code: def _reference_vicreg_loss(
      x: Tensor,
      y: Tensor,
      sim_coeff: float = 25.0,
      std_coeff: float = 25.0,
      cov_coeff: float = 1.0,
  ):
      # Original VICReg loss from:
      # https://github.com/facebookresearch/vicreg/blob/4e12602fd495af83efd1631fbe82523e6db092e0/main_vicreg.py#L194
      def off_diagonal(x):
          n, m = x.shape
          assert n == m
          return x.flatten()[:-1].view(n - 1, n + 1)[:, 1:].flatten()
  
      batch_size = x.shape[0]
      num_features = x.shape[-1]
      repr_loss = F.mse_loss(x, y)
  
      x = x - x.mean(dim=0)
      y = y - y.mean(dim=0)
  
      std_x = torch.sqrt(x.var(dim=0) + 0.0001)
      std_y = torch.sqrt(y.var(dim=0) + 0.0001)
      std_loss = (
          torch.mean(F.relu(1 - std_x)) / 2
          + torch.mean(F.relu(1 - std_y)) / 2
      )
  
      cov_x = (x.T @ x) / (batch_size - 1)
      cov_y = (y.T @ y) / (batch_size - 1)
      cov_loss = off_diagonal(cov_x).pow_(2).sum().div(
          num_features
      ) + off_diagonal(cov_y).pow_(2).sum().div(num_features)
  
      loss = (
          sim_coeff * repr_loss
          + std_coeff * std_loss
          + cov_coeff * cov_loss
      )
      return loss
  
imports: import unittest
  import pytest
  import torch
  import torch.nn.functional
  from pytest_mock import MockerFixture
  from torch import Tensor
  from torch import distributed
  from lightly.loss import VICRegLoss
label_desc: Use image node_id 1 for calling a global function with example usage: _reference_vicreg_loss(x, y, sim_coeff, std_coeff, cov_coeff) and returns: loss, x