What loss functions does PyTorch provide and how do you choose the right one?

import torch
import torch.nn as nn

# ── Regression: MSE
mse = nn.MSELoss()
pred = torch.tensor([2.5, 3.0, 4.1])
target = torch.tensor([3.0, 3.0, 4.0])
loss = mse(pred, target)   # mean((pred-target)^2)

# ── Multi-class classification: CrossEntropyLoss
ce = nn.CrossEntropyLoss()
logits = torch.randn(8, 5)         # batch=8, 5 classes — RAW logits
targets = torch.randint(0, 5, (8,))  # class indices, dtype long
loss = ce(logits, targets)

# ── Binary classification: BCEWithLogitsLoss (preferred over BCELoss)
bce = nn.BCEWithLogitsLoss()       # combines Sigmoid + BCE, numerically stable
logits_binary = torch.randn(8, 1)
targets_binary = torch.randint(0, 2, (8, 1)).float()
loss = bce(logits_binary, targets_binary)

# ── Class-weighted CrossEntropy for imbalanced data
class_weights = torch.tensor([1.0, 1.0, 5.0, 1.0, 1.0])  # upweight class 2
ce_weighted = nn.CrossEntropyLoss(weight=class_weights)

# ── Custom loss function
class FocalLoss(nn.Module):
    def __init__(self, gamma=2.0):
        super().__init__()
        self.gamma = gamma
        self.ce = nn.CrossEntropyLoss(reduction="none")

    def forward(self, logits, targets):
        ce_loss = self.ce(logits, targets)
        pt = torch.exp(-ce_loss)
        focal = ((1 - pt) ** self.gamma * ce_loss).mean()
        return focal