LLM各层参数详细分析（以LLaMA为例）

网上大多分析LLM参数的文章都比较粗粒度，对于LLM的精确部署不太友好，在这里记录一下分析LLM参数的过程。

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首先看QKV。先上transformer原文

也就是说，当h（heads） = 1时，在默认情况下，$W_i^Q$、$W_i^K$、$W_i^V$都是2维方阵，方阵维度是$d_{model}\times d_{model}$.

结合llama源码 (https://github.com/facebookresearch/llama/blob/main/llama/model.py)

class ModelArgs:
    dim: int = 4096
    n_layers: int = 32
    n_heads: int = 32
    n_kv_heads: Optional[int] = None
    vocab_size: int = -1  # defined later by tokenizer
    multiple_of: int = 256  # make SwiGLU hidden layer size multiple of large power of 2
    ffn_dim_multiplier: Optional[float] = None
    norm_eps: float = 1e-5

    max_batch_size: int = 32
    max_seq_len: int = 2048
# ...

class Attention(nn.Module):
    """Multi-head attention module."""
    def __init__(self, args: ModelArgs):
        """
        Initialize the Attention module.

        Args:
            args (ModelArgs): Model configuration parameters.

        Attributes:
            n_kv_heads (int): Number of key and value heads.
            n_local_heads (int): Number of local query heads.
            n_local_kv_heads (int): Number of local key and value heads.
            n_rep (int): Number of repetitions for local heads.
            head_dim (int): Dimension size of each attention head.
            wq (ColumnParallelLinear): Linear transformation for queries.
            wk (ColumnParallelLinear): Linear transformation for keys.
            wv (ColumnParallelLinear): Linear transformation for values.
            wo (RowParallelLinear): Linear transformation for output.
            cache_k (torch.Tensor): Cached keys for attention.
            cache_v (torch.Tensor): Cached values for attention.

        """
        super().__init__()
        self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads
        model_parallel_size = fs_init.get_model_parallel_world_size()
        self.n_local_heads = args.n_heads // model_parallel_size
        self.n_local_kv_heads = self.n_kv_heads // model_parallel_size
        self.n_rep = self.n_local_heads // self.n_local_kv_heads
        self.head_dim = args.dim // args.n_heads

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计算出
self.n_kv_heads = h = 32
self.head_dim = 4096/32=128
所以$W_i^Q$、$W_i^K$、$W_i^V$ 大小都为(4096, 128).（在未拆分前$W^Q$，$W^K$和$W^V$都是$(dim,dim)=(4096,4096)$大小）。

$Q,K,V$的大小都是 $(n_{ctx},dim)=(2048,4096)$ （在多头公式里。在self-attention里，其实他们都是同一个值：输入X），所以$Q\times W_i^Q$ 和 $K\times W_i^K$ 和 $Q\times W_i^Q$ 都是$(n_{ctx},d_k)=(2048,128)$。带入原文attention公式后，大小为(2048, 128)不变。Attention不改变大小（在默认$d_k=d_v$情况下）。

经过Cancat，分开的头又合并，大小变为(2048, 4096)矩阵，经过$W^O$ （大小是（4096，4096））全连接，还是(2048, 4096)矩阵。

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然后看Feed forward.根据源码，

class FeedForward(nn.Module):
    def __init__(
        self,
        dim: int,
        hidden_dim: int,
        multiple_of: int,
        ffn_dim_multiplier: Optional[float],
    ):
        """
        Initialize the FeedForward module.

        Args:
            dim (int): Input dimension.
            hidden_dim (int): Hidden dimension of the feedforward layer.
            multiple_of (int): Value to ensure hidden dimension is a multiple of this value.
            ffn_dim_multiplier (float, optional): Custom multiplier for hidden dimension. Defaults to None.

        Attributes:
            w1 (ColumnParallelLinear): Linear transformation for the first layer.
            w2 (RowParallelLinear): Linear transformation for the second layer.
            w3 (ColumnParallelLinear): Linear transformation for the third layer.

        """
        super().__init__()
        hidden_dim = int(2 * hidden_dim / 3)
        # custom dim factor multiplier
        if ffn_dim_multiplier is not None:
            hidden_dim = int(ffn_dim_multiplier * hidden_dim)
        hidden_dim = multiple_of * ((hidden_dim + multiple_of - 1) // multiple_of)

        self.w1 = ColumnParallelLinear(
            dim, hidden_dim, bias=False, gather_output=False, init_method=lambda x: x
        )
        self.w2 = RowParallelLinear(
            hidden_dim, dim, bias=False, input_is_parallel=True, init_method=lambda x: x
        )
        self.w3 = ColumnParallelLinear(
            dim, hidden_dim, bias=False, gather_output=False, init_method=lambda x: x
        )

    def forward(self, x):
        return self.w2(F.silu(self.w1(x)) * self.w3(x))

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multiattention layer过后，经过加法和normlayer（RMS norm），进入feed_forward前馈网络。注意这里的前馈网络其中一个维度会有8/3≈2.7的放缩，然后multiple_of又保证必须是256的倍数，所以这里算出来hidden_dim是256的倍数中与8/3*4096最接近的，是11008。以这里的w1,w3大小为（4096，11008），w2大小为（11008，4096）. 输出结果大小

整个decode layer计算如图所示，

来源：https://github.com/microsoft/Llama-2-Onnx/blob/main/Images/DecoderLayer.png