Drop in performance from using nn.Linear(...) to nn.Parameter(torch.tensor(...))

I am doing some experiments on transformer models using pytorch and need to make some modifications that require me to look at different weight matrices seperately. To this end I tried replacing some of the nn.Linear() blocks in the self attention computation with nn.Parameter(torch.tensor()), but I'm finding a substantial drop in performance. Here's the different implementations:

First (with nn.Linear()):

class Attention(nn.Module):
    def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
        super().__init__()
        inner_dim = dim_head *  heads
        project_out = not (heads == 1 and dim_head == dim)

        self.heads = heads
        self.scale = dim_head ** -0.5

        self.attend = nn.Softmax(dim = -1)
        self.to_qkv = nn.Linear(dim, inner_dim * 3, bias = False)

        self.to_out = nn.Sequential(
            nn.Linear(inner_dim, dim),
            nn.Dropout(dropout)
        ) if project_out else nn.Identity()

    def forward(self, x):
        qkv = self.to_qkv(x).chunk(3, dim = -1)
        q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h = self.heads), qkv)
        dots = torch.matmul(q, k.transpose(-1, -2)) * self.scale

        attn = self.attend(dots)


        out = torch.matmul(attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')
        return self.to_out(out)

Second(with nn.Parameter(torch.tensor())):

class Attention(nn.Module):
    def __init__(self, dim, heads = 8, dim_head = 64, dropout = 0.):
        super().__init__()
        inner_dim = dim_head *  heads
        project_out = not (heads == 1 and dim_head == dim)
        self.dim_head = dim_head
        self.heads = heads
        self.scale = dim_head ** -0.5

        self.attend = nn.Softmax(dim = -1)
        self.to_q = nn.Parameter(torch.randn(dim, inner_dim))
        self.to_k = nn.Parameter(torch.randn(dim, inner_dim))
        self.to_v = nn.Parameter(torch.randn(dim, inner_dim))
        self.projection = nn.Parameter(torch.randn(inner_dim, dim))
        self.dropout = nn.Dropout(dropout)

    def forward(self, x):
        q,k,v = x @ self.to_q, x @ self.to_k, x @ self.to_v
        q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h = self.heads), (q,k,v))
        dots = torch.matmul(q, k.transpose(-1, -2)) * self.scale
        attn = self.attend(dots)  
        out = torch.matmul(attn, v)
        out = rearrange(out, 'b h n d -> b n (h d)')
        out = out @ self.projection
        out = self.dropout(out)
        return out

Any explanation for why these two methods perform differently would help a lot. Thanks.

My guess is that weight initialization might be a problem. Note that nn.Linear will, by default, initialize the weights of the layer using a scaled uniform distribution in order to keep the variance small. While in your second implementation you initialize from a standard gaussian, which has quite high variance (std=1).

I would suggest to try this and see if the issue is fixed:

self.to_q = nn.Parameter(torch.randn(dim, inner_dim) * (2 / np.sqrt(dim + inner_dim)))
self.to_k = nn.Parameter(torch.randn(dim, inner_dim) * (2 / np.sqrt(dim + inner_dim)))
self.to_v = nn.Parameter(torch.randn(dim, inner_dim) * (2 / np.sqrt(dim + inner_dim)))

This will apply xavier initialization to the weights of your layer. The same effect can be achieved with:

nn.init.xavier_normal_(self.to_q)

If you want to now more about why we should initialize the Q, K, V matrices this way please see this: https://pi-tau.github.io/posts/transformer/#multi-head-attention-layer. There you will also find an explanation about why we need to scale the scores with dim_head ** -0.5.

Also if you only want access to the weight matrix then I see no reason why you should replace nn.Linear with something else. You can get the weights of the layer with self.to_qkv.wight.data