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。
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^Q
WiQ、
W
i
K
W_i^K
WiK、
W
i
V
W_i^V
WiV都是2维方阵，方阵维度是
d
m
o
d
e
l
×
d
m
o
d
e
l
d_{model} \times d_{model}
dmodel×dmodel.
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
计算出 self.n_kv_heads = h = 32 self.head_dim = 4096/32=128 所以
W
i
Q
W_i^Q
WiQ、
W
i
K
W_i^K
WiK、
W
i
V
W_i^V
WiV 大小都为(4096, 128).（在未拆分前
W
Q
W^Q
WQ，
W
K
W^K
WK和
W
V
W^V
WV都是
(
d
i
m
,
d
i
m
)
=
(
4096
,
4096
)
(dim, dim) = (4096,4096)
(dim,dim)=(4096,4096)大小）。
Q
,
K
,
V
Q,K,V
Q,K,V的大小都是
(
n
c
t
x
,
d
i
m
)
=
(
2048
,
4096
)
(n_{ctx}, dim) = (2048,4096)
(nctx,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
×
W
i
Q
Q×W_i^Q
Q×WiQ 和
K
×
W
i
K
K×W_i^K
K×WiK 和
Q
×
W
i
Q
Q×W_i^Q
Q×WiQ 都是
(
n
c
t
x
,
d
k
)
=
(
2048
,
128
)
(n_{ctx}, d_k)=(2048,128)
(nctx,dk)=(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
d_k=d_v
dk=dv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
W^O
WO （大小是（4096，4096））全连接，还是(2048, 4096)矩阵。
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))
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
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