不吐果冻皮：大模型分布式训练并行技术（八）-MOE并行
孟繁续：Mixtral-8x7B 模型挖坑
Mixtral-of-experts
Mistral-7B
Gshard
Switch Transformers
sMoE
Transformers-Mixtral-of-Experts
DeepSpeed-MoE
Megablocks
LLaMA-MoE

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