Cross-Entropy — AI의 성적표

import numpy as np

def cross_entropy(true_label_idx, predicted_probs):
    """모델의 예측이 정답과 얼마나 다른지 측정"""
    return -np.log(predicted_probs[true_label_idx] + 1e-10)

words = ["좋다", "나쁘다", "덥다", "춥다", "흐리다"]
true_answer = 0  # 정답: "좋다"

# 학습 단계별 모델의 예측
early_probs = np.array([0.20, 0.20, 0.20, 0.20, 0.20])
mid_probs   = np.array([0.45, 0.20, 0.15, 0.12, 0.08])
late_probs  = np.array([0.85, 0.06, 0.04, 0.03, 0.02])

print("=== 학습 단계별 Cross-Entropy 손실 ===\n")
for name, probs in [("학습 초기", early_probs),
                     ("학습 중기", mid_probs),
                     ("학습 후기", late_probs)]:
    loss = cross_entropy(true_answer, probs)
    bar = "█" * int(loss * 10)
    print(f"{name}: 손실 = {loss:.4f}  {bar}")
    print(f"  '좋다' 예측 확률: {probs[0]:.2f}")
    print()

# Cross-Entropy 손실 직접 계산
import math

def cross_entropy(true_idx, probs):
    # -log(정답 확률)
    p = max(probs[true_idx], 1e-10)  # 0 방지
    return -math.log(p)

def softmax(logits):
    max_val = max(logits)
    exps = [math.exp(x - max_val) for x in logits]
    total = sum(exps)
    return [e / total for e in exps]

words = ["사과", "바나나", "포도", "딸기"]
true_answer = 0  # 정답: "사과"

# 학습 단계별 logits 시뮬레이션
stages = {
    "초기 (랜덤)":  [0.2, 0.3, 0.1, 0.4],
    "학습 10회":     [1.5, 0.8, 0.3, 0.2],
    "학습 100회":    [3.0, 0.5, 0.2, 0.1],
    "학습 1000회":   [6.0, 0.3, 0.1, 0.05],
}

for stage, logits in stages.items():
    probs = softmax(logits)
    loss = cross_entropy(true_answer, probs)
    print(f"\n[{stage}]")
    for w, p in zip(words, probs):
        marker = " <-- 정답" if w == words[true_answer] else ""
        print(f"  {w}: {p:.4f}{marker}")
    print(f"  손실(loss): {loss:.4f}")