Neural networks have become a fundamental aspect of solving complex problems in various fields, including computer vision. One crucial component of neural networks is the activation function, which plays a vital role in transforming inputs into meaningful outputs. In this article, we will explore the limitations of the traditional step function activation and discover how the sigmoid neuron can offer a more flexible and predictable alternative.
The Limitations of the Step Function Activation
Before we delve into the limitations, let’s briefly recap the step function activation. In a perceptron network, the activation function is represented by a step function or a Heaviside function. However, this type of activation function poses certain challenges.
Consider a perceptron network with multiple weights and biases, as shown in the image below:
The goal is to find the optimal weights and biases to solve a specific problem, such as a computer vision task. To measure the impact of changing a parameter, let’s focus on a single weight.
If we change this particular weight, denoted as w1, by a small delta w, we expect to observe a corresponding change in the output, a. However, with the step function activation, the output remains unchanged if the resulting value of z (wx + b) is less than 0. This means that even if we modify w1, the output doesn’t reflect the impact of that change.
On the other hand, if we increase w1 sufficiently, the output suddenly flips from 0 to 1, making the system highly unstable. This instability becomes even more evident when dealing with larger networks consisting of millions of perceptrons.
Introducing the Sigmoid Neuron
To address the limitations of the step function activation, let’s introduce the sigmoid neuron. The activation function, denoted as sigma, is now defined by the sigmoid function: 1 / (1 + e^(-z)). This function appears as a blurred version of the step function, offering a smoother transition between outputs.
With the sigmoid activation, changing the weight w1 results in a measurable change in the output a. If we increase w1, the activation increases, and if we decrease it, the activation decreases accordingly. This behavior allows for a more predictable and manageable adjustment of weights and biases to achieve the desired output.
FAQs
Q: What is the purpose of an activation function in a neural network?
A: The activation function transforms the summed inputs of a neuron into an output, enabling the network to learn complex patterns and make predictions.
Q: Why is the step function activation limited in perceptron networks?
A: The step function activation lacks smoothness and makes it challenging to measure the impact of parameter changes, leading to unstable systems.
Q: How does the sigmoid activation function improve upon the step function?
A: The sigmoid activation offers a smoother transition between outputs, allowing for more predictable changes based on parameter adjustments.
Conclusion
Activation functions are essential components of neural networks, influencing the system’s ability to learn and make accurate predictions. While the step function activation has limitations, the sigmoid neuron provides a more flexible and stable alternative. By adopting smooth activation functions like the sigmoid, neural networks can achieve better performance and facilitate the training process.
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