Das Softmax function is a mathematical function often im maschinellen Lernen, particularly in classification tasks. It takes a vector of real-valued numbers and converts them into a probability distribution. The output values are in the range (0, 1) and sum to 1, making them interpretable as probabilities.
Mathematisch ist die Softmax-Funktion definiert als:
Softmax(zi) = (e^(zi)) / (Σ e^(zj))
where z is the Eingangsvektor, zi is the ith element of the vector, and the sum in the denominator is taken over all elements in the vector. The exponential function (e) is used to ensure that all output values are positive, which is essential for interpreting the results as probabilities.
In der Praxis wird Softmax häufig in der letzten Schicht eines neuronales Netzwerk designed for Mehrklassenklassifikation problems. By using Softmax, the model can output a probability distribution over multiple classes, allowing it to predict the most likely class for a given input. For example, if a model predicts three classes (A, B, and C) with scores (2.0, 1.0, and 0.1), applying Softmax will convert these scores into probabilities that sum to 1, indicating the model’s confidence in each class.
It is important to note that while Softmax is useful for multi-class problems, it can lead to issues such as numerische Instabilität if the input values are very large or very small. Techniques like subtracting the maximum value from the input vector (known as the log-sum-exp trick) can help mitigate these issues.