1.整体流程
先上一张图来整体理解下MLA的计算过程
2.实现代码
python
import math
import torch
import torch.nn as nn
# rms归一化
class RMSNorm(nn.Module):
"""
"""
def __init__(self, hidden_size, eps=1e-6):
super().__init__()
self.weight = nn.Parameter(torch.ones(hidden_size))
self.variance_epsilon = eps
def forward(self, hidden_states):
hidden_states = hidden_states.float()
variance = hidden_states.pow(2).mean(-1, keepdim=True)
hidden_states = hidden_states * torch.rsqrt(variance + self.variance_epsilon)
return self.weight * hidden_states.float()
def rotate_half(x):
x1, x2 = x.chunk(2, dim=-1)
return torch.cat((-x2, x1), dim=-1)
def apply_rotate_pos_emb(q, k, cos, sin, unsqueeze_dim=2):
cos = cos.unsqueeze(unsqueeze_dim)
sin = sin.unsqueeze(unsqueeze_dim)
q_embed = (q * cos) + (rotate_half(q) * sin)
k_embed = (k * cos) + (rotate_half(k) * sin)
return q_embed, k_embed
# 旋转位置编码
class RotaryEmbedding(nn.Module):
def __init__(self, dim, max_seq_len=1024):
super(RotaryEmbedding, self).__init__()
self.dim = dim
self.max_seq_len = max_seq_len
inv_freq = 1.0 / (10000 ** (torch.arange(0, dim, 2).float() / dim))
t = torch.arange(max_seq_len).float().unsqueeze(1)
freqs = t @ inv_freq.unsqueeze(0)
freqs = torch.cat((freqs, freqs), dim=-1)
self.register_buffer("cos_cached", freqs.cos())
self.register_buffer("sin_cached", freqs.sin())
def forward(self, q, k):
cos = self.cos_cached[:q.shape[1], :].unsqueeze(0)
sin = self.sin_cached[:q.shape[1], :].unsqueeze(0)
return apply_rotate_pos_emb(q, k, cos, sin)
class MLA(nn.Module):
def __init__(self,
dim,
n_heads,
q_lora_rank,
kv_lora_rank,
qk_nope_head_dim,
qk_rope_head_dim,
v_head_dim,
max_seq_len,
max_batch_size,
mode):
super().__init__()
self.dim = dim # 隐藏层维度
self.n_heads = n_heads # 总头数
self.q_lora_rank = q_lora_rank # q低秩压缩到的维度
self.kv_lora_rank = kv_lora_rank # k/v低秩压缩到的维度
self.qk_nope_head_dim = qk_nope_head_dim # q/k不带旋转位置编码的维度
self.qk_rope_head_dim = qk_rope_head_dim # q/k带旋转位置编码的维度
self.qk_head_dim = qk_nope_head_dim + qk_rope_head_dim # q/k的总维度，不带旋转位置编码的维度加上带旋转位置编码的维度
self.v_head_dim = v_head_dim # value的维度，等于不带旋转位置编码的k维度
self.mode = mode
self.max_seq_len = max_seq_len
self.max_batch_size = max_batch_size
self.wq_a = nn.Linear(self.dim, self.q_lora_rank) # q的降维矩阵
self.q_norm = RMSNorm(self.q_lora_rank)
self.wq_b = nn.Linear(self.q_lora_rank, self.n_heads * self.qk_head_dim) # q的升维矩阵
# 4096*128+128*4864 = 524,288 + 622592 = 1146880 4096*4864 = 19,922,944
self.wkv_a = nn.Linear(self.dim, self.kv_lora_rank + self.qk_rope_head_dim) # k/v的降维矩阵
# nn.Linear(self.dim, self.kv_lora_rank)
# nn.Linear(self.dim, self.qk_rope_head_dim)
self.kv_norm = RMSNorm(self.kv_lora_rank)
self.wkv_b = nn.Linear(self.kv_lora_rank, self.n_heads * (self.qk_nope_head_dim + self.v_head_dim)) # k/v的升维矩阵
self.wo = nn.Linear(self.n_heads * self.v_head_dim, self.dim)
self.rotary_emb = RotaryEmbedding(self.qk_rope_head_dim) # 旋转位置编码
# 没有矩阵融合
if self.mode == 'naive':
self.register_buffer('k_cache',
torch.zeros(self.max_batch_size, self.max_seq_len, self.n_heads, self.qk_head_dim),
persistent=False)
self.register_buffer('v_cache',
torch.zeros(self.max_batch_size, self.max_seq_len, self.n_heads, self.v_head_dim),
persistent=False)
# 有矩阵融合
else:
self.register_buffer('kv_cache', torch.zeros(self.max_batch_size, self.max_seq_len, self.kv_lora_rank),
persistent=False)
self.register_buffer('pe_cache', torch.zeros(self.max_batch_size, self.max_seq_len, self.qk_rope_head_dim),
persistent=False)
def forward(self, x, mask=None):
bs, seq_len, _ = x.shape
q = self.wq_a(x) # [bs, seq_len, q_lora_rank]
q = self.q_norm(q) # [bs, seq_len, q_lora_rank]
q = self.wq_b(q) # [bs, seq_len, n_heads * qk_head_dim]
q = q.view(bs, seq_len, self.n_heads, self.qk_head_dim) # [bs, seq_len, n_heads, qk_head_dim]
q_nope, q_pe = torch.split(q, [self.qk_nope_head_dim, self.qk_rope_head_dim],
dim=-1) # q_nope shape:[bs, seq_len, n_heads, qk_nope_head_dim] q_pe shape:[bs, seq_len, n_heads, qk_rope_head_dim]
kv = self.wkv_a(x) # [bs, seq_len, kv_lora_rank + qk_rope_head_dim]
kv, k_pe = torch.split(kv, [self.kv_lora_rank, self.qk_rope_head_dim],
dim=-1) # kv shape:[bs, seq_len, kv_lora_rank] k_pe shape:[bs, seq_len, qk_rope_head_dim]
k_pe = k_pe.unsqueeze(2) # k_pe shape:[bs, seq_len, 1, qk_rope_head_dim] 一层共享一个key
q_pe, k_pe = self.rotary_emb(q_pe, k_pe)
if self.mode == 'naive':
q = torch.cat([q_nope, q_pe], dim=-1) # * [bs, seq_len, n_heads, qk_head_dim]
kv = self.kv_norm(kv) # [bs, seq_len, kv_lora_rank)]
kv = self.wkv_b(kv) # [bs, seq_len, n_heads * (qk_nope_head_dim + v_head_dim)]
kv = kv.view(bs, seq_len, self.n_heads, self.qk_nope_head_dim + self.v_head_dim)
k_nope, v = torch.split(kv, [self.qk_nope_head_dim, self.v_head_dim], dim=-1)
k = torch.cat([k_nope, k_pe.expand(-1, -1, self.n_heads, -1)], dim=-1)
# k shape:[bs, seq_len, n_heads, qk_head_dim]
self.k_cache[:bs, :seq_len, :, :] = k
self.v_cache[:bs, :seq_len, :, :] = v
# scores = torch.einsum("bshd,bthd->bsht", q, self.k_cache[:bs, :seq_len]) / math.sqrt(self.qk_nope_head_dim + self.qk_rope_head_dim)
scores = torch.matmul(q.transpose(1, 2),
self.k_cache[:bs, :seq_len, :, :].transpose(1, 2).transpose(2, 3) / math.sqrt(
self.qk_nope_head_dim + self.qk_rope_head_dim))
scores = scores.transpose(1, 2)
else:
k_pe = k_pe.squeeze(2)
wkv_b = self.wkv_b.weight # [n_heads * (qk_nope_head_dim + v_head_dim), kv_lora_rank]
wkv_b = wkv_b.view(self.n_heads, -1,
self.kv_lora_rank) # [n_heads, qk_nope_head_dim + v_head_dim, kv_lora_rank]
q_nope = torch.einsum("bshd,hdc->bshc", q_nope,
wkv_b[:, :self.qk_nope_head_dim]) # q_nope shape:[bs, seq_len, n_heads, kv_lora_rank]
# q*k(T) = x*wq*(c*wkv_b[:, :self.qk_nope_head_dim])(T) = x*wq*wkv_b[:, :self.qk_nope_head_dim](T)*c(T) c为压缩后的k/v
# wq*wkv_b[:, :self.qk_nope_head_dim](T)作为q的投影矩阵 c可以替代原先的k，这样就可以直接使用压缩后的k/v计算注意力了，kv_cache时也只需存储压缩后的k/v
kv = self.kv_norm(kv)
self.kv_cache[:bs, :seq_len, :] = kv # kv shape:[bs, seq_len, kv_lora_rank]
self.pe_cache[:bs, :seq_len, :] = k_pe # k_pe shape:[bs, seq_len, qk_rope_head_dim]
scores_nope = torch.einsum("bshc,btc->bsht", q_nope,
self.kv_cache[:bs, :seq_len, :]) # bshc btc -> bshc bct -> bsht
scores_pe = torch.einsum("bshr,btr->bsht", q_pe,
self.pe_cache[:bs, :seq_len, :]) # bshr btr -> bshr bt1r -> bshr bthr -> bsht
scores = (scores_nope + scores_pe) / math.sqrt(
self.qk_nope_head_dim + self.qk_rope_head_dim) # [bs, seq_len, n_heads, seq_len]
if mask is not None:
# mask shape:[bs, seq_len, seq_len]
scores += mask.unsqueeze(2)
scores = scores.softmax(dim=-1)
if self.mode == 'naive':
x = torch.einsum("bsht,bthd->bshd", scores,
self.v_cache[:bs, :seq_len]) # bsht,bthd -> bhst, bhtd -> bhsd -> bshd
else:
# scores * v = scores * c * wkv_b[:, -self.v_head_dim:]
x = torch.einsum("bsht,btc->bshc", scores,
self.kv_cache[:bs, :seq_len]) # x shape:[bs, seq_len, n_heads, kv_lora_rank]
x = torch.einsum("bshc,hdc->bshd", x, wkv_b[:, -self.v_head_dim:]) # bshc, hdc -> bshc,dch -> bsdh -> bshd
x = x.contiguous().view(bs, seq_len, -1)
x = self.wo(x)
return x
if __name__ == '__main__':
torch.manual_seed(0)
torch.set_printoptions(precision=3, sci_mode=False)
x = torch.randn(1, 4, 16)
dim = 16
n_heads = 2
q_lora_rank = 10
kv_lora_rank = 6
qk_nope_head_dim = 8
qk_rope_head_dim = 4
v_head_dim = 8
max_seq_len = 10
max_batch_size = 4
mode = 'none'
mla = MLA(dim=dim,
n_heads=n_heads,
q_lora_rank=q_lora_rank,
kv_lora_rank=kv_lora_rank,
qk_nope_head_dim=qk_nope_head_dim,
qk_rope_head_dim=qk_rope_head_dim,
v_head_dim=v_head_dim,
max_seq_len=max_seq_len,
max_batch_size=max_batch_size,
mode=mode)
print(mla(x))
print(mla.kv_cache)参考资料：
https://zhuanlan.zhihu.com/p/16730036197
https://github.com/wyf3/llm_related/tree/main/deepseek_learn