# 交叉熵损失可视化

交互式探索机器学习中最常用的损失函数

> 标准页面: https://elysiatools.com/zh/visualizations/cross-entropy-loss

- **分类:** Math

## 概述

Comprehensive interactive visualization of cross-entropy loss, the most commonly used loss function for classification tasks in machine learning. Features three main sections: (1) Binary Cross-Entropy - Interactive exploration with adjustable true label (0/1) and predicted probability (0-1), real-time loss calculation using L = -[y·log(ŷ) + (1-y)·log(1-ŷ)], gradient visualization, and dynamic loss curve plotting showing both y=0 and y=1 cases. (2) Categorical Cross-Entropy - Multi-class demonstration with interactive 3-class softmax visualization, adjustable logits inputs with real-time probability distribution updates, true class selection, and softmax formula σ(z)_i = e^(z_i) / Σ(e^(z_j)). (3) Loss Function Comparison - Side-by-side comparison of cross-entropy vs Mean Squared Error (MSE), interactive loss curves comparison (y=1 scenario), pros/cons table analyzing gradient behavior, convexity, probabilistic interpretation, and best use cases. Educational content covers information theory perspective (KL divergence relation: H(p,q) = D_KL(p||q) + H(p)), why MSE is unsuitable for classification (weak gradient signals), numerical stability tips (log-sum-exp trick), label smoothing, class imbalance handling, and activation function selection (sigmoid for binary, softmax for multi-class). Uses Chart.js for interactive plots and KaTeX for formula rendering. Multi-language support (zh, en, es, fr, de, ru, pt).

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