# Loss and Miners¶

When training your embedding model, it is crucial that the model learns to embed similar items close together in the latent space, and different items far from each other.

For that, you can train your model using the Triplet or Siamese loss. By default, these losses will look at all possible triplets/pairs of embeddings in the batch. As we can expect there to be many “easy” triplets/pairs, you may want to select only the hard ones, to make the model learn faster. For that, you can use tuple mining.

## Triplet and Siamese Loss¶

Triplet and Siamese loss both compare the distances between the embeddings of similar and dissimilar items, and create a loss that penalizes similar items being too far apart, or dissimilar ones being too close to each other.

### Triplet Loss¶

Triplet loss works with a triplet composed of an anchor, a positive sample (item similar to the anchor) and a negative sample (item dis-similar from the anchor). The loss for a single such triplet is then computed as

$\ell_{i, p, n}=\max(0, d(\mathbf{x}_i, \mathbf{x}_p)-d(\mathbf{x}_i, \mathbf{x}_n)+m)$

Here $$\mathbf{x}_i, \mathbf{x}_p, \mathbf{x}_n$$ and the embeddings of the anchor, positive and negative sample, respectively, $$d$$ is a distance function, and $$m$$ is a desired wedge between the distances of similar and dis-similar items.

### Siamese Loss¶

Siamese loss works with a tuple of items, an anchor and either a positive or a negative sample. The loss for a single pair is computed as

$\ell_{i,j} = \mathrm{sim}(i,j)d(\mathbf{x}_i, \mathbf{x}_j) + (1 - \mathrm{sim}(i,j))\max(m - d(\mathbf{x}_i, \mathbf{x}_j))$

Here $$\mathrm{sim}(i,j)$$ denotes the similarity function, which returns 1 if items $$i$$ and $$j$$ are similar, and 0 if they are dis-similar.

### Use with Tuner¶

It’s straightforward to use these loss functions with the Tuner. You can just give the name of the loss function (as a string) as the loss argument on initialization, or you can instantiate the loss object, which allows you to customize parameters (including miners)

from finetuner.tuner.pytorch import PytorchTuner
from finetuner.tuner.pytorch.losses import TripletLoss

loss = TripletLoss(distance='cosine', margin=0.5)

tuner = PytorchTuner(..., loss=loss)

from finetuner.tuner.keras import KerasTuner
from finetuner.tuner.keras.losses import TripletLoss

loss = TripletLoss(distance='cosine', margin=0.5)

tuner = KerasTuner(..., loss=loss)

from finetuner.tuner.paddle import PaddleTuner

loss = TripletLoss(distance='cosine', margin=0.5)



## Tuple Miners¶

In order to support siamese and triplet training, the Finetuner implements different mining strategies.

This paper provides a thorough investigation of which mining strategies should be used and why. The image below illustrates the relative position of samples in the case of triplet training and will help us to define the necessary terminology.

The white circle in the middle (A) denotes our anchor sample $$\mathrm{x}_i$$ and the white circle on the left (P) denotes our positive sample $$\mathrm{x}_p$$. Depending on where our negative sample will fall, inside the encoding space, it will be either hard, semihard or an easy sample. More precisely, a negative sample is considered to be

• hard, when its distance to the anchor sample is smaller than the distance between the anchor and the positive sample, formally $$d(\mathrm{x}_i,\mathrm{x}_n) < d(\mathrm{x}_i,\mathrm{x}_p)$$.

• semihard, when it is just a little further from the postive sample $$\mathrm{x}_i$$, but within the margin, formally

$d(\mathrm{x}_i,\mathrm{x}_p) < d(\mathrm{x}_i,\mathrm{x}_n) < d(\mathrm{x}_i,\mathrm{x}_p) + \mathrm{m}$

• easy, when it is even further away from the anchor, formally $$d(\mathrm{x}_i,\mathrm{x}_n) > d(\mathrm{x}_i,\mathrm{x}_p) + \mathrm{m}$$.

The strategies presented here were given for the negative sample, taking the positive one as given. Analogous strategies for selecting the positive sample, having the negative one already give, are also possible. We enable the use of both positive and negative mining strategy in Tuner.

In order to apply mining, during siamese- or triplet training with the Finetuner, you simply need to add the desired miner to your loss. Please mind, that mining is only supported when using a Class Dataset.

from finetuner.tuner.pytorch import PytorchTuner
from finetuner.tuner.pytorch.miner import TripletEasyHardMiner
from finetuner.tuner.pytorch.losses import TripletLoss

loss = TripletLoss(miner=TripletEasyHardMiner(pos_strategy='easy', neg_strategy='hard'))

tuner = PytorchTuner(..., loss=loss)

from finetuner.tuner.keras import KerasTuner
from finetuner.tuner.keras.miner import TripletEasyHardMiner
from finetuner.tuner.keras.losses import TripletLoss

loss = TripletLoss(miner=TripletEasyHardMiner(pos_strategy='easy', neg_strategy='hard'))

tuner = KerasTuner(..., loss=loss)

from finetuner.tuner.paddle import PaddleTuner

loss = TripletLoss(miner=TripletEasyHardMiner(pos_strategy='easy', neg_strategy='hard'))



## NTXent Loss¶

The NTXent (normalized cross-entropy) loss is a popular loss function used in self-supervised training. If is defined as

$\ell_{i} = -\log \left(\frac{\exp (\mathrm{cossim}(\mathbf{x}_i, \mathbf{x}_{p_i})/ \tau)}{\sum_{k=1}^{2N}1_{k \neq i}\exp (\mathrm{cossim}(\mathbf{x}_i, \mathbf{x}_{k})/ \tau)}\right),$

where $$\mathbf{x}_i$$ is the embedding of the i-th element, $$\mathrm{cossim(\cdot, \cdot)}$$ is the cosine similarity function, and $$\tau$$ is the temperature parameter.

### Use with Tuner¶

The use of this loss function with tuner is straightforward, as shown in the snippet below. Note that this loss will only work with the Instance dataset.

from finetuner.tuner.pytorch import PytorchTuner
from finetuner.tuner.pytorch.losses import NTXentLoss

loss = NTXentLoss(temperature=0.5)

tuner = PytorchTuner(..., loss=loss)