content: 
  ### 因果掩码
  - 限制序列长度block_size=1024
  
  self.register_buffer("bias", torch.tril(torch.ones(config.block_size, config.block_size))
                                          .view(1, 1, config.block_size, config.block_size))
  
  att = (q @ k.transpose(-2, -1)) * (1.0 / math.sqrt(k.size(-1)))
              att = att.masked_fill(self.bias[:,:,:T,:T] == 0, float('-inf'))
              att = F.softmax(att, dim=-1)
              att = self.attn_dropout(att)
              y = att @ v # (B, nh, T, T) x (B, nh, T, hs) -> (B, nh, T, hs)
  
  ### 工程技巧
  
  k = k.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
  q = q.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
  v = v.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
  
  ### 模型
  
  class Block(nn.Module):
  
      def __init__(self, config):
          super().__init__()
          self.ln_1 = LayerNorm(config.n_embd, bias=config.bias)
          self.attn = CausalSelfAttention(config)
          self.ln_2 = LayerNorm(config.n_embd, bias=config.bias)
          self.mlp = MLP(config)
  
      def forward(self, x):
          x = x + self.attn(self.ln_1(x))
          x = x + self.mlp(self.ln_2(x))
          return x
  
  class CausalSelfAttention(nn.Module):
  
      def __init__(self, config):
          super().__init__()
          assert config.n_embd % config.n_head == 0
          # key, query, value projections for all heads, but in a batch
          self.c_attn = nn.Linear(config.n_embd, 3 * config.n_embd, bias=config.bias)
          # output projection
          self.c_proj = nn.Linear(config.n_embd, config.n_embd, bias=config.bias)
          # regularization
          self.attn_dropout = nn.Dropout(config.dropout)
          self.resid_dropout = nn.Dropout(config.dropout)
          self.n_head = config.n_head
          self.n_embd = config.n_embd
          self.dropout = config.dropout
          # flash attention make GPU go brrrrr but support is only in PyTorch >= 2.0
          self.flash = hasattr(torch.nn.functional, 'scaled_dot_product_attention')
          if not self.flash:
              print("WARNING: using slow attention. Flash Attention requires PyTorch >= 2.0")
              # causal mask to ensure that attention is only applied to the left in the input sequence
              self.register_buffer("bias", torch.tril(torch.ones(config.block_size, config.block_size))
                                          .view(1, 1, config.block_size, config.block_size))
  
      def forward(self, x):
          B, T, C = x.size() # batch size, sequence length, embedding dimensionality (n_embd)
  
          # calculate query, key, values for all heads in batch and move head forward to be the batch dim
          q, k, v  = self.c_attn(x).split(self.n_embd, dim=2)
          k = k.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
          q = q.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
          v = v.view(B, T, self.n_head, C // self.n_head).transpose(1, 2) # (B, nh, T, hs)
  
          # causal self-attention; Self-attend: (B, nh, T, hs) x (B, nh, hs, T) -> (B, nh, T, T)
          if self.flash:
              # efficient attention using Flash Attention CUDA kernels
              y = torch.nn.functional.scaled_dot_product_attention(q, k, v, attn_mask=None, dropout_p=self.dropout if self.training else 0, is_causal=True)
          else:
              # manual implementation of attention
              att = (q @ k.transpose(-2, -1)) * (1.0 / math.sqrt(k.size(-1)))
              att = att.masked_fill(self.bias[:,:,:T,:T] == 0, float('-inf'))
              att = F.softmax(att, dim=-1)
              att = self.attn_dropout(att)
              y = att @ v # (B, nh, T, T) x (B, nh, T, hs) -> (B, nh, T, hs)
          y = y.transpose(1, 2).contiguous().view(B, T, C) # re-assemble all head outputs side by side
  
          # output projection
          y = self.resid_dropout(self.c_proj(y))
          return y
  
  
  
  class GPT(nn.Module):
  
  - 分析self.wte和推荐系统稀疏词表的异同
      - 输入侧：地位相似
      - 生成侧：
          - 计算：有点像召回，但由于词表小，会进行完整的矩阵乘法
          - 模型：稠密而非稀疏，词汇表中的所有词的嵌入向量都会在每个训练步骤中得到更新
              - 换一种角度，RQ-VAE是让稀疏推荐模型更像稠密LLM模型
  
  - weight tying
      - self.transformer.wte.weight = self.lm_head.weight
  
  
      def __init__(self, config):
          super().__init__()
          self.config = config
  
          self.transformer = nn.ModuleDict(dict(
              wte = nn.Embedding(config.vocab_size, config.n_embd),
              wpe = nn.Embedding(config.block_size, config.n_embd),
              h = nn.ModuleList([Block(config) for _ in range(config.n_layer)]),
              ln_f = nn.LayerNorm(config.n_embd),
          ))
          self.lm_head = nn.Linear(config.n_embd, config.vocab_size, bias=False)
          self.transformer.wte.weight = self.lm_head.weight # https://paperswithcode.com/method/weight-tying
  
      def forward(self, idx, targets=None):
          device = idx.device
          b, t = idx.size()
          assert t <= self.config.block_size, f"Cannot forward sequence of length {t}, block size is only {self.config.block_size}"
          pos = torch.arange(0, t, dtype=torch.long, device=device) # shape (t)
  
          # forward the GPT model itself
          tok_emb = self.transformer.wte(idx) # token embeddings of shape (b, t, n_embd)
          pos_emb = self.transformer.wpe(pos) # position embeddings of shape (t, n_embd)
          x = tok_emb + pos_emb
  
          for block in self.transformer.h:
              x = block(x)
          x = self.transformer.ln_f(x)
  
          if targets is not None:
              # if we are given some desired targets also calculate the loss
              logits = self.lm_head(x)
              loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1)
          else:
              # inference-time mini-optimization: only forward the lm_head on the very last position
              logits = self.lm_head(x[:, [-1], :]) # note: using list [-1] to preserve the time dim
              loss = None
  
          return logits, loss
  
      def from_pretrained(...):
          和openai的定义差异、忽略buffer
          .copy_
  
      @torch.no_grad()
      def generate(self, idx, max_new_tokens, temperature=1.0, top_k=None):
          """
          Take a conditioning sequence of indices idx (LongTensor of shape (b,t)) and complete
          the sequence max_new_tokens times, feeding the predictions back into the model each time.
          Most likely you'll want to make sure to be in model.eval() mode of operation for this.
          """
          for _ in range(max_new_tokens):
              # if the sequence context is growing too long we must crop it at block_size
              idx_cond = idx if idx.size(1) <= self.config.block_size else idx[:, -self.config.block_size:]
              # forward the model to get the logits for the index in the sequence
              logits, _ = self(idx_cond)
              # pluck the logits at the final step and scale by desired temperature
              logits = logits[:, -1, :] / temperature
              # optionally crop the logits to only the top k options
              if top_k is not None:
                  v, _ = torch.topk(logits, min(top_k, logits.size(-1)))
                  logits[logits < v[:, [-1]]] = -float('Inf')
              # apply softmax to convert logits to (normalized) probabilities
              probs = F.softmax(logits, dim=-1)
              # sample from the distribution
              idx_next = torch.multinomial(probs, num_samples=1)
              # append sampled index to the running sequence and continue
              idx = torch.cat((idx, idx_next), dim=1)
  
          return idx
  
  