Sigmoid 函数

S形函数是机器学习（ML） 和深度学习（DL）领域广泛应用的基础数学组件。它常被称为"压平函数"，能将任意实数值作为输入，映射为0到1之间的数值。这种独特的"S"形曲线特性使其在将原始模型输出转换为可解释概率时具有非凡价值。 在神经网络（NN）中， S形函数作为激活函数发挥作用， 引入非线性特性使模型能够学习 超越简单线性关系的复杂模式。 尽管在深度隐藏层中已被其他函数 广泛取代，它仍是二元分类任务 中输出层的标准选择。

人工智能中S型曲线的运作机制

在核心层面，S形函数将输入数据（通常称为logits）转换为标准化范围。这种转换对于需要预测事件发生概率的任务至关重要。通过将输出值限制在0到1之间，该函数能提供清晰的概率评分。

• 逻辑回归：在传统统计建模中，Sigmoid函数是逻辑回归的核心引擎。它使数据科学家能够估计二元结果的概率，例如客户是否会流失或留存。
• 二元分类：对于 设计用于区分两个类别（例如"猫"与"狗"）的神经网络，最终层通常采用 Sigmoid激活函数。若输出值大于阈值（通常为0.5），模型则预测为正类。
• 多标签分类： 与类别互斥的多类问题不同，多标签任务允许图像或文本同时属于多个类别。在此，Sigmoid函数独立应用于每个输出节点，使模型能够在同一场景中detect "和"人"而不产生冲突。

Key Differences from Other Activation Functions

While Sigmoid was once the default for all layers, researchers discovered limitations like the vanishing gradient problem, where gradients become too small to update weights effectively in deep networks. This led to the adoption of alternatives for hidden layers.

• Sigmoid vs. ReLU (Rectified Linear Unit): ReLU is computationally faster and avoids vanishing gradients by outputting the input directly if positive, and zero otherwise. It is the preferred choice for hidden layers in modern architectures like YOLO26, whereas Sigmoid is reserved for the final output layer in specific tasks.
• Sigmoid vs. Softmax: Both map outputs to a 0-1 range, but they serve different purposes. Sigmoid treats each output independently, making it ideal for binary or multi-label tasks. Softmax forces all outputs to sum to 1, creating a probability distribution used for multi-class classification where only one class is correct.

实际应用

The utility of the Sigmoid function extends across various industries where probability estimation is required.

1. Medical Diagnosis: AI models used in medical image analysis often use Sigmoid outputs to predict the probability of a disease being present in an X-ray or MRI scan. For example, a model might output 0.85, indicating an 85% likelihood of a tumor, aiding doctors in early detection.
2. Spam Detection: Email filtering systems utilize natural language processing (NLP) models with Sigmoid classifiers to determine if an incoming message is "spam" or "not spam." The model analyzes keywords and metadata, outputting a score that determines whether the email lands in the inbox or the junk folder.

具体实施

You can observe how Sigmoid transforms data using PyTorch, a popular library for building deep learning models. This simple example demonstrates the "squashing" effect on a range of input values.

import torch
import torch.nn as nn

# Create a Sigmoid layer
sigmoid = nn.Sigmoid()

# Define input data (logits) ranging from negative to positive
input_data = torch.tensor([-5.0, -1.0, 0.0, 1.0, 5.0])

# Apply Sigmoid to squash values between 0 and 1
output = sigmoid(input_data)

print(f"Input: {input_data}")
print(f"Output: {output}")
# Output values near 0 for negative inputs, 0.5 for 0, and near 1 for positive inputs

For those looking to train models that utilize these concepts without writing low-level code, the Ultralytics Platform offers an intuitive interface to manage datasets and train state-of-the-art models like YOLO26. By handling the architectural complexities automatically, it allows users to focus on gathering high-quality training data for their specific computer vision applications.