Why are all my similarities close to 1?

qcr1t: <p>I am trying to build a simple two tower recommender system on the MovieLens 100k dataset. The user tower is just a simple embedding layer. The item tower uses an embedding layer and concats that with a binary vector corresponding to genres. The concated features are then passed through a feed forward network. Given a user_id, item_id, item_features, I am trying to predict the user-item rating.</p>
<p><strong>Q1:</strong> One thing I am unsure about is whether the embedding dimension is too large since I have more parameters in my model than I have user-item-rating pairs.</p>
<pre><code class="lang-auto">Model Parameters: 99440
Train Pairs size: 80668
Total Users x Total Items: 5942620
</code></pre>
<p><strong>Q2:</strong> The other issue is: if I look at the cosine similarity score between the item embeddings (output of <code>item_tower(item_id, item_feature)</code>), I see that all of them are close to 1 even the items that are supposed to be least similar. I am not sure what is causing this behavior.</p>
<pre><code class="lang-auto">TOP 4
title 	scores
Aladdin (1992) 	 	            1.000000
Hercules (1997)  	            0.999938
Muppet Treasure Island (1996) 	0.999860
Little Mermaid, The (1989)  	0.999844

BOT 3
Underworld: Awakening (2012)  	    0.988776
The Witch (2015) 	[Horror] 	    0.988495
Resident Evil: Retribution (2012) 	0.987383
</code></pre>
<p>The code is below:</p>
<pre><code class="lang-python">class TwoTower(torch.nn.Module):
    def __init__(self, user_input, item_emb_input, item_emb_output, item_feat_input, embedding_dim):
        super(TwoTower, self).__init__()
        
        self.user_tower = UserTower(user_input, embedding_dim)
        self.item_tower = ItemTower(item_emb_input, item_emb_output, item_feat_input, embedding_dim)
        
    def forward(self, usr, itm, itm_feat):
        return torch.sum(self.user_tower(usr) * self.item_tower(itm, itm_feat), dim=1)

class ItemTower(torch.nn.Module):
    def __init__(self,
                 emb_in, emb_out,
                 feat_in,
                 embedding_dim
                ):
        super(ItemTower, self).__init__()
        
        self.item_embedding = torch.nn.Embedding(emb_in, emb_out)
        self.ff = torch.nn.Sequential(
            torch.nn.Linear(emb_out + feat_in, embedding_dim),
            torch.nn.ReLU(),
            torch.nn.Linear(embedding_dim, embedding_dim),
        )
        
    def forward(self, item_id, item_feat):
        x = torch.cat((self.item_embedding(item_id), item_feat), dim=1)
        return self.ff(x)

class UserTower(torch.nn.Module):
    def __init__(self, input_dim, embedding_dim):
        super(UserTower, self).__init__()
        
        self.user_embedding = torch.nn.Embedding(input_dim, embedding_dim)
        
    def forward(self, x):
        return self.user_embedding(x)
</code></pre>
<p>The initialization</p>
<pre><code class="lang-python">model = TwoTower(len(user_id_map), len(ds_movies), 8, len(ds_movies.columns[4:]), 32)
optimizer = torch.optim.SGD(model.parameters(), lr=1e-2)
criterion = torch.nn.MSELoss()
</code></pre>
<p>Train loop</p>
<pre><code class="lang-python">loss_trn = []
loss_tst = []

num_epoch = 15
lam = 1e-1

for i in range(num_epoch):
    for batch, (usr, itm, itm_feat, rat) in enumerate(ratings_dataloader_trn):
        pred = model(usr, itm, itm_feat)
        loss = criterion(pred, rat) + (
            + lam * torch.mean(torch.sum(model.user_tower.user_embedding.weight ** 2, dim=1))
            + lam * torch.mean(torch.sum(model.item_tower.item_embedding.weight ** 2, dim=1))
        )
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()
        
        if batch % 100 == 0:
            loss_trn.append(criterion(pred, rat).item())
            
    with torch.no_grad():
        test_loss = 0.0
        for (usr, itm, itm_feat, rat) in ratings_dataloader_tst:
            pred = model(usr, itm, itm_feat)
            test_loss += criterion(pred, rat).item()

        test_loss /= len(ratings_dataloader_tst)
        loss_tst.append(test_loss)
</code></pre>