用注意力机制中学习到的Value向量作为反射基准，通过Householder反射来"归一化"特征表示，从而避免使用LayerNorm。.从复杂度上来讲，其实要比layernorm要高，但是更简明和几何化。
具体来说，
reflection_v = W2(softmax(W1)x)
reflection_v = normalize(reflection_v)
x = x - (2 * reflection_v * x) * reflection_v。
python
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
class ReflectionAttention(nn.Module):
"""
使用反射操作的注意力机制，替代LayerNorm
"""
def __init__(self, dim, num_heads=8, dropout=0.1):
super().__init__()
self.dim = dim
self.num_heads = num_heads
self.head_dim = dim // num_heads
# QKV投影
self.qkv = nn.Linear(dim, 3 * dim)
self.proj = nn.Linear(dim, dim)
self.dropout = nn.Dropout(dropout)
# 缩放因子
self.scale = self.head_dim ** -0.5
def householder_reflection(self, x, reflection_vector):
"""
Householder反射变换
x: [batch_size, seq_len, dim]
reflection_vector: [batch_size, seq_len, dim] 或 [batch_size, 1, dim]
"""
# 归一化反射向量
v = F.normalize(reflection_vector, p=2, dim=-1)
# 计算反射: x - 2 * (x·v) * v
v_dot_x = torch.sum(x * v, dim=-1, keepdim=True)
reflected_x = x - 2 * v_dot_x * v
return reflected_x
def forward(self, x, attention_mask=None):
"""
参数:
x: [batch_size, seq_len, dim]
"""
batch_size, seq_len, dim = x.shape
# 1. 生成QKV
qkv = self.qkv(x).reshape(batch_size, seq_len, 3, self.num_heads, self.head_dim)
q, k, v = qkv.unbind(2) # 每个都是 [batch_size, seq_len, num_heads, head_dim]
# 2. 计算注意力分数
q = q.transpose(1, 2) # [batch_size, num_heads, seq_len, head_dim]
k = k.transpose(1, 2)
v = v.transpose(1, 2)
attn_scores = torch.matmul(q, k.transpose(-2, -1)) * self.scale
if attention_mask is not None:
attn_scores = attn_scores + attention_mask
attn_weights = F.softmax(attn_scores, dim=-1)
attn_weights = self.dropout(attn_weights)
# 3. 应用注意力到V
attn_output = torch.matmul(attn_weights, v) # [batch_size, num_heads, seq_len, head_dim]
# 4. 合并多头
attn_output = attn_output.transpose(1, 2).contiguous().view(batch_size, seq_len, dim)
# 5. 使用V对原始输入x进行反射（替代LayerNorm的核心操作）
# 从注意力输出中提取反射信息
v_combined = v.transpose(1, 2).contiguous().view(batch_size, seq_len, dim)
# 对原始输入x进行反射变换
reflected_x = self.householder_reflection(x, v_combined)
# 6. 残差连接 + 投影
output = self.proj(reflected_x)
return output
class ReflectionTransformerBlock(nn.Module):
"""
使用反射注意力替代LayerNorm的Transformer块
"""
def __init__(self, dim, num_heads, mlp_ratio=4, dropout=0.1):
super().__init__()
self.dim = dim
self.num_heads = num_heads
# 反射注意力
self.attention = ReflectionAttention(dim, num_heads, dropout)
# 前馈网络（不使用LayerNorm）
mlp_hidden_dim = int(dim * mlp_ratio)
self.mlp = nn.Sequential(
nn.Linear(dim, mlp_hidden_dim),
nn.GELU(),
nn.Dropout(dropout),
nn.Linear(mlp_hidden_dim, dim),
nn.Dropout(dropout)
)
# 可选的轻量级稳定化（不是完整的LayerNorm）
self.pre_mlp_stabilizer = nn.LayerNorm(dim, elementwise_affine=False)
def forward(self, x, attention_mask=None):
# 自注意力部分（内部包含反射操作）
attn_output = self.attention(x, attention_mask)
x = x + attn_output # 残差连接
# 前馈网络部分（可选轻量级稳定化）
mlp_input = self.pre_mlp_stabilizer(x) if hasattr(self, 'pre_mlp_stabilizer') else x
mlp_output = self.mlp(mlp_input)
x = x + mlp_output # 残差连接
return x
class ReflectionTransformer(nn.Module):
"""
完整的反射Transformer
"""
def __init__(self, vocab_size, dim, num_layers, num_heads, mlp_ratio=4,
max_seq_len=512, dropout=0.1):
super().__init__()
self.dim = dim
self.num_layers = num_layers
# 词嵌入
self.token_embedding = nn.Embedding(vocab_size, dim)
self.position_embedding = nn.Embedding(max_seq_len, dim)
# Transformer层
self.layers = nn.ModuleList([
ReflectionTransformerBlock(dim, num_heads, mlp_ratio, dropout)
for _ in range(num_layers)
])
# 输出层
self.output_norm = nn.LayerNorm(dim) # 最终输出还是需要归一化
self.head = nn.Linear(dim, vocab_size)
self.dropout = nn.Dropout(dropout)
# 初始化
self.apply(self._init_weights)
def _init_weights(self, module):
if isinstance(module, nn.Linear):
torch.nn.init.normal_(module.weight, mean=0.0, std=0.02)
if module.bias is not None:
torch.nn.init.zeros_(module.bias)
elif isinstance(module, nn.Embedding):
torch.nn.init.normal_(module.weight, mean=0.0, std=0.02)
def forward(self, input_ids, attention_mask=None):
batch_size, seq_len = input_ids.shape
# 创建位置编码
positions = torch.arange(0, seq_len, dtype=torch.long, device=input_ids.device)
positions = positions.unsqueeze(0).expand(batch_size, seq_len)
# 嵌入层
x = self.token_embedding(input_ids)
x = x + self.position_embedding(positions)
x = self.dropout(x)
# 通过反射Transformer层
for layer in self.layers:
x = layer(x, attention_mask)
# 输出
x = self.output_norm(x)
logits = self.head(x)
return logits理论分析
反射 vs LayerNorm 的对比
| 特性 | LayerNorm | 反射变换 |
|---|---|---|
| 信息保持 | 有信息损失（缩放） | 无损（等距变换） |
| 训练稳定性 | 优秀 | 需要验证 |
| 计算复杂度 | O(n) | O(n) |
| 几何意义 | 统计归一化 | 几何变换 |
| 可解释性 | 中等 | 高 |
反射变换的优势
-
几何一致性：反射保持向量空间结构
-
信息无损：严格的等距变换
-
注意力融合：反射向量来自注意力机制本身
-
理论优雅：有坚实的数学基础