What loss functions does PyTorch provide for classification and regression, and which to use when?

The choice of loss function should match the output type and the probabilistic assumption about the data-generating process — it is the mathematical link between model predictions and the training signal.

import torch
import torch.nn as nn

# Binary classification — output is a single logit (no sigmoid)
bce = nn.BCEWithLogitsLoss()  # applies sigmoid internally
logit = torch.tensor([2.0, -1.0, 0.5])
label = torch.tensor([1.0, 0.0, 1.0])
loss = bce(logit, label)

# Multi-class — outputs are raw logits per class (no softmax)
ce = nn.CrossEntropyLoss()
logits = torch.randn(8, 10)    # batch of 8, 10 classes
targets = torch.randint(0, 10, (8,))  # class indices 0-9
loss = ce(logits, targets)

# Class-weighted cross-entropy — for imbalanced datasets
weights = torch.tensor([1.0]*9 + [10.0])  # up-weight class 9
ce_weighted = nn.CrossEntropyLoss(weight=weights)

# Regression
mse = nn.MSELoss()
huber = nn.HuberLoss(delta=1.0)  # L2 for |error|<1, L1 for |error|>1
pred = torch.randn(32, 1)
true = torch.randn(32, 1)
print(mse(pred, true), huber(pred, true))