238 lines
8.3 KiB
Python
238 lines
8.3 KiB
Python
import numpy as np
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def softmax(x, axis=-1):
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"""Softmax激活函数，用于将 logits 转换为概率分布"""
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# 减去最大值防止数值溢出
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e_x = np.exp(x - np.max(x, axis=axis, keepdims=True))
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return e_x / np.sum(e_x, axis=axis, keepdims=True)
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def relu(x):
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"""ReLU激活函数"""
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return np.maximum(0, x)
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class Linear:
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"""全连接层（线性层）"""
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def __init__(self, in_features, out_features):
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# 使用He初始化权重
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self.weight = np.random.randn(in_features, out_features) * np.sqrt(2.0 / in_features)
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# 偏置初始化为0
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self.bias = np.zeros(out_features)
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def forward(self, x):
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"""前向传播：y = xW + b"""
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return x @ self.weight + self.bias
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class LayerNorm:
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"""层归一化（Layer Normalization）"""
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def __init__(self, d_model, eps=1e-6):
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# 缩放参数
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self.gamma = np.ones(d_model)
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# 偏移参数
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self.beta = np.zeros(d_model)
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# 防止除零的小常数
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self.eps = eps
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def forward(self, x):
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"""前向传播：对最后一个维度进行归一化"""
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mean = np.mean(x, axis=-1, keepdims=True)
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std = np.std(x, axis=-1, keepdims=True)
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return self.gamma * (x - mean) / (std + self.eps) + self.beta
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class MultiHeadAttention:
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"""多头注意力机制"""
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def __init__(self, d_model, num_heads):
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self.d_model = d_model # 模型维度
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self.num_heads = num_heads # 注意力头数
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self.d_k = d_model // num_heads # 每个头的维度
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# 定义Q、K、V的线性变换层
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self.W_q = Linear(d_model, d_model) # Query变换
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self.W_k = Linear(d_model, d_model) # Key变换
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self.W_v = Linear(d_model, d_model) # Value变换
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self.W_o = Linear(d_model, d_model) # 输出变换
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def forward(self, Q, K, V, mask=None):
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"""
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前向传播
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Q: Query张量 [batch_size, seq_len, d_model]
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K: Key张量 [batch_size, seq_len, d_model]
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V: Value张量 [batch_size, seq_len, d_model]
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mask: 注意力掩码
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"""
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batch_size = Q.shape[0]
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seq_len = Q.shape[1]
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# 线性变换并分割成多头
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Q = self.W_q.forward(Q).reshape(batch_size, seq_len, self.num_heads, self.d_k).transpose(0, 2, 1, 3)
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K = self.W_k.forward(K).reshape(batch_size, seq_len, self.num_heads, self.d_k).transpose(0, 2, 1, 3)
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V = self.W_v.forward(V).reshape(batch_size, seq_len, self.num_heads, self.d_k).transpose(0, 2, 1, 3)
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# 计算缩放点积注意力分数
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attn_scores = Q @ K.transpose(0, 1, 3, 2) / np.sqrt(self.d_k)
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# 应用掩码（如果提供）
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if mask is not None:
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attn_scores = np.where(mask == 0, -1e9, attn_scores)
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# Softmax得到注意力权重
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attn_probs = softmax(attn_scores, axis=-1)
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# 加权求和
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attn_output = attn_probs @ V
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# 拼接多头输出
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attn_output = attn_output.transpose(0, 2, 1, 3).reshape(batch_size, seq_len, self.d_model)
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# 最终线性变换
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output = self.W_o.forward(attn_output)
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return output
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class FeedForward:
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"""前馈神经网络（两层全连接网络）"""
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def __init__(self, d_model, d_ff):
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# 第一层：扩展维度
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self.linear1 = Linear(d_model, d_ff)
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# 第二层：恢复维度
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self.linear2 = Linear(d_ff, d_model)
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def forward(self, x):
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"""前向传播：线性 -> ReLU -> 线性"""
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return self.linear2.forward(relu(self.linear1.forward(x)))
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class TransformerBlock:
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"""Transformer编码器块"""
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def __init__(self, d_model, num_heads, d_ff):
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# 多头自注意力层
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self.attention = MultiHeadAttention(d_model, num_heads)
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# 前馈网络层
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self.feed_forward = FeedForward(d_model, d_ff)
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# 两个层归一化
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self.norm1 = LayerNorm(d_model)
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self.norm2 = LayerNorm(d_model)
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def forward(self, x, mask=None):
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"""
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前向传播（残差连接 + 层归一化）
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1. 自注意力 -> 残差连接 -> 层归一化
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2. 前馈网络 -> 残差连接 -> 层归一化
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"""
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# 自注意力子层
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attn_output = self.attention.forward(x, x, x, mask)
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x = self.norm1.forward(x + attn_output)
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# 前馈网络子层
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ff_output = self.feed_forward.forward(x)
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x = self.norm2.forward(x + ff_output)
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return x
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class SimpleTransformer:
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"""简化的Transformer编码器模型"""
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def __init__(self, vocab_size, d_model, num_heads, num_layers, d_ff, max_seq_len):
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self.d_model = d_model
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# 词嵌入层
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self.embedding = np.random.randn(vocab_size, d_model) * 0.01
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# 位置编码
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self.positional_encoding = self._create_positional_encoding(max_seq_len, d_model)
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# Transformer编码器层堆叠
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self.transformer_blocks = [
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TransformerBlock(d_model, num_heads, d_ff) for _ in range(num_layers)
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]
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def _create_positional_encoding(self, max_seq_len, d_model):
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"""
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创建正弦余弦位置编码
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使用不同频率的正弦和余弦函数生成位置信息
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"""
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pe = np.zeros((max_seq_len, d_model))
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position = np.arange(0, max_seq_len).reshape(-1, 1).astype(float)
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div_term = np.exp(np.arange(0, d_model, 2).astype(float) * -(np.log(10000.0) / d_model))
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pe[:, 0::2] = np.sin(position * div_term) # 偶数维度用正弦
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pe[:, 1::2] = np.cos(position * div_term) # 奇数维度用余弦
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return pe
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def forward(self, x, mask=None):
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"""
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前向传播
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x: 输入序列 [batch_size, seq_len]
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mask: 注意力掩码
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"""
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seq_len = x.shape[1]
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# 词嵌入 + 缩放
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x = self.embedding[x] * np.sqrt(self.d_model)
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# 加上位置编码
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x = x + self.positional_encoding[:seq_len, :]
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# 通过所有Transformer块
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for block in self.transformer_blocks:
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x = block.forward(x, mask)
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return x
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def count_parameters(self):
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"""统计模型参数数量"""
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count = 0
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count += self.embedding.size # 嵌入层参数
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for block in self.transformer_blocks:
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# 注意力层参数
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count += block.attention.W_q.weight.size + block.attention.W_q.bias.size
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count += block.attention.W_k.weight.size + block.attention.W_k.bias.size
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count += block.attention.W_v.weight.size + block.attention.W_v.bias.size
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count += block.attention.W_o.weight.size + block.attention.W_o.bias.size
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# 前馈网络参数
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count += block.feed_forward.linear1.weight.size + block.feed_forward.linear1.bias.size
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count += block.feed_forward.linear2.weight.size + block.feed_forward.linear2.bias.size
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# 层归一化参数
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count += block.norm1.gamma.size + block.norm1.beta.size
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count += block.norm2.gamma.size + block.norm2.beta.size
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return count
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def create_padding_mask(seq, pad_idx=0):
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"""
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创建填充掩码
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用于忽略序列中的填充位置（padding tokens）
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"""
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return (seq != pad_idx).astype(float)[:, np.newaxis, np.newaxis, :]
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def create_look_ahead_mask(size):
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"""
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创建前瞻掩码（下三角掩码）
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用于解码器中，防止位置i看到i之后的信息
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"""
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mask = np.triu(np.ones((size, size)), k=1).astype(bool)
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return (~mask).astype(float)
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if __name__ == "__main__":
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# 模型超参数
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vocab_size = 1000 # 词汇表大小
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d_model = 512 # 模型维度
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num_heads = 8 # 注意力头数
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num_layers = 6 # Transformer层数
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d_ff = 2048 # 前馈网络隐藏层维度
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max_seq_len = 100 # 最大序列长度
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# 创建模型
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model = SimpleTransformer(vocab_size, d_model, num_heads, num_layers, d_ff, max_seq_len)
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# 创建随机输入
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batch_size = 2
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seq_len = 10
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x = np.random.randint(0, vocab_size, (batch_size, seq_len))
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# 前向传播
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output = model.forward(x)
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print(f"输入形状: {x.shape}")
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print(f"输出形状: {output.shape}")
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print(f"模型参数量: {model.count_parameters():,}") |