Sigmoid vs Softmax: So sánh hai hàm kích hoạt quan trọng nhất trong Deep Learning

1import numpy as np
2
3def sigmoid(x):
4    return 1 / (1 + np.exp(-x))
5
6# Ví dụ: Binary classification
7logit = 2.0
8prob = sigmoid(logit)
9print(f"Logit: {logit} → Sigmoid: {prob:.4f}")
10# Output: Logit: 2.0 → Sigmoid: 0.8808
11
12# Ví dụ: Multi-label (mỗi label độc lập)
13logits = np.array([2.0, -1.0, 0.5, 3.0])
14labels = ["Chó", "Mèo", "Ngoài trời", "Dễ thương"]
15probs = sigmoid(logits)
16
17print("\nMulti-label Classification:")
18for label, p in zip(labels, probs):
19    status = "✅" if p > 0.5 else "❌"
20    print(f"  {label}: {p:.1%} {status}")
21# Chó: 88.1% ✅ | Mèo: 26.9% ❌ | Ngoài trời: 62.2% ✅ | Dễ thương: 95.3% ✅

1import numpy as np
2
3def softmax(x):
4    # Trừ max để tránh overflow (numerical stability)
5    e_x = np.exp(x - np.max(x))
6    return e_x / e_x.sum()
7
8# Ví dụ: Multi-class classification
9logits = np.array([2.0, 1.0, 0.1])
10classes = ["🐕 Chó", "🐱 Mèo", "🐦 Chim"]
11probs = softmax(logits)
12
13print("Multi-class Classification:")
14for cls, p in zip(classes, probs):
15    print(f"  {cls}: {p:.1%}")
16print(f"\nTổng xác suất: {probs.sum():.4f}")
17# 🐕 Chó: 65.9% | 🐱 Mèo: 24.2% | 🐦 Chim: 9.9%
18# Tổng: 1.0000

1import torch
2import torch.nn as nn
3
4# === SIGMOID: Binary / Multi-label ===
5sigmoid = nn.Sigmoid()
6logits = torch.tensor([2.0, -1.0, 0.5])
7print("Sigmoid:", sigmoid(logits))
8# tensor([0.8808, 0.2689, 0.6225])
9
10# === SOFTMAX: Multi-class ===
11softmax = nn.Softmax(dim=0)
12logits = torch.tensor([2.0, 1.0, 0.1])
13print("Softmax:", softmax(logits))
14# tensor([0.6590, 0.2424, 0.0986])
15
16# Thực tế: dùng loss function có sẵn sigmoid/softmax
17# Binary / Multi-label
18loss_fn = nn.BCEWithLogitsLoss()  # Sigmoid built-in
19
20# Multi-class
21loss_fn = nn.CrossEntropyLoss()  # Softmax built-in