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[ PyTorch torch.nn Reference Manual](#) * * * `torch.nn.MSELoss` is the Mean Squared Error loss function in PyTorch. It calculates the mean of the squared differences between predicted values and target values, and is commonly used for regression tasks. ### Function Definition torch.nn.MSELoss(reduction='mean') **Parameter Description:** * `reduction` (str): Loss aggregation method. Options are `'mean'`, `'sum'`, `'none'`. Default is `'mean'`. ### Mathematical Principle MSE loss formula: MSE = (1/n) * Σ(y_pred - y_true)² * * * ## Usage Examples ### Example 1: Basic Usage Calculating regression loss: ## Instance import torch import torch.nn as nn # Create MSE loss criterion = nn.MSELoss() # Predicted values and true values predictions = torch.tensor([3.0,4.0,5.0]) targets = torch.tensor([2.8,4.2,4.9]) # Calculate loss loss = criterion(predictions, targets) print("Predicted values:", predictions.tolist()) print("Target values:", targets.tolist()) print("MSE loss:", loss.item()) # Manual verification manual_mse =((predictions - targets) ** 2).mean() print("Manual calculation:", manual_mse.item()) ### Example 2: Complete Regression Training Regression task training process: ## Instance import torch import torch.nn as nn import torch.optim as optim # Simple regression model class RegressionNet(nn.Module): def __init__ (self): super(RegressionNet,self). __init__ () self.fc= nn.Linear(10,1) def forward(self, x): return self.fc(x) model = RegressionNet() criterion = nn.MSELoss() optimizer = optim.Adam(model.parameters(), lr=0.01) # Training data X = torch.randn(100,10) y = torch.randn(100,1) # Training step model.train() optimizer.zero_grad() predictions = model(X) loss = criterion(predictions, y) loss.backward() optimizer.step() print("Training loss:", loss.item()) ### Example 3: reduction Parameter Different aggregation methods: ## Instance import torch import torch.nn as nn pred = torch.tensor([3.0,4.0,5.0,6.0]) target = torch.tensor([3.5,3.8,5.2,5.5]) # mean: average loss loss_mean = nn.MSELoss(reduction='mean')(pred, target) # sum: total loss loss_sum = nn.MSELoss(reduction='sum')(pred, target) # none: no aggregation loss_none = nn.MSELoss(reduction='none')(pred, target) print("Mean:", loss_mean.item()) print("Sum:", loss_sum.item()) print("None:", loss_none.tolist()) ### Example 4: Handling Multi-dimensional Output Multi-dimensional regression: ## Instance import torch import torch.nn as nn # Multi-dimensional output pred = torch.randn(4,3)# batch=4, 3 outputs target = torch.randn(4,3) criterion = nn.MSELoss() loss = criterion(pred, target) print("Prediction shape:", pred.shape) print("Target shape:", target.shape) print("MSE loss:", loss.item()) * * * ## Common Questions ### Q1: Which is better, MSE or MAE? * MSE: Sensitive to outliers, stable gradients * MAE (L1): Robust to outliers, unstable gradients ### Q2: Can MSE be used if the output has negative values? Yes, MSE does not restrict the output range. ### Q3: What loss to use for classification tasks? Use CrossEntropyLoss for classification tasks. * * * ## Use Cases The main application scenarios for `nn.MSELoss` include: * **Regression tasks**: House price prediction, numerical estimation * **Continuous value prediction**: Object tracking * **Generative models**: Certain losses in VAE, GAN * * PyTorch torch.nn Reference Manual](#)