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)
python
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,
python
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