LLaMA架构深度探析

LLaMA架构的设计可以说是引领了整个开源社区，其架构设计主要为以下几个方面：

Pre-Normalization（GPT3）
SwiGLU（PaLM）
RoPE（GPTNeo）
RMSNorm

在其实际设计中，还使用了GQA，KV-Cache等技术。

我们直接从代码中汲取营养吧。

1 RMSNorm

相比LayerNorm，不需要减去mean

class RMSNorm(torch.nn.Module):
    def __init__(self, dim: int, eps: float = 1e-6):
        super().__init__()
        self.eps = eps
        self.weight = nn.Parameter(torch.ones(dim))

    def _norm(self, x):
        return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)

    def forward(self, x):
        output = self._norm(x.float()).type_as(x)
        return output * self.weight

2 RoPE

RoPE的计算分为两部分：该种RoPE的计算方法利用了向量的计算。

1 计算弧度
2 计算x_q和x_v

precompute_freqs_cis的作用是将freqs_cis reshape到可以和xq_计算的维度：

xq_的维度： [batch_size, seq_len, n_head, hidden_size/2]
freqs_cis [seq_len, hidden_size/2] -> [1, seq_len, 1, hidden_size/2]

其他细节可以具体查看下述代码注释：

def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0):
    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))
    t = torch.arange(end, device=freqs.device)  # type: ignore
    freqs = torch.outer(t, freqs).float()  # type: ignore
    freqs_cis = torch.polar(torch.ones_like(freqs), freqs)  # complex64
    return freqs_cis

def reshape_for_broadcast(freqs_cis: torch.Tensor, x: torch.Tensor):
    ndim = x.ndim
    assert 0 <= 1 < ndim
    assert freqs_cis.shape == (x.shape[1], x.shape[-1])
    shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)]
    return freqs_cis.view(*shape)

def apply_rotary_emb(
    xq: torch.Tensor,
    xk: torch.Tensor,
    freqs_cis: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor]:
    # xq_ [batch_size, seq_len, n_head, hidden/2, 2] -> [batch_size, seq_len, n_head, hidden/2]
    xq_ = torch.view_as_complex(xq.float().reshape(*xq.shape[:-1], -1, 2))
    xk_ = torch.view_as_complex(xk.float().reshape(*xk.shape[:-1], -1, 2))
    # freqs_cis [seq_len, hidden/2] -> [1, seq_len, 1, hidden/2]
    freqs_cis = reshape_for_broadcast(freqs_cis, xq_)
    # xq_ [batch_size, seq_len, n_head, hidden/2, 2] -> [batch_size, seq_len, n_head, hidden]
    xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(3)
    xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(3)
    return xq_out.type_as(xq), xk_out.type_as(xk)

3 SwiGLU

不同于之前FFN的两层MLP，而是采用双线性单元+MLP进行取代。

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

4 Pre-Normalization

x输入就经过Layer Normalization，之后是Self-Attention计算或者SwiGLU单元+MLP计算

class TransformerBlock(nn.Module):
    def __init__(self, layer_id: int, args: ModelArgs):
        super().__init__()
        self.n_heads = args.n_heads
        self.dim = args.dim
        self.head_dim = args.dim // args.n_heads
        self.attention = Attention(args)
        self.feed_forward = FeedForward(
            dim=args.dim,
            hidden_dim=4 * args.dim,
            multiple_of=args.multiple_of,
            ffn_dim_multiplier=args.ffn_dim_multiplier,
        )
        self.layer_id = layer_id
        self.attention_norm = RMSNorm(args.dim, eps=args.norm_eps)
        self.ffn_norm = RMSNorm(args.dim, eps=args.norm_eps)

    def forward(
        self,
        x: torch.Tensor,
        start_pos: int,
        freqs_cis: torch.Tensor,
        mask: Optional[torch.Tensor],
    ):
        h = x + self.attention(
            self.attention_norm(x), start_pos, freqs_cis, mask
        )
        out = h + self.feed_forward(self.ffn_norm(h))
        return out

5 LLaMA Attention

Self-Attention最难的点在于如何将Multi-head Attention, GQA, KV Cache, RoPE合一。

class Attention(nn.Module):
        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

        self.wq = ColumnParallelLinear(
            args.dim,
            args.n_heads * self.head_dim,
            bias=False,
            gather_output=False,
            init_method=lambda x: x,
        )
        self.wk = ColumnParallelLinear(
            args.dim,
            self.n_kv_heads * self.head_dim,
            bias=False,
            gather_output=False,
            init_method=lambda x: x,
        )
        self.wv = ColumnParallelLinear(
            args.dim,
            self.n_kv_heads * self.head_dim,
            bias=False,
            gather_output=False,
            init_method=lambda x: x,
        )
        self.wo = RowParallelLinear(
            args.n_heads * self.head_dim,
            args.dim,
            bias=False,
            input_is_parallel=True,
            init_method=lambda x: x,
        )

        self.cache_k = torch.zeros(
            (
                args.max_batch_size,
                args.max_seq_len,
                self.n_local_kv_heads,
                self.head_dim,
            )
        ).cuda()
        self.cache_v = torch.zeros(
            (
                args.max_batch_size,
                args.max_seq_len,
                self.n_local_kv_heads,
                self.head_dim,
            )
        ).cuda()

    def forward(
        self,
        x: torch.Tensor,
        start_pos: int,
        freqs_cis: torch.Tensor,
        mask: Optional[torch.Tensor],
    ):
        bsz, seqlen, _ = x.shape
        xq, xk, xv = self.wq(x), self.wk(x), self.wv(x)

        xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim)
        xk = xk.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)
        xv = xv.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)

        xq, xk = apply_rotary_emb(xq, xk, freqs_cis=freqs_cis)

        self.cache_k = self.cache_k.to(xq)
        self.cache_v = self.cache_v.to(xq)

        self.cache_k[:bsz, start_pos : start_pos + seqlen] = xk
        self.cache_v[:bsz, start_pos : start_pos + seqlen] = xv

        keys = self.cache_k[:bsz, : start_pos + seqlen]
        values = self.cache_v[:bsz, : start_pos + seqlen]

        # repeat k/v heads if n_kv_heads < n_heads
        keys = repeat_kv(keys, self.n_rep)  # (bs, cache_len + seqlen, n_local_heads, head_dim)
        values = repeat_kv(values, self.n_rep)  # (bs, cache_len + seqlen, n_local_heads, head_dim)

        xq = xq.transpose(1, 2)  # (bs, n_local_heads, seqlen, head_dim)
        keys = keys.transpose(1, 2) # (bs, n_local_heads, cache_len + seqlen, head_dim)
        values = values.transpose(1, 2) # (bs, n_local_heads, cache_len + seqlen, head_dim)
        scores = torch.matmul(xq, keys.transpose(2, 3)) / math.sqrt(self.head_dim)
        if mask is not None:
            scores = scores + mask  # (bs, n_local_heads, seqlen, cache_len + seqlen)
        scores = F.softmax(scores.float(), dim=-1).type_as(xq)
        output = torch.matmul(scores, values)  # (bs, n_local_heads, seqlen, head_dim)
        output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1)
        return self.wo(output)

假设输入x的维度为 : [batch_size, seq_len, n_head, hidden_size]

为什么RoPE、GQA和KV Cache相处这么融洽呢，从其作用维度上可见一斑：

RoPE作用于hidden_size
GQA作用于n_head
KV Cache作用于seq_len

重点关注forward的计算过程：

1 先GQA计算Attention
2 xq和xk进行RoPE的位置编码融合
3 xk, xv放入KV Cache
4 从KV Cache总拿到全体xk和xv
5 全体xk和xv进行expand（由于GQA节省了部分k,v计算）
6 计算Selt-Attention
7 Self-Attention + mask
8 得到最终value

Mask的生成，mask为右上三角矩阵，内部元素为-inf，同时需要考虑KV Cache：


mask = torch.full(
                (seqlen, seqlen), float("-inf"), device=tokens.device
            )

            mask = torch.triu(mask, diagonal=1)

            # When performing key-value caching, we compute the attention scores
            # only for the new sequence. Thus, the matrix of scores is of size
            # (seqlen, cache_len + seqlen), and the only masked entries are (i, j) for
            # j > cache_len + i, since row i corresponds to token cache_len + i.
            mask = torch.hstack([
                torch.zeros((seqlen, start_pos), device=tokens.device),
                mask
            ]).type_as(h)

LLaMA架构深度探析

1 RMSNorm

2 RoPE

3 SwiGLU

4 Pre-Normalization

5 LLaMA Attention

By crabboss

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