Ask for help

[Yzichen]

The indicators obtained by pytorch's topk operation are not differentiable. How can I use the topk here to obtain differentiable indicators? My application cannot tolerate changes in embeddings. So I can't directly use the example you gave

[pietruh]

Hi, there are two ways to approach this problem that I will briefly sketch for you:

1. If your application can tolerate non-discrete indicators.
2. Other

Ad 1. If your application can tolerate non-discrete indicators.

You can prepend one-hot encoded vectors to embeddings, and after soft top-k selection, the top-k indicators will be recoverable. You will not get the exact discrete values, but this should be close enough with a high enough base(200 or bigger). Here is a sample code:

k = 256     # your k
n = 8192    # your n
depth = 32  # depth of the representations(vectors, embeddings etc.)
#Build operator and configure it
topk = TopKOperator()
cfg = TopKConfig(input_len=n,
                 pooled_len=k,
                 base=200,       # the bigger, the better approximation, but can be unstable
                 )
topk.set_config(cfg)
# Prepare data (Note: sample embeddings from range [-1, 1], so that cosine similarity is fairly unbiased)
embeddings = torch.rand((1, n, depth)) * 2 - 1
embeddings = torch.cat((torch.eye(n).unsqueeze(0), embeddings), dim=-1)    # <- Modifications of embeddings (prefixing them with one-hot vectors)
scores = torch.rand((1, n, 1))
# Select with Soft TopK operator we proposed
out_embs, out_scores = topk(embeddings, scores)
out_scores.unsqueeze_(2)
soft_indicators = (torch.arange(0,n)*out_embs[0,:,:n]).sum(1)    # <- Recovering the original indicators (here, you can try performing a softmax)
hard_indicators = scores[0,:,0].topk(10)
print(f'Soft indicators(top10): {soft_indicators[:10].tolist()}\n Hard indicators(top10): {hard_indicators.indices.tolist()}')

that will give you results:

Soft indicators(top10): [2863.00439453125, 2764.00537109375, 6665.99658203125, 4511.99755859375, 4813.0, 7624.9921875, 6757.98876953125, 2194.999267578125, 3649.0009765625, 7820.99072265625]
Hard indicators(top10): [2863, 2764, 6666, 4512, 4813, 7625, 6758, 2195, 3649, 7821]

Ad 2. Other

If you need to have discrete indicator values, you should probably use RL to achieve that.

[Yzichen]

Can I directly use rounding to get a discrete index?