Add Barlow Twins loss for representation learning (Project-MONAI#7530)

### Description

Addition of the BarlowTwinsLoss class. This cost function is introduced
in the http://proceedings.mlr.press/v139/zbontar21a/zbontar21a.pdf paper
with the aim of disentangling the representations learned on two views
of the same sample, making it a powerful tool for multimodal and
unsupervised learning.
This cost function is similar to the InfoNCE Loss function already
implemented in MONAI
(https://docs.monai.io/en/latest/_modules/monai/losses/contrastive.html#ContrastiveLoss).
However, it differs in several respects: there is no l2-normalisation,
but rather a z-normalisation. In addition, rather than working between
pairs of embeddings, Barlow Twins seeks to decorrelate the components of
the representations.

```math
\mathcal{L}_{BT} := \sum_i (1 - \mathcal{C}_{ii})^2 + \lambda \sum_i \sum_{i\neq j} \mathcal{C}_{ij}^2
```
with $\lambda$ a positive hyperparameters and $\mathcal{C}$ the
cross-correlation matrix

### Types of changes
<!--- Put an `x` in all the boxes that apply, and remove the not
applicable items -->
- [x] Non-breaking change (fix or new feature that would not break
existing functionality).
- [ ] Breaking change (fix or new feature that would cause existing
functionality to change).
- [x] New tests added to cover the changes.
- [x] Integration tests passed locally by running `./runtests.sh -f -u
--net --coverage`.
- [x] Quick tests passed locally by running `./runtests.sh --quick
--unittests --disttests`.
- [x] In-line docstrings updated.
- [x] Documentation updated, tested `make html` command in the `docs/`
folder.

---------

Signed-off-by: Lucas Robinet <robinet.lucas@iuct-oncopole.fr>
Signed-off-by: Lucas Robinet <67736918+Lucas-rbnt@users.noreply.github.com>
Co-authored-by: Lucas Robinet <robinet.lucas@iuct-oncopole.fr>
Co-authored-by: Eric Kerfoot <17726042+ericspod@users.noreply.github.com>
Co-authored-by: YunLiu <55491388+KumoLiu@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Signed-off-by: Juan Pablo de la Cruz Gutiérrez <juampatronics@gmail.com>

docs/source/losses.rst

@@ -73,6 +73,11 @@ Segmentation Losses
 .. autoclass:: ContrastiveLoss
     :members:
 
+`BarlowTwinsLoss`
+~~~~~~~~~~~~~~~~~
+.. autoclass:: BarlowTwinsLoss
+    :members:
+
 `HausdorffDTLoss`
 ~~~~~~~~~~~~~~~~~
 .. autoclass:: HausdorffDTLoss

monai/losses/__init__.py

@@ -12,6 +12,7 @@
 from __future__ import annotations
 
 from .adversarial_loss import PatchAdversarialLoss
+from .barlow_twins import BarlowTwinsLoss
 from .cldice import SoftclDiceLoss, SoftDiceclDiceLoss
 from .contrastive import ContrastiveLoss
 from .deform import BendingEnergyLoss, DiffusionLoss

monai/losses/barlow_twins.py

@@ -0,0 +1,84 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import torch
+from torch.nn.modules.loss import _Loss
+
+
+class BarlowTwinsLoss(_Loss):
+    """
+    The Barlow Twins cost function takes the representations extracted by a neural network from two
+    distorted views and seeks to make the cross-correlation matrix of the two representations tend
+    towards identity. This encourages the neural network to learn similar representations with the least
+    amount of redundancy. This cost function can be used in particular in multimodal learning to work on
+    representations from two modalities. The most common use case is for unsupervised learning, where data
+    augmentations are used to generate 2 distorted views of the same sample to force the encoder to
+    extract useful features for downstream tasks.
+
+    Zbontar, Jure, et al. "Barlow Twins: Self-Supervised Learning via Redundancy Reduction" International
+    conference on machine learning. PMLR, 2020. (http://proceedings.mlr.press/v139/zbontar21a/zbontar21a.pdf)
+
+    Adapted from:
+        https://github.com/facebookresearch/barlowtwins
+
+    """
+
+    def __init__(self, lambd: float = 5e-3) -> None:
+        """
+        Args:
+            lamb: Can be any float to handle the informativeness and invariance trade-off. Ideally set to 5e-3.
+
+        Raises:
+            ValueError: When an input of dimension length > 2 is passed
+            ValueError: When input and target are of different shapes
+            ValueError: When batch size is less than or equal to 1
+
+        """
+        super().__init__()
+        self.lambd = lambd
+
+    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
+        """
+        Args:
+            input: the shape should be B[F].
+            target: the shape should be B[F].
+        """
+        if len(target.shape) > 2 or len(input.shape) > 2:
+            raise ValueError(
+                f"Either target or input has dimensions greater than 2 where target "
+                f"shape is ({target.shape}) and input shape is ({input.shape})"
+            )
+
+        if target.shape != input.shape:
+            raise ValueError(f"ground truth has differing shape ({target.shape}) from input ({input.shape})")
+
+        if target.size(0) <= 1:
+            raise ValueError(
+                f"Batch size must be greater than 1 to compute Barlow Twins Loss, but got {target.size(0)}"
+            )
+
+        lambd_tensor = torch.as_tensor(self.lambd).to(input.device)
+        batch_size = input.shape[0]
+
+        # normalize input and target
+        input_norm = (input - input.mean(0)) / input.std(0).add(1e-6)
+        target_norm = (target - target.mean(0)) / target.std(0).add(1e-6)
+
+        # cross-correlation matrix
+        c = torch.mm(input_norm.t(), target_norm) / batch_size  # input_norm.t() is FxB, target_norm is BxF so c is FxF
+
+        # loss
+        c_diff = (c - torch.eye(c.size(0), device=c.device)).pow_(2)  # FxF
+        c_diff[~torch.eye(c.size(0), device=c.device).bool()] *= lambd_tensor
+
+        return c_diff.sum()

tests/test_barlow_twins_loss.py

@@ -0,0 +1,109 @@
+# Copyright (c) MONAI Consortium
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#     http://www.apache.org/licenses/LICENSE-2.0
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import annotations
+
+import unittest
+
+import numpy as np
+import torch
+from parameterized import parameterized
+
+from monai.losses import BarlowTwinsLoss
+
+TEST_CASES = [
+    [  # shape: (2, 4), (2, 4)
+        {"lambd": 5e-3},
+        {
+            "input": torch.tensor([[1.0, 1.0, 0.0, 0.0], [1.0, 1.0, 0.0, 0.0]]),
+            "target": torch.tensor([[1.0, 1.0, 0.0, 0.0], [1.0, 1.0, 0.0, 0.0]]),
+        },
+        4.0,
+    ],
+    [  # shape: (2, 4), (2, 4)
+        {"lambd": 5e-3},
+        {
+            "input": torch.tensor([[0.0, 0.0, 1.0, 1.0], [0.0, 0.0, 1.0, 1.0]]),
+            "target": torch.tensor([[1.0, 1.0, 0.0, 0.0], [1.0, 1.0, 0.0, 0.0]]),
+        },
+        4.0,
+    ],
+    [  # shape: (2, 4), (2, 4)
+        {"lambd": 5e-3},
+        {
+            "input": torch.tensor([[1.0, 0.0, 1.0, 1.0], [0.0, 1.0, 1.0, 0.0]]),
+            "target": torch.tensor([[1.0, 1.0, 1.0, 0.0], [1.0, 1.0, 0.0, 1.0]]),
+        },
+        5.2562,
+    ],
+    [  # shape: (2, 4), (2, 4)
+        {"lambd": 5e-4},
+        {
+            "input": torch.tensor([[2.0, 3.0, 1.0, 2.0], [0.0, 1.0, 2.0, 5.0]]),
+            "target": torch.tensor([[1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0]]),
+        },
+        5.0015,
+    ],
+    [  # shape: (4, 4), (4, 4)
+        {"lambd": 5e-3},
+        {
+            "input": torch.tensor(
+                [[1.0, 2.0, 1.0, 1.0], [3.0, 1.0, 1.0, 2.0], [1.0, 1.0, 1.0, 1.0], [2.0, 1.0, 1.0, 0.0]]
+            ),
+            "target": torch.tensor(
+                [
+                    [0.0, 1.0, -1.0, 0.0],
+                    [1 / 3, 0.0, -2 / 3, 1 / 3],
+                    [-2 / 3, -1.0, 7 / 3, 1 / 3],
+                    [1 / 3, 0.0, 1 / 3, -2 / 3],
+                ]
+            ),
+        },
+        1.4736,
+    ],
+]
+
+
+class TestBarlowTwinsLoss(unittest.TestCase):
+
+    @parameterized.expand(TEST_CASES)
+    def test_result(self, input_param, input_data, expected_val):
+        barlowtwinsloss = BarlowTwinsLoss(**input_param)
+        result = barlowtwinsloss(**input_data)
+        np.testing.assert_allclose(result.detach().cpu().numpy(), expected_val, atol=1e-4, rtol=1e-4)
+
+    def test_ill_shape(self):
+        loss = BarlowTwinsLoss(lambd=5e-3)
+        with self.assertRaises(ValueError):
+            loss(torch.ones((1, 2, 3)), torch.ones((1, 1, 2, 3)))
+
+    def test_ill_batch_size(self):
+        loss = BarlowTwinsLoss(lambd=5e-3)
+        with self.assertRaises(ValueError):
+            loss(torch.ones((1, 2)), torch.ones((1, 2)))
+
+    def test_with_cuda(self):
+        loss = BarlowTwinsLoss(lambd=5e-3)
+        i = torch.ones((2, 10))
+        j = torch.ones((2, 10))
+        if torch.cuda.is_available():
+            i = i.cuda()
+            j = j.cuda()
+        output = loss(i, j)
+        np.testing.assert_allclose(output.detach().cpu().numpy(), 10.0, atol=1e-4, rtol=1e-4)
+
+    def check_warning_raised(self):
+        with self.assertWarns(Warning):
+            BarlowTwinsLoss(lambd=5e-3, batch_size=1)
+
+
+if __name__ == "__main__":
+    unittest.main()