关于llama架构的分析
ViperEkura Lv1

1. 整体架构概览

Llama 3采用了经典的纯解码器Transformer架构,整体设计围绕自回归语言生成任务进行深度优化。模型核心由词嵌入层、多个堆叠的Transformer块以及输出层构成,每个Transformer块内部包含多头注意力机制和前馈网络两部分。特别值得注意的是其位置编码方案——使用了改进版的旋转位置编码,基础频率参数设定为50万,这比原始RoPE的1万要高出许多,使得模型能够更好地处理长序列文本并具备更强的位置外推能力。

在注意力机制方面,Llama 3引入了分组查询注意力设计,允许键值头的数量少于查询头,通过重复利用键值头来匹配查询头的数量,这种设计在保持模型性能的同时显著降低了内存占用。前馈网络采用了SwiGLU激活函数,其独特的门控机制提供了比传统MLP更强的表达能力。整个模型还采用了RMSNorm进行层归一化,计算效率高于标准的LayerNorm,同时配合模型并行策略和KV缓存技术,在训练和推理过程中都实现了优异的速度表现和内存效率。

1.1 模型初始化

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class Transformer(nn.Module):
def __init__(self, params: ModelArgs):
super().__init__()
self.params = params
self.vocab_size = params.vocab_size
self.n_layers = params.n_layers

# 1. 词嵌入层(并行化)
self.tok_embeddings = VocabParallelEmbedding(
params.vocab_size, params.dim, init_method=lambda x: x
)

# 2. Transformer层堆叠
self.layers = torch.nn.ModuleList()
for layer_id in range(params.n_layers):
self.layers.append(TransformerBlock(layer_id, params))

# 3. 输出层
self.norm = RMSNorm(params.dim, eps=params.norm_eps)
self.output = ColumnParallelLinear(
params.dim, params.vocab_size, bias=False, init_method=lambda x: x
)

# 4. 预计算旋转位置编码
self.freqs_cis = precompute_freqs_cis(
params.dim // params.n_heads, # 每个头的维度
params.max_seq_len * 2, # 两倍序列长度,用于缓存
params.rope_theta, # RoPE基础频率
)

关键点

  • 使用 VocabParallelEmbedding 将词表分割到多个GPU
  • 每层都是独立的 TransformerBlock
  • 输出前进行 RMSNorm 归一化
  • 预先计算旋转位置编码,减少运行时计算

2. 注意力机制详解

2.1 注意力头配置

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class Attention(nn.Module):
def __init__(self, args: ModelArgs):
super().__init__()
# GQA(分组查询注意力)配置
self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads

# 模型并行配置
model_parallel_size = fs_init.get_model_parallel_world_size()
self.n_local_heads = args.n_heads // model_parallel_size
self.n_local_kv_heads = self.n_kv_heads // model_parallel_size
self.n_rep = self.n_local_heads // self.n_local_kv_heads # 重复因子

# 投影层(模型并行)
self.wq = ColumnParallelLinear(args.dim, args.n_heads * self.head_dim, bias=False)
self.wk = ColumnParallelLinear(args.dim, self.n_kv_heads * self.head_dim, bias=False)
self.wv = ColumnParallelLinear(args.dim, self.n_kv_heads * self.head_dim, bias=False)
self.wo = RowParallelLinear(args.n_heads * self.head_dim, args.dim, bias=False)

# KV缓存(用于推理加速)
self.cache_k = torch.zeros((args.max_batch_size, args.max_seq_len,
self.n_local_kv_heads, self.head_dim)).cuda()
self.cache_v = torch.zeros((args.max_batch_size, args.max_seq_len,
self.n_local_kv_heads, self.head_dim)).cuda()

关键点

  • 支持 GQA:当 n_kv_heads < n_heads 时,KV头会被复用
  • 每个GPU只计算部分注意力头(n_local_heads
  • KV缓存预分配内存,加速自回归生成

2.2 注意力前向传播

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def forward(self, x: torch.Tensor, start_pos: int, freqs_cis: torch.Tensor, mask: Optional[torch.Tensor]):
bsz, seqlen, _ = x.shape

# 1. 线性投影得到 Q, K, V
xq, xk, xv = self.wq(x), self.wk(x), self.wv(x)

# 2. 重塑为多头格式
xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim)
xk = xk.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)
xv = xv.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)

# 3. 应用旋转位置编码(RoPE)
xq, xk = apply_rotary_emb(xq, xk, freqs_cis=freqs_cis)

# 4. 更新KV缓存
self.cache_k[:bsz, start_pos : start_pos + seqlen] = xk
self.cache_v[:bsz, start_pos : start_pos + seqlen] = xv

# 5. 获取缓存的KV(包含历史所有token)
keys = self.cache_k[:bsz, : start_pos + seqlen]
values = self.cache_v[:bsz, : start_pos + seqlen]

# 6. 如果使用GQA,复制KV头以匹配Q头数量
keys = repeat_kv(keys, self.n_rep) # (bs, seqlen, n_local_heads, head_dim)
values = repeat_kv(values, self.n_rep) # (bs, seqlen, n_local_heads, head_dim)

# 7. 注意力计算
xq = xq.transpose(1, 2) # (bs, n_local_heads, seqlen, head_dim)
keys = keys.transpose(1, 2) # (bs, n_local_heads, cache_len, head_dim)
values = values.transpose(1, 2)

# 8. 缩放点积注意力
scores = torch.matmul(xq, keys.transpose(2, 3)) / math.sqrt(self.head_dim)

# 9. 应用因果掩码
if mask is not None:
scores = scores + mask # mask是下三角矩阵,包含 -inf

# 10. Softmax和输出
scores = F.softmax(scores.float(), dim=-1).type_as(xq)
output = torch.matmul(scores, values) # (bs, n_local_heads, seqlen, head_dim)

# 11. 合并多头输出
output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1)
return self.wo(output) # 输出投影

3. RoPE(旋转位置编码)实现

3.1 预计算旋转矩阵

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def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0):
# 1. 计算基础频率(公式:theta^{-2i/dim})
freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))

# 2. 创建位置序列
t = torch.arange(end, device=freqs.device, dtype=torch.float32)

# 3. 计算外积:每个位置 * 每个频率
freqs = torch.outer(t, freqs) # (end, dim//2)

# 4. 转换为复数形式:e^{i*θ} = cosθ + i*sinθ
freqs_cis = torch.polar(torch.ones_like(freqs), freqs) # complex64

return freqs_cis

数学原理

  • 对于位置 m 和维度 i,旋转角度为:m * theta^{-2i/d}
  • 复数形式:(cos(mθ), sin(mθ)) 应用于 Q 和 K 的相邻维度对

3.2 应用旋转位置编码

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def apply_rotary_emb(xq: torch.Tensor, xk: torch.Tensor, freqs_cis: torch.Tensor):
# 1. 将最后两个维度重塑为复数形式
# 输入形状: (batch, seqlen, n_heads, head_dim)
# 重塑为: (batch, seqlen, n_heads, head_dim//2, 2)
# 然后转换为复数: (batch, seqlen, n_heads, head_dim//2)
xq_ = torch.view_as_complex(xq.float().reshape(*xq.shape[:-1], -1, 2))
xk_ = torch.view_as_complex(xk.float().reshape(*xk.shape[:-1], -1, 2))

# 2. 广播频率到合适的形状
freqs_cis = reshape_for_broadcast(freqs_cis, xq_)

# 3. 复数乘法实现旋转
# 对于复数 a+bi 和 cosθ+isinθ,乘法实现旋转
xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(3)
xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(3)

return xq_out.type_as(xq), xk_out.type_as(xk)

4. 前馈网络(SwiGLU)

4.1 FeedForward 实现

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class FeedForward(nn.Module):
def __init__(self, dim: int, hidden_dim: int, multiple_of: int, ffn_dim_multiplier: Optional[float]):
super().__init__()
# 1. 计算隐藏层维度(默认是 4/3 * dim)
hidden_dim = int(2 * hidden_dim / 3)

# 2. 可选的隐藏层缩放因子
if ffn_dim_multiplier is not None:
hidden_dim = int(ffn_dim_multiplier * hidden_dim)

# 3. 对齐到 multiple_of 的倍数(内存优化)
hidden_dim = multiple_of * ((hidden_dim + multiple_of - 1) // multiple_of)

# 4. SwiGLU 的三个投影层
self.w1 = ColumnParallelLinear(dim, hidden_dim, bias=False, gather_output=False)
self.w2 = RowParallelLinear(hidden_dim, dim, bias=False, input_is_parallel=True)
self.w3 = ColumnParallelLinear(dim, hidden_dim, bias=False, gather_output=False)

def forward(self, x):
# SwiGLU: w2 * (silu(w1(x)) * w3(x))
return self.w2(F.silu(self.w1(x)) * self.w3(x))

SwiGLU 公式

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FFN(x) = W₂ · (silu(W₁·x) ⊙ W₃·x)

其中 silu 是 Swish 激活函数:x * sigmoid(x)

5. Transformer Block 结构

5.1 单层 Transformer

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class TransformerBlock(nn.Module):
def __init__(self, layer_id: int, args: ModelArgs):
super().__init__()
self.n_heads = args.n_heads
self.dim = args.dim
self.head_dim = args.dim // args.n_heads
self.attention = Attention(args)
self.feed_forward = FeedForward(
dim=args.dim,
hidden_dim=4 * args.dim, # 默认 4倍扩展
multiple_of=args.multiple_of,
ffn_dim_multiplier=args.ffn_dim_multiplier,
)
self.layer_id = layer_id
self.attention_norm = RMSNorm(args.dim, eps=args.norm_eps)
self.ffn_norm = RMSNorm(args.dim, eps=args.norm_eps)

def forward(self, x: torch.Tensor, start_pos: int, freqs_cis: torch.Tensor, mask: Optional[torch.Tensor]):
# 1. 残差连接 + 注意力(Pre-Norm)
h = x + self.attention(self.attention_norm(x), start_pos, freqs_cis, mask)

# 2. 残差连接 + FFN(Pre-Norm)
out = h + self.feed_forward(self.ffn_norm(h))
return out

架构特点

  • Pre-LayerNorm:归一化在子层之前
  • 残差连接:每个子层都有残差连接
  • 并行计算:注意力头和FFN都支持模型并行
 REWARD AUTHOR