GQA: Grouped-Query Attention

URL

• paper: https://arxiv.org/pdf/2305.13245

TL;DR

• 本质是标准 Multi-Head Attention 和 Multi-Query Attention 的一个折衷。
  
• 目的是 降低 Attention 过程内存带宽成本，并没有降低计算复杂度，计算复杂度依然是 $\mathcal{O}(n^2)$

Algorithm

import torch
import torch.nn.functional as F
def multiquery_attention_batched(X, M, mask, P_q, P_k, P_v, P_o, num_groups):
    # b: batch size
    # n: number of querys
    # m: number of keys / values
    # d: input dimension
    # H: number of heads
    # g: number of groups
    # h: number of heads per group
    # k: key / query dimention
    # v: value dimention
    assert 0 == P_q.size(0) % num_groups
    heads_per_group = P_q.size(0) // num_groups
    # 应用线性变换获取查询Q（multi-head）
    Q = torch.einsum("bnd,Hdk->bHkn", X, P_q).view(
        -1, num_groups, heads_per_group, P_q.size(2), X.size(1)
    )
    # 应用线性变换获取键K和值V（single-head）
    K = torch.einsum("bmd,gdk->bgmk", M, P_k)
    V = torch.einsum("bmd,gdv->bgmv", M, P_v)
    # 计算注意力得分并应用掩码
    logits = torch.einsum("bghkn,bgmk->bghnm", Q, K)
    # mask 分组
    mask = mask.view(-1, num_groups, heads_per_group, mask.size(-2), mask.size(-1))
    weights = F.softmax(logits + mask, dim=-1)
    # 计算加权的值
    O = torch.einsum("bghnm,bgmv->bghnv", weights, V)
    # P_o 分组
    P_o = P_o.view(num_groups, heads_per_group, P_o.size(-2), P_o.size(-1))
    # 应用输出变换
    Y = torch.einsum("bghnv,ghvd->bnd", O, P_o)
    return Y
# 假设参数和维度
batch_size = 2
num_queries = 5
num_keys = 7  # 同时也是 num_values
dim = 64
key_dim = 32  # 同时也是 query_dim
value_dim = 48
num_heads = 8
num_groups = 4  # head 分成多少组，必须整除 num_heads
# 随机初始化输入数据和参数
X = torch.randn(batch_size, num_queries, dim)
M = torch.randn(batch_size, num_keys, dim)
mask = torch.randn(batch_size, num_heads, num_queries, num_keys)
P_q = torch.randn(num_heads, dim, key_dim)
P_k = torch.randn(num_groups, dim, key_dim)     # 组件 key / value 不共享
P_v = torch.randn(num_groups, dim, value_dim)
P_o = torch.randn(num_heads, value_dim, dim)
# 运行多查询注意力机制
output = multiquery_attention_batched(X, M, mask, P_q, P_k, P_v, P_o, num_groups)
print(output.shape)  # 应该输出: torch.Size([2, 5, 64])

Thought

• GQA 介于 MHA 和 MQA 之间，每个 group 内部实际上是 MQA