We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
VICReg Loss De-Means Twice?
https://github.com/lightly-ai/lightly/blob/66ad1b40ebf3b53512703c774988211ce283211f/lightly/loss/vicreg_loss.py#L128-L129

I think the VICReg loss removes the mean, then calls `.var()` which also de-means (see: https://pytorch.org/docs/stable/generated/torch.var.html). 

If I understand correctly, that seems unnecessary?

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `lightly/loss/vicreg_loss.py`
Content:
```
1 import torch
2 import torch.distributed as dist
3 import torch.nn.functional as F
4 from torch import Tensor
5 
6 from lightly.utils.dist import gather
7 
8 
9 class VICRegLoss(torch.nn.Module):
10     """Implementation of the VICReg loss [0].
11 
12     This implementation is based on the code published by the authors [1].
13 
14     - [0] VICReg, 2022, https://arxiv.org/abs/2105.04906
15     - [1] https://github.com/facebookresearch/vicreg/
16 
17     Attributes:
18         lambda_param:
19             Scaling coefficient for the invariance term of the loss.
20         mu_param:
21             Scaling coefficient for the variance term of the loss.
22         nu_param:
23             Scaling coefficient for the covariance term of the loss.
24         gather_distributed:
25             If True then the cross-correlation matrices from all gpus are gathered and
26             summed before the loss calculation.
27         eps:
28             Epsilon for numerical stability.
29 
30     Examples:
31 
32         >>> # initialize loss function
33         >>> loss_fn = VICRegLoss()
34         >>>
35         >>> # generate two random transforms of images
36         >>> t0 = transforms(images)
37         >>> t1 = transforms(images)
38         >>>
39         >>> # feed through model
40         >>> out0, out1 = model(t0, t1)
41         >>>
42         >>> # calculate loss
43         >>> loss = loss_fn(out0, out1)
44     """
45 
46     def __init__(
47         self,
48         lambda_param: float = 25.0,
49         mu_param: float = 25.0,
50         nu_param: float = 1.0,
51         gather_distributed: bool = False,
52         eps=0.0001,
53     ):
54         super(VICRegLoss, self).__init__()
55         if gather_distributed and not dist.is_available():
56             raise ValueError(
57                 "gather_distributed is True but torch.distributed is not available. "
58                 "Please set gather_distributed=False or install a torch version with "
59                 "distributed support."
60             )
61 
62         self.lambda_param = lambda_param
63         self.mu_param = mu_param
64         self.nu_param = nu_param
65         self.gather_distributed = gather_distributed
66         self.eps = eps
67 
68     def forward(self, z_a: torch.Tensor, z_b: torch.Tensor) -> torch.Tensor:
69         """Returns VICReg loss.
70 
71         Args:
72             z_a:
73                 Tensor with shape (batch_size, ..., dim).
74             z_b:
75                 Tensor with shape (batch_size, ..., dim).
76         """
77         assert (
78             z_a.shape[0] > 1 and z_b.shape[0] > 1
79         ), f"z_a and z_b must have batch size > 1 but found {z_a.shape[0]} and {z_b.shape[0]}"
80         assert (
81             z_a.shape == z_b.shape
82         ), f"z_a and z_b must have same shape but found {z_a.shape} and {z_b.shape}."
83 
84         # invariance term of the loss
85         inv_loss = invariance_loss(x=z_a, y=z_b)
86 
87         # gather all batches
88         if self.gather_distributed and dist.is_initialized():
89             world_size = dist.get_world_size()
90             if world_size > 1:
91                 z_a = torch.cat(gather(z_a), dim=0)
92                 z_b = torch.cat(gather(z_b), dim=0)
93 
94         var_loss = 0.5 * (
95             variance_loss(x=z_a, eps=self.eps) + variance_loss(x=z_b, eps=self.eps)
96         )
97         cov_loss = covariance_loss(x=z_a) + covariance_loss(x=z_b)
98 
99         loss = (
100             self.lambda_param * inv_loss
101             + self.mu_param * var_loss
102             + self.nu_param * cov_loss
103         )
104         return loss
105 
106 
107 def invariance_loss(x: Tensor, y: Tensor) -> Tensor:
108     """Returns VICReg invariance loss.
109 
110     Args:
111         x:
112             Tensor with shape (batch_size, ..., dim).
113         y:
114             Tensor with shape (batch_size, ..., dim).
115     """
116     return F.mse_loss(x, y)
117 
118 
119 def variance_loss(x: Tensor, eps: float = 0.0001) -> Tensor:
120     """Returns VICReg variance loss.
121 
122     Args:
123         x:
124             Tensor with shape (batch_size, ..., dim).
125         eps:
126             Epsilon for numerical stability.
127     """
128     x = x - x.mean(dim=0)
129     std = torch.sqrt(x.var(dim=0) + eps)
130     loss = torch.mean(F.relu(1.0 - std))
131     return loss
132 
133 
134 def covariance_loss(x: Tensor) -> Tensor:
135     """Returns VICReg covariance loss.
136 
137     Generalized version of the covariance loss with support for tensors with more than
138     two dimensions. Adapted from VICRegL:
139     https://github.com/facebookresearch/VICRegL/blob/803ae4c8cd1649a820f03afb4793763e95317620/main_vicregl.py#L299
140 
141     Args:
142         x:
143             Tensor with shape (batch_size, ..., dim).
144     """
145     x = x - x.mean(dim=0)
146     batch_size = x.size(0)
147     dim = x.size(-1)
148     # nondiag_mask has shape (dim, dim) with 1s on all non-diagonal entries.
149     nondiag_mask = ~torch.eye(dim, device=x.device, dtype=torch.bool)
150     # cov has shape (..., dim, dim)
151     cov = torch.einsum("b...c,b...d->...cd", x, x) / (batch_size - 1)
152     loss = cov[..., nondiag_mask].pow(2).sum(-1) / dim
153     return loss.mean()
154
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/lightly/loss/vicreg_loss.py b/lightly/loss/vicreg_loss.py
--- a/lightly/loss/vicreg_loss.py
+++ b/lightly/loss/vicreg_loss.py
@@ -125,7 +125,6 @@
         eps:
             Epsilon for numerical stability.
     """
-    x = x - x.mean(dim=0)
     std = torch.sqrt(x.var(dim=0) + eps)
     loss = torch.mean(F.relu(1.0 - std))
     return loss

{"golden_diff": "diff --git a/lightly/loss/vicreg_loss.py b/lightly/loss/vicreg_loss.py\n--- a/lightly/loss/vicreg_loss.py\n+++ b/lightly/loss/vicreg_loss.py\n@@ -125,7 +125,6 @@\n         eps:\n             Epsilon for numerical stability.\n     \"\"\"\n-    x = x - x.mean(dim=0)\n     std = torch.sqrt(x.var(dim=0) + eps)\n     loss = torch.mean(F.relu(1.0 - std))\n     return loss\n", "issue": "VICReg Loss De-Means Twice?\nhttps://github.com/lightly-ai/lightly/blob/66ad1b40ebf3b53512703c774988211ce283211f/lightly/loss/vicreg_loss.py#L128-L129\r\n\r\nI think the VICReg loss removes the mean, then calls `.var()` which also de-means (see: https://pytorch.org/docs/stable/generated/torch.var.html). \r\n\r\nIf I understand correctly, that seems unnecessary?\n", "before_files": [{"content": "import torch\nimport torch.distributed as dist\nimport torch.nn.functional as F\nfrom torch import Tensor\n\nfrom lightly.utils.dist import gather\n\n\nclass VICRegLoss(torch.nn.Module):\n    \"\"\"Implementation of the VICReg loss [0].\n\n    This implementation is based on the code published by the authors [1].\n\n    - [0] VICReg, 2022, https://arxiv.org/abs/2105.04906\n    - [1] https://github.com/facebookresearch/vicreg/\n\n    Attributes:\n        lambda_param:\n            Scaling coefficient for the invariance term of the loss.\n        mu_param:\n            Scaling coefficient for the variance term of the loss.\n        nu_param:\n            Scaling coefficient for the covariance term of the loss.\n        gather_distributed:\n            If True then the cross-correlation matrices from all gpus are gathered and\n            summed before the loss calculation.\n        eps:\n            Epsilon for numerical stability.\n\n    Examples:\n\n        >>> # initialize loss function\n        >>> loss_fn = VICRegLoss()\n        >>>\n        >>> # generate two random transforms of images\n        >>> t0 = transforms(images)\n        >>> t1 = transforms(images)\n        >>>\n        >>> # feed through model\n        >>> out0, out1 = model(t0, t1)\n        >>>\n        >>> # calculate loss\n        >>> loss = loss_fn(out0, out1)\n    \"\"\"\n\n    def __init__(\n        self,\n        lambda_param: float = 25.0,\n        mu_param: float = 25.0,\n        nu_param: float = 1.0,\n        gather_distributed: bool = False,\n        eps=0.0001,\n    ):\n        super(VICRegLoss, self).__init__()\n        if gather_distributed and not dist.is_available():\n            raise ValueError(\n                \"gather_distributed is True but torch.distributed is not available. \"\n                \"Please set gather_distributed=False or install a torch version with \"\n                \"distributed support.\"\n            )\n\n        self.lambda_param = lambda_param\n        self.mu_param = mu_param\n        self.nu_param = nu_param\n        self.gather_distributed = gather_distributed\n        self.eps = eps\n\n    def forward(self, z_a: torch.Tensor, z_b: torch.Tensor) -> torch.Tensor:\n        \"\"\"Returns VICReg loss.\n\n        Args:\n            z_a:\n                Tensor with shape (batch_size, ..., dim).\n            z_b:\n                Tensor with shape (batch_size, ..., dim).\n        \"\"\"\n        assert (\n            z_a.shape[0] > 1 and z_b.shape[0] > 1\n        ), f\"z_a and z_b must have batch size > 1 but found {z_a.shape[0]} and {z_b.shape[0]}\"\n        assert (\n            z_a.shape == z_b.shape\n        ), f\"z_a and z_b must have same shape but found {z_a.shape} and {z_b.shape}.\"\n\n        # invariance term of the loss\n        inv_loss = invariance_loss(x=z_a, y=z_b)\n\n        # gather all batches\n        if self.gather_distributed and dist.is_initialized():\n            world_size = dist.get_world_size()\n            if world_size > 1:\n                z_a = torch.cat(gather(z_a), dim=0)\n                z_b = torch.cat(gather(z_b), dim=0)\n\n        var_loss = 0.5 * (\n            variance_loss(x=z_a, eps=self.eps) + variance_loss(x=z_b, eps=self.eps)\n        )\n        cov_loss = covariance_loss(x=z_a) + covariance_loss(x=z_b)\n\n        loss = (\n            self.lambda_param * inv_loss\n            + self.mu_param * var_loss\n            + self.nu_param * cov_loss\n        )\n        return loss\n\n\ndef invariance_loss(x: Tensor, y: Tensor) -> Tensor:\n    \"\"\"Returns VICReg invariance loss.\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n        y:\n            Tensor with shape (batch_size, ..., dim).\n    \"\"\"\n    return F.mse_loss(x, y)\n\n\ndef variance_loss(x: Tensor, eps: float = 0.0001) -> Tensor:\n    \"\"\"Returns VICReg variance loss.\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n        eps:\n            Epsilon for numerical stability.\n    \"\"\"\n    x = x - x.mean(dim=0)\n    std = torch.sqrt(x.var(dim=0) + eps)\n    loss = torch.mean(F.relu(1.0 - std))\n    return loss\n\n\ndef covariance_loss(x: Tensor) -> Tensor:\n    \"\"\"Returns VICReg covariance loss.\n\n    Generalized version of the covariance loss with support for tensors with more than\n    two dimensions. Adapted from VICRegL:\n    https://github.com/facebookresearch/VICRegL/blob/803ae4c8cd1649a820f03afb4793763e95317620/main_vicregl.py#L299\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n    \"\"\"\n    x = x - x.mean(dim=0)\n    batch_size = x.size(0)\n    dim = x.size(-1)\n    # nondiag_mask has shape (dim, dim) with 1s on all non-diagonal entries.\n    nondiag_mask = ~torch.eye(dim, device=x.device, dtype=torch.bool)\n    # cov has shape (..., dim, dim)\n    cov = torch.einsum(\"b...c,b...d->...cd\", x, x) / (batch_size - 1)\n    loss = cov[..., nondiag_mask].pow(2).sum(-1) / dim\n    return loss.mean()\n", "path": "lightly/loss/vicreg_loss.py"}], "after_files": [{"content": "import torch\nimport torch.distributed as dist\nimport torch.nn.functional as F\nfrom torch import Tensor\n\nfrom lightly.utils.dist import gather\n\n\nclass VICRegLoss(torch.nn.Module):\n    \"\"\"Implementation of the VICReg loss [0].\n\n    This implementation is based on the code published by the authors [1].\n\n    - [0] VICReg, 2022, https://arxiv.org/abs/2105.04906\n    - [1] https://github.com/facebookresearch/vicreg/\n\n    Attributes:\n        lambda_param:\n            Scaling coefficient for the invariance term of the loss.\n        mu_param:\n            Scaling coefficient for the variance term of the loss.\n        nu_param:\n            Scaling coefficient for the covariance term of the loss.\n        gather_distributed:\n            If True then the cross-correlation matrices from all gpus are gathered and\n            summed before the loss calculation.\n        eps:\n            Epsilon for numerical stability.\n\n    Examples:\n\n        >>> # initialize loss function\n        >>> loss_fn = VICRegLoss()\n        >>>\n        >>> # generate two random transforms of images\n        >>> t0 = transforms(images)\n        >>> t1 = transforms(images)\n        >>>\n        >>> # feed through model\n        >>> out0, out1 = model(t0, t1)\n        >>>\n        >>> # calculate loss\n        >>> loss = loss_fn(out0, out1)\n    \"\"\"\n\n    def __init__(\n        self,\n        lambda_param: float = 25.0,\n        mu_param: float = 25.0,\n        nu_param: float = 1.0,\n        gather_distributed: bool = False,\n        eps=0.0001,\n    ):\n        super(VICRegLoss, self).__init__()\n        if gather_distributed and not dist.is_available():\n            raise ValueError(\n                \"gather_distributed is True but torch.distributed is not available. \"\n                \"Please set gather_distributed=False or install a torch version with \"\n                \"distributed support.\"\n            )\n\n        self.lambda_param = lambda_param\n        self.mu_param = mu_param\n        self.nu_param = nu_param\n        self.gather_distributed = gather_distributed\n        self.eps = eps\n\n    def forward(self, z_a: torch.Tensor, z_b: torch.Tensor) -> torch.Tensor:\n        \"\"\"Returns VICReg loss.\n\n        Args:\n            z_a:\n                Tensor with shape (batch_size, ..., dim).\n            z_b:\n                Tensor with shape (batch_size, ..., dim).\n        \"\"\"\n        assert (\n            z_a.shape[0] > 1 and z_b.shape[0] > 1\n        ), f\"z_a and z_b must have batch size > 1 but found {z_a.shape[0]} and {z_b.shape[0]}\"\n        assert (\n            z_a.shape == z_b.shape\n        ), f\"z_a and z_b must have same shape but found {z_a.shape} and {z_b.shape}.\"\n\n        # invariance term of the loss\n        inv_loss = invariance_loss(x=z_a, y=z_b)\n\n        # gather all batches\n        if self.gather_distributed and dist.is_initialized():\n            world_size = dist.get_world_size()\n            if world_size > 1:\n                z_a = torch.cat(gather(z_a), dim=0)\n                z_b = torch.cat(gather(z_b), dim=0)\n\n        var_loss = 0.5 * (\n            variance_loss(x=z_a, eps=self.eps) + variance_loss(x=z_b, eps=self.eps)\n        )\n        cov_loss = covariance_loss(x=z_a) + covariance_loss(x=z_b)\n\n        loss = (\n            self.lambda_param * inv_loss\n            + self.mu_param * var_loss\n            + self.nu_param * cov_loss\n        )\n        return loss\n\n\ndef invariance_loss(x: Tensor, y: Tensor) -> Tensor:\n    \"\"\"Returns VICReg invariance loss.\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n        y:\n            Tensor with shape (batch_size, ..., dim).\n    \"\"\"\n    return F.mse_loss(x, y)\n\n\ndef variance_loss(x: Tensor, eps: float = 0.0001) -> Tensor:\n    \"\"\"Returns VICReg variance loss.\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n        eps:\n            Epsilon for numerical stability.\n    \"\"\"\n    std = torch.sqrt(x.var(dim=0) + eps)\n    loss = torch.mean(F.relu(1.0 - std))\n    return loss\n\n\ndef covariance_loss(x: Tensor) -> Tensor:\n    \"\"\"Returns VICReg covariance loss.\n\n    Generalized version of the covariance loss with support for tensors with more than\n    two dimensions. Adapted from VICRegL:\n    https://github.com/facebookresearch/VICRegL/blob/803ae4c8cd1649a820f03afb4793763e95317620/main_vicregl.py#L299\n\n    Args:\n        x:\n            Tensor with shape (batch_size, ..., dim).\n    \"\"\"\n    x = x - x.mean(dim=0)\n    batch_size = x.size(0)\n    dim = x.size(-1)\n    # nondiag_mask has shape (dim, dim) with 1s on all non-diagonal entries.\n    nondiag_mask = ~torch.eye(dim, device=x.device, dtype=torch.bool)\n    # cov has shape (..., dim, dim)\n    cov = torch.einsum(\"b...c,b...d->...cd\", x, x) / (batch_size - 1)\n    loss = cov[..., nondiag_mask].pow(2).sum(-1) / dim\n    return loss.mean()\n", "path": "lightly/loss/vicreg_loss.py"}]}