prompt: 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()
  
  ```
  
golden_diff: 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
  
verification_info: {"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"}]}