What loss functions does PyTorch provide and when do you use each?

import torch, torch.nn as nn

# Multi-class classification: CrossEntropyLoss
# Input: (N, C) logits — raw, before softmax
# Target: (N,) class indices — dtype=long
ce = nn.CrossEntropyLoss()
logits  = torch.randn(4, 10)              # 4 samples, 10 classes
targets = torch.tensor([2, 5, 0, 9])      # true class indices
loss = ce(logits, targets)

# Binary classification: BCEWithLogitsLoss
# Numerically stable (fuses sigmoid + BCE)
bce = nn.BCEWithLogitsLoss()
preds = torch.randn(4)       # logits, NOT sigmoid output
true  = torch.tensor([1.,0.,1.,0.])
loss_b = bce(preds, true)

# Class weighting for imbalanced datasets
weights = torch.tensor([1.0]*9 + [10.0])   # class 9 is rare
ce_w = nn.CrossEntropyLoss(weight=weights)

# Label smoothing (reduces overconfidence)
ce_ls = nn.CrossEntropyLoss(label_smoothing=0.1)

# Regression: MSE vs Huber
mseLoss   = nn.MSELoss()
huberLoss = nn.HuberLoss(delta=1.0)   # L2 near 0, L1 for large errors
pred_r = torch.randn(4)
true_r = torch.randn(4)
print(mseLoss(pred_r, true_r))
print(huberLoss(pred_r, true_r))

Critical gotcha: nn.CrossEntropyLoss expects raw logits (before softmax), not probabilities. It internally applies log-softmax, so applying softmax first leads to double-softmax and incorrect training.